The production level that will maximize profit is 80 units
To find the production level that will maximize profit given the cost function C(q) = 660 + 5q + 0.03q^2 and demand function p = 10 - q/400, follow these steps:
1. Write down the revenue function: Revenue (R) is the product of price (p) and quantity (q). So, R(q) = p * q.
2. Substitute the demand function into the revenue function: R(q) = (10 - q/400) * q
3. Simplify the revenue function: R(q) = 10q - q^2/400
4. Write down the profit function: Profit (P) is the difference between revenue and cost. So, P(q) = R(q) - C(q).
5. Substitute the revenue and cost functions into the profit function: P(q) = (10q - q^2/400) - (660 + 5q + 0.03q^2)
6. Simplify the profit function: P(q) = 10q - q^2/400 - 660 - 5q - 0.03q^2
7. Combine like terms: P(q) = 5q - q^2/400 - 0.03q^2 - 660
8. Differentiate the profit function with respect to q to find the first derivative: P'(q) = 5 - q/200 - 0.06q
9. Set the first derivative equal to 0 and solve for q: 5 - q/200 - 0.06q = 0
10. Solve for q: q ≈ 80
The production level that will maximize profit is approximately 80 units (rounded to the nearest whole number).
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The point k lies on the segment JL. Find the coordinates of k so that the ratios of JK to KL is 3 to 4
After considering all the given data we conclude that the coordinates of k so that the ratios of JK to KL is 3 to 4 is (-16x₁x₂-16y₁y₂)
The two values of X and Y are the coordinates of K. Let us assume that the coordinates of points J and L are (x₁, y₁) and (x₂, y₂) respectively.
Then, the coordinates of point K can be placed as (x, y), here x and y are unknowns that we need to find.
Now, we know that the ratio of JK to KL is 3:4. This means that:
JK/KL = 3/4
We can use the distance formula to find the distances JK and KL in terms of their coordinates:
JK = √((x-x₁)²+(y-y₁²) KL = √((x-x₂)²+(y- y₂)²)
Staging these distances into the above equation, we get:
√(x-x₁)²+(y-y₁))/√((x-x₂)²+(y-y₂)²) = 3/4
Squaring both sides and simplifying, we get:
16(x-x1)²+16(y-y₁)²= 9(x-x₂)²+9(y-y₂)²
Expanding and simplifying, we get:
7x²-14xx₁-9x₂²+ 7y2-14yy₁-9y₂²= -16x₁x₂-16y₁y₂
This is a quadratic equation in x and y. We can solve this equation to find the values of x and y that satisfy the given conditions. The solution to this quadratic equation gives two values of x and y, which are the coordinates of point K.
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Find Tn centered at x = 23 for all n for the function f(x) = ex. (Use symbolic notation and fractions where needed.)
For a function f(x) = e^x, we can find its Taylor series expansion Tn centered at x = 23 using the formula:
Tn(x) = Σ (f^(k)(23) * (x - 23)^k) / k!, for k = 0 to n
Since the derivative of e^x is always e^x, the k-th derivative evaluated at 23 is f^(k)(23) = e^23 for all k. Therefore, the Taylor series expansion becomes:
Tn(x) = Σ (e^23 * (x - 23)^k) / k!, for k = 0 to n
This is the Tn centered at x = 23 for all n for the function f(x) = e^x, with symbolic notation and fractions as requested.
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A company manufactures and sells x microwaves per month. The monthly price-demand equation is: p(x) = 280 – 0.4z (a) Assuming that the manufacture would like to charge between $100 and $500 for microwaves, find the price that maximizes the revenue. (b) What is the maximum revenue from selling microwaves?
The price that maximizes revenue for the given monthly price-demand equation with price range between $100 and $500 is $220.
(b) The maximum revenue from selling microwaves can be found by multiplying the price that maximizes revenue by the corresponding quantity of microwaves sold. Using the price-demand equation p(x) = 280 - 0.4x, we can find the quantity that corresponds to the price that maximizes revenue as follows:p(x) = 280 - 0.4x220 = 280 - 0.4x0.4x = 60x = 150Therefore, the quantity that corresponds to the price that maximizes revenue is x = 150. The maximum revenue can be found by multiplying the price and quantity:Revenue = Price * QuantityRevenue = $220 * 150Revenue = $33,000Therefore, the maximum revenue from selling microwaves is $33,000.
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Tammy knits blankets and scarves. On the first day of a craft fair, she sells 2 blankets and 5 scarves for $104. On the second day of the craft fair, she sells 3 blankets and 4 scarves for $128. How much does 1 blanket cost?
The cost of one blanket after calculations sums up as $32.
