Find the average rate of change of the function on the interval, specified for real number b ???

The value of r'(1) = 60 for the given function, using the chain rule.

By adding the derivatives of f(x) with regard to g(x) and g(x) with respect to the variable x, one may get the derivative of the composite function h(x) = f(g(x)). The chain rule of differentiation can be used to derive derivatives of composite functions. Now, let's go over what composite functions are. When a function is expressed in terms of another function, it is said to have a composite function. This suggests that a function can be changed into another function in a composite function.

Using the chain rule of derivatives we have:

r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)

Substituting the values we have:

r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1)

r'(1) = f'(g(3)) * g'(3) * 3

r'(1) = f'(4) * 4 * 3

r'(1) = 5 * 4 * 3

r'(1) = 60

Hence, the value of r'(1) = 60 for the given function, using the chain rule.

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The cuboidal prism has a volume of 40.625 cubic centimeters

Multiplying the cuboidal prism's length, width, and height yields its volume. Assuming that the width b and height h are both 2.5 cm and the length l is 6.5 cm. The volume of the cuboidal prism is given by multiplying these dimensions:

V = l b h = 6.5cm x 2.5cm x 2.5cm

 = [tex]40.625cm^3.[/tex]

As a result, the cuboidal prism has a volume of 40.625 cubic centimeters. As a result, the prism can be utilized for a variety of purposes, including packaging, storage, and transportation, and it can accommodate 40.625 cubic centimeters of material inside its boundaries.

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Answer:

1. 7/16 = 43.75%

2. 4/5 = 80%

3. 55% = 55/100 = 11/20

4. 248% = 2 48/100 = 2 12/25

5. 0.00031 = 0.031%

6. 6.005 = 600.5%

7. 12% = 12/100 = 3/25 (Gigi spent 3/25 of her birthday money on the new sunglasses)

8. The total bill for pizza and soft drinks was $27.50. With a 20% tip, the amount of tip left would be:

Tip = 20% of total bill

Tip = 20/100 * $27.50

Tip = $5.50

Therefore, Veronica and her friends left a $5.50 tip for their server.

Step-by-step explanation:

Answer:

1. 43.75%

2. 60%

3. 11/20

4. 2 and 12/25

5. 0.031%

6. 600.5%

7. 3/25

8. $5.50

Step-by-step explanation:

1. 7 ÷ 16 = 0.4375

0.4375 x 100 = 43.75%

2. 3 ÷ 5 = 0.6

0.6 x 100 = 60%

3. 55/100

11x25 / 20x5 = 11/20

4.248/100

62x4 / 25x4

62/25

62/25 = 2R12

2 12/25

5. 0.00031 x 100 = 0.031%

6. 6.005 x 100 = 600.5%

7. 12% = 12/100.

12/100 simplified = 3/25

8. $27.50 x 20% = $5.50

Using the equation, A = 6,000(1+0.029t) The number of years that is the investment period is: D 8 years.

Investment period refers to the length of time during which an individual or organization invests money in a particular investment vehicle or asset. It can also be referred to as the holding period, and it is the duration for which an investment is held or maintained before it is sold or liquidated.

We can start by setting the equation for the final account balance, A, to $7,392:

7,392 = 6,000(1 + 0.029t)

Divide both sides by 6,000:

1.232 = 1 + 0.029t

Subtract 1 from both sides:

0.232 = 0.029t

Divide both sides by 0.029:

t ≈ 8

Therefore, the investment period is approximately 8 years.

So the answer is option D) 8 years.

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we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12).

HOW TO SOLVE THE QUESTION?

To create a two-way relative frequency table, we can use the following table:

       | English | Mathematics | Total

--------|---------|-------------|-------

Male    |   x     |     24      |   30

Female  |   y     |     11      |   20

--------|---------|-------------|-------

Total   |   35    |     35      |   50

Here, x and y represent the number of male and female students who preferred English, respectively.

To calculate the values for x and y, we can use the fact that there were 35 students who preferred mathematics, and 24 of them were male. Therefore, the number of females who preferred mathematics is 35 - 24 = 11. Since there are a total of 20 female students, the number of females who preferred English is 20 - 11 = 9. Similarly, the number of male students who preferred English is 30 - 24 = 6.

To calculate the relative frequencies, we can divide each cell by the total number of students (50). For example, the relative frequency of male students who preferred mathematics is 24/50 = 0.48.

The resulting two-way relative frequency table is as follows:

       | English | Mathematics | Total

--------|---------|-------------|-------

Male    |   0.12  |     0.48    |  0.60

Female  |   0.18  |     0.22    |  0.40

--------|---------|-------------|-------

Total   |   0.30  |     0.70    |  1.00

From this table, we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12). However, it would not be safe to assume that all females prefer English and all males prefer mathematics based on this data alone, as there may be individual variations and exceptions to this trend.

