The slopes and y-intercept of a graph are two key components of the equation that describes the relationship between two variables.
The slope of a graph is the measure of how steeply the line is rising or falling. It is calculated by dividing the change in the y-axis by the change in the x-axis between two points on the line. A positive slope indicates that the line is rising, while a negative slope indicates that the line is falling.
The y-intercept of a graph is the point where the line crosses the y-axis. It is the value of y when x=0. The y-intercept is a fixed point on the line and is used to help determine the equation of the line.
Together, the slope and y-intercept of a graph can be used to write an equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
7*. All lengths are in cm. Find the area of the right angled
triangle.
x-14( shortest side)
2x+5( hypotenuse)
2x+3( remaining side)
Answer:
504 cm^2.
Step-by-step explanation:
By Pythagoras:
(2x + 5)^2 = (2x + 3)^2 + (x - 14)^2
4x^2 + 20x + 25 = 4x^2 + 12x + 9 + x^2 - 28x + 196
20x - 12x + 28x + 25 - 9 - 196 = x^2
x^2 - 36x + 180 = 0
(x - 6)(x - 30) = 0
x = 6, 30.
As one of the sides is x - 14, x mst be 30 as its length has to be positive.
So the area of the triangle
= 1/2 * (x - 14) 8 (2x + 3)
= 1/2 * (30-14)(60 + 3)
= 1/2 * 16 * 63
= 504 cm^2.
tomas earns 0.5% commision on the sale price of a new car. On wednesday, he sells a new car for $24,500. How much commison does tomas earn on this sale
Tomas earns a commission of $122.50 on the sale of the new car.
Tomas earns a 0.5% commission on the sale price of a new car. On Wednesday, he sells a new car for $24,500. To determine the commission Tomas earns, we need to multiply the sale price by the commission rate. The commission rate is given as 0.5%, which can be expressed as a decimal by dividing by 100. So, 0.5% is equal to 0.005 as a decimal.
Now, we can calculate Tomas's commission by multiplying the sale price by the commission rate. In this case, we multiply $24,500 by 0.005:
$24,500 x 0.005 = $122.50
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In 3 minutes, a conveyor belt moves 200 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area
If both belts are used, it will take 2.25 minutes to move the cans to the storage area
To solve this problem, we need to use the concept of rate of work. We know that the larger belt can move 200 pounds of aluminum in 3 minutes, which means its rate of work is 200/3 = 66.67 pounds per minute. Similarly, the smaller belt can move the same quantity of cans in 9 minutes, which means its rate of work is 200/9 = 22.22 pounds per minute.
When both belts are used together, their rates of work add up, so the total rate of work is 66.67 + 22.22 = 88.89 pounds per minute. We can use this rate of work to find how long it will take to move the cans to the storage area.
Let's assume that it takes x minutes to move the cans using both belts. Then, we can set up the following equation:
88.89x = 200
Solving for x, we get:
x = 2.25 minutes
Therefore, it will take 2.25 minutes to move the cans to the storage area using both belts.
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The mean of a sample is a. always equal to the mean of the population. b. always smaller than the mean of the population c. computed by summing the data values and dividing the sum by (n - 1) d. computed by summing all the data values and dividing the sum by the number of items
The mean of a sample is computed by summing all the data values and dividing the sum by the number of items in the sample. Thus, the correct answer is d.
Option a is incorrect because the mean of a sample is not always equal to the mean of the population, unless the sample is a complete representation of the population (which is often not the case).
Option b is incorrect because the mean of a sample can be greater than, equal to, or smaller than the mean of the population, depending on the sampling method and the characteristics of the population.
Option c is incorrect because the sample mean is computed by summing the data values and dividing the sum by the number of items in the sample minus one only if the sample is taken from a normally distributed population and the standard deviation of the population is unknown. Otherwise, the sample mean is computed by dividing the sum of the data values by the number of items in the sample.
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The area of triangle ABC is 4 root 2. Work out the value of x
Question is from mathswatch
if you pay $ for a 20-year zero coupon bond with a face value of $, what is your annual compound rate of return?
