Suppose you physically simulate the random process of rolling a single die. ​(a) After 1010 rolls of the​ die, you observe a​ "one" 44 times. What proportion of the rolls resulted in a​ "one"? ​(b) After 2020 rolls of the​ die, you observe a​ "one" 22 times. What proportion of the rolls resulted in a​ "one"?

The equations when solved would have the solutions of:

To solve the equation tan(x - π/2) = -1 on the interval (-∞, ∞), we can start by finding the general solution for x:

x - π/2 = -π/4 + kπ, where k is an integer.

Now, we can solve for x:

x = π/2 - π/4 + kπ

x = π/4 + kπ

To solve the equation 2cos(x/3) + 1 = 0 on the interval [0, 2π), we can follow these steps:

2cos(x/3) + 1 = 0

cos(x/3) = -1/2

x/3 = 2π/3, 4π/3

x = 2π, 4π

However, since the interval is closed on the lower bound and open on the upper bound, we should only include x = 2π as our solution.

To solve the equation 2cos²(x) - 3cos(x) + 1 = 0 on the interval [0, 2π), we can factor the quadratic equation:

(2cos(x) - 1)(cos(x) - 1) = 0

Now, we have two cases to consider:

Case 1: 2cos(x) - 1 = 0

cos(x) = 1/2

x = π/3, 5π/3

Case 2: cos(x) - 1 = 0

cos(x) = 1

x = 0

So, the solutions on the interval [0, 2π) are x = 0, π/3, and 5π/3.

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Step-by-step explanation:

We can use the binomial distribution to compute the probability that exactly 91 out of 153 registered voters will vote in the presidential election, assuming that the probability that any given registered voter will vote in the presidential election is 59%.

The probability mass function of the binomial distribution is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

- n is the number of trials (in this case, the number of registered voters)

- k is the number of successes (in this case, the number of registered voters who will vote in the election)

- p is the probability of success on any individual trial (in this case, the probability that a given registered voter will vote in the election)

Using this formula, we can calculate:

P(exactly 91 out of 153 voters will vote) = (153 choose 91) * 0.59^91 * (1 - 0.59)^(153 - 91)

= 0.037

Therefore, the probability that exactly 91 out of 153 registered voters will vote in the presidential election is approximately 0.037, or about 3.7%.

Tom has jogged 9 29/30 miles in all.

Just add the values that tells us all the distamnce that he jogged

Write the values as improper fraction

(25/6) + (29/5)

To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 6 and 5. The LCM of 6 and 5 is 30. Now we can convert each fraction to an equivalent fraction with a denominator of 30:

(25/6) * (5/5) = 125/30

(29/5) * (6/6) = 174/30

Now, add the fractions:

(125/30) + (174/30) = (125 + 174) / 30 = 299/30

Now, let's convert this improper fraction back into a mixed number:

299 ÷ 30 = 9 (remainder 29)

So, the mixed number is 9 29/30.

Tom has jogged 9 29/30 miles in all.

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The surface area of the pyramid is 128.2cm².

What is the surface area of the pyramid?

A pyramid is a three-dimensional building with triangular lateral faces and a polygonal base. A pyramid's surface area is simply the total area of all of its faces.

Here, we have

Given:  A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.

We have to find the surface area of the pyramid.

The rectangular base of the pyramid has a length of 7 centimeters and a width of 5 centimeters, so the area of the rectangular base is 35 cm².

The two large triangular faces have a height of 7.6 centimeters, so the area of each of these faces can be calculated as:

= (1/2)×7×7.6

= 26.6 cm²

Similarly, the two small triangular faces have a height of 8 centimeters, so the area of each of these faces can be calculated as:

= (1/2)×5×8

= 20cm²

The total surface area of the rectangular pyramid is:

= 35cm² + 2×26.6 cm² + 2×20 cm²

= 128.2cm²

Hence, the surface area of the pyramid is 128.2cm².

