Which expression represents the sum of (2x

Average rate of change help!!

frez [133]

Given that the function is $f(x)=x^{3}-6 x^{2}+4 x+7$

We need to determine the average rate of change over the interval $0 \leq x \leq 5$

Value of f(x) when x = 0:

Substituting x = 0 in the function $f(x)=x^{3}-6 x^{2}+4 x+7$ , we have;

$f(0)=(0)^{3}-6 (0)^{2}+4 (0)+7$

$f(0)=0-0+0+7$

$f(0)=7$

Thus, the value of f(0) is 7.

Value of f(x) when x = 5:

Substituting x = 5 in the function $f(x)=x^{3}-6 x^{2}+4 x+7$ , we have;

$f(5)=(5)^{3}-6 (5)^{2}+4 (5)+7$

$f(5)=125-150+20+7$

$f(5)=2$

Thus, the value of f(5) is 2.

Average rate of change:

The average rate of change can be determined using the formula,

$Rate \ of \ change=\frac{f(b)-f(a)}{b-a}$

where $a=0$ and $b=5$

Thus, we have;

$Rate \ of \ change=\frac{f(5)-f(0)}{5-0}$

$Rate \ of \ change=\frac{2-7}{5-0}$

$Rate \ of \ change=\frac{-5}{5}$

$Rate \ of \ change=-1$

Thus, the average rate of change over the interval $0 \leq x \leq 5$ is -1.

3 0

3 years ago

What is EQUATION of the line below?

julia-pushkina [17]

3, -1 !!!!!!!!!!!!!!

5 0

3 years ago

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 48,564 miles, with a standard

DerKrebs [107]

Answer:

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 48564, \sigma = 3293, n = 281, s = \frac{3293}{\sqrt{281}} = 196.44$

What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct?

This is the pvalue of Z when X = 48101. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{48101 - 48564}{196.44}$

$Z = -2.36$

$Z = -2.36$ has a pvalue of 0.0091

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

6 0

3 years ago

The sum of two consecutive odd intergers is 32. Find the intergers.

elena-14-01-66 [18.8K]

So let the smaller integer be 2x+1 and the larger one be 2x+3. So 2x+1+2x+3 is 32. Simplifying, we get 4x+4=32. So subtracting 2 from both sides we get 4x+2=30. So dividing by 2 we get 2x+1=15. So 2x+3 is 17. So the numbers are 15 and 17

4 0

3 years ago

Use a two-column proof to prove the Triangle Proportionality Theorem:

photoshop1234 [79]

Answer:

Step-by-step explanation:

From the picture attached,

Statements Reasons

1). In ΔABC, DE intersects AB and AC 1). Given

2). DE║BC 2). Given

3). ∠ADE ≅ ABC 3). Corresponding angles postulate

4). ∠AED ≅ ∠ACB 4). Corresponding angles postulate

5). ΔADE ~ ΔABC 5). AA similarity postulate

6). $\frac{AD}{AB}=\frac{AE}{AC}$ 6). Definition of two similar triangles

Hence proved.

4 0

3 years ago

Which expression represents the sum of (2x - 5y) and (x + y)?