The annual compound rate of return on this 20-year zero coupon bond is 6%. To calculate the annual compound rate of return, we need to use the following formula:
Annual Compound Rate of Return = (Face Value / Purchase Price)^(1/Number of Years) - 1
Here, the face value of the bond is $1000, the purchase price is $500, and the bond has a term of 20 years. Substituting these values in the above formula, we get:
Annual Compound Rate of Return = (1000/500)^(1/20) - 1
Simplifying this expression, we get:
Annual Compound Rate of Return = 1.06 - 1
Annual Compound Rate of Return = 0.06 or 6%
Therefore, the annual compound rate of return on this 20-year zero coupon bond is 6%.
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Which expression is equivalent to: (5²)⁴ ?
(Exponent Form Only, please)
.....................
Which equation represents a line that is perpendicular to the line
represented by 2x - y = 7?
(1) y = -x + 6
(2) y = x + 6
(3) y = -2x + 6
(4) y = 2x + 6
In a hypothesis test for a mean in one population, where you have H subscript 0 colon space mu space equals space 40 comma space H subscript A colon space mu space not equal to space 40 and the population standard deviation is sigma space equals space 12, what are the critical value(s) of the sample mean x with bar on top if your sample size is 36 and the significance level alpha = 0. 05?
Group of answer choices
Using the t-distribution table with a sample size of 36 and a significance level of 0.05, we find the critical t-value to be ±2.03 (with 34 degrees of freedom, which is n-1).
What are the critical values of the sample mean for a hypothesis test with a sample size of 36, population standard deviation of 12, significance level of 0.05, and null hypothesis of μ = 40?
To explain, we use the t-distribution to find the critical values because the population standard deviation is known. Since the alternative hypothesis is two-tailed (H_A: μ ≠ 40), we need to find two critical values.
With a sample size of 36, the degrees of freedom are 34 (n-1), so we use a t-distribution table with 34 degrees of freedom and a significance level of 0.05. From the table, we find the critical t-value to be ±2.03.
Therefore, if the calculated t-value falls outside of this range, we can reject the null hypothesis H0: μ = 40 in favor of the alternative hypothesis H_A: μ ≠ 40.
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Hello! Help please thank you
Answer:
2(2(3) + 2(5) + 3(5)) = 2(6 + 10 + 15) = 2(31)
= 62
D is the correct answer.
Sally earns a weekly salary of $450 plus a 6. 5% commission on sales at a boutique. How much would she make in a work week if she sold $650 worth of merchandise?
To find out Sally's total earnings for the week, we need to consider her base salary and the commission on her sales. Her base salary is $450, and she earns a 6.5% commission on $650 worth of merchandise.
First, let's calculate her commission:
6.5% of $650 = 0.065 * $650 = $42.25
Now, we can add her base salary to the commission:
Total earnings = Base salary + Commission
Total earnings = $450 + $42.25
Total earnings = $492.25
So, Sally would make $492.25 in a work week if she sold $650 worth of merchandise.
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3. Compute the integral JSS, udv, where U is the part of the ball of radius 3, centered at 0,0,0), that lies in the 1st octant. Recall that the first octant is the part of the 3d space where all three coordinates I, y, z are nonnegative. (Hint: You may use cylindrical or spherical coordinates for this computation, but note that the computation with cylindrical coordinates will involve a trigonometric substitution - 30 spherical cooridnates should be preferable.)
To compute the integral JSS, udv, where U is the part of the ball of radius 3, centered at 0,0,0), that lies in the 1st octant, we can use spherical coordinates. Since the region is defined as having all three coordinates nonnegative, we can set our limits of integration as follows: 0 ≤ ρ ≤ 3, 0 ≤ θ ≤ π/2, and 0 ≤ φ ≤ π/2.
Using the Jacobian transformation, we have:
JSS, udv = ∫∫∫U ρ²sinφ dρdθdφ
Substituting in our limits of integration, we get:
JSS, udv = ∫0^π/2 ∫0^π/2 ∫0³ ρ²sinφ dρdθdφ
Evaluating the integral, we get:
JSS, udv = (3³/3) [(sin(π/2) - sin(0))] [(1/2) (π/2 - 0)]
JSS, udv = 9/2 π
Therefore, the value of the integral JSS, udv, over the part of the ball of radius 3 that lies in the 1st octant is 9/2π.
To compute the integral JSS, udv, over the region U, which is the part of the ball of radius 3 centered at (0,0,0) and lies in the first octant, we will use spherical coordinates for this computation as it's more preferable.
