Find the average rate of change of each of the following functions over the interval 1 < × < 5.h(x)=3(2)×

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Step-by-step explanation:

the slope is the y/x ratio of the x and y coordinate differences when going from one point to the other. it is in the line equation always the factor of x.

(-7, -6) to (3, -6)

x changes by 10 units (from -7 to 3).

y changes by 0 units.

so, the slope is 0/10 = 0

it is a horizontal line at y = -6

(8, 2) to (8, -3)

x changes by 0 units.

y changes by 5 units (from 2 to -3).

so, the slope is 5/0 which is infinite.

it is a vertical line at x = 8

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(5,-3) and (-4,7)

The midpoint is

We have the final answer as

Hope this helps you

Answer:

36.5 hours

Step-by-step explanation:

It is 36.5 because 7.3x5 would equal 36.5 which tells you that Salma worked 36.5 hours in the last five days.

Answer:

To graph the line with slope -1 passing through the point (-2,4), we can use the point-slope form of the equation of a line, which is:

where m is the slope of the line, and (x1, y1) is the given point on the line. Substituting the given values, we get:

Simplifying this equation, we get:

Now we can graph this line by plotting the given point (-2,4), and then using the slope of -1 to find one or more additional points on the line. We can do this by starting at the given point and then moving one unit down (since the slope is negative) and one unit to the right (since the slope is -1). This gives us the point (-1,3). We can then connect these two points to graph the line.

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Answer:

Step-by-step explanation:

a. x is negative: x < 0

b. y is nonnegative: y ≥ 0

c. q is less than or equal to π: q ≤ π

Answer:

a.

2. x < 0

b.

2. y ≥ 0

c.

5. q ≤ π

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

a. The statement "x is negative" means that x is less than 0. Mathematically, we can represent this as x < 0.

b. The statement "y is nonnegative" means that y is greater than or equal to 0. Mathematically, we can represent this as y ≥ 0.

c. The statement "q is less than or equal to π" means that the value of q is either equal to π or less than π. Mathematically, we can represent this as q ≤ π.

The series converges to -3/5.The given series is -2/6 + 4/36 - 8/216 + 16/1296 + ...

To determine if the series converges, we need to check if the sequence of its partial sums converges. Let Sn be the nth partial sum of the series. Then we have:

S1 = -1/3

S2 = -1/9

S3 = -1/27

S4 = -1/81 + 16/1296 = -65/1458

S5 = -1/243 + 16/1296 - 32/7776 = -385/59049

It appears that the sequence of partial sums is converging to a finite value as n increases. To find the limit, we can use the formula for the sum of an infinite geometric series:

S = a/(1-r)

where a is the first term and r is the common ratio. Here, a = -2/6 and r = -1/6. Plugging in these values, we get:

S = (-2/6)/(1-(-1/6)) = -3/5

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Answer:

the answer is 1,530

Step-by-step explanation:

I uses a calculator.

Explanation: There is 1 side that has what we want (rolling a 2) out of 6 sides total.

The rational function representing the graph is \(f(x) = \dfrac{x}{(x-5)(x+2)}\). The correct option is C.

Any function that can be expressed mathematically as a rational fraction an algebraic fraction in which both the numerator and the denominator are polynomials is referred to as a rational function.

One curve is at x = 5 and the second curve is at x = -2. The numerator value is x = 0.

The function can be written as,

\(f(x) = \dfrac{x}{(x-5)(x+2)}\)

The graph of the function is attached with the answer below.

Therefore, the correct option will be C, for the given graph in the image.

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Answer: 584 yds

Step-by-step explanation:

3mi-3mi=0

1622-1038=584yds

Answer:

28.26

hop thats better the the first anser

Answer: 4/30

Step-by-step explanation:

it does

If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x). Then the parent function is f(x) = √x .

The value of the absolute function is always positive.

The absolute function is given as

f(x) = a√x

The function g is related to one of the parent functions g(x) = 2 √x

Then the parent function f(x);

f(x) = √x

If the function f(x) is shifted right upward by 2 units, then the function f(x) will be equal to the function g(x).

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Answer:

\(\cos(W) = \frac{9}{41}\)

Step-by-step explanation:

Given

\(\angle Y = 90^o\)

\(YX = 40; XW = 41; WY = 9\)

Required

Determine \(\cos(W)\)

The question is illustrated with the attached image.

So:

\(\cos(W) = \frac{Adajacent}{Hypotenuse}\)

\(\cos(W) = \frac{WY}{XW}\)

This gives:

\(\cos(W) = \frac{9}{41}\)

Answer:

A.

Lateral area (LA) = 324 cm²

Surface area = 432 cm²

Step-by-step explanation:

✔️Lateral area of the triangular prism = perimeter of the base (P) × height of prism (L)

Perimeter (P) = 9 + 12 + 15

Perimeter (P) = 36 cm

height of prism (L) = 9 cm

Lateral area (LA) = 36 × 9 = 324 cm²

✔️Surface area = bh + LA

b = 9 cm

h = 12 cm

LA = 324 cm²

Surface area = 9*12 + 324

= 108 + 324

Surface area = 432 cm²

Answer:

vertex

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

See image

L side goes from    3 units   to   6 units    so scale factor is 2

Answer:

She swam for 3 hours 10 minutes

Answer:

Jaidens walk was 2 4/8 miles long and

Miyas walk was 4 3/8 miles long so

Miyas walk was 2 1/8 mile longer than Jaidens

Step-by-step explanation:

Answer:

-156

Step-by-step explanation:

Subtracting 6 from each side, we get

-x/6 = 26

Then multiplying by 6 from each side, we get

-x = 156

Then dividing by negative one from each side, we get

x = -156

Answer:

x=−156

Step-by-step explanation:

See picture...

