Prism A and prism B are similar.
6 yd
Prism A
S = 225 yd²
Prism B
8 yd
Part A: What is the scale factor from Prism A to Prism B?
Part B: What is the surface area of Prism B?

The distance between the mirror and the 20-foot tree is 32 feet.

The idea of comparable triangles can be used to calculate the separation between the mirror and the 20-foot tree.

Let's think about the triangles the man, the mirror, and the tree created. Similar triangles have comparable sides that are equal in ratio.

The dude is standing 8 feet away from the mirror and is 5 feet tall. As a result, we may establish the following ratio:

(Height of the man) / (Distance of the man from the mirror) = (Height of the tree) / (Distance of the tree from the mirror)

Substituting the known values:

5 / 8 = 20 / x

Where x represents the distance of the tree from the mirror.

Now, we can solve for x:

5x = 8 * 20

5x = 160

x = 160 / 5

x = 32

Therefore, the distance between the mirror and the 20-foot tree is 32 feet.

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B

H

E

C

Standard form must be between 1 and 9

Answer:

43,624 mm cubed

Volume of Prisms Equation:

V=(Areabase)(height)

Volume of Triangular Prisms:

V=(1/2×base×height)(HEIGHT OF PRISM)

Step by Step Explanation:

V=(1/2×38×28)(82)

Cancelling:

cancel 2 and 28 making it 1 and 14

since the fraction is now 1/1 it is not needed

Back to Solving:

=38×14×82

=43,624 mm cubed

Answer:

Step-by-step explanation:

To calculate the probability of rolling a sum of 10 with two dice, we need to find the number of ways we can get a sum of 10 and divide that by the total number of possible outcomes. The sum of 10 can be obtained in three ways: (4, 6), (5, 5), and (6, 4). There are 36 possible outcomes when rolling two dice, since there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. Therefore, the probability of rolling a sum of 10 is 3/36, which simplifies to 1/12.

The probability you will roll a sum of 10 is 1/12.

We have,

Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

To calculate the probability of rolling a sum of 10 with two dice, we need to find the number of ways we can get a sum of 10 and divide that by the total number of possible outcomes.

The sum of 10 can be obtained in three ways: (4, 6), (5, 5), and (6, 4).

The probability you will roll a sum of 10 = total times a sum of 10 is derived / total sample spaces

so, we get,

total times a sum of 10 is derived = (4 + 6) , (6 +4) , (5 + 5)

There are 36 possible outcomes when rolling two dice, since there are 6 possible outcomes for the first die and 6 possible outcomes for the second die.

Total sample spaces = 36

The probability you will roll a sum of 10 = 3/36 = 1/12

Therefore, the probability of rolling a sum of 10 is 3/36, which simplifies to 1/12.

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Answer:

18.136 units of distance

Step-by-step explanation:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) = (2, 1) and (x2, y2) = (12, 18)

d = sqrt((12 - 2)^2 + (18 - 1)^2)

= sqrt(10^2 + 17^2)

= sqrt(329)

≈ 18.136

Therefore, the rock traveled approximately 18.136 units of distance.

The box plot that represents the data on the sandwiches sold by Super Sandwiches is Box Plot 1.

The box plot that shows the data of sandwiches is the one that has the correct measure of the value of Q1 or the lower quartile. This is because the box plots are similar except for the lower quartile.

To find the lower quartile, arrange the numbers;

50, 66, 74, 88, 100, 109, 113, 127, 150

The lower quartile would be the median of the lower half of :

50, 66, 74, 88

The lower quartile is:

= ( 66 + 74 ) / 2

= 70

The first box plot has this Q1 value and so is correct.

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Answer:

Step-by-step explanation:

total number of sticks = 47+36+31= 114

Because you draw with replacement to find the probability of two events happening you simply just multiply them

p(books without pics) = #books without pics /#sticks

47/114 = 41.2280702%

p(audiobooks)= #audiobooks/ #sticks

31/114= 27.1929825%

p(books without pics and audiobooks)= p(books without pics) * p(audiobooks)

41.2280702%*27.1929825% = 11.21%

If every matchbox contains no more than 20% defective matches, then at least 80% of the matches in a box must be intact. The minimum number of intact matches in a 43-match box manufactured by that factory is 34.