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Answer:

If the y value decreases while the x value remains the same over time, then the correct answer would be A. Y decreases and X decreases.

Step-by-step explanation:

Sure! A slope is a measure of the steepness of a line. It is calculated by dividing the change in the y-coordinates (rise) by the change in the x-coordinates (run) between two points on a line. The formula for slope is m = (y2 - y1) / (x2 - x1).

In your question, if the y value decreases while the x value remains the same over time, it means that the change in y-coordinates (rise) is negative while the change in x-coordinates (run) is zero. This results in a vertical line with an undefined slope. Therefore, the correct answer would be A. Y decreases and X decreases.

Peter’s new salary by the given data is $36,400.

We are given that;

Salary= 35000

Percentage= 4%

Now,

To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).

The amount of his raise is:

0.04 × 35000

= 1400

35000 + 1400

= 36400

Therefore, by the given percentage the answer will be $36,400.

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Peter’s new salary by the given data is $36,400.

We are given that;

Salary= 35000

Percentage= 4%

Now,

To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).

The amount of his raise is:

0.04 × 35000

= 1400

35000 + 1400

= 36400

Therefore, by the given percentage the answer will be $36,400.

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The probability of pulling out a number which is divisible by 2 or 3 will be 7/10 which is not given here. So, option D will be the answer.

How do we find Probability?

The measurement through which we find the likelihood of an event to occur is called probability. We cannot predict a lot of events with total certainty. And thus, the chance of a event to occur (i.e. how likely they re going to happen) can be predicted using probability.

Probability of any event to happen can be find as: No of favorable outcomes/Total number of outcomes.

Here,

The total no of outcomes = 1,2,3,4,5,6,7,8,9,10

No of favorable outcomes ={2,3,4,6,8,9,10} = 7

Therefore, P(E) = 7/10

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Answer:

To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.

Setting x^2 - 10x + 31 equal to x + 1:

x^2 - 10x + 31 = x + 1

Rearranging the equation to standard quadratic form:

x^2 - 10x + 30 = 0

Now, we can factorize the quadratic expression:

(x - 5)(x - 6) = 0

Setting each factor equal to zero and solving for x:

x - 5 = 0 or x - 6 = 0

x = 5 or x = 6

So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.

Answer:

To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.

Setting x^2 - 10x + 31 equal to x + 1:

x^2 - 10x + 31 = x + 1

Rearranging the equation to standard quadratic form:

x^2 - 10x + 30 = 0

Now, we can factorize the quadratic expression:

(x - 5)(x - 6) = 0

Setting each factor equal to zero and solving for x:

x - 5 = 0 or x - 6 = 0

x = 5 or x = 6

So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.

Answer:

x = 5 or x = 6

Step-by-step explanation:

Given expressions:

[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]

To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:

[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]

Factor the quadratic:

[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]

Using the zero-product property, set each factor equal to zero and solve for x:

[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]

Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.

Answer:

x = 5 or x = 6

Step-by-step explanation:

Given expressions:

[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]

To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:

[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]

Factor the quadratic:

[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]

Using the zero-product property, set each factor equal to zero and solve for x:

[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]

Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.

Answer:

The two triangles are related by Angle-Angle-Side (AAS), so the triangles are congruent.

Answer:

17cm

Step-by-step explanation:

Perimeter is the sum of all the sides.

4.5+4.5=9

4+4=8

9+8=17

It will take the acrobat 1/4 of a second to land safely on the net.