It's also important to note that the sample size is relatively small, with only 50 students surveyed, and may not be representative of the larger population. Further research with a larger and more diverse sample size would be needed to make more accurate conclusions about gender-based preferences in this population

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Answer:

s = 8 mi

Step-by-step explanation:

We know that the ratio of side lengths of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

     x       :    x√3     :        2x

We can apply this information to the given triangle. We know that the length of the short leg is 4 mi. This can be substituted for x:

x = 4 mi

We are trying to solve for s, which is the triangle's hypotenuse. So, we can apply the ratio to x.

s = 2x = 2(4 mi) = 8 mi

Answer: To find the average of x, y, and z in terms of m, we first need to find expressions for x, y, and z in terms of m:

x = (m + 9)/2

y = (2m + 15)/2

z = (3m + 18)/3 = (m + 6)

To find the average of x, y, and z, we add them up and divide by the number of terms:

average = (x + y + z)/3

Substituting the expressions for x, y, and z, we get:

average = [(m + 9)/2 + (2m + 15)/2 + (m + 6)]/3

Simplifying the expression by combining like terms, we get:

average = (4m + 30)/6

Simplifying further by dividing both the numerator and denominator by 2, we get:

average = (2m + 15)/3

Therefore, the average of x, y, and z in terms of m is (2m + 15)/3.

Step-by-step explanation:

Answer:

Without knowing the number of pieces that the pizzas were cut into, it is not possible to determine the fraction of a whole pizza that is left.

Step-by-step explanation:

simple interest

1 year: [tex]3.6\% \cdot 150,000 = \dfrac{3.6}{100} \cdot 150,000 = 5,400[/tex]

5 years: [tex]5,400(5) = 27,000[/tex]

the maturation value:

[tex]150,000 + 27,000 = \$ 177,000[/tex]

Answer:

The probability that exactly 5 of the 7 selected smartphone users use their phones in meetings or classes is approximately 0.0127 or 1.27%.

The final amount after 5 years is $ 49521.98.  

Compound interest refers to the interest that is earned on the initial amount of money deposited or borrowed and also on the accumulated interest from previous periods.  

The formula for calculating compound interest is:

Where

Where:

A = Final amount

P = Principal amount

r = Annual interest rate

n = Number of times the interest is compounded per year

t = Time period

Here we have

The deposited amount, P= $200.00  

Rate of interest, r = 9% = 9/100 = 0.09%

Number of compounds per year, n = 1

Time period, t = 5 years

Using the formula,

A = 2000(1 + 0.09/1)⁽¹⁽⁵⁾⁾

A = 2000(1.09)⁵

A = 49521.98  

Therefore,

The final amount after 5 years is $ 49521.98.  

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Answer: To evaluate 13 - 0.75w + 8x when w = 12 and x = 1/2, we substitute these values into the expression:

13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2)

Simplifying the expression inside the parentheses first:

13 - 9 + 4 = 8

Substituting this value into the expression:

13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2) = 13 - 9 + 4 = 8 + 4 = 12

Therefore, the value of 13 - 0.75w + 8x when w = 12 and x = 1/2 is 12.

Answer:

8

Step-by-step explanation:

Given expression is
[tex]13-0.75w\:+\:8x[/tex]

and we are asked to evaluate this expression when
[tex]w = 12 ,\: x = \dfrac{1}{2}[/tex]

[tex]0.75w = 0.75 \times 12 = 9[/tex]

[tex]8x = \8 \times \dfrac{1}{2} = 4[/tex]

[tex]\text{So the expression at $w = 12 \; , x= \dfrac{1}{2}$ evaluates to}[/tex]

13 - 9 + 4 = 8

Answer: 8

Answer: 275,400

Step-by-step explanation:

- First we do 18 multiplied by 20 which would get us the answer of 360

- Next we do 45 multiplied by 17 which would get us the answer of 765

- Now we multiply both 360 and 765 and get the answer of 275,400

The percent increase in the amount of interest paid between a household with a 780 credit score and one with a 589 credit score is approximately 0.8%, which is closest to option B, 0.8% or 39.9%.

Finding the entire amount paid by each family and comparing the difference in total amount paid will allow us to determine the percentage rise in the amount of interest paid between a household with a credit score of 780 and one with a score of 589.

The overall cost for a FICO score of 780 is:

$12,650 for the principal balance and all installments plus (33 x $60) to get $14,930.

With a 589 FICO score, the total cost is:

Total payments plus principal balance equal $12,650 plus (40 x $60) = $15,050.

The two households' combined total outlays differ in the following ways:

$15,050 - $14,930 = $120

We multiply by 100 and divide the difference by the initial sum to determine the percent increase:

($120 / $14,930) x 100% = 0.802% ≈ 0.8%

In light of this, the difference in interest rates between a family with a 780 credit score and one with a 589 credit score is roughly 0.8%, which is closest to option B, 0.8% or 39.9%.