Answer:

Graph 2

Step-by-step explanation:

See image attached. Hope this helps.

The second graph shown the polar curve at r = 7.

Given ,

Equation of polar curve = r = 2 + 5sin(θ)

We have to find ,

Which of following graph show polar curve ,

At  r = 2 + 5sin(θ)

The area between two curves in the polar coordinate system, first find the points of intersection, then subtract the corresponding areas.

First graph ;  r = 2 + 5sin(θ)

Where ,

\(\theta = 0\)

r = 2 + 5sin0

r = 2 + 5 (0)

r = 2

Second graph : r = 2 + 5sin(θ)

Where

\(\theta = \frac{\pi }{2}\)

Then,

r = 2 + sin\(\frac{\pi }{2}\)

r = 2 +5 ( 1 )

r = 2+5

r = 7

Third graph ;  r = 2 + 5sin(θ)

where

\(\theta = \pi\)

Then,

r = 2 + 5sin\(\pi\)

r = 2 + 5(0)

r = 2

Fourth graph ; r = 2 + 5sin(θ)

Where

r = 2 + 5sin\(\frac{3\pi }{2}\)

r = 2 + 5 (-1)

r = -3

Fifth graph ; r = 2 + 5sin(θ)

Where

\(\theta = 2\pi\)

r = 2 + 5sin(2π)

r = 2+ 5 (0)

r = 2

Comparing all the value of the graph ,the second graph shown the polar curve at r = 7.

Hence, The second graph shown the polar curve at r = 7.

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Robert can make a maximum of 8 milkshakes with the remaining chocolate syrup.

Converting the mixed number 2 2/5 to an improper fraction: 2 2/5 = 12/5

Subtracting the amount of chocolate syrup used per milkshake from the total amount of chocolate syrup:

12/5 - 1/4 = (48 - 5) / 20 = 43/20

Therefore, Robert has 43/20 cups of chocolate syrup left, which is the maximum amount he can use to make milkshakes.

For maximum number of milkshakes:

(43/20) / (1/4) = (43/20) x (4/1) = 172/20 = 8.6

Since Robert cannot make a fraction of a milkshake, he can make a maximum of 8 milkshakes with the remaining chocolate syrup.

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Answer:

The mean is 24 ( I think)

Step-by-step explanation:

SO in all, there were 96 magazines sold. So if there are just those 4 categories divide the 96 by 4. 96 divided by 4 = 24.

The mean of magazines he sold is 24

The value of 12x in the expression is 10

You multiply 5 = 6x  by 2 to get 12x

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

2x + 5 = 8x

You subtract 2X from each side to get

5 = 6x

Then multiply both sides by 2

This gives

10 = 12x

So, we have

12x = 10

Why do you multiply both sides by 2

You multiply by 2 because the question requests for the value of 12x

Since, we have solved for 6x, the next step is to multiply 6x by 2 to get 12x

i.e. 6x * 2 = 12x

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The way the flashback in these paragraphs advance the plot is C. It introduces Evan's motivation for working in the garden with Grandfather.

The technique of flashback in storytelling involves interrupting the chronological order of events to depict an earlier event or scene. It uses time travel to furnish the audience with necessary backstory, context, or a deeper understanding of the characters.

The technique of flashbacks is frequently employed as a means of divulging previous occurrences, recollections, or incidents that hold significance to the present narrative being conveyed.

Hence, it can be seen from the given text that the use of flashback helps show the motivation which Evans had for working in the garden with Grandfather

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Answer:

24

Step-by-step explanation:

i dont know if its correct

Step-by-step explanation: because they need to have atleast 2500 calories a day

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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For binomial probability mass function formula and compound interest formula, These both involve the use of exponents, they are not otherwise related to each other in any significant way.

What is Compound interest?

Compound interest is the interest that is earned not only on the initial principal amount of an investment, but also on any interest that has accumulated over time. In other words, it is interest that is "compounded" or added to the principal amount at specific intervals, such as daily, monthly, quarterly, or annually.

Now,

The binomial probability mass function formula and the compound interest formula are not directly related to each other, as they are used to model different types of phenomena.

The binomial probability mass function is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure) and the probability is same. The binomial probability mass function is

P(x) = pˣ (1-p)ⁿ⁻ˣ

where X is the number of successes, k is the specific number of successes we are interested in, n is the total number of trials, p is the probability of success on each trial, and represents the binomial coefficient.

The compound interest formula, on the other hand, is used to calculate the value of an investment over time, assuming a fixed interest rate and compounding periods. The future value is

FV = PV x (1 + r/n)ⁿˣ

where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), n = number of times interest is compounded per year, and x = number of years.

While both formulas involve the use of exponents, they are not otherwise related to each other in any significant way.

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The binomial probability mass function formula and the compound interest formula are not directly related to each other.

The binomial probability mass function formula is used to calculate the probability of observing a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant across all trials. The formula is:

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

where X is the random variable representing the number of successes, k is the number of successes we want to observe, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

On the other hand, the compound interest formula is used to calculate the value of an investment that earns a fixed interest rate over a certain period of time, assuming that the interest is compounded at regular intervals. The formula is:

A = P * (1 + r/n)^(nt)

where A is the final amount of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the number of years, and (1 + r/n)^(nt) represents the growth factor of the investment.

While both formulas involve exponents and use the terms (1 - p) and (1 + r/n), they are fundamentally different in their purpose and application.