The sculpture was worth £332.80 three years ago when it depreciates by 20% each year
To determine how much the sculpture was worth 3 years ago, we need to apply the depreciation rate of 20% per year for the past three years.
First, we need to calculate how much the sculpture would be worth after one year of depreciation:
650 - (0.20)(650) = 520
This means that after the first year, the sculpture would be worth £520.
Next, we can calculate the value of the sculpture after the second year of depreciation:
520 - (0.20)(520) = 416
After two years, the sculpture would be worth £416.
Finally, we can calculate the value of the sculpture after the third year of depreciation:
416 - (0.20)(416) = 332.8
Therefore, the sculpture was worth £332.80 three years ago.
To check this answer, we can also use another method: We can calculate the value of the sculpture using the compound interest formula, where the initial value is £x, the annual depreciation rate is 20%, and the time period is three years:
650 = x[tex](1-0.20)^{2}[/tex]
Simplifying this equation, we get:
x = 650 / [tex]0.80^{2}[/tex] = 332.80
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find the missing side length
Answer:
Step-by-step explanation:
[tex]x^{2}[/tex]=a²+b²
x²=6²+2.5²
x²=36+6.25
x²=42.25
√x=√42.25
x=6.5
Answer:
6.5
Step-by-step explanation:
6^2 + 2.5^2 = c^2
•36 + 6.25 = c^2
•42.25 = c^2
• find square root of 42.25 = 6.5
• 6.5 = C
The ratio of an objects weight on earth to its weight on the moon is 6:1 the first person to walk on the moon was neil armstrong. he weighed 165 pounds on earth. what would be the proportion of this word problem?
The proportion of this word problem is 6 : 1 where Neil Armstrong weighed approximately 27.5 pounds on the moon.
The proportion of a word problem represents the relationship between two or more quantities. In this case, the proportion can be set up as:
Weight on Earth : Weight on Moon = 6 : 1
Using the information provided in the problem, we know that Neil Armstrong weighed 165 pounds on Earth. We can use this information to find his weight on the moon by setting up a proportion:
165 : x = 6 : 1
where x represents his weight on the moon. To solve for x, we can cross-multiply and simplify:
165 * 1 = 6 * x
x = 165/6
x ≈ 27.5
Therefore, Neil Armstrong weighed approximately 27.5 pounds on the moon.
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Andre is playing greatest product. he says the greatest product it’s possible to make in the game is 987x65 do you agree or disagree with andre
Andre's claim that the greatest product possible in the game is 987x65 is incorrect.
Why is Andre's claim incorrect?
While 987x65 is a large product, it is not the greatest possible product in the game. In fact, a larger product can be obtained by multiplying the two largest numbers available in the game. Without knowing the specific rules of the game, it is impossible to determine the exact greatest product, but it is certain that 987x65 is not it.
To elaborate, the game likely has certain constraints or rules that limit the numbers that can be multiplied. It may be possible to combine multiple numbers to create a larger product, or to find a different pair of numbers that yield a larger product. Therefore, without knowing the specifics of the game's rules, it is impossible to determine the greatest possible product.
The actual greatest product possible in the game will depend on the specific rules and constraints that are in place. It may be possible to combine multiple numbers to create an even larger product, or to find a different pair of numbers that yield a larger product. Without knowing the specifics of the game's rules, it is impossible to determine the greatest possible product.
In mathematics, the concept of maximum or greatest products is important and is studied in various areas such as algebra, number theory, and calculus. In real-world applications, maximum products play a critical role in determining profits, yields, and returns on investments in economics and finance. In engineering, the concept of maximum product is used in optimization problems, where the goal is to maximize or minimize a certain function or output.
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Find the probability that a randomly selected point within the circle falls in the white area. R=4 cm 2. 5 cm 3 cm 3 cm [?]% Round to the nearest tenth of a percent.
The probability is approximately 45.4% (rounded to the nearest tenth of a percent).
