The correct answer is Part A: The dimensions of the new deck are 9 feet for the base and 5.4 feet for the height.Part B: The area of the original deck is 67.5 square feet, and the area of the new deck is 24.3 square feet.Part C: The ratio of the areas (new deck to original deck) is 0.36, which is different from the scale factor of 3:5.
Part A: To find the dimensions of the new deck, we need to scale the base and height of the original deck by a factor of 3:5.
The scale factor from the original deck to the new deck is 3:5.
The scaled base of the new deck can be found by multiplying the original base by the scale factor:
Scaled base = Original base * Scale factor = 15 feet * (3/5) = 9 feet
The scaled height of the new deck can be found by multiplying the original height by the scale factor:
Scaled height = Original height * Scale factor = 9 feet * (3/5) = 5.4 feet
Therefore, the dimensions of the new deck are 9 feet for the base and 5.4 feet for the height.
Part B: To find the area of the original deck and the new deck, we'll use the formula for the area of a triangle:
Area = (base * height) / 2
For the original deck:
Area of original deck = (15 feet * 9 feet) / 2 = 67.5 square feet
For the new deck:
Area of new deck = (9 feet * 5.4 feet) / 2 = 24.3 square feet
Part C: To compare the ratio of the areas to the scale factor, we'll divide the area of the new deck by the area of the original deck:
Ratio of areas = Area of new deck / Area of original deckRatio of areas = 24.3 square feet / 67.5 square feet = 0.36
The ratio of the areas is 0.36.
Comparing this ratio to the scale factor (3:5), we can see that they are not equal. The scale factor represents the ratio of the corresponding sides, not the ratio of the areas.
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Graph the function f(x) = 32. Plot the key features including any x- and y-intercepts, any vertical, horizontal, or slant asymptotes, and any holes.
The graph of the function f(x) = 32 is attached accordingly.
How would you describe the above graph ?X - Intercept - There is no x-intercept since the function is a horizontal line.
Y -Interept - The y-intercept is (0, 32), since the line intersects the y-axis at y = 32.
Vertical Asymptotes - There are 0 vertical asymptotes, since t function is defined for all values of x.
Horizontal Asymptotes - There are 0 horizontal asymptotes, since the function is a horizontal line.
Slant Asymptotes - There are zeroslant asymptotes, since the function is a horizontal line.
Holes - There are zeroholes in the graph, since the function is a horizontal line with no breaks or discontinuities.
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Answer: see below
Step-by-step explanation:
got it right on quiz
5/6 + 2/3 = ?
your answer
Answer:
3/2 or 1.5 or 1 1/2
Step-by-step explanation:
5/6 + 2/3 = ?
5/6 + 4/6 =
9/6
semplify
3/2 or 1.5 or 1 1/2
A Stock Clerk's income is $832.00 a month and his total expenses are $668. How much money does he have left for savings?
Answer:
$164
Step-by-step explanation:
you take the clerk's income ($832.00) and subtract it with the total expenses ($668) to get the savings
suppose that initially c = 2 0.75 × gdp, i = 3, g = 2, and nx = 1. compute the equilibrium value of spending.
The equilibrium value of spending is 72.
To compute the equilibrium value of spending, we need to use the equation for the expenditure approach to GDP:
GDP = C + I + G + NX
Where:
C = consumption
I = investment
G = government spending
NX = net exports
Given the values of c, i, g, and nx, we can substitute them into the equation:
GDP = 2.75 × GDP + 3 + 2 + 1
Simplifying the equation, we get:
GDP = 2.75 × GDP + 6
Now, we can solve for GDP:
GDP - 2.75 × GDP = 6
0.25 × GDP = 6
GDP = 24
Therefore, the equilibrium value of spending is:
C + I + G + NX = 2.75 × GDP + 3 + 2 + 1 = 2.75 × 24 + 6 = 72
The equilibrium value of spending is 72.
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Use the Maclaurin series for cos(x) to compute cos(3) correct to five decimal places. (Round your answer to five decimal places.) 0.99862
Maclaurin series for cos(x) to compute [tex]\cos(3) \approx 0.99862$.[/tex]
What is Maclaurin series?