Velocity is a physical quantity that measures the rate at which an object moves in a particular direction. It is measured in terms of distance traveled per unit of time, usually expressed in terms of meters per second (m/s). Velocity is a vector quantity, meaning it has both a magnitude and a direction. It is an important concept in physics and is used to understand the motion of objects and forces.
The quadratic equation representing the height h of the acrobat t seconds after the jump can be written as follows: [tex]h=-16t^2+4t+25[/tex].
To find the time it takes for the acrobat to land safely on the net, we need to solve for t when h=5. We can do this by substituting 5 for h into the equation and solving for t:
[tex]h=-16t^2+4t+25\\\\5=-16t^2+4t+25\\\\=-16t^2+4t-20=0\\\\(4+\sqrt{64})/(-32)=t\\ \\t=(4+8)/(-32)\\\\t=1/4[/tex]
Therefore, it will take the acrobat 1/4 of a second to land safely on the net.
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Answer:

9/7, 6/5

Step-by-step explanation:

An improper fraction is a fraction whose numerator is greater than the denominator.

Answer: 9/7, 6/5

We can see here that the probability that a randomly selected customer did not purchase a Toes Knows shoe or is not displeased is: 0.939

Mathematics' study of random events and their likelihood of happening is known as probability.

We can calculate the probability thus:

We will use: P(not Toes Knows or not displeased) = 1 - P(Toes Knows and displeased)

Calculating P(Toes Knows and displeased), we have:

P(Toes Knows and displeased) = P(Toes Knows) × P(displeased | Toes Knows).

We can find  P(Toes Knows)  which will give us:

P(Toes Knows) =  (8+3)/(12+13+10+3+8+3) = 11/49

P(displeased | Toes Knows) = 3/11

Thus, P(Toes Knows and displeased) = (11/49) × (3/11) = 3/49

So, we can now find  the probability that a randomly selected customer did not purchase a Toes Knows shoe or is not displeased which is:

P(not Toes Knows or not displeased) =

1 - P(Toes Knows and displeased) =

1 - 3/49 = 46/49 ≈ 0.939

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The rate of change of the quantity is 90%.

What is the rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.  The pace at which one quantity changes in relation to another quantity is known as the rate of change function.

Here, we have

Given: The function f(t) = [tex]300(1.9)^{t}[/tex] represents the change in a quantity over t months.

Since the base of the exponent 1.9 is greater than 1.

The nature of f(t) is increasing.

Now,

f(t+1) = [tex]300(1.9)^{t+1}[/tex]

f(t+1)/f(t) =  [tex]((1.9)^{t+1})/((1.9)^{t}[/tex] = 1.9

Hence, an increase in f(t)

(f(t+1) -f(t))/f(t) = f(t+1)/f(t) - 1

= 1.9 - 1

= 0.9

% increase = 0.9 × 100 = 90%

Hence, the rate of change in the quantity is 90%.

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Answer:

20 days

Step-by-step explanation:

We can model this situation using the linear equation, whose general form is

f(x) = mx + b, where m is the slope and b is the y-intercept

f(x) = -5/8x + 25/2, where f(x) is the amount remaining in the vitamin bottle and x is the number of days

Explaining the formula:

We essentially want to find the x value that will make f(x) = 0 since that is when the bottle will be empty:

0 = -5/8x + 25/2

-25/2 = -5/8x

20 = x

We can check by plugging in 20 for x and see whether we get 0:

0 = -5/8(20) + 25/2

0 = -25/2 + 25/2

0 = 0

The coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3).

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

To find the coordinates of polygon A'B'C'D' after a 180° rotation, we need to reflect each vertex across the x-axis and then the y-axis.

To reflect a point across the x-axis, we change the sign of the y-coordinate.

To reflect a point across the y-axis, we change the sign of the x-coordinate.

Using this method, we can find the coordinates of A'B'C'D':

A(0, 0) reflects to A'(0, 0) (no change)

B(5, 2) reflects to B'(-5, 2) (reflect across y-axis)

C(5, -5) reflects to C'(-5, -5) (reflect across y-axis)

D(0, -3) reflects to D'(0, 3) (reflect across x-axis)

Therefore, the coordinates of polygon A'B'C'D' are:

A'(0, 0), B'(-5, 2), C'(-5, -5), D'(0, 3)

Hence,  the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3) and the graph is attached is in the attached image.

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In the most recent reporting period, the amount of cash paid by Nike for property, plant and equipment was $4,904 million. The Option D is correct.