Let b be the cost of one blanket and s be the cost of one scarf in dollars. We can set up a system of equations based on the information given:
2b + 5s = 104
3b + 4s = 128
We want to solve for the cost of one blanket, so we'll solve for b in terms of s. We can start by multiplying the first equation by 3 and the second equation by 2 to create a system of equations where the coefficients of b will cancel each other out when we subtract the two equations:
6b + 15s = 312
6b + 8s = 256
Subtracting the second equation from the first, we get:
7s = 56
Dividing both sides by 7, we get:
s = 8
Now we can substitute s = 8 into either of the original equations to solve for b:
2b + 5(8) = 104
2b + 40 = 104
2b = 64
b = 32
Therefore, one blanket costs $32.
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A triangle has vertices at (–4, 0), (2, 8), and (8, 0). What are the coordinates of the centroid, circumcenter, and orthocenter? If needed, write mixed numbers with a single space between the whole number and the fractional parts.
The centroid of the given triangle (2, 8/3), the circumcenter of the triangle is (0,2), the orthocenter of the triangle is (2,8).
What is centroid?
In geometry, the centroid of a triangle is the point where the three medians of the triangle intersect.
To find the centroid of a triangle with vertices at (x1,y1), (x2,y2), and (x3,y3), we can use the formula:
(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3
Using this formula, we get the centroid of the given triangle as:
((-4 + 2 + 8)/3 , (0 + 8 + 0)/3) = (2, 8/3)
To find the circumcenter, we first need to find the equations of the perpendicular bisectors of any two sides of the triangle. Let's choose the sides formed by the points (-4,0) and (2,8), and (2,8) and (8,0).
The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1,4), and the slope of the line passing through (-4,0) and (2,8) is (8-0)/(2-(-4)) = 8/6 = 4/3. So the equation of the perpendicular bisector of this side is y-4 = -(3/4)(x+1), or 3x + 4y = 8.
Similarly, the midpoint of the second side is ((2+8)/2, (8+0)/2) = (5,4), and the slope of the line passing through (2,8) and (8,0) is (0-8)/(8-2) = -8/6 = -4/3. So the equation of the perpendicular bisector of this side is y-4 = (3/4)(x-5), or 3x - 4y = -8.
The intersection of these two lines gives us the circumcenter of the triangle. Solving the system of equations:
3x + 4y = 8
3x - 4y = -8
We get x = 0, y = 2. So the circumcenter of the triangle is (0,2).
To find the orthocenter, we first need to find the equations of the altitudes from any two vertices of the triangle. Let's choose the vertices (2,8) and (8,0).
The altitude from (2,8) is perpendicular to the side formed by the points (-4,0) and (8,0), so its slope is 0. Therefore, its equation is y = 8.
The altitude from (8,0) is perpendicular to the side formed by the points (-4,0) and (2,8), so its slope is the negative reciprocal of the slope of that side, which is -4/3. Using the point-slope form, we get the equation:
y - 0 = (-4/3)(x - 8)
y = -4x/3 + 32/3
To find the intersection of these two lines, we can substitute y = 8 into the second equation:
8 = -4x/3 + 32/3
-8/3 = -4x/3
x = 2
Substituting x = 2 into either equation gives us y = 8, so the orthocenter of the triangle is (2,8).
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The first two terms in an arthemetic progression are 2 and 9. The last term in the progression is the only number greater than 150. Find the sum of all the terms in the progression
The sum of all the terms in the arithmetic progression is 3507.
The common difference in an arithmetic progression is the difference between any two consecutive terms. Let the common difference be d. Then, the third term is 2 + d, the fourth term is 2 + 2d, and so on. Also, let the last term be n.
Since the last term is greater than 150, we can write n = 2 + (n-2)d > 150. Solving this inequality, we get d < 74. Therefore, the common difference can be 1, 2, 3, ..., 73.
Using the formula for the sum of an arithmetic progression, we get the sum of all the terms as (n/2)(first term + last term) = (n/2)(2 + n d) = (n/2)(11 + (n-1)d).
We can substitute n = (last term - first term)/d + 1 and solve for the sum. This gives us the final answer of 3507.
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Let f be a differentiable function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3. f 6 . The function g is differentiable and g(x) = f-1(x) for all x. What is the value of g'(4) =
The value of g'(4) is -1/3 if f is a differential function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3.
First, let's use the information given to find the equation of the tangent line to f at x=2. We know that f(2) = 4 and f'(2) = -4, so the equation of the tangent line at x=2 is
y - 4 = -4(x - 2)
Simplifying, we get
y = -4x + 12
Now let's use the fact that g(x) = f-1(x) for all x. This means that g(f(x)) = x for all x. We want to find g'(4), which is the derivative of g at x=4.