The Maclaurin series is a special case of the Taylor series, which is a power series expansion of a function about 0. The Maclaurin series is obtained by setting the center of the Taylor series to 0. It is named after the Scottish mathematician Colin Maclaurin.
The Maclaurin series of a function f(x) is given by:
[tex]f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ... + (f^{(n)}(0)/n!)x^n + ...[/tex]
where [tex]f^{(n)}(0)[/tex] denotes the nth derivative of f evaluated at 0.
Using the Maclaurin series for [tex]$\cos(x)$[/tex], we have:
[tex]\cos(x) &= \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!}(x)^{2n}[/tex]
Substituting [tex]$x=3$[/tex] into this series, we get:
[tex]\cos(3) &= \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!}(3)^{2n}[/tex]
[tex]&= 1 - \frac{3^2}{2!} + \frac{3^4}{4!} - \frac{3^6}{6!} + \frac{3^8}{8!} - \cdots[/tex]
[tex]&\approx 0.99862 \quad\text{(correct to five decimal places)}[/tex]
Therefore, [tex]\cos(3) \approx 0.99862$.[/tex]
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use formula for arc length to show that the circumference of a circle x^2+y^2=1 is 2pi
The circumference of the circle x² + y² = 1 is 2π.
To show that the circumference of the circle x² + y² = 1 is 2π, we can use the arc length formula. The formula for arc length (s) in a circle is given by:
s = r × θ
where r is the radius of the circle and θ is the central angle in radians.
For the circle x² + y² = 1, the radius (r) is equal to 1 (since the equation is already in the standard form). To find the circumference, we need to find the arc length for a complete circle. A complete circle has a central angle of 2π radians. Therefore, we can plug these values into the arc length formula:
Circumference = s = r × θ
Circumference = 1 × 2π
Circumference = 2π
Thus, the circumference of the circle x² + y² = 1 is 2π.
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Answer:
2
Step-by-step explanation:
Select true or false.
(a) T/F 22 ≡ 8 (mod 7)
(b) T/F −13 ≡ 9 (mod 12)
(c) T/F −13 ≡ 9 (mod 11)
(d) T/F −13 ≡ 12 (mod 2)
Hence, a and c are true .
What is the modulo?When two numbers are split, the modulo operation in computing the remainder of the division. A modulo n is the remainder of the Euclidean division of two positive numbers, a and n, where a is the dividend and n is the divisor.
What is the congruent modulo ?A congruence relation is an equivalence relation that is symbol of addition, subtraction, and multiplication. Congruence modulo n is one one map connection. The symbol for congruence modulo n is: The brackets indicate that (mod n) applies to both sides of the equation, not only the right-hand side of the equation.
True,because they are congruent modulo 7 because 22 divided by 7 leaves a remainder of 1, and the divided of 8 by 7 leaves a remainder of 1.False because they are not congruent modulo 12 because 13 divided by 12 leaves a remainder of 1, and 9 divided by 12 leaves a remainder of 9.True because they are congruent modulo 11 and 13 divided by 11 leaves a remainder of 2 and 9 divided by 11 leaves a remainder of 9.False because they are not congruent modulo 2 since 13 divided by 2 leaves a remainder of 1, and 12 divided by 2 leaves a remainder of 0.Learn more about mod here:
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The degrees of freedom for the sample variance A.are equal to the sample size B.are equal to the sample size C.can vary between - [infinity] and + [infinity] D.both B and C
The degrees of freedom for the sample variance can vary between - [infinity] and + [infinity]. This means that the number of degrees of freedom is not dependent on the sample size, but rather on the amount of variance in the data.
The degrees of freedom for sample variance A. is equal to the sample size minus 1. This means that the correct answer is not provided in your given options. To clarify, let's define the terms:
1. Degrees of freedom: The number of independent values in a statistical calculation that are free to vary.
2. Variance: A measure of dispersion that represents the average squared difference between the values in a dataset and the mean of the dataset.