To find the minimum number of intact matches in a 43-match box, we need to multiply 43 by 80% (or 0.8):
43 x 0.8 = 34.4
Since we can't have a fraction of a match, we round down to the nearest whole number. Therefore, the minimum number of intact matches in a 43-match box manufactured by that factory is 34.
In a 43-match box manufactured by that factory, no more than 20% of the matches can be defective. To find the minimum number of intact matches, we can calculate the number of defective matches and subtract it from the total.
20% of 43 matches = (20/100) * 43 = 8.6
Since there can't be a fraction of a match, we round up to the nearest whole number, which is 9 defective matches. Now, subtract the number of defective matches from the total:
43 matches - 9 defective matches = 34 intact matches
The minimum number of intact matches in a 43-match box manufactured by that factory is 34.

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We can see that the pattern progresses by adding 3 to the previous perfect square to obtain the next term. The next few terms of the sequence would be:

25 (16 + 3)

36 (25 + 3)

49 (36 + 3)

64 (49 + 3)

81 (64 + 3)

...

We can continue this pattern to find as many terms as desired.

What is Number Sequences?

In mathematics, a number sequence is an ordered list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term, and the position of a term in the sequence is called its index.

The given pattern appears to be a sequence of perfect squares starting from 1 and increasing by 3 at each step. We can verify this by observing that:

The first term is 1 which is a perfect square.

The second term is 4 which is a perfect square and is obtained by adding 3 to the previous term 1.

The third term is 9 which is a perfect square and is obtained by adding 3 to the previous term 4.

The fourth term is 16 which is a perfect square and is obtained by adding 3 to the previous term 9.

Therefore, we can see that the pattern progresses by adding 3 to the previous perfect square to obtain the next term. The next few terms of the sequence would be:

25 (16 + 3)

36 (25 + 3)

49 (36 + 3)

64 (49 + 3)

81 (64 + 3)

...

We can continue this pattern to find as many terms as desired.

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if Jacob wants to make a square or rectangular garden, each side can be up to 16.5 feet long, allowing for a total perimeter of 33 feet.

What is Perimeter?

Perimeter is the total distance around the edge of a two-dimensional shape, such as a polygon or a circle, and it is calculated by adding up the lengths of all of the sides of the shape.

A measuring cup is a kitchen tool used to measure the volume of liquid or bulk solid ingredients, typically made of glass or plastic and marked with graduated lines to indicate different measurements, such as milliliters, fluid ounces, and cups.

Jacob is planning a garden. He has 12 fence posts and plans to place them 3 feet apart. How many feet of fence will this allow for the perimeter of the garden?

If Jacob has 12 fence posts and plans to place them 3 feet apart, the perimeter of the garden will be 33 feet.

To see why, we can start with the fact that Jacob has 12 fence posts. Since he wants to place them 3 feet apart, we can imagine a straight line fence where each post is 3 feet away from the next one. The length of this line would be:

11 distances between posts x 3 feet per distance = 33 feet

However, a garden typically has four sides, so we need to divide this length by two to get the length of one side:

33 feet / 2 = 16.5 feet

Therefore, if Jacob wants to make a square or rectangular garden, each side can be up to 16.5 feet long, allowing for a total perimeter of 33 feet.

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The equation for g(x) in vertex form is [tex]g(x) = ax^2[/tex], where "a" represents a constant that determines the shape and direction of the parabola.

The vertex form of a quadratic equation is given by:

[tex]g(x) = a(x - h)^2 + k[/tex]

where (h, k) represents the vertex of the parabola.

Since g(x) is a translation of [tex]f(x) = x^2[/tex], the vertex of g(x) will be the same as the vertex of f(x). The vertex of [tex]f(x) = x^2[/tex] is (0, 0).

So, the equation for g(x) in vertex form is:

[tex]g(x) = a(x - 0)^2 + 0\\g(x) = a(x^2)\\g(x) = ax^2[/tex]

Therefore, the equation for g(x) in vertex form is [tex]g(x) = ax^2[/tex], where "a" represents a constant that determines the shape and direction of the parabola.

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Finding the fixed points, classifying them, sketching the neighboring trajectories, and filling in the rest of the phase portrait can help us understand the behavior of a dynamical system and make predictions.

To find the fixed points of a system, we need to solve for the values of the variables that make the derivatives equal to zero. Once we have found the fixed points, we can classify them by analyzing the sign of the derivatives near each point. If the derivatives are positive on one side and negative on the other, then the fixed point is unstable, meaning nearby trajectories will move away from it. If the derivatives are negative on both sides, then the fixed point is stable, meaning nearby trajectories will move towards it. If the derivatives are zero on one side and positive or negative on the other, then the fixed point is semi-stable or semi-unstable, respectively.