Using the chain rule, we have
g'(4) = [g(f(4))]'
Since f(4) = 6 and g(f(4)) = g(6) (since g(x) = f-1(x)), we can rewrite this as
g'(4) = [g(6)]'
Now we can use the fact that g(x) = f-1(x) to rewrite g(6) as f-1(6)
g'(4) = [f-1(6)]'
Now we need to find the derivative of f-1(x) with respect to x. To do this, we can use the fact that f(f-1(x)) = x for all x. Differentiating both sides with respect to x using the chain rule, we get
f'(f-1(x)) * (f-1)'(x) = 1
Solving for (f-1)'(x), we get
(f-1)'(x) = 1 / f'(f-1(x))
Now we can plug in x=6 and use the information given to find f'(f-1(6)). Since f(4) = 6, we know that f-1(6) = 4. Therefore
f'(f-1(6)) = f'(4)
Using the tangent line equation we found earlier, we know that f(2) = 4 and f'(2) = -4. Therefore, the slope of the line connecting (2,4) and (4,6) is
(6 - 4) / (4 - 2) = 1
Since the line connecting (2,4) and (4,6) is the tangent line to f at x=2, we know that this slope is equal to f'(2). Therefore
f'(4) = f'(f-1(6)) = f'(4)
Now we can plug in x=6 and f'(4) into our expression for (f-1)'(x)
(f-1)'(6) = 1 / f'(4)
Substituting this into our expression for g'(4), we get
g'(4) = [f-1(6)]' = (f-1)'(6) = 1 / f'(4)
Plugging in f'(4) = f'(f-1(6)) = f'(4), we get
g'(4) = 1 / f'(4) = 1 / (-3) = -1/3
Therefore, g'(4) = -1/3.
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Gross Monthly Income: Jackson works for a pipe line company and is paid $18. 50 per hour. Although he will have overtime, it is not guaranteed when or where, so Jackson will only build a budget on 40 hours per week. What is Jackson’s gross monthly income for 40 hours per week? Type in the correct dollar amount to the nearest cent. Do not include the dollar sign or letters.
A. Gross Annual Income: $
B. Gross Monthly Income: $
To find Jackson's gross monthly income for 40 hours per week, follow these steps:
1. Calculate his weekly income: Multiply his hourly wage ($18.50) by the number of hours he works each week (40 hours).
2. Calculate his monthly income: Multiply his weekly income by the number of weeks in a month (4 weeks).
A. Gross Annual Income: To find this, multiply his monthly income by 12 (the number of months in a year).
B. Gross Monthly Income: This is the answer we need to find.
Step-by-step calculations:
1. Weekly income = $18.50 * 40 hours = $740
2. Monthly income = $740 * 4 weeks = $2,960
A. Gross Annual Income: $2,960 * 12 = $35,520
B. Gross Monthly Income: $2,960
The answer:
A. Gross Annual Income: $35,520
B. Gross Monthly Income: $2,960
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Rewrite this equation without absolute value. y=|x-5|+|x+5| if -5
The equation y = |x - 5| + |x + 5| can be rewritten as:
y = { -2x - 10, for x < -5,
{ 10, for -5 ≤ x ≤ 5,
{ 2x + 10, for x > 5.
When -5 < x < 5, both |x - 5| and |x + 5| are non-negative. So we can rewrite y = |x - 5| + |x + 5| as follows:
If x < -5, then x - 5 < -5 and x + 5 < 0, so we have:
y = -(x - 5) - (x + 5) = -2x - 10
If -5 ≤ x ≤ 5, then x - 5 < 0 and x + 5 ≥ 0, so we have:
y = -(x - 5) + (x + 5) = 10
If x > 5, then x - 5 ≥ 0 and x + 5 > 5, so we have:
y = (x - 5) + (x + 5) = 2x + 10
Therefore, the equation y = |x - 5| + |x + 5| can be rewritten as:
y = { -2x - 10, for x < -5,
{ 10, for -5 ≤ x ≤ 5,
{ 2x + 10, for x > 5.
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Given question is incomplete, the complete question is below
Rewrite each equation without absolute value for the given conditions. y = |x-5| + |x+5| if -5 < x < 5
can yall help me with this and this is due today!
a) The experimental probability of rolling an even number is given as follows: 12/25.
b) The theoretical probability of rolling an even number is given as follows: 1/2.
c) With a large number of trials, there might be a difference between the experimental and the theoretical probabilities, but the difference should be small.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The number of trials in which an even number is rolled is given as follows:
88 + 69 + 83 = 240.