3. Sample size: The number of observations in a sample.
As the variance increases, the degrees of freedom decrease, which can impact the accuracy of the results. However, it is important to note that a larger sample size can often lead to a more accurate estimate of the population variance, even if the degrees of freedom are not directly related to the sample size.
When calculating the sample variance, the degrees of freedom is equal to the sample size (n) minus 1, often denoted as (n-1). This is because we lose one degree of freedom when estimating the population means using the sample mean.
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help me out pls!!! :)
Answer: 254.34
Step-by-step explanation:
First we can fine the radius by dividing the diameter (18in) by 2: 18/2=9
Then we can use the formula to find the area of the circle (pi*r^2):9*9*pi=81pi
Finally, approximate pi to 3.14 and multiple: 81*3.14=254.34
Therefore, the answer is 254.34
Answer:1017.36
Step-by-step explanation:
I really need help with this, pls answer it as fast as possible!
Answer:
A) Tamara's work is correct.
Step-by-step explanation:
To determine whether a function is even, odd, or neither, we need to check whether f(-x) is equal to f(x) or -f(x).
In this case, Tamara correctly found the expression for f(-x) in step 1, and then in step 2, she checked whether f(-x) is equal to f(x) or -f(x).
Since f(-x) is equal to f(x), Tamara correctly concluded that f is an even function.
Find the Z-scores for which 90% of the distribution's area lies between -z and Z. A) (-1.96, 1.96)B) (-2.33, 2.33) C) (-0.99, 0.99) D) (-1.645, 1.645)
The correct Z-scores for which 90% of the distribution's area lies between -z and Z are D) (-1.645, 1.645).
The Z-score is a measure of how many standard deviations a particular value is from the mean of a distribution. In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the Z-score represents the number of standard deviations a value is away from the mean.
To find the Z-scores for which 90% of the distribution's area lies between -z and Z, we need to find the Z-scores that correspond to the 5th and 95th percentiles of the standard normal distribution.
Since the distribution is symmetric, we can find the Z-scores for the lower and upper tails of the distribution and use them to determine the range between -z and Z.
Using a standard normal distribution table or a Z-table calculator, we can find that the Z-score corresponding to the 5th percentile (i.e., the value of -z) is approximately -1.645, and the Z-score corresponding to the 95th percentile (i.e., the value of Z) is also approximately 1.645.
Therefore, the correct Z-scores for which 90% of the distribution's area lies between -z and Z are (-1.645, 1.645).
Note: The other options given in the question (A) (-1.96, 1.96), (B) (-2.33, 2.33), and (C) (-0.99, 0.99) do not correspond to the Z-scores for which 90% of the distribution's area lies between -z and Z. Option (D) (-1.645, 1.645) is the correct answer.
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find the least squares regression line for the points. (0, 0), (2, 2), (3, 6), (4, 7), (5, 9)
Answer:
Use the graphing calculator to plot the points and then generate the least squares regression line.
y = 1.87837878 - .4594594595
Dee wants to buy 2 pens from the catalog. The retail price of the pens is $15.99 each. The pens are on sale. If you buy 2 or more pens, the price is reduced to $11.50 each. What will Dee write for the Total Price in the catalog?
Answer:
23 dollar in total
Step-by-step explanation:
since 11.50 for one if u buy 2 it would be 23dollar total
The sum of three numbers $x$, $y$, $z$ is $165$. When the smallest number $x$ is multiplied by $7$, the result is $n$. The value $n$ is obtained by subtracting $9$ from the largest number $y$. This number $n$ also results by adding $9$ to the third number $z$. What is the product of the three numbers?
Hint: It's not 12295
The product of the three numbers under the given circumstances is 49,483.
How are products of numbers determined?Let's start by setting up the equations based on the given information:
x + y + z = 165 (equation 1)
7x = n (equation 2)
y - 9 = n (equation 3)
z + 9 = n (equation 4)
We want to find the product of x, y, and z, which is simply:
x * y * z
We can use equations 2, 3, and 4 to substitute n in terms of y and z:
7x = y - 9 (substituting equation 3)
7x = z + 9 (substituting equation 4)
Now we can substitute these expressions for y and z into equation 1 to get an equation in terms of x:
x + (7x + 9) + (7x - 9) = 165
15x = 165
x = 11
Substituting x = 11 into equations 2, 3, and 4, we get:
7(11) = n
n = 68
y = n + 9 = 68 + 9 = 77
z = n - 9 = 68 - 9 = 59
Now we can calculate the product of x, y, and z:
x * y * z = 11 * 77 * 59 = 49,483
Therefore, the product of the three numbers is 49,483.