To find the probability that a randomly selected point within the circle falls in the white area, we need to find the area of the white region and divide it by the total area of the circle.
The total area of the circle is:
A = πr² = π(4 cm)² = 16π cm²
The area of the white region can be found by subtracting the area of the two semicircles from the area of the circle:
White area = A - 2(1/2π(2.5 cm)²) = 16π - 2(4.375π) = 7.25π cm²
So, the probability that a randomly selected point within the circle falls in the white area is:
P(white area) = (white area)/(total area) = (7.25π)/(16π) ≈ 45.4%
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Dominic and his parents plan to share the cost of his college education. The annual
tuition cost for the college he wants to attend is $7,260 per year. His parents will pay 80%
of the annual tuition. He has one year to save his portion of the first year's tuition. What is
the minimum monthly amount he needs to save?
Dominic will need to save a minimum of $121 per month to pay for his portion of the first year's tuition.
Dominic's parents will pay 80% of the annual tuition cost, which is:
0.8 x $7,260 = $5,808
So, Dominic will need to pay the remaining 20% of the tuition cost, which is:
0.2 x $7,260 = $1,452
Since Dominic has one year to save his portion of the tuition, he will need to save:
$1,452 / 12 months = $121 per month
Therefore, Dominic will need to save a minimum of $121 per month to pay for his portion of the first year's tuition.
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The library in natchitoches had about 60000 volumes in march 2004 and was adding about 400 volumes per month Write an equation expressing y, the total number of volumes in the library, in terms of x, the number of mouths after march 2004
The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is y = 400x + 60,000.
What is the equation for the volumes in library?The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is determined as follows;
Using general linear equation;
y = mx + b
where:
y is the total number of volumes in the libraryx is number of months after March 2004m is the rate of change b is the initial number of volumes in the library in March 2004The initial volume as at March = 60,000
the rate = 400 volumes / month
The equation is determined as;
y = 400x + 60,000
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Identify the equation of the line that passes through the pair of points (−3, 6) and (−5, 9) in slope-intercept form.
Therefore, the equation of the line that passes through the points (-3, 6) and (-5, 9) in slope-intercept form is:
y = -3/2 x + 3/2
Step-by-step explanation:
To find the equation of the line that passes through the points (-3, 6) and (-5, 9) in slope-intercept form (y = mx + b), we need to first find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-3, 6) and (x2, y2) = (-5, 9).
m = (9 - 6) / (-5 - (-3))
m = 3 / (-2)
m = -3/2
Now that we have the slope, we can use either of the two given points and the slope to find the y-intercept (b) of the line:
y = mx + b
6 = (-3/2)(-3) + b
6 = 9/2 + b
b = 6 - 9/2
b = 3/2
from a circular sheet of a radius 5cm, a circle of radius 3cm is removed. find the area of the remaining sheet
Check the picture below.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=5\\ r=3 \end{cases}\implies A=\pi (5^2-3^2)\implies A\approx 50.27~cm^2[/tex]
If a data set has many very large data values, then the mean wil be
the median
a larger than
b. the same as
c. equal to
d. smaller than
A data set has many very large data values, then the mean will be larger than the median. The correct option is a.
In a dataset with large values, the mean is influenced by outliers and extreme values, whereas the median is not. The median is the value that divides the data into two equal halves, while the mean is calculated by summing up all values and dividing by the total number of values.
Thus, in a skewed dataset with large values, the mean tends to be pulled towards the larger values, resulting in a larger mean than the median. This effect is more pronounced in datasets with a high variance. Therefore, option (a) is the correct answer.
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please answer, i have 5 mins
Use each of these rules to create 4 ordered pairs using the two sequences.
The first rule is add 12, then divide by 2, starting from 4.
The second rule is multiply by 2, then subtract 2, starting from 3.
Which table shows the 4 ordered pairs created using the two sequences?