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The angle x opposite to the side measuring 17 is approximately 20.68 degrees using trigonometry.

Let x stand for the side that is the shortest. The Pythagorean theorem yields the following result: x2 + 172 = 19.

When we simplify this equation, we obtain:

[tex]x^2 = 19^2 - 17^2[/tex]

[tex]x^2 = 36x = 6[/tex]

Hence, the shortest side is six inches long.

Using the inverse trigonometric function tangent, we can determine the angle opposite the side measuring 17. (tan).

tan = adjacent/opposite = x/17

By changing the value of x, we obtain:

[tex]tanθ = 6/17[/tex]

We may determine the angle whose tangent is 6/17 using a calculator or a trigonometric table.

[tex]θ = 20.68°[/tex]

As a result, the angle that is opposite the side that measures 17 is roughly 20.68 degrees.

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Answer: 2x-6

Step-by-step explanation:

If Astrid says the function being graphed is y=-4+1/3. Matt is correct, while Astrid is incorrect.

Astrid's equation y = -4 + 1/3 is incorrect because it is missing the variable x. The equation is missing a term that represents the x variable, so the equation does not represent a line.

On the other hand, Matt's equation y = 1/3x is correct, and the slope of the line represented by this equation is indeed 1/3. This can be seen from the fact that the equation is in the form y = mx, where m is the slope of the line. In this case, m = 1/3, so Matt is correct.

Therefore, Matt is correct, while Astrid is incorrect.

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Answer:

The equation x = 5 represents a vertical line passing through the point (5, 0) on the x-axis. A vertical line has an undefined slope because the rise (change in y) is undefined when the run (change in x) is zero. Therefore, the slope of the line x = 5 is undefined.

Answer:

y = x + 6

Step-by-step explanation:

We can put the equation of the line in slope intercept form [tex]y=mx+b[/tex] where m is the slope and b is the y intercept.

The line passes through (0,6) which means that is our y intercept. Now we have to count the slope. To do this, we can either evaluate the slope given 2 points or count it if given a graph. We have a graph, so the convenient thing to do is to count it. If we count, we see that our slope is [tex]\frac{1}{1}[/tex] or simply 1. All we have to do now is write it in slope intercept form.

[tex]y=x+6[/tex]

Answer:

They will need 6 vans to hold all 44 people.

Step-by-step explanation:

1 bus holds : 8

2 bus holds : 16

3 bus holds : 24

4 bus holds : 32

5 bus holds : 40

6 bus holds : 48 (4 extra seats)

Answer:

To find the total balance after three years, we can use the formula for continuous compounding:

A = Pe^(rt)

Where A is the total balance, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.

In this case, P = $12,000, r = 0.0125 (1.25% expressed as a decimal), and t = 3. Plugging these values into the formula, we get:

A = $12,000 x e^(0.0125 x 3)

A = $12,000 x e^(0.0375)

A = $12,000 x 1.038163

A = $12,458.54

Therefore, the total balance after three years is $12,458.54.

Based on the information in the graph, we can infer that the tax that Melvin and Sylvia must pay if they pay federal income taxes when filling it out together would be 11,631.

To identify the value of the federal income taxes we must take into account how much money the income of the two of them is. In this case, on the left side, they indicate that they are $77,000.

So, once we know the income we must look at the right side of the graph. In this case we must look for the value that matches the row that says "Married filling jointly" and the value of income (77,000). According to the above, these values coincide in the box that says 11,631.

From the above, we can infer that the tax they must pay would be 11,631

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The product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.

The given expression is:

-2³ + x - 5 x (x³ -3x +4)

We need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, let's simplify -2³, which means -2 x 2 x 2 = -8, so we have:

-8 + x - 5 x (x³ -3x +4)

Next, we need to distribute the -5 to the terms inside the parentheses:

-8 + x - 5x³ + 15x - 20

Now we can combine like terms:

-5x³ + 16x - 28

Therefore, the product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.

Now, to answer the second part of the question, we need to check if:

-2³ + x - 5 x (x³ -3x +4) = (x³ -3x +4) * (-2³ + x - 5)

We can simplify both expressions first:

-8 + x - 5x³ + 15x - 20 = -8 + x - 5x³ + 15x - 20

We can see that both expressions are identical, which means that the product of -2³ + x - 5 and x³ -3x +4 is equal to the product of x³ -3x +4 and -2³ + x - 5, regardless of the order in which we multiply the factors.

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Answer:

4 Outcomes.

Step-by-step explanation:

Both land tails.

Both land heads.

First coin lands Tails while the Second lands Heads.

First lands Heads while the Second lands Tails.

