If a town with a population of 10,000 doubles in size every 17 years. What will the population be 68 years from now?

We specify the one-way anova model in the model statement of proc glm is model response variable; (the grouping variable is only specified in the class statement.)

So option b. is the correct option of the given statement.

Information that needs to be accessed and changed by a computer program is stored in variables. In order to make our programs more understandable to ourselves and the reader, they also offer a mechanism to label data with a descriptive name.

Values can be stored in variables. In order to use a variable, we must first declare it so the program is aware of it and then assign it so the program is aware of the value we are storing in the variable.

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The measure of angle Z is 47.19°.

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given a triangle XYZ.

m ∠Y = 78°, XY = 9, XZ = 12

We have to find the measure of angle Z.

Using the law of sines,

XZ / sin Y = XY / sin Z

12 / sin (78°) = 9 / sin Z

Cross multiplying,

12 × sin Z = 9 × sin (78°)

sin Z = (9 × sin (78°)) / 12

sin Z = 0.7336

Z = sin⁻¹ (0.7336)

Z = 0.8236 radians

  = 47.19°

Hence the measure of Z is 47.19°.

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An equation of the plane tangent to the following surface at the given points (5,6, ln(31)) and (-5, -6, ln(31)) is (6/31)(x-5) + (5/31)(y-6) + (z-ln(31)) = 0 and (-6/31)(x+5) + (-5/31)(y+6) + (z-ln(31)) = 0 respectively.

The equation of the plane tangent to the surface z = ln(1+xy) at the given points (5,6, ln(31)) and (-5, -6, ln(31)) can be found using the gradient vector and the point-normal form of a plane equation.

To find the equation of the plane tangent to the surface at the given points, we need to find the normal vector to the surface at those points. The normal vector can be obtained by taking the gradient of the surface function.

The gradient of the surface function z = ln(1+xy) is given by:

∇z = (∂z/∂x, ∂z/∂y) = (y/(1+xy), x/(1+xy))

At the points (5,6, ln(31)) and (-5, -6, ln(31)), we can substitute the respective x and y values into the gradient expression to obtain the normal vectors.

For the point (5,6, ln(31)):

∇z = (6/(1+56), 5/(1+56)) = (6/31, 5/31)

Similarly, for the point (-5, -6, ln(31)):

∇z = (-6/(1-56), -5/(1-56)) = (-6/31, -5/31)

Now, we have the normal vectors to the surface at the given points. We can use the point-normal form of the plane equation to find the equation of the tangent plane.

Using the point-normal form: A(x-x0) + B(y-y0) + C(z-z0) = 0, where (x0, y0, z0) is a point on the plane and (A, B, C) is the normal vector, we can substitute the values from the points and normal vectors:

For the point (5,6, ln(31)):

(6/31)(x-5) + (5/31)(y-6) + (z-ln(31)) = 0

For the point (-5, -6, ln(31)):

(-6/31)(x+5) + (-5/31)(y+6) + (z-ln(31)) = 0

These equations represent the planes tangent to the surface z = ln(1+xy) at the given points.

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Answer: y = x - 6

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Since the line has a slope of 1, we can substitute m = 1 into the equation.

y = 1x + b

To find the y-intercept b, we can use the fact that the line passes through the point (-1,-7). Substituting x = -1 and y = -7, we get:

-7 = 1(-1) + b

b = -6

Now we can substitute m = 1 and b = -6 into the slope-intercept form of the equation:

y = 1x - 6

Simplifying the equation gives us:

y = x - 6

Answer:

A

Step-by-step explanation:

There are six equally likely outcomes when rolling a six-sided die: 1, 2, 3, 4, 5, or 6.

Since we want to find the probability of rolling a 3 or a 4, we can count the number of favorable outcomes, which is 2 (a 3 or a 4), and divide by the total number of possible outcomes, which is 6. So the probability of rolling a 3 or a 4 is 2/6 or 1/3, which is approximately 0.333 or 33.3%.

Answer:

n = 1/5

Step-by-step explanation:

5/12n + 2/3 = 3/4

5/12n = 3/4 - 2/3

5/12n = 9/12 - 8/12

5/12n = 1/12

n = 1/12 × 12/5

n = 1/5

I hope this helped!

Answer:

I'm not sure but I guess I will go with A.