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers zero, four, six, and seven. Under column rule 2 are the numbers three, five, nine, and seventeen. Under the column labeled ordered pair are zero and three, four and five, six and nine, and seven and seventeen.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers two, six, eight, and nine. Under column rule 2 are the numbers two, four, ten, and twenty-eight. Under the column labeled ordered pair are two and two, six and four, eight and ten, and nine and twenty-eight.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers four, eight, ten, and eleven. Under column rule 2 are the numbers three, four, six, and ten. Under the column labeled ordered pair are four and three, eight and four, ten and six, and eleven and ten.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers six, eight, twelve, and twenty. Under column rule 2 are the numbers one, eight, twenty-two, and fifty. Under the column labeled ordered pair are six and one, eight and eight, twelve and twenty-two, and twenty and fifty.
Ordered pairs must be placed in the following order: (6, 1), (8, 8), (12, 22). (20, 50). The right answer is D.
What is arithmetic?According to the assertions, it deals with a number of operations in mathematics.
For the first series, let the number be x, and for the second, let it be y.
The first rule is to multiply by 2, then, beginning with 6, remove 4.
The sequence can be written as 6 is the first number: = 2x - 4
next number = 2(6) - 4
= 12-4
= 8
The following phrase is thus 8. The following two terms can be written as 12 and 20.
Values of x = 6, 8, 12, 20
The second rule is to add three and then multiply by two, counting backward from one.
= (y + 3)2
First term = 1
Next term = (1 + 3)2
= 8
The next two words can be acquired in a similar manner.
y = 1, 8, 22, 50
Therefore, ordered pairs must be placed in the following order: (6, 1), (8, 8), and (12, 22). (20, 50). The right answer is D.
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Correct question:
The first rule is to multiply by 2, then subtract 4 starting from 6. The second rule is to add 3, then multiply by 2 starting from 1. What are the first four ordered pairs using the two sequences?
A. (0, 0) (6, 1), (8, 2), (12, 22)
B. (6, 1), (10, 8), (14,22), (22, 50)
C. (6, 1), (8, 8), (12, 20), (20, 45)
D. (6, 1), (8, 8), (12, 22), (20, 50)
Solve for the unknown value.
x
61
42
degrees.
Hi! To solve for the unknown value in the equation "x + 61 + 42 = degrees", follow these steps:
1. Combine the known values (61 and 42) by adding them together: 61 + 42 = 103.
2. Rewrite the equation with the combined values: x + 103 = degrees.
3. To isolate the unknown value (x), subtract 103 from both sides of the equation: x = degrees - 103.
So, the unknown value x can be found by subtracting 103 from the given degrees value.
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Help please! I'm really struggling here ((40 points))
Answer:
k = - 0.36 or k = 30.36
Step-by-step explanation:
k² - 30k = 11
to complete the square
add ( half the coefficient of the k- term )² to both sides
k² + 2(- 15)k + 225 = 11 + 225
(k - 15)² = 236 ( take square root of both sides )
k - 15 = ± [tex]\sqrt{236}[/tex] ≈ ± 15.36 ( to the nearest hundredth )
add 15 to both sides
k = 15 ± 15.36
Then
k = 15 - 15.36 = - 0.36
or
k = 15 + 15.36 = 30.36
Determine how long it will take for 650 mg of a sample of chromium-51, which has a half life of 28 days, to decay to 200 mg.
It will take approximately 60.9 days for 650 mg of chromium-51 to decay to 200 mg.
What is Equation ?
An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
The decay of a radioactive substance can be modeled by the following equation:
N(t) = N₀ * [tex](1/2)^{(t/T) }[/tex]
where:
N(t) is the amount of the substance remaining after time t
N₀ is the initial amount of the substance
T is the half-life of the substance
We can use this equation to find how long it will take for 650 mg of chromium-51 to decay to 200 mg.