Hence the experimental probability is given as follows:
240/500 = 12/25.
For each roll, 3 out of 6 numbers are even, hence the theoretical probability is given as follows:
p = 3/6
p = 1/2.
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Your supervisor asks you to separate 4,780 castings into 25 piles. When you complete the job, how many castings will you have left over
Answer:5
Step-by-step explanation:
4780/25=191.2
You don't want an odd amount of castings in different piles.
191*25=4755
4780-4755=5
I think i read the question wrong. Sorry if i did
When separating 4,780 castings into 25 piles, there will be 5 castings left over.
Explanation:A fraction is a numerical expression representing a part of a whole. It consists of a numerator (the top number) that indicates how many parts are considered, and a denominator (the bottom number) that shows the total number of equal parts in the whole. Fractions are typically expressed as a/b, where "a" is the numerator and "b" is the denominator. They are used in various mathematical operations, including addition, subtraction, multiplication, and division, and in real-life scenarios involving proportions and portions.
In order to determine the number of castings left over when separating 4,780 castings into 25 piles, we can use division. Divide 4,780 by 25 to find the number of castings in each pile.
The quotient is 191.2. Since we can't have a fraction of a casting, we round down to 191.
To find the number of castings left over, subtract the total number of castings in the piles from the original total. 4,780 - (191 x 25)
= 4,780 - 4,775
= 5
Therefore, when you complete the job, you will have 5 castings left over.
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A machine has an initial cost of $40,000 and operating costs of $3500 each year. Its salvage value decreases by $4,000 each year. The machine is now 4 years old.
Assuming an effective annual interest rate of 12%, what is the cost of owning and operating the machine for one more year.
The cost of owning and operating the machine for one more year is approximately $11,160.71.
To calculate the cost of owning and operating the machine for one more year, we need to consider both the operating costs and the decrease in salvage value.
The operating costs for one more year will be $3,500.
To calculate the decrease in salvage value, we need to know the salvage value of the machine after 4 years of use. If the salvage value decreased by $4,000 each year, then after 4 years the salvage value will have decreased by $16,000. Therefore, the salvage value of the machine after 4 years is:
Salvage value after 4 years = Initial salvage value - Total decrease in salvage value
Salvage value after 4 years = $40,000 - $16,000
Salvage value after 4 years = $24,000
To calculate the cost of owning and operating the machine for one more year, we need to consider the difference between the salvage value at the end of the additional year and the salvage value after 4 years. Assuming a straight-line depreciation model, the salvage value of the machine after one more year will be:
Salvage value after one more year = Salvage value after 4 years - (4 x $4,000)
Salvage value after one more year = $24,000 - $16,000
Salvage value after one more year = $8,000
To calculate the cost of owning and operating the machine for one more year, we need to calculate the present value of the difference between the salvage values, plus the operating costs for one more year. Assuming an effective annual interest rate of 12%, the present value can be calculated using the formula:
PV = FV / (1 + r[tex])^n[/tex]
where PV is the present value, FV is the future value, r is the effective annual interest rate, and n is the number of years.
The future value of the salvage value difference plus the operating costs for one more year is:
FV = Salvage value after one more year - Salvage value after 4 years + Operating costs for one more year
FV = $8,000 - $24,000 + $3,500
FV = -$12,500
(Note that the negative value indicates a cost.)
Plugging in the values, we get:
PV = -$12,500 / (1 + 0.12[tex])^1[/tex]
PV = -$11,160.71
Therefore, the cost of owning and operating the machine for one more year is approximately $11,160.71.
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As a reward for Musa's diligence and agreement, his father decided to distribute a sum of money amounting to 5,800 dinars to him and his brothers, the one with the highest average taking the largest amount, while that the one with the third rank gets an amount that is half of what the one with the first rank takes. Translate this situation as an equation with an unknown X, where X is the amount that the first rank takes. Solve the resulting equation , Solve an exact value . Gives exclusively between two consecutive natural numbers Each of the three sums
The amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
Let's assume that there are three brothers, including Musa. Let X be the amount of money that the brother with the highest average takes, and let Y be the amount of money that the brother with the third rank takes.
According to the given conditions, we can write the following equations:
X + Y + (5800 - X - Y) = 5800 (The total amount of money distributed should be equal to 5800 dinars)X > Y (The brother with the highest average should take the largest amount)X is an integer valueLet's simplify equation 1:
X + Y = 2900
Also, we know that:
X = (2Y + X)/2
(The amount that the third rank takes is half of what the first rank takes)
Simplifying this equation:
2X = 2Y + X
X = 2Y
Substituting this value of X in equation X + Y = 2900:
3Y = 2900
Y = 2900/3
Y ≈ 966.67
As the amount given must be a whole number between two consecutive natural numbers, we can round Y to the nearest natural number:
Y = 967
Then, X = 2Y = 2*967 = 1934
Therefore, the amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
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A hexagon has 4 sides of length 3x +5 and the other 2 sides are each 3 units shorter than the other 4 sides. What is the perimeter, P, of the hexagon in terms of x?