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suppose p is invertible and a = pbp−1 . solve for b in terms of a
1. Multiply both sides by the inverse of p on the left: p^(-1)a = p^(-1)(pbp^(-1))
2. Simplify: p^(-1)a = bp^(-1)
3. Multiplying both sides by the inverse of p^(-1) on the right: (p^(-1)a)p = b
So, b = (p^(-1)a)p.
Given that p is invertible and a = pbp^(-1), we want to solve for b in terms of a.
First, let's multiply both sides of the equation by p:
ap = pb
Now, we can substitute pb with ap from the given equation:
a = apbp^(-1)
Multiplying both sides by p:
ap = apbp^(-1)p
ap = ab
Dividing both sides by a:
b = p^(-1)
Therefore, b is equal to the inverse of p.
In conclusion, b = p^(-1) in terms of a.
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to find p(0 ≤ z ≤ 1.37) using appendix c-1, find the row containing 0.1 in the far left column. then find the column containing .037 in the top row. (round the values to 2 decimal places.)
The value of p(0 ≤ z ≤ 1.37) is approximately 0.41 (rounded to 2 decimal places).
What is Probability ?
Probability is a branch of mathematics that deals with the study of the likelihood or chance of an event occurring. It is the measure of the likelihood that a particular event or set of events will occur.
To find the value of p(0 ≤ z ≤ 1.37) using Appendix C-1, we need to locate the row containing 0.1 in the far-left column and the column containing 0.37 in the top row.
Starting with the row containing 0.1 in the far-left column, we can locate the value closest to 1.3 in the row, which is 1.37. Moving along the row to the right, we can find the corresponding value of the cumulative distribution function (CDF) for this value of z, which is 0.9147.
Next, we need to find the column containing 0.37 in the top row. The closest value in the column is 0.3707. Moving down the column to the row containing the CDF value we just found, we can read off the value of the CDF for z = 0, which is 0.5000.
To find the value of p(0 ≤ z ≤ 1.37), we subtract the CDF value for z = 0 from the CDF value for z = 1.37:
p(0 ≤ z ≤ 1.37) = 0.9147 - 0.5000 = 0.4147
Therefore, the value of p(0 ≤ z ≤ 1.37) is approximately 0.41 (rounded to 2 decimal places).
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. The graph of a quadratic function has a vertex at (-6, -24) and passes through the points (-9, -6) and (-3, -6). Write an equation for the function in standard form.
Answer:
y = -1/2(x + 6)^2 - 6
Step-by-step explanation:
0_0
Multiply. (w-2v)(w+2v) simply your answer
Answer:
w^2-4v^2
Step-by-step explanation:
w*w=w^2
w*2v=2vw
-2v*w=-2vw
-2v*2v=-4v^2
w^2+2vw-2vw-4v^2
w^2-4v^2
In a certain year, according to a national Census Bureau, the number of people in a household had a mean of 4.664.66 and a standard deviation of 1.941.94.
This is based on census information for the population. Suppose the Census Bureau instead had estimated this mean using a random sample of 225 homes. Suppose the sample had a sample mean of 4.8 and standard deviation of 2.1
Describe the center and variability of the data distribution. what would you predict as the shape of the data distribution? explain. The center of the data distribution is ______.
The variability of the population distribution is _____.
It's reasonable to assume the sample distribution's shape would be similar to the population distribution's shape. However, without more information, we cannot confirm the exact shape of the distribution.
The center of the data distribution is represented by the mean. According to the national Census Bureau, the mean number of people in a household for the entire population is 4.66.
The variability of the population distribution is represented by the standard deviation. In this case, the standard deviation provided by the Census Bureau is 1.94.