Let's first find the decay constant (λ) for chromium-51:
λ = ㏒(2) ÷ T = ㏒(2) ÷ 28 = 0.0248 (rounded to 4 decimal places)
Now we can use the equation:
N(t) = N₀ * [tex]e^{(-λ*t)}[/tex]
We know that N₀ = 650 mg and N(t) = 200 mg, so we can solve for t:
200 = 650 * [tex]e^{(-0.0248*t)}[/tex]
Dividing both sides by 650:
0.3077 = [tex]e^{(-0.0248*t)}[/tex]
Taking the natural logarithm of both sides:
㏒(0.3077) = -0.0248*t
Solving for t:
t = ㏒(0.3077) : (-0.0248) ≈ 60.9 days
Therefore, it will take approximately 60.9 days for 650 mg of chromium-51 to decay to 200 mg.
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If a cone with a volume of 6 cm3 is enlarged by a scale factor of 2, what is the volume, in cubic centimeters, of the similar, larger cone?
The volume of the larger cone will be 48 cm³.
This is because when a shape is enlarged by a scale factor of 2, the volume is increased by a factor of 2³ (or 8). So, 6 x 8 = 48.
When we enlarge a shape by a scale factor, we are multiplying all of its dimensions by that factor. In the case of a cone, this means that we are increasing the radius and the height of the cone by a factor of 2.
We can use the formula for the volume of a cone to find out how the volume changes when we enlarge it. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.
If we multiply the radius and the height of the cone by 2, we get a new cone with a radius of 2r and a height of 2h. Plugging these new values into the formula for the volume of a cone, we get:
V' = (1/3)π(2r)²(2h) = (1/3)π(4r²)(2h) = (8/3)πr²h
We can simplify this expression by multiplying the original volume by 8/3:
V' = (8/3) x 6 = 48
So the volume of the larger cone is 48 cubic centimeters.
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Helps me please What is most likely to push the price of a company's stock higher?
O A. An increase in demand for the company's stock
OB. An increase in demand for the company's products
O C. An increase in tariffs paid by the company's competitors
O D. An increase in the exchange rate for the US dollar
SUBMIT
PREVIOUS
e to search
O
RI
The most likely factor to push the price of a company's stock higher is an increase in demand for the company's stock. Option A.
A stock's price will often increase when there is greater demand than there is supply. Various things, such as good news about the company's financial performance, new product releases or innovations, positive analyst reports, or general market trends, can contribute to this increased demand.
The company's financial performance may benefit from a rise in product demand, but if investors do not view it as a key growth engine for the business, it may not necessarily transfer into a higher stock price.
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NEED HELP FAST!!!! Please answer both questions
Therefore, the molarity of the sugar solution is 0.3704 M at 25°C. Therefore, the molality of the NaCl solution is 1.8994 mol/kg.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=). The expressions on either side of the equal sign may contain variables, constants, coefficients, and mathematical operations.
Here,
1. To calculate the molarity of a sugar solution, we need to first determine the number of moles of solute (glucose, C6H12O6) present in the solution. We can then divide this number of moles by the volume of the solution in liters to obtain the molarity. The number of moles of glucose in the solution can be calculated as follows:
Number of moles = mass of solute / molar mass of solute
Number of moles = 100.0 g / 180 g/mol
Number of moles = 0.5556 mol
Next, we can calculate the molarity of the solution using the following formula:
Molarity = number of moles / volume of solution (in L)
Molarity = 0.5556 mol / 1.50 L
Molarity = 0.3704 M
2. To calculate the molality of a solution, we need to know the number of moles of solute (NaCl) per kilogram of solvent (water).
First, let's calculate the number of moles of NaCl:
Number of moles = mass of NaCl / molar mass of NaCl
Number of moles = 200.0 g / 58.5 g/mol
Number of moles = 3.4188 mol
Next, we need to calculate the mass of the solvent (water) in kilograms:
Mass of solvent = 2.00 kg - 0.200 kg
Mass of solvent = 1.80 kg
Note that we subtracted the mass of the NaCl from the total mass of the solution to obtain the mass of the solvent.
