Which of the following represents the factored form of f(x) = x^3 − 64x?f(x) = x(x + 8)(x − 8)
f(x) = (x − 8)(x + 8)
f(x) = x(x − 8)^2
f(x) = x(x^2 − 8)

Answers

Answer 1

Answer: the first answer is the right factors

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A person came to work at 8:30 AM, went out at 11:45 AM, had lunch, came in at 12:30 PM, and left work at 5:15 PM. The total number of hours worked by this person was
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Richard has 5 markers in a backpack. One of them is black and one is red. Find the probability Richard will reach into the backpack without looking and grab the black marker and then reach in a second time and grab the red marker. Express your answer as a fraction in simplest form.
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Find the next term of the given sequence. 1.31, 2.54, 3.77, ... 4.90 5.00 5.10

Answers

Answer:

Option B is correct.

the next term of the sequence is 5.00

Explanation:

Arithmetic progression(A.P) is a sequence of numbers in which the consecutive terms are formed by adding a constant quantity with the preceding term.

Common difference(d) is the constant quantity stated in the above definition of arithmetic progression. it is given by;

$d=a_(n+1) - a_n$ for all n∈N

Given sequence:- 1.31, 2.54 , 3.77 , ___ ;

we have;

$a_1 = 1.31$ , $a_2= 2.54$ and $a_3 = 3.77$

First find the common difference;

$d =a_2 - a_1$ = $2.54-1.31 = 1.23$

d = $=a_3-a_2 = 3.77-2.54 =1.23$

Therefore, by the definition of arithmetic progression,

the given sequence is Arithmetic progression

Now, to find the fourth term of the sequence, add constant quantity (d) to the third term;

$a_4 = 3.77+1.23 = 5.00$

Therefore, in the given sequence next term will be 5.00.

It is A.P. with common difference = 2.54-1.31 = 1.23

So, next term would be 3.77+1.23 = 5.00

OPTION B IS YOUR ANSWER

the environmental protection agency has determined that safe drinking water should contain no more than 1.3 milligrams per liter (mg/l) of copper, on average. to test water from a new source, you collect water in small bottles at each of 30 randomly selected locations. the mean copper content of your bottles is 1.36 mg/l and the standard deviation is 0.18 mg/l. you perform a test of

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The EPA has set the safe drinking water limit for copper at 1.3 milligrams per liter (mg/L). In your sample, the mean copper content is 1.36 mg/L with a standard deviation of 0.18 mg/L from 30 randomly selected locations.

To determine if the new water source meets the EPA's standard, you should perform a hypothesis test using the provided sample data. The null hypothesis (H0) would be that the mean copper content is less than or equal to 1.3 mg/L, while the alternative hypothesis (H1) is that the mean copper content is greater than 1.3 mg/L.

With the given sample size, mean, and standard deviation, you can calculate the test statistic and compare it to a critical value to determine whether to accept or reject the null hypothesis. If the test statistic is greater than the critical value, you would reject the null hypothesis and conclude that the mean copper content of the new water source exceeds the EPA's safe limit.

It's important to remember that statistical tests can only provide evidence for or against a hypothesis, but cannot definitively prove that the new water source is safe or unsafe. Additional testing and monitoring would be necessary to make a well-informed decision about the safety of the water source.

To learn more about null hypothesis : brainly.com/question/28920252

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If the edges of a cube add up to 4 feet in length, what is the volume of the cube?

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4ft=48 inches and there are 12 edges on a cube, so each edge is 4 inches. And the volume is 64 cubic inches.

Let f(x)=4x-1 and g(x)=2x^2+3. Perform each function operations and then find the domain.1. (f+g)(x) 2. (f-g)(x) 3. (g-f)(x) 4. (f times g)(x) 5. f/g(x) 6. g/f(x)

Answers

The domain of a function is the set of input values, the function can take.

