Find the circumference leave the answer in terms of pi

Simplify the following expression<br> by combining like terms.<br> 3b + 8 – 3- b = 2b + [?]

babymother [125]

The missing term is 5

3 0

3 years ago

What product is positive ?

s344n2d4d5 [400]

<h3>Answer: Choice D</h3>

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Explanation:

The long way to do this is to multiply all the fractions out by hand, or use a calculator to make shorter work of this.

The shortest way is to simply count how many negative signs each expression has.

The rule is: if there are an even number of negative signs, then the product will be positive. Otherwise, the product is negative.

For choice A, we have 3 negative signs. The result (whatever number it is) is negative. Choice B is a similar story. Choice C is also negative because we have 1 negative sign. Choices A through C have an odd number of negative signs.

Only choice D has an even number of negative signs. The two negatives multiply to cancel to a positive. The negative is like undoing the positive. So two negatives just undo each other. This is why the multiplied version of choice D will be some positive number.

Or you can think of it as opposites. If you are looking up (positive direction) and say "do the opposite" then you must look down (negative direction). Then if you say "do the opposite", then you must look back up in the positive direction.

5 0

3 years ago

What is meant by the term 'domain'?

damaskus [11]

B the set of input values for the function.

4 0

3 years ago

The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio

kap26 [50]

Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

the translation

∵ The general form of the quadratic function is

f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

(h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right

by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left

by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up

by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down

by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)² ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

5 0

3 years ago

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Some college graduates employed full-time work more than hours per week, and some work fewer than hours per week. We suspect tha

Alex_Xolod [135]

Answer:

a)Null hypothesis: $\mu =40$

Alternative hypothesis: $\mu \neq 40$

b) A Type of error I is reject the hypothesis that $\mu$ is equal to 40 when is fact $\mu is equal to 40c) We can commit a Type II Error, since by definition "A type II error is the non-rejection of a false null hypothesis and is known as "false negative" conclusion"Step-by-step explanation:Assuming this problem: "Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, [tex]\mu$ , is different from 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 43 hours and that the standard deviation is 4 hours. Based on this information, answer the questions below"

Data given

$\bar X=43$ represent the sample mean

$\mu$ population mean (variable of interest)

s=4 represent the sample standard deviation

n represent the sample size

Part a: System of hypothesis

We need to conduct a hypothesis in order to determine if actual mean is different from 40 , the system of hypothesis would be:

Null hypothesis: $\mu =40$

Alternative hypothesis: $\mu \neq 40$

Part b

In th context of this tes, what is a Type I error?

A Type of error I is reject the hypothesis that $\mu$ is equal to 40 when is fact [tex]\mu is equal to 40

Part c

Suppose that we decide not to reject the null hypothesis. What sort of error might we be making.

We can commit a Type II Error, since by definition "A type II error is the non-rejection of a false null hypothesis and is known as "false negative" conclusion"

5 0

3 years ago

Read 2 more answers