The perimeter, P, of the hexagon in terms of x is 18x + 24.
To find the perimeter, P, of the hexagon in terms of x, we'll consider the given side lengths.
The hexagon has 4 sides of length 3x + 5. The other 2 sides are each 3 units shorter than the other 4 sides, so their length is (3x + 5) - 3 = 3x + 2.
Now, we can calculate the perimeter by adding the lengths of all 6 sides:
P = (4 * (3x + 5)) + (2 * (3x + 2))
First, distribute the numbers to the expressions inside the parentheses:
P = (12x + 20) + (6x + 4)
Next, combine like terms:
P = 18x + 24
So, the perimeter, P, of the hexagon in terms of x is 18x + 24.
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If a card never cost to ask what the first minimum payment would be for $3000 balance transfer at 4. 99% there is currently no balance on the account and the fee is 4% the minimum payment would be what
The first minimum payment would be $62.40 as it is higher than $25.
To determine the first minimum payment for a $3000 balance transfer at 4.99% with a 4% fee, you need to first calculate the balance transfer fee and add it to the initial balance. Then, you'll need to determine the minimum payment based on the credit card issuer's policy.
1. Calculate the balance transfer fee: $3000 * 4% = $120
2. Add the balance transfer fee to the initial balance: $3000 + $120 = $3120
3. The minimum payment depends on the credit card issuer's policy. Typically, the minimum payment is a percentage of the balance or a fixed amount, whichever is higher. For example, if the issuer requires a minimum payment of 2% of the balance or $25, whichever is higher:
- Calculate 2% of the balance: $3120 * 2% = $62.40
- Since $62.40 is higher than $25, the first minimum payment would be $62.40.
Please note that the actual minimum payment may vary depending on the specific credit card issuer's policy.
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100%
A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were
repaired during the first year of ownership.
How many of the 960 DVD players were repaired in the first year?
If 5 out of every 24 players were repaired during the first year of ownership, then 200 of the 960 DVD players were repaired in the first year.
Based on the manufacturer's records, we know that 5 out of every 24 players were repaired in the first year of ownership. To find out how many out of the 960 DVD players were repaired in the first year, we can set up a proportion:
5/24 = x/960
To solve for x, we can cross-multiply:
5 * 960 = 24x
4800 = 24x
x = 200
Therefore, 200 of the 960 DVD players were repaired in the first year, which is approximately 20.8% of the total shipped.
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Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 78 students in the highest quartile of the distribution, the mean score was x = 177. 30. Assume a population standard deviation of = 8. 19. These students were all classified as high on their need for closure. Assume that the 78 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 1. 8 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number. )
We need a sample size of at least n = 214 students to estimate the population mean score if we wish to be 99% confident that the sample mean score is within 1. 8 points of the population mean score for students who are high on the need for closure
We are given that the population standard deviation is σ = 8.19 and the sample mean is X = 177.30 for a sample of n = 78 students in the highest quartile of the "need for closure" scale.
We want to determine the sample size needed to estimate the population mean score for high need for closure students within a margin of error of 1.8 points, with 99% confidence.
Since we do not know the population mean score, we will use a t-distribution to calculate the margin of error. We can use the formula:
margin of error = t_(α/2) * (σ/√n)
where t_(α/2) is the critical value from the t-distribution for a 99% confidence level with (n - 1) degrees of freedom. We can find this value using a t-table or a calculator, and we get t_(α/2) = 2.64 (rounded to two decimal places) for n - 1 = 77 degrees of freedom.
Substituting the given values into the formula, we have:
1.8 = 2.64 * (8.19/√n)
Solving for n, we get:
n = [2.64 * (8.19/1.8)]^2 = 214 (rounded up to the nearest whole number)
Therefore, we need a sample size of at least n = 214 students to estimate the population mean score for high need for closure students within a margin of error of 1.8 points, with 99% confidence.
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What is the answer?
What is the gradient of the blue line?
Step-by-step explanation:
the gradient = the slope = the incline = ...
many different names for the same thing.
however you call it, it is the ratio
y coordinate change / x coordinate change
whet going from one point on the line to another.
for questions like this we should look for points with integer coordinates (going through a vertex of the coordinate grid squares).