Once we have classified the fixed points, we can sketch the neighboring trajectories by analyzing the sign of the derivatives along those trajectories. If the derivatives are positive, then the trajectory will move in the positive direction, and if they are negative, then it will move in the negative direction. By sketching the neighboring trajectories, we can get a sense of how the system behaves in different regions of the phase space.

Finally, we can try to fill in the rest of the phase portrait by looking for other features such as limit cycles, separatrices, or regions of phase space where trajectories diverge or converge.

Overall, finding the fixed points, classifying them, sketching the neighboring trajectories, and filling in the rest of the phase portrait can help us understand the behavior of a dynamical system and make predictions about its future evolution.

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The given series is ∑(n!)(k^n)((kn)!)x^n. To find the radius of convergence, the radius of convergence for the given series is 0.

The given series is ∑(n!)(k^n)((kn)!)x^n. To find the radius of convergence, we can use the Ratio Test. The Ratio Test states that the radius of convergence R is given by:
R = 1/lim (n→∞) |(a_(n+1))/a_n|
where a_n represents the nth term of the series. For our series, a_n = (n!)(k^n)((kn)!)x^n. Let's find the ratio
|(a_(n+1))/a_n| = |[((n+1)!)(k^(n+1))((k(n+1))!)x^(n+1)]/[(n!)(k^n)((kn)!)x^n]|
Simplifying, we get
|(a_(n+1))/a_n| = |(n+1)(k)(((k(n+1))!))/((kn)!)x|
Now, let's take the limit as n approaches infinity:
lim (n→∞) |(n+1)(k)(((k(n+1))!))/((kn)!)x|
Since both the numerator and the denominator have factorials that grow rapidly, this limit is infinity. Therefore, the radius of convergence is:
R = 1/∞ = 0
So, the radius of convergence for the given series is 0.

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Answer:

b = 4[tex]\sqrt{3}[/tex] , c = 8

Step-by-step explanation:

using the tangent and cosine ratios in the right triangle and the exact values

tan60° = [tex]\sqrt{3}[/tex] , cos60° = [tex]\frac{1}{2}[/tex] , then

tan60° = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{b}{4}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 4 )

b = 4[tex]\sqrt{3}[/tex]

then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{c}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

c = 4 × 2 = 8

The variable c indicates the number of crimes in a city with two neighborhoods—one rich and one poor—both of the same size, where the city employs a police force of 20 officers and p represents the number of police officers. Here option C is the correct answer.

To allocate police resources effectively between rich and poor neighborhoods, crime rates, severity, and community policing should be considered to ensure the safety and well-being of all residents.

The allocation of police resources in a city with two neighborhoods - one rich and one poor - presents a challenging issue. In this scenario, both neighborhoods have the same population size, but different socio-economic characteristics. The rich neighborhood may have lower crime rates due to better security measures and access to resources, while the poor neighborhood may experience higher crime rates due to factors such as poverty, lack of education, and unemployment.

Given the budgetary restrictions, the city employs a police force of 20 officers. This raises the question of how to allocate these officers between the two neighborhoods to ensure the most effective use of resources.

One approach to this issue is to allocate officers based on crime rates. If the rich neighborhood has lower crime rates, then fewer officers can be assigned there, while more officers can be allocated to the poor neighborhood where crime rates are higher. This approach ensures that police resources are used where they are most needed.

Another approach is to allocate officers based on the severity of crimes. If the rich neighborhood has fewer but more severe crimes, then more officers may need to be assigned there to handle these cases. On the other hand, if the poor neighborhood has more but less severe crimes, then fewer officers may be required, but they may need to be more vigilant and proactive in preventing crime.

It is also important to consider community policing as a strategy to improve relationships between police officers and residents in both neighborhoods. By building trust and fostering communication, residents may be more willing to work with law enforcement to prevent crime and promote safety.

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Complete question:

What does the variable c denote in a city with two neighborhoods - one rich and one poor - both with equal-sized populations, where the city employs a police force of 20 officers and p represents the number of police officers?

A) The number of police officers

B) The population of the rich neighborhood

C) The population of the poor neighborhood

D) The number of crimes.

The gradient field of a function is a vector field that points in the direction of the maximum increase of the function.  In the case of f(x,y,z) = x^2/4 + y^2/4 + z^2 - 1/2, the gradient field is given by <x/2, y, 2z>.

The gradient of a scalar field is a vector field that points in the direction of the maximum rate of increase of the scalar field, and its magnitude represents the rate of increase.