Step-by-step explanation:

The probability of receiving two calls in a 5-minute interval is:

P(X = 2) = (e^-4 * 4^2) / 2! = 0.0902

The probability of receiving exactly 10 calls in 15 minutes is:

P(Y = 10) = (e^-12 * 12^10) / 10! = 0.1143

(a) Let X be the number of calls received in a 5-minute interval. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, X follows a Poisson distribution with mean λ = 0.8 * 5 = 4. The probability of receiving two calls in a 5-minute interval is:

P(X = 2) = (e^-4 * 4^2) / 2! = 0.0902

(b) Let Y be the number of calls received in a 15-minute interval. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, Y follows a Poisson distribution with mean λ = 0.8 * 15 = 12. The probability of receiving exactly 10 calls in 15 minutes is:

P(Y = 10) = (e^-12 * 12^10) / 10! = 0.1143

(c) Let Z be the number of callers waiting after 5 minutes. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, Z follows a Poisson distribution with mean λ = 0.8 * 5 = 4. The expected number of callers waiting after 5 minutes is:

E(Z) = λ = 4

The probability that none will be waiting is:

P(Z = 0) = e^-4 = 0.0183

(d) Let W be the waiting time until the next call. The time between calls follows an exponential distribution with rate λ = 48/60 = 0.8 calls per minute. Then, the probability that the agent can take 2 minutes for personal time without being interrupted by a call is:

P(W > 2) = e^(-0.8 * 2) = 0.4493

Alternatively, we can use the memoryless property of the exponential distribution to calculate:

P(W > 2) = P(W > 1 + 1) = P(W > 1) * P(W > 1) = e^(-0.8 * 1) * e^(-0.8 * 1) = 0.4493.

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Answer:

X - 3 = 5

Step-by-step explanation:

X decreased by 3 means X-3.

If X - 3 is 5, then it can be written as X - 3 = 5

Answer: 8

Step-by-step explanation: 8 decreased (subtracted) by 3 is 5.

if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter.

If the sample size is 28 and the population standard deviation is increased, there will be a direct impact on the confidence interval. This is because the confidence interval is calculated based on the sample mean and the standard deviation. If the population standard deviation is increased, it means that there is more variability in the population. This increase in variability will lead to wider confidence intervals.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the confidence interval is determined by the sample size, the standard deviation, and the level of confidence.
In this case, if the population standard deviation is increased, it means that the sample standard deviation will also increase. The sample mean will be relatively more variable than it would be if the population standard deviation was lower. This increase in variability will cause the confidence interval to become wider, as there is more uncertainty in the estimate of the population parameter.
In summary, if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter. It is important to note that increasing the sample size can help to reduce the impact of increased population standard deviation on the confidence interval, as a larger sample size provides more accurate estimates of the population parameter.

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Answer:

D

Step-by-step explanation:

The volume of the pool is 528 cubic feet.

Determine the volumes of each rectangular prism separately and then add them up to determine the volume of Joanie's pool. The rectangular prisms have the following measurements:

4 ft x 8 ft x 6 ft

12 ft x 2 ft x 10 ft

4 ft x 4 ft x 6 ft

Multiply the first rectangular prism's length, width, and height to determine its volume:

4 ft x 8 ft x 6 ft = 192 cubic feet

Multiply the length, width, and height to determine the volume of the second rectangular prism:

12 ft x 2 ft x 10 ft = 240 cubic feet

Multiply the third rectangular prism's length, width, and height to determine its volume:

4 ft x 4 ft x 6 ft = 96 cubic feet

The volumes of the three rectangular prisms are now added up:

192 cubic feet + 240 cubic feet + 96 cubic feet = 528 cubic feet

Therefore, the pool can hold 528 cubic feet of water.

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The slope of the line c is - 92.

The points via which the line b passes are:

(-20, 4) and (-21, 96).

The slope of the line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Slope of the line b passing through these points are:

m = (96 - 4) / (- 21 + 20)

m = (92) / (-1)

m = - 92

Since, line b is parallel to line c,

Slope of line b = slope of line c

So, the slope of line c is also:

m' = - 92

Therefore, we get that, the slope of the line c is - 92.

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The required answer is ∫ Cydx−xdy = ∬ D (−1) dA = − area(D) = −8.

To evaluate the given line integral using Green's theorem, we need to first find the curl of the vector field F = (−x, y).

∂Fy/∂x = 1, and ∂Fx/∂y = 1, so curl(F) = ∂Fy/∂x − ∂Fx/∂y = 0.

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. It is the two-dimensional special case of Stokes' theorem.

Since the curl is zero, we can apply Green's theorem to get

∫ Cydx−xdy = ∬ D (−∂Fx/∂y − ∂Fy/∂x) dA = ∬ D (−1 − 0) dA

where D is the square [−1,1]×[−1,1].