I see for example right at the left beginning (0, 1).
the next one is then (4, 2).
when going from (0, 1) to (4, 2) :
x changes by +4 (from 0 to 4).
y changes by +1 (from 1 to 2).
so, the slope or gradient is
+1/+4 = 1/4
When a figure is translated on the coordinate plane you should add or subtract x and y? Is this statement true or false?
Answer: True
Step-by-step explanation:
A rectangular garden has an area of 100 square meters. The length of the garden is 10 meters more than the width. What is the perimeter of the garden?
Answer:
40 meters
Step-by-step explanation:
Let's assume the width of the garden is x meters, then the length of the garden would be (x+10) meters since we know that the length is 10 meters more than the width.
We also know that the area of the garden is 100 square meters, therefore:
Area = Length x Width
100 = (x+10) x x
Expanding the equation we get:
100 = x^2 + 10x
Rearranging the terms we have:
x^2 + 10x - 100 = 0
Solving for x using the quadratic formula, we get:
x = 5 or x = -20
Since the width cannot be negative, we discard the negative solution and conclude that the width of the garden is 5 meters. Therefore, the length of the garden is (5+10) = 15 meters.
The perimeter of the garden is the sum of the four sides, which is:
Perimeter = 2 x (Length + Width)
Perimeter = 2 x (15 + 5)
Perimeter = 2 x 20
Perimeter = 40 meters
Therefore, the perimeter of the garden is 40 meters.
Answer:
Let's start by using algebra to solve for the width of the garden:
- Let w be the width of the garden.
- Then the length of the garden is w + 10.
- The area of the garden is length x width, so we can write the equation: (w + 10)w = 100.
- Expanding the left side of the equation, we get: w^2 + 10w = 100.
- Rearranging the equation, we get: w^2 + 10w - 100 = 0.
- Factoring the left side of the equation, we get: (w + 20)(w - 10) = 0.
- Solving for w, we get: w = -20 or w = 10. Since the width cannot be negative, we have w = 10.
Now that we know the width of the garden is 10 meters, we can find the length by adding 10 meters:
- Length = width + 10 = 10 + 10 = 20 meters.
Finally, we can find the perimeter of the garden by adding up the lengths of all four sides:
- Perimeter = 2(length + width) = 2(20 + 10) = 2(30) = 60 meters.
Therefore, the perimeter of the garden is 60 meters.
Explain how you can determine if (x + 3) is a factor of the given polynomial through factoring and polynomial division:
(A-APR. 2) (A1. 26. A, A1. 26. B)
x3-x2-12x
fast with step by step explanation if possible please!
To determine whether (x + 3) is a factor of the polynomial x^3 - x^2 - 12x, we can use polynomial division.
Step 1: Write the divisor, (x + 3), on the left side of a long division symbol and the dividend, x^3 - x^2 - 12x, on the right side.
x + 3 | x^3 - x^2 - 12x
Step 2: Divide the first term of the dividend, x^3, by the first term of the divisor, x, and write the result, x^2, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the dividend.
lua
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2
Step 3: Bring down the next term of the dividend, -12x, and write it next to the remainder, -4x^2.
lua
Copy code
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2 - 12x
Step 4: Divide the first term of the new dividend, -4x^2, by the first term of the divisor, x, and write the result, -4x, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the previous subtraction.
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Para medir lo largo de un lago se construyeron los siguientes triangulos semejantes, en los cuales se tiene que : AC = 215m, A 'C= 50m, A'B=112m. Cual es la longitud del lago?
using the given similar triangles, the length of the lake is approximately 26.05 meters.
We have,
In the given similar triangles, we have the following information:
Length of the longer side of the larger triangle: AC = 215m
Length of the longer side of the smaller triangle: A'C = 50m
Length of the corresponding shorter side of the smaller triangle: A'B = 112m
Let's denote the length of the lake (the longer side of the smaller triangle) as x.
Now, we can set up a proportion between the sides of the two triangles:
AC / A'C = A'B / x
Substitute the given values:
215 / 50 = 112 / x
Now, solve for x:
215x = 50 * 112
Divide both sides by 215:
x = (50 * 112) / 215
x ≈ 26.05
Thus,
The length of the lake is approximately 26.05 meters.
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The complete question:
To measure the length of a lake, the following similar triangles were built, in which it is necessary to: AC = 215m, A'C= 50m, A'B=112m. What is the length of the lake?
What is the probability that the drug will wear off between 200 and 220 minutes?
P(200
The probability that the drug will wear off between 200 and 220 minutes is 0.4.
To calculate the probability that the drug will wear off between 200 and 220 minutes, we need to know the cumulative distribution function (CDF) of the drug's effect duration. Let's say the CDF is denoted by F(t), where t is the time in minutes.
