Calculate the average rate of change of a function over a specified interval.


Which expression can be used to determine the average rate of change in f(x) over the interval 2, 9?


On a coordinate plane, a curve opens down and to the right. The curve starts at (0, 0) and goes through (1, 3), (4, 6), and (7, 8).

f(9 – 2)

f(9) – f(2)

StartFraction f (9 minus 2) Over 9 minus 2 EndFraction

StartFraction f (9) minus f (2) Over 9 minus 2 EndFraction

The vertical component of the initial velocity will basically decide where the vertices will be. that is how the initial velocity is related to the vertex of the parabola.

A parabola is a symmetrical curve that is formed by the intersection of a plane and a cone, where the plane is parallel to one of the cone's generating lines. The shape of a parabola is similar to that of a U-shaped curve, but with a sharper curve near the bottom of the U.

The parabola has several important properties, including a focus and a directrix. The focus is a point on the axis of symmetry of the parabola that is equidistant from every point on the curve. The directrix is a line that is perpendicular to the axis of symmetry and is equidistant from every point on the curve.

The equation of a parabola in standard form is y = ax² + bx + c, where "a" determines the direction and shape of the parabola, "b" determines the horizontal shift of the parabola, and "c" determines the vertical shift of the parabola.

The initial velocity will have two component basically, a horizontal component and a vertical component. The vertical component will decide how high the object will go, or in other words the vertical component of the velocity will decide the position of the vertex of the parabolis path which the object is going to follow.

When the vertical component of the velocity becomes 0, the object will be at it's maximum height (i.e the object will be at the vertex of the parabola)

The vertical component of the initial velocity will basically decide where the verties will be. that is how the initial velocity is related to the vertex of the parabola.

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Answer:

9636.66666665,or, 9637

Step-by-step explanation:

The company only has 172 pounds of dye, which is not enough to color 5 rolls of fabric. Therefore, the company cannot color 5 rolls of fabric with the amount of dye it currently has.

What is fabric?

Fabric is a material that is typically made by weaving, knitting, or felting fibers or yarns together. Fabrics can be made from a wide variety of fibers, including cotton, wool, silk, linen, polyester, and many others. The type of fiber used to make a fabric affects its characteristics, such as its softness, durability, and ability to absorb moisture.

To answer this question, we need to determine how much dye is needed to color one roll of fabric, and then see if the 4 buckets of dye will provide enough dye to color 5 rolls of fabric.

The question tells us that a 43 pound bucket of dye is used to color a roll of fabric that is 1,067 feet long. We can use this information to find the amount of dye needed per foot of fabric:

43 pounds of dye / 1 roll of fabric = 43 pounds of dye / 1,067 feet of fabric

= 0.0403 pounds of dye per foot of fabric

Now, we can use this rate to find how much dye is needed to color 5 rolls of fabric:

5 rolls of fabric x 1,067 feet of fabric per roll = 5,335 feet of fabric

5,335 feet of fabric x 0.0403 pounds of dye per foot of fabric = 215.03 pounds of dye

Therefore, the company would need 215.03 pounds of dye to color 5 rolls of fabric.

However, the company only has 4 buckets of dye, and we need to convert this to pounds of dye to see if it is enough:

4 buckets of dye x 43 pounds of dye per bucket = 172 pounds of dye

So, the company only has 172 pounds of dye, which is not enough to color 5 rolls of fabric. Therefore, the company cannot color 5 rolls of fabric with the amount of dye it currently has.

Fabrics are used for many different purposes, including clothing, bedding, curtains, upholstery, and many others. The properties of a fabric, such as its weight, texture, and color, can be manipulated through the weaving or knitting process, as well as through treatments such as dyeing, printing, and finishing.

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Complete question is: A textile factory uses a 43 pound bucket of dye to color a roll of fabric that is 1,067 feet long. If the company has 4 buckets of dye, the company cannot color 5 rolls of fabric.

Answer:

(3,8) and (5,12) in other words C.

Step-by-step explanation:

l4ynhrnhebegbyev3tv3tv3tv3g 3f eg ef ev3tv3tv

Answer:

yes

Step-by-step explanation:

half of 6 is 3 so

By using a² + b² = c² this formula we can find the missing side of a triangle.

A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.

If we know two other sides of the right triangle, all you need to do is apply the Pythagorean theorem:

a² + b² = c²

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root:

a = √(c² - b²)

If leg b is unknown, then:

b = √(c² - a²)

For hypotenuse c missing, the formula is:

c = √(a² + b²)

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The equilibrium constant can be determined using the concentrations of reactants and products at equilibrium. In this case, the initial concentrations of substances A, B, and C are given as [A] = 0.50 M, [B] = 0.75 M, and [C] = 1.2 M, while the equilibrium concentration of C is [C] = 1.0 M.