To find the gradient field of f(x,y,z), we first calculate the partial derivatives of f with respect to x, y, and z. The partial derivative of f with respect to x is 2x/4y2/4z2, the partial derivative of f with respect to y is -x2/2y3/4z2, and the partial derivative of f with respect to z is -x2/4y2/2z3/2. The gradient of f is then given by the vector field (2x/4y2/4z2)i - (x2/2y3/4z2)j - (x2/4y2/2z3/2)k, where i, j, and k are the unit vectors in the x, y, and z directions, respectively. This vector field represents the direction and magnitude of the maximum rate of increase of f at any point in space.

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Therefore, the solution to the given IVP is, y(t) = 1/2 * [e^t - e^(-t)]

Explanation:
To solve the given IVP using Laplace transforms, we need to take the Laplace transform of both sides of the differential equation. This gives us:
s^2 Y(s) - s(0) - (0) - Y(s) = 0
s^2 Y(s) - Y(s) = 1
Y(s)(s^2 - 1) = 1
Y(s) = 1/(s^2 - 1)
Now, we need to find the inverse Laplace transform of Y(s) to get the solution in the time domain. Using partial fraction decomposition, we can write Y(s) as:
Y(s) = 1/2 * [1/(s-1) - 1/(s+1)]
Taking the inverse Laplace transform of this expression gives us:
y(t) = 1/2 * [e^t - e^(-t)]

Therefore, the solution to the given IVP is, y(t) = 1/2 * [e^t - e^(-t)]

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-2 is the equivalent average rate of change of f(x) with the interval.

The formula for calculating the rate of change of a function is expressed as:

[tex]f'(x) = \frac{f(b)-f(a)}{b-a}[/tex]

Given the function f(x) = 2x² + 12x + 16 with the interval [-3, -2]

f(-3) =  2(-3)² + 12(-3) + 16

f(-3) = 2(9) - 36 + 16

f(-3) = 18 - 20

f(-3) = -2

Similarly:

f(-2) =  2(-2)^2 + 12(-2) + 16

f(-2) = 2(4) - 24 + 16

f(-2) = 8 - 8

f(-2) = 0

Substitute the resulting values:

[tex]f'(x) = \frac{f(-3)-f(-2)}{-3-(-2)}\\f'(x)=\frac{-2-0}{-1}\\f'(x)=-2[/tex]

Hence the average rate of change of f(x) within the given interval is -2.

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The graph of y = -5x + 10 is a function because (d) yes, because it passes the vertical line test.

From the question, we have the following parameters that can be used in our computation:

y = -5x + 10

The above equation is a linear function

As a general rule of functions and relations

All linear functions are functions

This is because they pass the vertical line test

So, the true statement is (d)

Hence, the relation y = -5x + 10 is a function because (d) yes, because it passes the vertical line test.

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Complete question

Does this graph show a function? Explain how you know.

y = -5x + 10

A. No; there are y-values that have more than one x-value.

B. Yes; there are no y-values that have more than one x-value.

C. No; the graph fails the vertical line test.

D. Yes; the graph passes the vertical line test.

The areas of the circular sectors are listed below:

Case 7: A = 50π / 3 in²

Case 8: A = 177.884 cm²

Case 9: A = 937.312 m²

Case 10: A = 10π / 3 ft²

In this problem we must determine the areas of four circular sectors, whose area formula is equal to:

A = (θ / 360°) · π · r²

Where:

Now we proceed to determine the areas:

Case 7

A = (60 / 360) · π · (10 in)²

A = 50π / 3 in²

Case 8

A = (104 / 360) · π · (14 cm)²

A = 177.884 cm²

Case 9

A = (137 / 360) · π · (28 m)²

A = 937.312 m²

Case 10

A = (75 / 360) · π · (4 ft)²

A = 10π / 3 ft²

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Because x-bar is an unbiased estimator of μ, sample averages have the same variance as the individual observations in the population.

The sample mean or x-bar is a statistic that estimates the population mean or μ. When we say that x-bar is an unbiased estimator of μ, it means that on average, the sample mean is equal to the population mean. This property is desirable because it means that our estimates are not systematically too high or too low.

One consequence of the x-bar being an unbiased estimator of μ is that sample averages have the same variance as the individual observations in the population. This means that the spread or variability of the sample mean is equal to the spread or variability of the individual observations. However, the central limit theorem tells us that the distribution of sample averages is more Normal than the distribution of individual observations. This is because as the sample size increases,

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The 1st Quartile germination rate is 92%, the 1st Quartile germination rate represents the threshold below which 25% of the germination rates fall.