Then, the probability that the drug will wear off between 200 and 220 minutes is given by:
P(200 < T < 220) = F(220) - F(200)
This is because the probability of the drug wearing off between two specific times is equal to the difference between the CDF values at those times.
For example, if F(200) = 0.2 and F(220) = 0.6, then:
P(200 < T < 220) = 0.6 - 0.2 = 0.4
Therefore, the probability that the drug will wear off between 200 and 220 minutes is 0.4.
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The following relation is a function:
{(-2, 4), (3, 0), (-4, 3), (-2, -1), (0, -4)}
true
false
The relation of function is False.
This relation is not a function because the input value -2 is associated with two different output values (4 and -1). In a function, each input can only have one corresponding output.
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Fred bought 5 liters of liquid laundry detergent, 3,250 milliliters of fabric softener, and 2. 8 liters of bleach. Select true or false for each statement. Fred bought 45 milliliters more fabric softener than bleach. ?
Fred bought 2. 45 liters more laundry detergent than bleach. ?
Fred bought 450 milliliters more fabric softener than bleach. ?
Fred bought 220 milliliters more laundry detergent than bleach. ?
Fred bought 0. 45 liters more fabric softener than bleach. ?
Fred purchased more 2. 45 liters of laundry detergent than bleach is false statement, Fred took 450 milliliters more fabric softener than bleach is false, Fred placed 220 milliliters more laundry detergent than bleach is true, Fred has taken 0. 45 liters more fabric softener than bleach is false.
Fred in total bought 5 liters of liquid laundry detergent which is equal to 5000 milliliters. Then he bought 3,250 milliliters of fabric softener and 2.8 liters of bleach which is equal to 2800 milliliters.
Fred purchased 45 milliliters more fabric softener than bleach. This statement is false because Fred bought 250 milliliters less fabric softener than bleach.
Fred bought 2.45 liters more laundry detergent than bleach. This statement is false because Fred bought 2.2 liters more laundry detergent than bleach.
Fred has taken 450 milliliters more fabric softener than bleach. This statement is false because Fred bought 250 milliliters less fabric softener than bleach.
Fred on the event of taking 220 milliliters more laundry detergent than bleach is considered a true statement because Fred bought 2200 milliliters more laundry detergent than bleach.
Fred on the event of taking 0.45 liters more fabric softener than bleach is considered a false statement due to the fact that Fred bought 0.25 liters less fabric softener than bleach.
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A helicopter takes off from the roof of a building and travels at 100 mph on a bearing of 558°e. the flight takes 3. 8 hr. to the nearest mile, how far south and
how far east has the helicopter traveled?
can someone pls help me
The helicopter traveled approximately 175.5 miles east and 299.1 miles south.
How to find the helicopter traveled?Let's say the building is located at point A and the helicopter travels to point B. We know that the bearing of B from A is 558°e, which means the angle formed by the line AB and the east direction is 558°.
Next, we can use trigonometry to find the horizontal and vertical components of the distance traveled. Let x be the horizontal distance (in miles) traveled by the helicopter and y be the vertical distance (in miles) traveled. We can then use the following equations:
cos(558°) = x / d
sin(558°) = y / d
where d is the total distance traveled (in miles). We can also use the formula:
d = r * t
where r is the speed of the helicopter (100 mph) and t is the time taken for the flight (3.8 hours). Substituting this into the first two equations, we get:
x = d * cos(558°)
y = d * sin(558°)
d = r * t = 100 * 3.8 = 380 miles (rounded to the nearest mile)
Substituting the values of d and the angle into the equations for x and y, we get:
x = 380 * cos(558°) ≈ -175.5 miles
y = 380 * sin(558°) ≈ 299.1 miles
Note that the negative sign for x indicates that the helicopter traveled west, not east. We can take the absolute value of x to get the distance traveled east:
|x| ≈ 175.5 miles
Therefore, the helicopter traveled approximately 175.5 miles east and 299.1 miles south.
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PLEASE HELP ASAP I HAVE 10 MIN 30 PTS
A 72. 0-gram piece of metal at 96. 0 °C is placed in 130. 0 g of water in a calorimeter at 25. 5 °C. The final temperature in the calorimeter is 31. 0 °C. Determine the specific heat of the metal. Show your work by listing various steps, and explain how the law of conservation of energy applies to this situation.
The specific heat of the metal is approximately 0.392 J/g°C. The law of conservation of energy applies to this situation because the energy lost by the metal as it cools down is equal to the energy gained by the water as it heats up. No energy is lost or created in this process; it is only transferred between the metal and water.