So, the center of the data distribution is 4.66, and the variability of the population distribution is 1.94.
Since the Census Bureau has used a random sample of 225 homes, the sample mean (4.8) and standard deviation (2.1) could be used to estimate the population mean and standard deviation. However, these sample statistics are not necessarily equal to the population parameters.
As for the shape of the data distribution, it's difficult to predict without more information about the distribution itself. If the data is normally distributed, the shape would be bell-shaped. If the sample is representative of the population, it's reasonable to assume the sample distribution's shape would be similar to the population distribution's shape. However, without more information, we cannot confirm the exact shape of the distribution.
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solve and show explanation plsss i’ll make you brainlistt
The amount that Julian will save, when Julian makes $500 is $95
What will be the amount saved, when Julian makes $500The scattered points on the graph represents the given parameter
When the line of the best fit is drawn on the scattered graph, it passes through the points
(175, 30) and (25, 0)
A linear equation is represented as
y = mx + c
Using the given points, we have
25m + c = 0
175m = c = 30
Subtract the equations
So, we have
150m = 30
Divide
m = 0.2
Solving for c, we have
c = -25m
c = -25 * 0.2
c = -5
So, the equation is
y = 0.2x - 5
When Julian makes $500, we have
x = 500
This gives
y = 0.2 * 500 - 5
Evaluate
y = 95
Hence, the savings at $500 is $95
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given e z = xyz, find ∂z ∂x and ∂z ∂y
Sure! So, given e z = xyz, we can use the product rule of differentiation to find the partial derivatives of z with respect to x and y ∂z/∂x = yz + xz(∂y/∂x) .
∂z/∂y = xz + yz(∂x/∂y), Since there are no other given values or constraints, we cannot simplify these further. I hope this helps! Let me know if you have any other questions, Given the equation z = xyz, to find the partial derivatives ∂z/∂x and ∂z/∂y, we can use the following:
For ∂z/∂x, we differentiate z with respect to x while treating y as a constant:
∂z/∂x = y*(1) + xyz*(0) = y
For ∂z/∂y, we differentiate z with respect to y while treating x as a constant:
∂z/∂y = x*(1) + xyz*(0) = x
So, ∂z/∂x = y and ∂z/∂y = x.
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The equation D=200(1.16)^m models the number of total downloads,D, for an app Carrie created m month after its launch.Of the following,which equation models the number of total downloads y years after launch?
[tex]D = 200(1.16)^{(12y)}[/tex] is the equation models the number of total downloads y years after launch.
What is equation?
In mathematics, an equation is a statement that two expressions are equal. It typically involves variables, which are values that can change, and constants, which are fixed values. Equations are used to represent relationships between variables and to solve for unknown values.
The given equation is [tex]D = 200(1.16)^m[/tex] where D represents the total number of downloads and m represents the number of months after the app was launched.
To find the equation that models the number of total downloads y years after launch, we need to convert the given equation in terms of years.
We know that there are 12 months in a year. So, if we divide the time in months by 12, we get the time in years. Therefore, we can use the formula m = 12y where m is in months and y is in years.
Now, substituting m = 12y in the given equation,
[tex]D = 200(1.16)^{(12y)}[/tex]
Therefore, the equation that models the number of total downloads y years after launch is [tex]D = 200(1.16)^{(12y)}[/tex]
Option (d) represents the correct equation.
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determine the sample size n needed to construct a 90onfidence interval to estimate the population mean when = 36and the margin of error equals .4
You need a sample size of approximately 10,875 to construct a 90% confidence interval with a margin of error of 0.4 and a standard deviation of 36.
To determine the sample size (n) needed to construct a 90% confidence interval for estimating the population mean, given a standard deviation (σ) of 36 and a margin of error of 0.4, you can use the formula:
[tex]n = (Z * σ / E)^2[/tex]
where:
n = sample size
Z = Z-score corresponding to the desired confidence level (90%)
σ = standard deviation (36)
E = margin of error (0.4)
For a 90% confidence interval, the Z-score is 1.645. Now, plug in the values into the formula:
n = (1.645 * 36 / 0.4)^2
n ≈ 10874.09
Since sample size should be a whole number, round up to the nearest whole number: n ≈ 10875.