Finally, we can calculate the molality of the solution using the following formula:
Molality = number of moles of solute / mass of solvent (in kg)
Molality = 3.4188 mol / 1.80 kg
Molality = 1.8994 mol/kg
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1 A) (In(x) +1) 2x In(2) Denivate h(x) = √xen(x) h( 1 B) In() + V2V C) V 2. In(x) + 2 D) In (30) + 2ln()
The derivatives of the given functions are:
A) h'(x) = (1/2)√xen(x)[2+In(x)]
B) h'(x) = (1/x) - V2V
C) h'(x) = (2/x) + 2
D) h'(x) = 0
A) To find the derivative of h(x) = √xen(x), we use the product rule of differentiation. Let u = √x and v = en(x).
Then, h(x) = uv, and h'(x) = u'v + uv'.
We have u' = (1/2)x^(-1/2) and v' = en(x)(1/x).
Substituting the values, we get h'(x) = (1/2)√xen(x)[2+In(x)].
B) To find the derivative of h(x) = In(x) + V2V, we use the sum rule of differentiation.
Using the properties of logarithms, we rewrite the function as h(x) = In(x) + (1/2)ln(x).
Taking the derivative, we get h'(x) = (1/x) - V2V.
C) To find the derivative of h(x) = V2 In(x) + 2, we use the sum rule of differentiation.
Taking the derivative, we get h'(x) = (2/x) + 2.
D) To find the derivative of h(x) = In(30) + 2ln(x), we use the sum rule of differentiation.
Taking the derivative, we get h'(x) = 0, since the derivative of a constant is always zero.
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What is the shape of the height and weight distribution? A. The height and weight distribution exhibit a negative and a positive skew, respectively. B. Both the height and weight distribution exhibit a positive skew. C. Both the height and weight distribution exhibit a negative skew. D. Both the height and weight distribution are symmetric about the mean. E. The height and weight distribution exhibit a positive and a negative skew, respectively
D. Both the height and weight distribution are symmetric about the mean.
What is the shape of the height and weight distribution? If a distribution is symmetric about the mean, it means that the values are evenly distributed on either side of the mean, resulting in a bell-shaped curve. The height and weight of individuals in a population tend to follow this type of distribution, with the majority of individuals clustering around the mean height and weight values. This is known as a normal distribution, which is a type of symmetric distribution. Therefore, option D is the correct answer. Options A, B, C, and E are not correct because they indicate skewness in the distribution, which is not typically observed in height and weight data.Learn more about distribution,
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PLEASE HELP MEE
4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. Find the capacity of 1 thumb drive (x) and the capacity of 1 compact disk (y)
The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.
What is the capacity of 1 thumb drive and 1 compact disk?The first step is to form the system of equations that represent the information in the question:
4x + y = 18 equation 1
4x + 3y = 22 equation 2
The elimination method would be used to determined the required values.
Subtract equation 1 from equation 2
2y = 4
y = 4/2
y = 2
Substitute for y in equation 1: 4x + 2 = 18
4x = 18 - 2
4x = 16
x = 16/4
x = 4
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The surface area of the square pyramid is 84 square inches. The side length of the base is 6 what is the value of x
With the surface area of the square pyramid 84 square inches and side length of the base is 6, the value of x is 4 inches, by assuming x as the slant height of the square pyramid.
Assuming that x refers to the slant height of the square pyramid, we can use the formula for the surface area of a square pyramid to solve for x:
Surface area of a square pyramid = base area + (0.5 x perimeter of base x slant height)
Since the base of the square pyramid is a square with side length 6,
the base area is 6² = 36 square inches.
The perimeter of the base is 4 times the side length, so it is 4 x 6 = 24 inches.
Substituting these values into the formula and simplifying, we get:
84 = 36 + (0.5 x 24 x x)
84 - 36 = 12x
48 = 12x
x = 4
Therefore, the value of x, the slant height of the square pyramid, is 4 inches.