The equilibrium constant, denoted as K, is defined as the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients. In this case, the balanced chemical equation is not provided, so we cannot directly calculate the equilibrium constant.

To determine the equilibrium constant, we need the balanced chemical equation representing the reaction. Once the balanced equation is available, we can determine the stoichiometric coefficients and calculate the equilibrium constant using the concentrations at equilibrium. Without the specific reaction, we cannot provide a numerical value for the equilibrium constant.

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Answer:

GCF = 4

Find the prime factorization of 12

12 = 2 × 2 × 3

Find the prime factorization of 40

40 = 2 × 2 × 2 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2

GCF = 4

Answer:

Always true.

the meaning of a multiple is the product result of one number multiplied by another number, so if we are taling aout LCM ( Least common multiple) then it will always be a product of two numbers.

The function that represents the relationship between the number of bacteria in the Petri dish (P) and the number of hours (t) is: P(t) = 120 * 1.05^t

The function that represents the relationship between the number of bacteria in the Petri dish (P) and the number of hours (t) can be determined based on the given information. Since the bacteria are growing at a rate of 5% per hour, we can express this as an exponential growth function.

The general form of an exponential growth function is given by:

P(t) = P₀ * (1 + r)^t

Where:

P(t) is the number of bacteria at time t,

P₀ is the initial number of bacteria (120 in this case),

r is the growth rate per hour (5% or 0.05 as a decimal), and

t is the number of hours.

Substituting the given values into the equation, we have:

P(t) = 120 * (1 + 0.05)^t

Simplifying further, the function that represents the relationship between the number of bacteria in the Petri dish (P) and the number of hours (t) is:

P(t) = 120 * 1.05^t

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Answer:

Step-by-step explanation:

An absolute value function has the standard form

where h and k are the coordinates of the vertex (the pointy part of the graph) and the absolute value of a indicates whether or not the graph is the same width as the parent graph or if it is steeper or flatter. If the absolute value of a is greater than 1, the graph is steeper; if the absolute value of a is greater than 0 but less than 1 (in other words a fraction less than 1), the graph is flatter than the parent. If the graph is upside down, there will be a negative out in front of the absolute value of a. Because our graph is in fact upside down, we will choose one of the options that has a negative in front of it. The fact that it has moved UP from the origin, but not side to side, means that the k value is a +1.

If you are familiar with an absolute value parent graph, the lines go through each diagonal of the grid perfectly. It appears that our graph is steeper (or slimmer) than that. That means that not only is our graph upside down, it also has an a value greater than 1. Putting those 2 facts to use along with our k value of +1, makes our obvious choice the first one listed.

The given series, ∑(n=1 to ∞) √(n^5 + 41) + 1/n^6, converges conditionally.

To determine the convergence of the series, we will use the Direct Comparison Test. We need to find another series whose convergence behavior we already know, and which is greater than or equal to the given series for all terms beyond a certain point.

For the given series, ∑(n=1 to ∞) √(n^5 + 41) + 1/n^6, let's consider the series ∑(n=1 to ∞) 1/n^5. This series is a p-series with p = 5, and we know that p-series converge when p > 1.

Now, we will compare the given series with the series ∑(n=1 to ∞) 1/n^5. Taking the limit as n approaches infinity of the ratio of their terms, we get:

lim(n→∞) [(√(n^5 + 41) + 1/n^6) / (1/n^5)]

Simplifying the expression, we have:

lim(n→∞) (√(n^5 + 41) + 1/n^6) * (n^5)

Using the limit properties, we find that this limit is equal to infinity.

Since the series ∑(n=1 to ∞) 1/n^5 converges and the given series is greater than it for all terms beyond a certain point, we can conclude that the given series also converges. However, since the harmonic series ∑(n=1 to ∞) 1/n^6 diverges, the given series does not converge absolutely. Therefore, the given series converges conditionally.

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Answer:

708

Step-by-step explanation:

Answer

1.7/5

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Given:

The cost of the T.V. for Colin = £ 800.

The rate of depreciation per year = 4%

Time period = 3 years

To find:

How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate.

Solution:

To solve the above-given problem, we will use the following formula:

where

A = the final value after depreciation

P = the present value

R = rate of depreciation

n = time period

Now, on substituting the given values in the formula, we get

we will round the above answer to its nearest penny where appropriate

≈ £ 708

Thus, the worth of the t.v. in 3 years will be £ 708.

Answer:

Domain: -inf to +inf

Range: -inf to 4

Inc: - inf to 4

Dec: 4 to - inf

Answer:

Step-by-step explanation:

V = 1/3bh or V=bh/3

cross multiply

3V = bh

divide both sides by b

3V/b = h or h = 3V/b

Answer:

answer is 2

Step-by-step explanation:

20/10

divide both answers by ten

2/1

then one is meaningless so u remove it

The percentage of published studies that supported the tested hypothesis has changed from 70 to 85% over the past 25 years.