So, you need a sample size of approximately 10,875 to construct a 90% confidence interval with a margin of error of 0.4 and a standard deviation of 36.
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There are 23 rabbits in a valley. The rabbit population grows at a rate of approximately 18% per month. The approximate number of rabbits in the valley after n months is given by this formula: number of rabbits - 23 × 1.18n Use this formula to predict the number of rabbits in the valley after 25 months. Round your answer to the nearest integer.
Evaluating the exponential equation we can see that after 25 months there will be 1,441 rabbits after 25 months.
How to find the number of rabbits in the valley after 25 months?We know that the population of rabbits is modeled by the exponential equation below:
P(n) = 23*1.18^n
Where n is the number of months.
Then the population after 25 months is what we get when we evaluate the exponential equation in n = 25, we will get:
P(25) = 23*1.18^25 = 1,441
There will be 1,441 rabbits after 25 months.
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The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 2 comma negative 2, at 0 comma 2, at 1 comma 3, and at 5 comma 1
Is the relation a function? Explain.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Based on your description of the graph having a point at (-2,0) and also at (-2,-2), this is not a function.
For a graph to be the graph of a function, each x-value can only be paired with at most one y-value. In other words, you cannot have two points with the same x-value.
Answer:
No, because of each input there is not exactly one output.
Step-by-step explanation:
The input -2 has two outputs: 0 and -2
Helping in the name of Jesus.
A cylindrical tank, lying on its side, has a radius of 10 ft^2 and length 40ft. Assume that the tank is half-filled with water and that water leaks through a hole in the bottom of area B = 1 in^2. Determine the water level y(t) and the time te when the tank is empty. y(t) = te = seconds.
The water level y(t) = √(1000 - 80πt/3), te ≈ 11.8 seconds.
The water level y(t) in the cylindrical tank with radius 10 ft and length 40 ft decreases over time until the tank is empty at time t=te seconds can be found shown below:
First, find the volume of the half-filled tank: V = (1/2)π(10^2)(40) = 2000π ft³. The leakage rate Q = (1 in²)(1/144 ft²/in²) = 1/144 ft². Since Q = dV/dt, we have dV = -Qdy.
Integrating both sides gives V = -Qy + C. Initially, V = 2000π and y = 10, so C = 3000π. Thus, V = -Qy + 3000π. Solving for y, we get y(t) = √(1000 - 80πt/3). To find te, set V = 0 and solve for t: 0 = -80πt/3 + 1000, which gives te ≈ 11.8 seconds.
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The cumulative distribution function of random variable V is f_V (v) = {0, v < -5 (v + 1)^2/144, -5 lessthanorequalto v < 7 1, x greaterthanorequalto 7 What are the expected value and variance of V? What is E[V^3]?
The expected value of V is 1.75
The variance of V is 97.65
E[V³] is 193.083
To find the expected value and variance of V, we first need to find the distribution function of V. For -5 ≤ v < 7, the cumulative distribution function (CDF) F_V(v) can be found by integrating f_V(v):
F_V(v) = ∫ f_V(t) dt
= ∫ (t+1)²/144 dt
= (1/144) * ∫ (t² + 2t + 1) dt
= (1/144) * [(t³)/3 + t² + t]_(-5)^(v)
= (1/144) * [(v³)/3 + v² + v + 160]/3
For v ≥ 7, F_V(v) = 1.