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The price of a shirt after 25% discount is R480 calculate the original price of the shirt
discount amount= CP-Disount percentage
or,480=CP-25/100
or480×100+25 =CP
48025 is the original price of shirt
8. The table shows the number of different
kinds of sodas sold at a gas station on a
Monday.
A.
B.
Kind of Soda
18
If the gas station had 80 customers on
Tuesday, how many customers can be
predicted to get a Dr. Pepper?
C. 45
Coks
Sprite
Dr. Papper
7-Up
36
Number of
Bottles Sold
11
D. Not Here
Jack's bill at a restaurant came to $51.31 he wants to leave a 15% tip how much will the new total be including tip
The new total bill including the tip of 15% is $59.01.
Calculating the new bill including the tipTo find the amount of the tip, we can multiply the total bill by the percentage as a decimal:
tip = 0.15 * $51.31 = $7.70
To find the new total including the tip, we can add the tip to the original bill:
new total = $51.31 + $7.70 = $59.01
So the new total, including a 15% tip, will be $59.01.
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A food truck owner charges z dollars per burrito combo and $1. 50 for a side of guacamole. The expression 5 (x + 1. 50) represents the
total cost of 5 burrito combos and 5 sides of guacamole.
Which expression also represents the total cost of 5 burrito combos, which cost a dollars each, and 5 sides of guacamole, which cost $1. 50
each?
0
The expression that fits perfect for the given requirement is 5z + 7.50, under the condition that a food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole.
Here we have to apply the principles of solving algebraic equations, due to the expression provided.
From the given information, here the food truck owner charges z dollars per burrito combo along with $1.50 for a side of guacamole.
According to the information it is given that the expression is 5(z+1.50) which helps to state the total cost of 5 burrito combos and 5 sides of guacamole.
Lets now formulate the expression for the given required equation
= 5(z + 1.50)
= 5z + 7.50.
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A food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole. The expression 5(z+1.50) represents the total cost of 5 burrito combos and 5 sides of guacamole. What expression also represent the cost of 5 burrito combos and 5 sides if guacamole that cost 1.50 each.
A system of linear equations is shown on the graph.
The graph shows a line that passes through negative 10 comma 10, negative 5 comma 9, and 0 comma 8. The graph also shows another line that passes through negative 8 comma 12, negative 5 comma 9, and 0 comma 4.
What is the solution to the system of equations?
There are infinitely many solutions.
There is no solution.
There is one unique solution (−5, 9).
There is one unique solution (0, 8).
The correct statement regarding the solution to the system of equations is given as follows:
There is one unique solution (−5, 9).
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.For the first line, the points are given as follows:
(-10, 10) and (0,8).
Hence the equation is:
y = -0.2x + 8.
For the second line, the points are given as follows:
(-8, 12) and (0,4).
Hence the equation is:
y = -x + 4.
Then the x-coordinate of the solution is obtained as follows:
-0.2x + 8 = -x + 4
0.8x = -4
x = -5.
The y-coordinate is given as follows:
y = -(-5) + 4 = 9.
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Write an equation and solve to find the numbers and show work.
9. Doubling the difference between a number and 4 is 6 more than the number.
10. Five less than the opposite of a number is three times the sum of the number and -7.
9. Let's start by defining the variable.
Let's say the number we're trying to find is "x".
Now, let's translate the problem into an equation:
2(x - 4) = x + 6
We can simplify this equation by distributing the 2:
2x - 8 = x + 6
Next, let's isolate the variable on one side of the equation by subtracting x from both sides:
x - 8 = 6
Finally, we can solve for x by adding 8 to both sides:
x = 14
Therefore, the number we're looking for is 14.
10. Let's start by defining the variable.
Let's say the number we're trying to find is "x".