In spherical coordinates, the volume element is given by dv = ρ² * sin(φ) * dρ * dφ * dθ, where ρ is the radial distance, φ is the polar angle (between 0 and π/2 for the first octant), and θ is the azimuthal angle (between 0 and π/2 for the first octant).
Now, we need to set up the integral for the volume of the region U:
JSS, udv = ∫∫∫ (ρ² * sin(φ) * dρ * dφ * dθ), with limits of integration as follows:
ρ: 0 to 3 (radius of the ball),
φ: 0 to π/2 (for the first octant),
θ: 0 to π/2 (for the first octant).
So, the integral becomes:
JSS, udv = ∫(0 to π/2) ∫(0 to π/2) ∫(0 to 3) (ρ² * sin(φ) * dρ * dφ * dθ)
By evaluating this integral, we will obtain the volume of the region U in the first octant.
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$3,900 at 1% compounded
annually for 6 years
_____________________________
A = P (1 + 1%) n = 3,900 (1 + 1%) ⁶= $4,139.92_____________________________
bacteria in a dirty glass triple every day. if there are 25 bacteria to start, how many are in the glass after 15 days
Answer:
Step-by-step explanation:
25x3x15
Determine where the absolute extrema of f(x)= 4x/ x²+1 on the interval [-4,0] occur. 1. The absolute maximum occurs at x= 2. The absolute minimum occurs at x =
The absolute maximum of f(x) = 4x / (x² + 1) on the interval [-4,0] occurs at x = 2 and the absolute minimum occurs at x = -4.
To find the absolute extrema, we first find the critical points by setting the derivative of f(x) equal to zero:
f'(x) = (4(x² + 1) - 8x²) / (x² + 1)² = 0
Simplifying, we get:
4 - 4x² = 0
x² = 1
x = ±1
Since x = -4 and x = 0 are also endpoints of the interval, we evaluate f(x) at these five points:
f(-4) = -8/17
f(-1) = -4/5
f(0) = 0
f(1) = 4/5
f(2) = 8/5
Thus, the absolute maximum occurs at x = 2, where f(x) = 8/5, and the absolute minimum occurs at x = -4, where f(x) = -8/17.
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If arc wvx=(13x+9) and angle wxz=(5x+36) find angle wxy
Angle WXY is vertical to angle WXZ, they are equal, therefore, angle WXY is also 141 degrees.
How to find the angle WXY using information about the arc WVX and angle WXZ in a circle?To find the angle WXY, we need to use the properties of angles formed by intersecting chords in a circle. The angles formed by intersecting chords are related to the arcs intercepted by those chords.
Given that the arc WVX is equal to (13x + 9) and the angle WXZ is equal to (5x + 36), we can set up an equation:
Angle WXZ = [tex]\frac{1}{2}[/tex] * Arc WVX
(5x + 36) = [tex]\frac{1}{2}[/tex] * (13x + 9)
To solve for x, we'll multiply both sides of the equation by 2 to eliminate the fraction:
2(5x + 36) = 13x + 9
10x + 72 = 13x + 9
Subtracting 10x and 9 from both sides, we get:
72 - 9 = 13x - 10x
63 = 3x
Dividing both sides by 3, we find:
x = 21
Now that we have the value of x, we can substitute it back into the equation for the angle WXZ to find its value:
Angle WXZ = 5x + 36 = 5(21) + 36 = 105 + 36 = 141 degrees
Since angle WXY is vertical to angle WXZ, they are equal. Therefore, the angle WXY is also 141 degrees.
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CAN somebody pl help
The expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.
How to evaluate for the area of the shaded regionThe area of the shaded region is the area of the semicircle subtracted from the area of the rectangle
radius of the semicircle is also the width of the rectangle, so;
area of the rectangle = 8 yd × 4 yd = 32 yd²
area of the semicircle = (π × 4 yd × 4 yd)/2
area of the semicircle = 8π yd²
area of the shaded region = 32 yd² - 8π yd²
area of the shaded region = 8(4 - π) yd²
Therefore, the expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.
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Which of the following statements proves the series –128 + 96 – 72 + 54 – … is geometric? r equals negative three fourths r equals three fourths r equals negative four thirds r equals four thirds
Answer: To determine if the series –128 + 96 – 72 + 54 – ... is a geometric series, we need to check if the ratio between consecutive terms is constant.