V's expected value is:
E[V] = ∫ v f_V(v) dv = ∫ (-∞ to -5) 0 dv + ∫ (-5 to 7) v*(v+1)²/144 dv + ∫ (7 to ∞) v dv
= (1/144) * ∫ (-5 to 7) (v³ + v²) dv + ∫ (7 to ∞) v dv
= (1/144) * [(7⁴ - (-5)⁴)/4 + (7³ - (-5)³)/3 + 7²*(7-(-5))]
= 1.75
V's variance is as follows:
Var[V] = E[V²] - (E[V])²
= ∫ v² f_V(v) dv - (E[V])²
= ∫ (-∞ to -5) 0 dv + ∫ (-5 to 7) v²*(v+1)²/144 dv + ∫ (7 to ∞) v² dv - (E[V])²
= (1/144) * ∫ (-5 to 7) (v⁴ + 2v³ + v²) dv + ∫ (7 to ∞) v² dv - (E[V])²
= (1/144) * [(7⁵ - (-5)⁵)/5 + 2*(7⁴ - (-5)⁴)/4 + (7³3 - (-5)³)/3 + 7*(7²*(7-(-5))) - (1.75)²]
= 97.65
Finally, we can find E[V³] using:
E[V³] = ∫ v³ f_V(v) dv
= ∫ (-∞ to -5) 0 dv + ∫ (-5 to 7) v³*(v+1)²/144 dv + ∫ (7 to ∞) v³ dv
= (1/144) * ∫ (-5 to 7) (v⁵ + 2v⁴ + v³) dv + ∫ (7 to ∞) v³ dv
= (1/144) * [(7⁶ - (-5)⁶)/6 + 2*(7⁵ - (-5)⁵)/5 + (7⁴ - (-5)⁴)/4 + 7*(7³ - (-5)³)/3]
= 193.083
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An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $5750 and her stock in Company B was worth $1200. The stock in Company A has decreased 16% since last year and the stock in Company B has decreased 2%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The total percentage decrease in the investor's stock account is 13.6%
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is denoted using the symbol "%". For example, 25% is the same as 25/100 or 0.25.
According to given information:To find the total percentage decrease in the investor's stock account, we need to first calculate the new values of the stocks after the decreases and then find the percentage decrease of the total value compared to the original value.
The new value of the stock in Company A is:
5750 - 0.16 * 5750 = 4830
The new value of the stock in Company B is:
1200 - 0.02 * 1200 = 1176
The total value of the stocks after the decreases is:
4830 + 1176 = 6006
The percentage decrease of the total value compared to the original value is:
(1 - 6006/6950) * 100% = 13.6%
Therefore, the total percentage decrease in the investor's stock account is 13.6% (rounded to the nearest tenth).
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similar to 3.10.1 in rogawski/adams. how fast is the water level rising if water is filling a rectangular bathtub with a base of 28 square feet at a rate of 5 cubic feet per minute? rate is =
The water level is rising at a rate of 0.006 feet per minute. This can be answered by the concept of Differentiation.
The formula for the volume of a rectangular box is V = lwh, where l, w, and h represent the length, width, and height respectively. Since the base of the bathtub is 28 square feet, we can assume that the length and width are both 28 feet. Let's say the height of the water in the bathtub is h at time t.
We know that the water is filling the bathtub at a rate of 5 cubic feet per minute, so the rate of change of the volume of water in the bathtub is 5. We want to find the rate of change of the height of the water, which we can call dh/dt.
Using the formula for the volume of a rectangular box, we can write:
V = lwh = 28wh
We can differentiate both sides with respect to time t:
dV/dt = 28w dh/dt
We know that dV/dt is 5, and w is also 28 since the base of the bathtub is a rectangle with sides of length 28 feet. Therefore, we can solve for dh/dt:
5 = 28(28) dh/dt
dh/dt = 5/(28×28)
dh/dt = 0.006 ft/min
Therefore, the water level is rising at a rate of 0.006 feet per minute.
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Once a week, Ms. Conrad selects one student at random from her class list to win a “no homework”
pass. There are 17 girls and 18 boys in the class. Rounded to the nearest percent, what is the
probability that a girl will win two weeks in a row?
The probability that a girl will win two weeks in a row is 24%.
What is probability?
Probability tells how many times something will happen or be present.
The probability of a girl winning in a given week is 17/35 since there are 17 girls and 35 students total. Assuming each week's selection is independent of previous selections, the probability of a girl winning two weeks in a row is (17/35) x (17/35) = 289/1225.
Rounding this to the nearest percent gives a probability of 24%.
Therefore, the probability is 24%.
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