Integrating over D, we get

∫ C ydx−xdy = ∬ D (−1) dA = − area(D) = −8.

Therefore, the value of the line integral is −8.

To evaluate the given line integral using Green's theorem, we first need to express the given integral as a double integral over the region enclosed by the curve C, which in this case is the square [-1, 1] x [-1, 1].

According to Green's theorem, for a line integral ∫C (P dx + Q dy), we have:

∫C (P dx + Q dy) = ∬D (dQ/dx - dP/dy) dA

In our case, P = y and Q = -x. So, we first find the partial derivatives dP/dy and dQ/dx:

dP/dy = d(y)/dy = 1
dQ/dx = d(-x)/dx = -1

Now, substitute these values into Green's theorem formula:

∫C (y dx - x dy) = ∬D (-1 - 1) dA

This simplifies to:

∫C (y dx - x dy) = ∬D (-2) dA

Now, evaluate the double integral over the region D (the square [-1, 1] x [-1, 1]):

∬D (-2) dA = -2 ∬D dA

Since D is a square with side length 2, the area is 2 * 2 = 4. Thus, we have:

-2 ∬D dA = -2 * 4 = -8

So, the value of the line integral ∫C y dx - x dy, where C is the boundary of the square [-1, 1] x [-1, 1] oriented in the counterclockwise direction, using Green's theorem is -8.

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Answer: 16 girls

Step-by-step explanation:

Step 1: Calculate the total number of students in the school by multiplying 32 by the ratio of girls to all the students, which is 5:8.

32 x (5/8) = 20

Step 2: Subtract the result from 32 to get the number of girls in the school.

32 - 20 = 12

Step 3: Multiply the result by the ratio of girls to all the students, which is 5:8.

12 x (5/8) = 16

A longitudinal study is a type of research method used to observe changes in a given behavior or condition of a group of individuals over a period of time.

It is especially useful in resolving the limitation of a traditional correlational study in that it can provide evidence for the direction of a possible causal relationship between the variables. This is because the study is conducted over a period of time, which allows for the observation of changes in the variables over time, and the ability to determine which variable is causing the changes in the other. This can be done through the use of statistical tests, such as regression analysis, which can measure the strength of the correlation and the direction of the relationship. Additionally, longitudinal studies can also help to determine whether the sample size is sufficient, as well as whether the relationship between the variables is statistically significant.

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Answer:

28 g. ................

The polynomial : y = 3.6088 x³  - 0.3494 x² + 7.7644 x + 2.1870

Given,

Table

MATLAB  code :

clc; clear all; x = [1.15; -1.95; 2.15; -0.8; 0.1]; y = [16.42; -41.1; 53.06; -5.8; 2.52]; % taking cube of x p =x³; % taking square of x q = x²; %combining all columns X = [p q x];  % model of the form ax³ + bX² + cx + d % fit model in linear model mdl = fitlm(X,y); % printing coeffecients of matrix mdl.Coefficients

The table is attached below .

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Answer:

The answser should be V = hπr2/3 if im not wrong if I am sorry lol Step-by-step explanation:

Answer:

The formula is \(\frac{1}{3}\)\(\pi\)r²h

Step-by-step explanation:

So, you will just have to plug in these values into the formula.

r = radius (of the circle base of the cone)

h= height

Then multiply by the fraction \(\frac{1}{3}\) as well as \(\pi\), and you will get the volume of the cone.

Answer:

Step-by-step explanation:

Comparing

This is not same as u = v, so the answer is false

Answer:

41

Step-by-step explanation:

2021 eng

a) To verify that the straight lines y = ±(1/2)x are solution curves of the given differential equation, we substitute these lines into the equation and check if they satisfy it.

Let's consider the positive slope line y = (1/2)x.