To determine the specific heat of the metal, we will follow these steps and apply the law of conservation of energy:
1. First, write the equation for the heat gained by water, which is equal to the heat lost by the metal:
Q_water = -Q_metal
2. Next, write the equations for heat gained by water and heat lost by the metal using the formula Q = mcΔT:
m_water * c_water * (T_final - T_initial, water) = -m_metal * c_metal * (T_final - T_initial, metal)
3. Plug in the known values:
(130.0 g) * (4.18 J/g°C) * (31.0 °C - 25.5 °C) = -(72.0 g) * c_metal * (31.0 °C - 96.0 °C)
4. Solve for the specific heat of the metal (c_metal):
c_metal = [(130.0 g) * (4.18 J/g°C) * (5.5 °C)] / [(72.0 g) * (-65.0 °C)]
5. Calculate the value:
c_metal = 0.392 J/g°C
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A)Irene purchased some earrings that regularly cost $55 for a friend’s birthday. Irene used a "20% Off" coupon.
How much did Irene pay for the earrings?
Show your work. Highlight your answer.
B)Irene’s friend did not like the gift so she tried to return the earrings. She did not have the receipt, so the store would only give her store credit for 50% of the purchase price.
How much credit did Irene’s friend receive?
Show your work. Highlight your answer.
C)What is the percent change from what Irene paid and what her friend returned it for?
Show your work. Highlight your answer
A) Irene pays $44 for the earrings.
B) Irene’s friend received $22 as credit.
C) Percent change from what Irene paid and what her friend returned it for is 50%
A) Cost of earing = $55
Discount coupon = 20%
Total cost Irene pay = 55 - (20% of 55)
Total cost Irene pay = 55 - ( 55 × 20/100)
Total cost Irene pay = 55 - 11
Total cost Irene pay = 44
B) Credit given by store = 50%
Credit received = 50% of 44
Credit received = 44 × 50/100
Credit received = 22
C) Percent change = [tex]\frac{final - initial }{initial}[/tex] × 100
Percent change = [tex]\frac{44-22}{44}[/tex] × 100
Percent change = 50%
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Let G be the center of the equilateral triangle XYZ. A dilation centered at G with scale factor -3/4 is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find A/the area of XYZ.
The calculated value of the expression A/the area of XYZ is [tex]\frac{49\sqrt3}{216}[/tex]
Finding the value of A/the area of XYZFrom the question, we have the following parameters that can be used in our computation:
Center of the equilateral triangle XYZ = GDilation centered at G with scale factor = 3/4By the ratio of corresponding sides (see attachment for figure), we have
(x + 2y)/(2x + y) = 3/4
By comparison, we have
x + 2y = 3
2x + y = 4
This gives
(x, y) = (5/3, 2/3)
The triangles are equilateral triangles
So, we have
Area of XYZ = 1/2 * side length² * sin(60)
This gives
Area of XYZ = 1/2 * (2x + y)² * sin(60)
Substitute the known values in the above equation
Area of XYZ = 1/2 * (4)² * sin(60)
Evaluate
Area of XYZ = 4√3
The region A is a trapezoid
So, the area is
A = 1/2 * Sum of parallel sides * height
So, we have
A = 1/2 * (x + y) * (x² - y²)
Recall that (x, y) = (5/3, 2/3)
So, we have
A = 1/2 * (5/3 + 2/3) * ((5/3)² - (2/3)²)
Evaluate
A = 49/18
Finding A/the area of XYZ, we have
A/the area of XYZ = 49/18 ÷ 4√3
This gives
A/the area of XYZ = 49/72 ÷ √3
Rationalize
A/the area of XYZ = [tex]\frac{49\sqrt3}{216}[/tex]
Hence, the value of the expression is [tex]\frac{49\sqrt3}{216}[/tex]
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Complete question
Let G be the center of the equilateral triangle XYZ. A dilation centered at G with scale factor -3/4 is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find A/the area of XYZ.
XY = 2x + y
X'Z' = x + 2y
Region A is a trapezoid with parallel sides y & x and height x² - y²
What is the meaning of a relative frequency of 0. 56
A relative frequency of 0.56 means that out of the total number of observations in a given sample or population, 56% of those observations belong to a particular category or have a certain characteristic.
In other words, it is the proportion or fraction of the observations that fall into that particular category or have that characteristic, relative to the total number of observations. For example, if we had a sample of 100 people and 56 of them had brown hair, then the relative frequency of brown hair would be 0.56 or 56%.
To calculate relative frequency, you divide the frequency of a specific event or category by the total number of observations. In this case, the specific event or category occurs 56% as often as the total events or categories observed.
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