The cash payments under property, plant, and equipment (PP&E) are recognized in a company's financial statements when they represent actual expenditures for acquiring, constructing, or improving long-term assets.

Some examples of cash payments that could be recognized under PP&E include the purchase price of land or buildings, expenses related to preparing land for its intended use, costs incurred to construct new buildings or renovate existing ones, expenditures to install or upgrade equipment etc.

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An equation that expresses the total cost in terms of the number of hours required to complete the job is [tex]C = 32h + 31.50[/tex]

We will use "h" to represent the number of hours required to complete the job.

As cost per hour is K32, so, if it takes "h" hours to complete the job, then the cost will b:

=  K32 *  h.

We have one-time charge of K31.50, which is added to the total cost. So, the equation that expresses the total cost "C" in terms of the number of hours required to complete the job "h" is C = 32h + 31.50

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Answer:

To find the probability of the next drink being an espresso, we need to know the total number of drinks sold.

In this case, the total number of drinks sold is:

3 cappuccinos + 7 espresso drinks = 10 drinks

The probability of the next drink being an espresso can be calculated by dividing the number of espresso drinks sold by the total number of drinks sold:

Probability of next drink being an espresso = Number of espresso drinks sold / Total number of drinks sold

Probability of next drink being an espresso = 7/10

Probability of next drink being an espresso = 0.7 or 70%

Therefore, the probability of the next drink being an espresso is 0.7 or 70%.

The highest temperature on Day 7 is equal to 60 degrees.

The day in which the highest temperature was 60 degrees is day 3.

Yes, the high temperature is a function of the day because it is dependent variable.

No, the day is not a function of the high temperature because it is an independent variable.

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter, scientist, or a researcher.

This ultimately implies that, an independent variable is always considered as the cause in an experiment and it is represented by the x-axis value on a graph.

In this context, we can reasonably infer and logically deduce that time measured in days represent the independent variable while the highest temperature measured in degree Fahrenheit represent the dependent variable.

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The total surface area of the pyramid from the net is 286 square cm

To calculate the total surface area of a pyramid from its net, you need to add up the areas of all its faces.

The net of a pyramid is a two-dimensional representation of the pyramid, where the edges of the net represent the edges of the pyramid.

In this case, the nets are

Using the above as a guide, we have the following:

Area = 10 * 7 + 2 * (1/2 * 10 * 12.5 + 1/2 * 7 * 13)

Evaluate

Area = 286

Hence, the surface area is 286 square cm

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The values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.

The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.

We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):

μ[tex]= 7000/16,780 = 0.4168[/tex]

We can use μ as the value of λ in the Poisson distribution since they are equal.

To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:

P(x=3) = (e^(-λ) * λ^x) / x!

where x = 3.

Substituting the values we have:

[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]

Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:

[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]

[tex]P(x=3) ≈ 0.000305[/tex]

Therefore, the values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

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The values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.

The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.

We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):

μ[tex]= 7000/16,780 = 0.4168[/tex]

We can use μ as the value of λ in the Poisson distribution since they are equal.

To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:

P(x=3) = (e^(-λ) * λ^x) / x!

where x = 3.

Substituting the values we have:

[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]

Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:

[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]

[tex]P(x=3) ≈ 0.000305[/tex]

Therefore, the values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

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A) cos 35⁰ = y/5

=> y = cos 35⁰ × 5 ≈ 0.82 × 5 ≈ 4,1

B) cos 45⁰ = y/6

=> y = cos 45⁰ × 6 = (√2)/2 × 6 = 3√2

Answer: a) 4,1 b) 3√2

Ok done. Thank to me >:333

The steps of "hypothesis-testing" for papers bought home are stating the Null and Alternate Hypothesis, find level-of-significance, collecting data, determining p-value, and making decision.

The "Hypothesis-Testing" is defined as a statistical method used to make inferences about a population based on a sample of data. It involves making a assumption about a population parameter (such as its mean or proportion) and then collecting data to test whether the hypothesis is likely to be true or false.