Taking the derivative of y with respect to x, we have dy/dx = 1/2. Substituting this into the equation dy/dx = x/(4y), we get 1/2 = x/(4(1/2)x), which simplifies to 1/2 = 1/2. Since both sides are equal, the positive slope line y = (1/2)x is a solution curve. Similarly, you can verify that the negative slope line y = -(1/2)x is also a solution curve.

b) To sketch the solution curve with the initial condition y(0) = -1, we start at the point (0, -1) and follow the direction field. At each point, we draw a small line segment that indicates the direction of the solution curve. Since the line y = -(1/2)x is a solution curve, it passes through the point (0, -1). We can sketch this line and other nearby solution curves that follow the direction field.

c) To sketch the solution curve with the initial condition y(3) = 1, we start at the point (3, 1) and follow the direction field. The direction field indicates the slope of the solution curve at each point. By following the directions given by the field, we can sketch the solution curve passing through the point (3, 1). The curve might cross or intersect with other solution curves, but the general behavior will be in accordance with the direction field.

d) As x approaches positive infinity, the solution curves will tend to approach the horizontal line y = 0. This can be observed from the direction field where the lines become more horizontal as x increases. On the other hand, as x approaches negative infinity, the solution curves will tend to approach the horizontal line y = 0 as well, but from below the x-axis. The slopes of the solution curves decrease as x moves away from zero in either direction, leading to the curves approaching the horizontal line. This behavior is consistent with the given differential equation dy/dx = x/(4y), where the slope is determined by the ratio of x and y.

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The empirical probability that a consumer will like this brand of sausage is 0.9 or 90%.

The ratio of the number of times an event occurs to all possible trials is the empirical probability that the event will occur. The occurrence in this instance is comparable to the brand of sausage.

The total number of consumers who tested was 700, and 630 of them rated the sausage favorably. As a result, the empirical likelihood that a customer will enjoy this brand of sausage is:

Empirical Probability = Number of consumers who liked the sausage / Total number of consumers tested

Empirical Probability = 630 / 700

Empirical Probability = 0.9

Therefore, the empirical probability that a consumer will like this brand of sausage is 0.9 or 90%.

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Answer:

a) \(P(148<X<175)=P(\frac{148-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{175-\mu}{\sigma})=P(\frac{148-160}{8}<Z<\frac{175-160}{8})=P(-1.5<z<1.875)\)

\(P(-1.5<z<1.875)=P(z<1.875)-P(z<-1.5)= 0.970-0.0668= 0.9032\)

b) \(P(X>164)=P(\frac{X-\mu}{\sigma}>\frac{164-\mu}{\sigma})=P(Z>\frac{164-160}{8})=P(z>0.5)\)

\(P(z>0.5)=1-P(z<0.5)= 1-0.691= 0.309\)

c) \(P(X<179)=P(\frac{X-\mu}{\sigma}<\frac{179-\mu}{\sigma})=P(Z<\frac{179-160}{8})=P(z<2.375)\)

\(P(z<2.375)= 0.991\)

Step-by-step explanation:

Let X the random variable that represent the heights of Guinean travels , and for this case we know the distribution for X is given by:

\(X \sim N(160,8)\)  

Where \(\mu=160\) and \(\sigma=8\)

Part a

We are interested on this probability

\(P(148<X<175)\)

We can ue the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

Using this formula we got:

\(P(148<X<175)=P(\frac{148-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{175-\mu}{\sigma})=P(\frac{148-160}{8}<Z<\frac{175-160}{8})=P(-1.5<z<1.875)\)

And we can find this probability with this difference using the normal standard distribution or excel:

\(P(-1.5<z<1.875)=P(z<1.875)-P(z<-1.5)= 0.970-0.0668= 0.9032\)

Part b

\(P(X>164)=P(\frac{X-\mu}{\sigma}>\frac{164-\mu}{\sigma})=P(Z>\frac{164-160}{8})=P(z>0.5)\)

And we can find this probability with this difference using the normal standard distribution or excel:

\(P(z>0.5)=1-P(z<0.5)= 1-0.691= 0.309\)

Part c

\(P(X<179)=P(\frac{X-\mu}{\sigma}<\frac{179-\mu}{\sigma})=P(Z<\frac{179-160}{8})=P(z<2.375)\)

And we can find this probability with this difference using the normal standard distribution or excel:

\(P(z<2.375)= 0.991\)

SOLUTIONS

The On- time departure are represented with 4 , 5 , 6 , 7 , 8 , 9

while the late departure are represented with 0 , 1, 2, 3

Correct answer = Option D

Answer:

40 students

Step-by-step explanation:

you have to minus 9 because of the cars then you have 320 divide 8 and you get 40.

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

Answer: unit of account

Step-by-step explanation:

I learned this in Macro Chapter 34.

Answer:

x > 24

Step-by-step explanation:

- 1/2 x < -12

Multiply each side by -2, remembering to flip the inequality

-2 * -1/2x > -12 *-2

x > 24

Answer:

\(x > 24\)

Step-by-step explanation:

\( - \frac{1}{2} x < - 12 \\ x < - 12 \times 2 \\ - x < - 24 \\ x > 24\)