Hypothesis testing:

A hypothesis testing means investigates a proposed mathematical model to determine whether there is sufficient evidence from a sample of data to reject the defined null hypothesis.

Given,

The percentage of published studies that supported the tested hypothesis has changed from _____ to _____ over the past 25 years.

Here we need to find the change in the percentage for the past 25 years.

Based on the details, the percentage of published studies that supported the tested hypothesis has changed from 70 to 85% over the past 25 years.

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If an independent event has four uncertain outcomes, their probabilities are 20%, 45%, 15%, and C: 20%.

In probability, the sum of the probabilities of all possible outcomes must equal 100%. In this case, the probabilities of the four uncertain outcomes are given as 20%, 45%, 15%, and 20%. This means that each of these outcomes has a chance of occurring equal to the given percentage, and the total probability of all four outcomes is 20% + 45% + 15% + 20% = 100%.

It is important to note that when calculating probabilities, the percentages must add up to 100% to ensure that the total chance of all possible outcomes occurring is equal to 1 or 100%.

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Answer: 72 miles

Step-by-step explanation:

The total distance from Smithville to Clarksville will be:

= 3 3/4 + 5 1/4

= 9 inches

Since the scale on the map is:

1/2 inch = 4 miles

1 inch = 4 × 2 = 8 miles

Therefore, 9 inches will be:

= 9 × 8 = 72 miles

The actual distance that the Patel family will travel by the time they reach Clarksville will be 72 miles.

Answer:

he should save $70 each week

Step-by-step explanation:

1200 - 640 = 560

560/8 = 70

The percent of oil that remains in terms of m and n is (n - m) / n × 100

The percent that was used is m/n × 100

A percentage is a value or ratio that may be stated as a fraction of 100.

In this case, there are n gallons of oil in a tank and then m gallons of oil are used.

The gallons used is m/n × 100.

The percentage that remains will be:

= Amount remain / Original gallon × 100

= (n - m) / n × 100

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Step-by-step explanation:

9/25 of 100 did not like the book.

so, (25-9)/25 of 100 liked the book (because 25/25 is the whole 100 students).

the corresponding number of students we get

(25-9)/25 × 100 = 16/25 × 100 = 16 × 4 = 64

so, 64 students liked the book.

A true/false test with 9 questions can be answered in 512 different ways.

The number of ways a true/false question can be answered is 2 (either true or false). By the theorem of counting, the number of ways to answer a series of independent events (such as a series of true/false questions) is equal to the product of the number of ways each event can occur.

In this case, the number of ways to answer 9 independent true/false questions is 2 raised to the power of 9, or 2⁹ = 512. This means that there are 512 possible combinations of answers for a 9-question true/false test.

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The ninth term of the given geometric sequence 8, 32, 128, ..... is 524288.

We know that the n th term of a geometric progression with first term 'a' and common ratio 'r' is given by,

aₙ = arⁿ⁻¹

Given the geometric sequence is 8, 32, 128, .....

Now we can see that the first term is (a) = 8

and the common ratio (r) = 32/8 = 128/32 = 4

Here we have to find the 9th term of the geometric progression.

So, value of n = 9.

Thus, the 9th term of the geometric progression is

= 8*(4)⁹⁻¹ = 8*4⁸ = 524288

Hence the ninth term of the given geometric sequence is 524288.

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Answer:

C. a 270° rotation about point B'

Step-by-step explanation:

I just got it right.

An estimated regression equation that can be used to predict a residence's average monthly gas bill for last year given its age is \($\hat{y} = 115.14 - 3.167x$\). The average monthly gas bill for last year increases by $0.2456 on average.

Using age as the predictor variable and average monthly gas bill as the response variable, we can use linear regression to develop an estimated regression equation:

\($\hat{y} = b_0 + b_1 x$\)

where \(\hat{y}\) is the predicted average monthly gas bill, x is the age of the residence, b₀ is the intercept and b₁ is the slope.

Using the given data, we can find the values of b₀ and b₁:

\($\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i = 17.6$\)

\($\bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i = 55.906$\)

\($s_x = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}} = 8.564$\)

\($s_y = \sqrt{\frac{\sum_{i=1}^{n} (y_i - \bar{y})^2}{n-1}} = 24.193$\)

\($r = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i - \bar{x})^2} \sqrt{\sum_{i=1}^{n} (y_i - \bar{y})^2}} = -0.577$\)

\($b_1 = r \frac{s_y}{s_x} = -3.167$\)

\($b_0 = \bar{y} - b_1 \bar{x} = 115.14$\)

Therefore, the estimated regression equation is:

\($\hat{y} = 115.14 - 3.167x$\)

where \(\hat{y}$\) is the predicted average monthly gas bill and x is the age of the residence.

This equation suggests that as the age of the residence increases by one year, the average monthly gas bill for last year increases by $0.2456 on average.

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