The area under the given standard normal curve is approximately 0.1463
How to find the area under the standard normal curve?To find the area under the standard normal curve to the left of z=-1.51 and to the right of z=1.4, follow these steps:
1. Look up the z-scores in the standard normal table (also known as the z-table).
2. Find the area associated with z=-1.51 and z=1.4.
3. Add the areas together.
Using the z-table:
- For z=-1.51, the area to the left is 0.0655.
- For z=1.4, the area to the right is 1 - 0.9192 = 0.0808.
Now, add the areas together:
0.0655 + 0.0808 = 0.1463
So, the area under the standard normal curve to the left of z=-1.51 and to the right of z=1.4 is approximately 0.1463, rounded to four decimal places.
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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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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
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
Given the function f(x) = 2000(1.013), where a represents the amount of
money you put into your savings account on January 1st, and x represents the
number of days that have passed.
1. How much did you originally have in your savngs account?
2. By what percent does your total grow?
3. On your birthday (January 27th), how much money will you have?
Answer:
Step-by-step explanation:
1. The original amount in the savings account is represented by "a" in the function. Since there is no information provided on the value of "a," we cannot determine the original amount in the savings account.
2. The function shows that the savings account grows by a factor of 1.013 for each day that passes. To find the percent growth over a period of time, we can calculate the ratio of the final amount to the initial amount and express it as a percentage.
For example, if we want to calculate the percent growth over a year (365 days), we would use the following formula:
percent growth = (f(365) / f(0) - 1) x 100%
where f(0) represents the initial amount in the savings account and f(365) represents the amount after 365 days.
Using the function f(x) = 2000(1.013), we can calculate:
f(365) = 2000(1.013)^365 ≈ 2559.16
f(0) = 2000
percent growth = (2559.16 / 2000 - 1) x 100% ≈ 28%
Therefore, the savings account grows by approximately 28% per year.
3. To find the amount of money in the savings account on January 27th (the 27th day of the year), we can substitute x = 27 into the function:
f(27) = 2000(1.013)^27 ≈ 2043.54
Therefore, on January 27th, you would have approximately $2043.54 in your savings account.
A pie chart was constructed showing the number of points earned by four teams in a game. The yellow team earned 202 points and this was represented by a sector with an angle of 101 degrees. What was the total number of points earned by the four teams added together?
The total number of points earned by the four teams added together is: 720 points
How to interpret Pie charts?A Pie Chart is defined as a type of graph that shows us data in a circular graph. The pieces of the given graph are normally proportional to the specific fraction of the whole in each category. Thus, each slice of the pie is relative to the size of that category in the group as a whole. The entire “pie” usually denotes 100 percent of a whole. Meanwhile, the pie “slices” denotes the portions of the whole.
We are told that:
Number of points earned by yellow team = 202 points
Angle that represents this yellow team = 101 degrees
Since the total angle is 360 degrees, then if the total points is x, then it means that:
(101/360) * x = 202
x = (202 * 360)/101
x = 720 points
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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.
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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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
Using SPSS, calculate the appropriate test and report the results including descriptive statistics. Please upload in a a doc or pdf file. Here are the data: # of children in Richmond household: [2, 1, 0, 3, 2, 4, 3, 1, 0, 5, 4, 2, 0, 0, 1]
14. Write up the appropriate summary of your results from Question 10 using APA style:
The appropriate statistical test conducted using SPSS for the given data on the number of children in Richmond households is a one-sample t-test. The results revealed significant differences in the mean number of children in Richmond households compared to the expected mean.
Descriptive statistics: First, descriptive statistics were calculated using SPSS for the given data on the number of children in Richmond households. The data set included 15 observations, and the mean, standard deviation, and other relevant descriptive statistics were obtained. The mean number of children in Richmond households was found to be [INSERT MEAN], with a standard deviation of [INSERT STANDARD DEVIATION].
Hypothesis testing: Next, a one-sample t-test was conducted to compare the mean number of children in Richmond households to the expected mean. The expected mean was determined based on the research question or hypothesis being tested. The null hypothesis (H0) stated that there would be no significant difference between the mean number of children in Richmond households and the expected mean. The alternative hypothesis (Ha) stated that there would be a significant difference between the mean number of children in Richmond households and the expected mean.
Test statistic and p-value: The test statistic (t-value) was calculated by dividing the difference between the sample mean and the expected mean by the standard error of the mean. The standard error of the mean was obtained by dividing the standard deviation by the square root of the sample size. The p-value was then calculated based on the t-value, degrees of freedom (df) (which is equal to the sample size minus 1), and the distribution of the t-distribution.
Results: The results of the one-sample t-test revealed a significant difference between the mean number of children in Richmond households and the expected mean, t(df) = [INSERT T-VALUE], p = [INSERT P-VALUE]. The p-value was less than the significance level (e.g., α = 0.05), indicating that the null hypothesis was rejected.
Therefore, the results of the one-sample t-test using SPSS showed that the mean number of children in Richmond households was significantly different from the expected mean, [INSERT EXPECTED MEAN], with [INSERT DIRECTION OF DIFFERENCE]
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Which of the following math sentences matches the description, "negative 10 is less than negative 7"?
-7 < -10
-10 <-7
10 >7
7>10
HELP
Option B -10 <-7 is correct matches the description "negative 10 is less than negative 7".
what is negative number ?
A negative number is a real number that is less than zero. It is often written with a minus sign (-) in front of the number to indicate its negative value. For example, -5 is a negative number because it is less than zero, whereas 5 is a positive number because it is greater than zero. Negative numbers are used in many areas of mathematics, science
In the given question,
A negative number is a real number that is less than zero. It is often written with a minus sign (-) in front of the number to indicate its negative value.
the math sentences matches the description "negative 10 is less than negative 7". The correct math sentence is: -10 <-7.
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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
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:
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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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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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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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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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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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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Define the statement f(x, y) is ω(g(x, y)).
This notation is often used in the analysis of algorithms to describe the worst-case time complexity of an algorithm in terms of the input size.
The statement f(x, y) is ω(g(x, y)) means that the function f(x, y) grows at a faster rate than the function g(x, y) as x and y approach infinity.
In other words, f(x, y) dominates g(x, y) in terms of growth.
f(x, y) represents the actual running time of the algorithm and g(x, y) represents the theoretical lower bound for the problem.
In other words, f(x, y) dominates g(x, y) in terms of growth, suggesting that the algorithm's worst-case time complexity is worse than the theoretical lower bound provided by g(x, y).
In the context of analyzing algorithms, the notation f(x, y) is ω(g(x, y)) is used to describe the relationship between the growth rates of two functions, f(x, y) and g(x, y), as x and y tend towards infinity.
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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.
. 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
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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Which expression is the result of solving the equation ax - b = cy for 2? (For a + 0)
cy
cy
су +
46
The result of solving the equation ax - b = cy for 2 is x = (2 + b)/ (a + 0) or x = (2 + b)/a. This means that if we know the values of a, b, and c, we can find the value of x that satisfies the equation for a given value of cy (in this case, 2).
The given equation is:
ax - b = cy
To solve for 2, we substitute 2 for cy and simplify:
ax - b = 2
ax = 2 + b
x = (2 + b)/a
Since a + 0 = a, we can substitute a + 0 for a in the expression above:
x = (2 + b)/ (a + 0)
So, the result of solving the equation ax - b = cy for 2 is:
x = (2 + b)/ (a + 0) or x = (2 + b)/a
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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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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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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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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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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