Let's calculate the ratio between the second and first terms:
96 / (-128) = -3/4
Now let's calculate the ratio between the third and second terms:
-72 / 96 = -3/4
The ratio between the fourth and third terms is:
54 / (-72) = -3/4
We can see that the ratio between consecutive terms is always the same: -3/4. Therefore, the series –128 + 96 – 72 + 54 – ... is a geometric series with a common ratio of -3/4.
So the answer is r equals negative three fourths.
Step-by-step explanation:
The series provided is a geometric series because each term after the first is found by multiplying the previous term by -3/4. Therefore, the common ratio 'r' equals -3/4.
Explanation:In a geometric series, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In the series given –128 + 96 – 72 + 54 – …, the second term (96) divided by the first term (-128) equals -3/4, the third term (-72) divided by the second term (96) also equals -3/4, and so on. This constant ratio between successive terms demonstrates that this is indeed a geometric series. Therefore, the statement that proves this is a geometric series is 'r equals negative three fourths' where r represents the common ratio.
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Pls help i really need help on this
Where the function f(x) = x² + 2x - 3 is given, note that the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4. See the attached graph.
What is the explanation for the above response?
To find the minimum and maximum points of the function f(x), we can complete the square:
f(x) = x^2 + 2x - 3
= (x + 1)^2 - 4
We can see that the function is in the vertex form f(x) = a(x - h)^2 + k, where the vertex is (-1, -4).
Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the vertex is the minimum point. Therefore, the minimum value of the function f(x) is -4.
To find the x-intercepts, we can set f(x) = 0:
(x + 1)^2 - 4 = 0
(x + 1)^2 = 4
Taking the square root of both sides, we get:
x + 1 = ±2
x = -1 ± 2
Therefore, the x-intercepts of the function f(x) are x = -3 and x = 1.
In summary, the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4, which occurs at the vertex (-1, -4).
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A basic pattern of 1 blue bead and 1 green bead is used to make a bracelet that is 37cm long. The bracelet is made by repeating the basic pattern 10 times. The length of a blue bead is Bcm. The length of a green bead is 1. 2cm. Complete the question to represent the length of the bracelet
Answer: Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:
10 × (2.5 + 1.2) = 37 cm.
Step-by-step explanation:
To represent the length of the bracelet, we need to determine the length of each repetition of the basic pattern and then multiply it by the number of times the pattern is repeated.
The length of each repetition of the basic pattern is the sum of the length of one blue bead and one green bead, which is:
B + 1.2 cm
Since the basic pattern is repeated 10 times, the total length of the bracelet is:
10 × (B + 1.2) cm
And we know that the total length of the bracelet is 37 cm, so we can set up an equation:
10 × (B + 1.2) = 37
Simplifying the equation, we can divide both sides by 10:
B + 1.2 = 3.7
Subtracting 1.2 from both sides, we get:
B = 2.5
Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:
10 × (2.5 + 1.2) = 37 cm.
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HELPPPPPPPPPp WILL GIVE BRAINLEISTTT!!!
Answer:
100
Step-by-step explanation:
i think this is right
Qn in attachment
.
..
Answer:
option d
Step-by-step explanation:
24
pls mrk me brainliest (*￣(ｴ)￣*)
From monday through friday, earl works in the bookstore on 1 and in the athletic center on another 2 days. on saturday and sunday, earl cooks food 50% of the days. how many days does earl work in a week? what percent of monday through friday does earl work?
Earl works a total of 3 days in a week. From Monday through Friday, he works in the bookstore on 1 day and in the athletic center on 2 days. On Saturday and Sunday, he cooks food on 50% of the days, which would be a total of 1 day. Therefore, he works a total of 3 days in a week.
To calculate the percentage of Monday through Friday that Earl works, we need to first calculate the total number of days in a week, which is 7. Then, we need to subtract the weekend days, which are Saturday and Sunday, leaving us with 5 days.
Finally, we can calculate the percentage by dividing the number of days Earl works from Monday through Friday (which is 1) by the total number of weekdays (which is 5), and multiplying by 100. So, Earl works 20% of Monday through Friday.
In summary, Earl works 3 days in a week, 1 day in the bookstore and 2 days in the athletic center. He also cooks food on 1 day during the weekend. Earl works 20% of Monday through Friday.