The steps of hypothesis testing are:

Step 1: State the "Null-Hypothesis"

The null hypothesis (H₀) is = average number of papers brought home by the kids at Little Kids Elementary School is the same as the average for the general population, which is 13.

⇒ H₀: µ = 13,

Step 2: State the alternative hypothesis

The "Alternative-Hypothesis" (Hₐ) is = average number of papers brought home by the kids at Little Kids Elementary School is different from 13.

⇒ Hₐ: µ ≠ 13,

Step 3: Determine the level of significance

Let "significance-level" be "α = 0.05". This means we accept a 5% chance of making a "Type I Error"

Step 4: Collect the data and calculate test-statistic

The sample mean of the number of papers brought home by the kids at Little Kids Elementary School is:

⇒ x' = (14 + 12 + 18 + 8 + 11)/5 = 12.6,

The sample standard deviation is:

⇒ s = √[((14-12.6)² + (12-12.6)² + (18-12.6)² + (8-12.6)² + (11-12.6)²)/4] ≈ 3.71

The "test-statistic" ⇒ t = (x' - µ)/(s/√n);

where n = sample size = (5),

⇒ t = (12.6 - 13)/(3.57/√5) = -0.25,

Step 5: Determine of "p-value",

The "degrees-of-freedom" = 4,   ..because 5 - 1 = 4,

We know that "p-value" for t = -0.63 with 4 "degrees-of-freedom" is approximately 0.8103.

Step 6: Making decision and interpreting results

The p-value is 0.8103 which is greater than "significance-level" of (0.05),

So we fail to reject the null hypothesis. and say that there is not enough evidence to conclude that the average number of papers brought home by the kids at Little Kids Elementary School is different from the population mean of 13.

Therefore, we can say that the digital work program did not have a statistically significant effect on the amount of papers brought home by the students at Little Kids Elementary School.

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Using a proof by contraposition we can see that the sum must be even.

Here we know that x and y are odd integers, then we can write thes two numbers as:

x = 2n + 1

y = 2m + 1

Where n and m are integers.

If we use the proof by contraposition, then we will assume that the outcome is also an odd number 2k + 1

Then we can write:

2n + 1 + 2m + 1 = 2k + 1

We can simplify this to get:

2n + 2m + 1= 2k

2(n + m) + 1 = 2k

So there we have an odd number is equal to an even number, that does not make sense, thus, the outcome of the sum can't be odd.

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Answer:

  -1

Step-by-step explanation:

You want the average rate of change of the function shown in the graph between x=-1 and x=2.

The y-value at x = -1 is 9.

The y-value at x = 2 is 6.

The graph changes by 6-9 = -3 units as x changes by 2 -(-1) = +3 units.

The average rate of change is ...

  (change in y) / (change in x) = -3/3 = -1

The average rate of change from x = -1 to x = 3 is -1.

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Applying the tangent ratio, the value of x, to the nearest degree is determined as: 41.8 degree.

The formula we would use to find the value of x is the tangent ratio, which is expressed as:

tan ∅ = length of opposite side / length of adjacent side.

reference angle (∅) = x

Length of opposite side = 17

Length of adjacent side = 19

Plug in the values:

tan x = 17/19

x = tan^(-1)(17/19)

x ≈ 41.8 degree (to nearest tenth of a degree)

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The measurement of KL is given as follows:

KL = 5.86.

Similar triangles are triangles that share these two features listed as follows:

Considering the similar triangles in this problem, the proportional relationship for the side lengths is given as follows:

8.7/KL = 7.8/LJ = 12.18/8.2

Hence the length KL is obtained as follows:

8.7/KL = 12.18/8.2

12.18KL = 8.2 x 8.7

KL = 8.2 x 8.7/12.18

KL = 5.86.

More can be learned about similar triangles at brainly.com/question/14285697

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