The values of the composite functions are:

$\mathbf{(f + g)(x) = 2x^2 + 4x +2}$

$\mathbf{(f - g)(x) = -2x^2 + 4x - 4}$

$\mathbf{(g - f)(x) = 2x^2 - 4x + 4}$

$\mathbf{(f * g)(x) = 8x^3 - 2x^2 -12x + 4}$

$\mathbf{(f / g)(x) = ((4x - 1 ))/((2x^2 - 3))}$

$\mathbf{(g / f)(x) = (2x^2 - 3)/(4x - 1 )}$

The functions are given as:

$\mathbf{f(x) = 4x - 1}$

$\mathbf{g(x) = 2x^2 + 3}$

$\mathbf{(1)\ (f + g)(x)}$

This is calculated as:

$\mathbf{(f + g)(x) = f(x)+ g(x)}$

So, we have:

$\mathbf{(f + g)(x) = 4x - 1 + 2x^2 + 3}$

Collect like terms

$\mathbf{(f + g)(x) = 2x^2 + 4x - 1 + 3}$

$\mathbf{(f + g)(x) = 2x^2 + 4x +2}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(2)\ (f - g)(x)}$

This is calculated as:

$\mathbf{(f - g)(x) = f(x) - g(x)}$

So, we have:

$\mathbf{(f - g)(x) = 4x - 1 - 2x^2 - 3}$

Collect like terms

$\mathbf{(f - g)(x) = -2x^2 + 4x - 1 - 3}$

$\mathbf{(f - g)(x) = -2x^2 + 4x - 4}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(3)\ (g - f)(x)}$

This is calculated as:

$\mathbf{(g - f)(x) = -(f - g)(x) }$

So, we have:

$\mathbf{(g - f)(x) = 2x^2 - 4x + 4}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(4)\ (f * g)(x)}$

This is calculated as:

$\mathbf{(f * g)(x) = f(x) * g(x)}$

So, we have:

$\mathbf{(f * g)(x) = (4x - 1 )* (2x^2 - 3)}$

$\mathbf{(f * g)(x) = 8x^3 - 2x^2 -12x + 4}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(5)\ (f /g)(x)}$

This is calculated as:

$\mathbf{(f /g)(x) = (f(x) )/(g(x))}$

So, we have:

$\mathbf{(f / g)(x) = ((4x - 1 ))/((2x^2 - 3))}$

There are restrictions to the value of x.

So, the domain is: $\mathbf{(-\infty,-\sqrt{(3)/(2)} ) \ u\ ( -\sqrt{(3)/(2)},\sqrt{(3)/(2)}})\ u\ (\sqrt{(3)/(2)},\ \infty)}$

$\mathbf{(6)\ (g /f)(x)}$

This is calculated as:

$\mathbf{(g /f)(x) =1 / (f(x) )/(g(x))}$

So, we have:

$\mathbf{(g / f)(x) = (2x^2 - 3)/(4x - 1 )}$

There are restrictions to the value of x.

So, the domain is: $\mathbf{(-\infty, (1)/(4))\ u\ ((1)/(4),\infty)}$

Answers

It would be:
5n - 2

Hope that helps :D

sophies math class has 6 fewer boys than girls , and there are g girls. write an expression for the number of boys

Answers

It is a known fact that there are 6 fewer boys than girls in Sophies class. We need to write an expression based on thi fact. It is also given in the question that there are "g" girls present in the class of Sophie. so there are several factors that we already know from the question given.Now
Number of girls in sophies class = g
Let the number of boys in Sophies class - b
Then the expression for the number of boys will be
b = g - 6
This is the final and only expression that can determine the number of boys in Sophies class.

The answer is g - 6

I hope this helps!

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Which of the following represents the factored form of f(x) = x^3 − 64x?f(x) = x(x + 8)(x − 8) f(x) = (x − 8)(x + 8) f(x) = x(x − 8)^2 f(x) = x(x^2 − 8)

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Which of the following represents the factored form of f(x) = x^3 − 64x?f(x) = x(x + 8)(x − 8)
f(x) = (x − 8)(x + 8)
f(x) = x(x − 8)^2
f(x) = x(x^2 − 8)