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Skyler has 4 1/3 hours until she needs to go to bed she watches a movie for 2 2/9 hours how much time does she have left
Step-by-step explanation:
just convert the 1/3 and times 3 to both it's numerator and denominator.
once you have the same denominator as the other mixed number, you can start to minus.
Answer:
2 1/9 hrs
Step-by-step explanation:
4 1/3 = 13/3 = 39/9
2 2/9 = 20/9
39/9 - 20/9 = 19/9 = 2 1/9 hrs
or,
(4 - 2) + (3/9 - 2/9) = 2 1/9 hrs
Given logaMN = 6, log aN/M = 2 and logaN^m = 16, find M.
The value of M is a^4.
Given the information, we can express the given logarithms as follows:
1) log_a(MN) = 6
2) log_a(N/M) = 2
3) log_a(N^m) = 16
From equation (1), we can write:
MN = a^6
From equation (2), we can write:
N/M = a^2 → N = a^2 * M
Now, substitute N from equation (2) into equation (3):
log_a((a^2 * M)^m) = 16
Using the power rule of logarithms, we get:
m * log_a(a^2 * M) = 16
Since log_a(a^2 * M) = 2log_a(a) + log_a(M) = 2 + log_a(M), we have:
m * (2 + log_a(M)) = 16
We don't have enough information to determine the value of 'm', but we don't need it to find the value of 'M'.
Now, substitute N back into the equation MN = a^6:
M * a^2 * M = a^6
Divide both sides by M * a^2:
M = a^(6-2) = a^4
So, the value of M is a^4.
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Find the values of x and y that make the quadrilateral a parallelogram
DEFG
5x-4
3y+9
10x-24
2y+16
Answer:
x = 4, y = 7
Step-by-step explanation:
3y + 9 = 2y + 16
y = 7
10x - 24 = 5x - 4
5x = 20
x = 4
values of x is 4 and y is 7
Identify the fractions between 1/16 and 5/8
The fractions between 1/16 and 5/8 are 3/16 and 5/16
Identifying the fractions between 1/16 and 5/8The fraction expressions are given as
1/16 and 5/8
The above fractions are proper fractions because numerator < denominator
Express the fraction 5/8 as a denominator of 16
So, we have the following equivalent fractions
1/16 and 10/16
This means that the fractions between 1/16 and 5/8 can be represented as
a/16
Where
1 < a < 10
So, we have
Possible fraction = 3/16 and 5/16
Hence, the fractions between 1/16 and 5/8 are 3/16 and 5/16
Note that there are other possible fractions too
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If a bag of marbles contains 6 yellow, 8 blue, and 6 red marbles, then what is the probability of not pulling out a
blue or yellow marble?
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases.
we have here a total of 6 + 8 + 6 = 20 marbles.
to not pull a blue or yellow marble is in this context the same event as pulling a red marble.
so, the desired cases are 6 (red).
which we can get directly from the 6 red marbles, or by counting off the undesired cases : 20 - 8 - 6 = 6.
and the probabilty for not pulling a blue or yellow marble (or simply pulling a red marble) is
6/20 = 3/10 = 0.3
WHATS THE AREA PLEASE HELP DUE in 5 minutes
Answer:
The answer to your problem is, 201.06 or 201.1
Step-by-step explanation:
To find the area you use the formula:
A = π [tex]r^2[/tex]
R = Radius
A = Area
We know the radius of the circle is 8
So replace A = π [tex]r^2[/tex]
= π × 8 ≈ 201.06193
Or 201.06 or 201.1
Thus the answer to your problem is, 201.06 or 201.1
6. Yu is considering two different banks for his $3,000 savings account: OPTION A 4% FOR 20 YEARS SIMPLE INTEREST OPTION B 2% FOR 10 YEARS COMPOUND INTEREST 8 What is the interest earned on option A? O What is the total value on option A? What is the interest earned on option B? O What is the total value on option B? 10 Which is the better option?
The interest earned on Option A is $2400 and Option B is $666.18. Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.
To calculate the interest earned and total value for each option, we can use the following formulas:
For Option A:
- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400
- Total value = principal + interest earned = 3000 + 2400 = $5400
For Option B:
- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18
- Total value = principal + interest earned = 3000 + 666.18 = $3666.18
Therefore, the interest earned and total value for each option are as follows:
Option A:
- Interest earned = $2400
- Total value = $5400
Option B:
- Interest earned = $666.18
- Total value = $3666.18
To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.
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