Answer:

∂z/∂x = 3x^2 + 6y

∂z/∂y = 6x - 3y^2

Now, we need to solve the system of equations:

3x^2 + 6y = 0

6x - 3y^2 = 0

From the first equation, we get:

y = -x^2/2

Substituting this into the second equation, we get:

6x - 3(-x^2/2)^2 = 0

Simplifying, we get:

6x - 3x^4/4 = 0

Multiplying by 4 and rearranging, we get:

3x^4 - 24x = 0

Factoring out 3x, we get:

3x(x^3 - 8) = 0

Therefore, the critical values of x are x = 0 and x = 2.

For x = 0, we have y = 0 (from y = -x^2/2). So, one critical point is (0, 0).

For x = 2, we have y = -2. So, the other critical point is (2, -2).

To find the critical values of the function, we need to evaluate the function at each critical point:

z(0, 0) = 0^3 + 6(0)(0) - 0^3 - 1 = -1

z(2, -2) = 2^3 + 6(2)(-2) - (-2)^3 - 1 = -13

Therefore, the critical values of the function are -1 and -13.

Hence, in response to the provided question, we can say that We discard the t = 0.003 solution since time cannot be negative. As a result, the discus takes around 2.375 seconds to strike the ground.

Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.

The specified function appears to have a typo. I believe it should be:

[tex]h = -16t^2 + 38t + 5[/tex]

a) The discus's initial height can be calculated by entering t = 0 into the function:

[tex]h = -16(0)^2 + 38(0) + 5 = 5[/tex]

As a result, the discus's starting height is 5 feet.

[tex]-16t^2 + 38t + 5 = 0[/tex]

[tex]t = (-b \sqrt(b2 - 4ac)) /[/tex]

t = 0.003 or 2.375

We discard the t = 0.003 solution since time cannot be negative. As a result, the discus takes around 2.375 seconds to strike the ground.

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Answer:

C) 260 square inches.

Step-by-step explanation:

To find the surface area of a pyramid, we can use the formula.

Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area

where l is the length of one side of the square base, s is the slant height, and Base Area is the area of the square base.

In this case, the base of the pyramid is a square with side length l = 10 inches, so its area is

Base Area = l^2 = 10^2 = 100 square inches

To find the perimeter of the base, we can simply multiply the length of one side by 4

Perimeter of Base = 4l = 4 x 10 = 40 inches

We are also given that the slant height of the pyramid is s = 8 inches.

Now we can substitute the values into the formula.

Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area

Surface Area = (1/2) x 40 x 8 + 100

Surface Area = 160 + 100

Surface Area = 260 square inches

Therefore, the surface area of the pyramid is 260 square inches.

Answer:360 in

Step-by-step explanation:

The 24 parking spοt length is 68 yards.

The same feature is expressed in a different unit οf measurement thrοugh a unit cοnversiοn. Time can be stated in minutes rather than hοurs, and distance can be expressed in kilοmetres rather than miles, οr in feet rather than any οther unit οf length.

Here the given width of One parking spot is eight and one-half feet.

Now  we know that 1 feet = [tex]\frac{1}{3}[/tex] yard,

Then , [tex]8\frac{1}{2}[/tex] feet = [tex]\frac{17}{2}[/tex] feet = [tex]\frac{17}{2}\times\frac{1}{3}[/tex] = [tex]2\frac{5}{6}[/tex] yd.

Now Parking lot have 24 parking spot, Then,

=> Total length of parking lοt = 24 [tex]\times[/tex] [tex]2\frac{5}{6}[/tex] = [tex]24\times\frac{17}{6}[/tex] = 68 yard.

Hence The length of parking lοt is 68 yard.

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As a result, the likelihood that the mean length of a random sample of 17 items is less than 10.9 inches is about 0.9265, or 92.65%.

Probability is a measure of how likely an event is to occur. It is a number between 0 and 1, with 0 suggesting that an occurrence is impossible and 1 indicating that an event is unavoidable. A given event's probability is computed by dividing the number of positive outcomes by the total number of potential possibilities.

In this case, we may utilize the central limit theorem to estimate the sample mean distribution. The central limit theorem states that if the sample size is high enough (n 30), the distribution of the sample mean will be normal.

Regardless of demographic distribution, the population is essentially typical.

In this scenario, the population has a normal distribution with a mean () of 9.8 inches and a standard deviation () of 2 inches. We wish to calculate the likelihood that the sample mean (x) of 17 objects is smaller than 10.9 inches.

The formula for calculating a sample mean's z-score is: z = (x - ) / ( / sqrt(n)), where n is the sample size.

We obtain: z = (10.9 - 9.8) / (2 / sqrt(17)) by substituting the numbers supplied in the problem.

z = 1.45

We may calculate the chance that a standard normal variable is smaller than 1.45 using a typical normal distribution table or calculator:

P(Z < 1.45) = 0.9265

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