Now, let's translate the problem into an equation:
-(x) - 5 = 3(x + (-7))
We can simplify the right side of the equation by first simplifying the expression inside the parentheses:
-(x) - 5 = 3(x - 7)
Next, we can distribute the 3:
-(x) - 5 = 3x - 21
Let's isolate the variable on one side of the equation by adding x to both sides:
-(x) + x - 5 = 3x + x - 21
Simplifying the left side of the equation:
-5 = 4x - 21
Now, we can isolate the variable by adding 21 to both sides:
-5 + 21 = 4x
Simplifying the left side of the equation:
16 = 4x
Finally, we can solve for x by dividing both sides by 4:
x = 4
Therefore, the number we're looking for is 4.
Solve the differential equation. dy + 6ydx=9e -⁶x dx y=
The general solution to the given differential equation:
[tex]y = (9x + C)e^(-6x)[/tex]
To solve the given differential equation, dy + 6ydx = 9e^(-6x)dx, we can first rewrite it as a first-order linear differential equation:
[tex]dy/dx + 6y = 9e^(-6x)[/tex]
Now, we will find the integrating factor, which is e^(∫P(x)dx), where P(x) is the coefficient of y in the equation:
Integrating factor =[tex]e^(∫6dx) = e^(6x)[/tex]
Next, we multiply the entire differential equation by the integrating factor:
[tex]e^(6x)(dy/dx + 6y) = 9e^(-6x)e^(6x)[/tex]
This simplifies to:
[tex]e^(6x)(dy/dx) + 6e^(6x)y = 9[/tex]
Now, the left side of the equation is the derivative of the product of y and the integrating factor:
[tex]d/dx(y * e^(6x)) = 9[/tex]
To solve for y, integrate both sides with respect to x:
[tex]∫[d/dx(y * e^(6x))]dx = ∫9dx[/tex]
This results in:
[tex]y * e^(6x) = 9x + C[/tex]
Finally, we solve for y by dividing by e^(6x):
[tex]y = (9x + C)e^(-6x)[/tex]
And that is the general solution to the given differential equation.
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What is the probability that a randomly selected participant dreams in black and white or color?
The evaluated probability of randomly choosing a participant dreams in black and white or color is 0.13, under the condition that the given Students are passing from psychology surveyed 200 of their fellow students regarding their dreams.
Probability means the possible chances of an event occurring in a particular time frame. It is a considered a branch of mathematics that deals with the occurrence of a random event.
The value is presented from zero to one. Probability has been induced in math to predict how prone are the events going to occur. The meaning of probability is basically the express something that is likely to happen.
Black Probability = 4/200=0.02
White Probability = 12/200=0.06
Probability of all other color = 10/200=0.05
So, probability of randomly choosing a participant dreams in black and white or color =0.02+0.06+0.05=0.13
Therefore, the probability of randomly selecting participant dreams in black and white or color = 0.13
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The complete question is
Students majoring in psychology surveyed 200 of their fellow students about their dreams. The results of the survey are shown in the Venn diagram. Let B be the event that the participant dreams in black and white and let C be the event that the participant dreams in color.
What is the probability that a randomly selected participant dreams in black and white or color?
Find the value of x.
Step-by-step explanation:
180° + 42° + x = 360°
222° + x = 360°
x = 138°
Answer:
138
Step-by-step explanation:
Since a circle is 360 degrees and it is split in half, each half would equal 180 degrees so you would subtract 42 from 180
Three students each calculated the volume of a sphere with a radius of 6 centimeters.
-Diego found the volume to be 288
cubic centimeters.
-Andre approximated 904 cubic centimeters.
-Noah calculated 226 cubic centimeters.
Do you agree with any of them? Explain your reasoning.
Answer:
It seems that the three students each calculated the volume of a sphere with a radius of 6 centimeters, but arrived at different results. Diego found the volume to be 288 cubic centimeters, Andre approximated it to be 904 cubic centimeters, and Noah calculated it to be 226 cubic centimeters. It's interesting to see the variation in their calculations.
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