To determine this, we need to arrange the germination rates in ascending order and find the value that corresponds to the 25th percentile.

In this case, we have a packet of 160 seeds with 95% germination rate. To find the 1st Quartile germination rate, we need to consider the germination rates of the remaining 5% of seeds that did not germinate.

Since 92% is the claimed germination rate mentioned on the seed packet, we can assume that the 5% of seeds that did not germinate fall below this claimed rate. Therefore, the 1st Quartile germination rate is 92%.

The 1st Quartile, also known as the lower quartile or 25th percentile, divides a dataset into four equal parts. It represents the threshold below which 25% of the data points fall.

In this scenario, we have a packet of 160 seeds with a 95% germination rate. This means that 95% of the seeds successfully germinated. To find the 1st Quartile germination rate, we need to consider the remaining 5% of seeds that did not germinate.

Since the information on the seed packet claims a germination rate of 92%, we can assume that the 5% of seeds that did not germinate fall below this claimed rate.

As a result, the 1st Quartile germination rate is 92%. This indicates that 25% of the seeds in the packet had a germination rate below 92% while the remaining 75% had a germination rate equal to or higher than 92%.

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Answer:

To test the null hypothesis that the mean mark is equal to 100 against the alternative that the mean mark is greater than 100, we can use a one-sample t-test since the population variance is unknown. Here's how you can perform the test:

Step 1: State the null and alternative hypotheses:

- Null hypothesis (H₀): The mean mark is equal to 100.

- Alternative hypothesis (H₁): The mean mark is greater than 100.

Step 2: Set the significance level (α):

In this case, the significance level is given as 0.05 or 5%.

Step 3: Compute the test statistic:

The test statistic for a one-sample t-test is calculated using the formula:

t = (X - μ) / (s / √n)

where X is the sample mean, μ is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

Given:

X = 110 (sample mean)

s = 8 (sample standard deviation)

n = 13 (sample size)

μ (population mean under the null hypothesis) = 100

Substituting the values into the formula, we get:

t = (110 - 100) / (8 / √13)

t = 10 / (8 / √13)

t ≈ 3.012

Step 4: Determine the critical value:

Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value for a one-tailed test at a 5% significance level with (n - 1) degrees of freedom. In this case, the degrees of freedom are 13 - 1 = 12.

Using a t-distribution table or statistical software, the critical value at α = 0.05 and 12 degrees of freedom is approximately 1.782.

Step 5: Make a decision:

If the test statistic t is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the test statistic t is approximately 3.012, which is greater than the critical value of 1.782. Therefore, we reject the null hypothesis.

Step 6: State the conclusion:

Based on the sample data, there is sufficient evidence to support the claim that the mean mark is greater than 100.

Step-by-step explanation:

Step-by-step explanation:

To find the equation of the tangent plane to the surface at (3, 4, ln 5), we need to first find the partial derivatives of h with respect to x and y:

hx(x, y) = 2y^2/x

hy(x, y) = 2x^2/y

Then, we can plug in the point (3, 4) to get the partial derivatives evaluated at that point:

hx(3, 4) = 2(4^2)/3 = 32/3

hy(3, 4) = 2(3^2)/4 = 9/2

Now we can use the point-normal form of the equation of a plane, where the normal vector is given by ⟨hx(3, 4), hy(3, 4), -1⟩:

hx(3, 4)(x - 3) + hy(3, 4)(y - 4) - (z - ln 5) = 0

Substituting in the values for hx(3, 4) and hy(3, 4), we get:

(32/3)(x - 3) + (9/2)(y - 4) - (z - ln 5) = 0

Simplifying, we get:

(32/3)x + (9/2)y - z = 55/6

So the equation of the tangent plane to the surface at (3, 4, ln 5) is (32/3)x + (9/2)y - z = 55/6.

The slope of the line that passes through the points ( -4,5) and (2,-3) is -4/3

The slope of a line is a measure of its steepness. It is also called gradient. It is the change in value on the vertical axis to the change in value on the horizontal axis.

Y axis is the vertical axis and x axis is the horizontal axis.

slope = [tex]y_2 -y_1)/x_2-x_1[/tex]

[tex]y_2[/tex] = -3

[tex]y_1[/tex]= 5x2 = 2x1 = -4

slope = -3-5/(2-(-4)

= -8/6

= -4/3

Therefore the slope of the line is -4/3

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Since f(g(x)) = g(f(x)) = x, functions f(x) and g(x) are inverse functions.

The pair of functions in is inverse functions. A.

To determine whether two functions are inverse functions need to check if the composition of the two functions gives the identity function.

To check whether f(g(x)) = x and g(f(x)) = x.

Let's check each pair of functions:

f(x) = x - 4 and g(x) = x + 4

f(g(x)) = (x + 4) - 4

= x

g(f(x)) = (x - 4) + 4

= x

Since f(g(x)) = g(f(x)) = x, functions f(x) and g(x) are inverse functions.

f(x) = x - 4 and g(x) = 4x - 1

f(g(x)) = 4x - 1 - 4

= 4x - 5

g(f(x)) = 4(x - 4) - 1

= 4x - 17

Since f(g(x)) ≠ x and g(f(x)) ≠ x, functions f(x) and g(x) are not inverse functions.

f(x) = x - 4 and g(x) = (x - 4)/4

f(g(x)) = ((x - 4)/4) - 4

= (x - 20)/4

g(f(x)) = ((x - 4) - 4)/4

= (x - 8)/4

Since f(g(x)) ≠ x and g(f(x)) ≠ x, functions f(x) and g(x) are not inverse functions.

f(x) = 4x - 1 and g(x) = 4x + 1

f(g(x)) = 4(4x + 1) - 1

= 16x + 3

g(f(x)) = 4(4x - 1) + 1

= 16x - 3

Since f(g(x)) ≠ x and g(f(x)) ≠ x functions f(x) and g(x) are not inverse functions.

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The geometric sequence is -6, 1, -1/6, 1/36.......

Given is a geometric sequence, -6, ?, ?, 1/36 we need to find the missing terms,

So, we know that the ratios between the terms of a geometric sequence are common,

Let the 2nd term be x and the 3rd term be y, so,

-x/6 = 1/36 / y

-x/6 = 1/36y

6 = -36xy

x·y = -1/6

So, we get x·y = -1/6,

Now if we see the options, the third option gives 1 × -1/6 = -1/6,
Therefore, the terms can be written as,

-6, 1, -1/6, 1/36.......

If we see the common ratio we get,

-1/6

-1/6/1 = -1/6

1/36 / (-1/6) = -1/6

Hence the geometric sequence is -6, 1, -1/6, 1/36.......

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The driver's speed is 37 miles per hour.

We have,

To determine the speed of the driver, we need to use the relationship between skid marks and speed.

One commonly used formula is the "skid-to-stop" formula, which relates the length of the skid mark to the initial speed of the vehicle.

The skid-to-stop formula is given by:

v = √(30 x d)

where:

v is the initial velocity or speed of the vehicle in feet per second,

d is the length of the skid mark in feet.

In this case, the skid mark is 96.42 feet long.

Let's plug in the value for d into the formula and solve for v:

v = √(30 x 96.42)

v = √(2892.6)

v ≈ 53.8 feet per second

To convert the speed to miles per hour, we can multiply it by a conversion factor of 0.681818

(since there are approximately 0.681818 feet per second in 1 mile per hour):

v ≈ 53.8 x 0.681818 ≈ 36.74 miles per hour

Therefore,

To the nearest mile per hour, the driver's speed is 37 miles per hour.

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See solution in the attached image.

For us to solve the system of equations using the substitution method, let us solve one equation for one variable and substitute it into the other equation.

Let's solve the second equation for y:

3x - y = 9

Let us Isolate y:

y = 3x - 9

substitute this expression for y in the first equation:

8x - 2(3x - 9) = 10

Let us simplify the equation:

8x - 6x + 18 = 10

add like terms:

2x + 18 = 10

Subtract 18 from both sides:

2x = 10 - 18

2x = -8

Divide both sides by 2:

x = -8/2

x = -4

Substitute this value of [tex]x[/tex] back to the 2nd equation in order to find y:

[tex]3(-4) - y = 9[/tex]

[tex]-12 - y = 9[/tex]

Subtract -12 from both sides:

[tex]-y = 9 + 12[/tex]

[tex]-y = 21[/tex]

Multiply both sides by -1 :

[tex]y = -21[/tex]

Therefore, the solution is x = -4 and y = -21.

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Answer:

1.2 seconds

Step-by-step explanation:

100-4=96

96/80 = 1.2

Answer:      1 24/80 of a second

Step-by-step explanation:

Well so if you are at 4 ft after 1 second you need 16/80 of a second to reach 100 feet above because 80 then plus 16 plus the addition 4 ft that you are above the water would be 100 feet.