A pyramid has a base off 100 m^2 and a height of 60 m. What is the volume of the pyramid?

What is the range of the function f(x)=(x+4)²+5

hammer [34]

Answer:

$Range=\left \{y|y\geq 5\right \}$

Step-by-step explanation:

Since given the expression, this represents graphically a parabola with arms pointing up, and a vertical translation of its vertex 5 units up, then the range of the function must be all the y values such that they are greater or equal to 5. This is written as:

$Range=\left \{y|y\geq 5\right \}$

8 0

4 years ago

g A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estim

kipiarov [429]

Answer:

a) n= 1045 computers

b) n= 442 computers

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

Step-by-step explanation:

Hello!

The variable of interest is

X: Number of computers that use the new operating system.

You need to find the best sample size to take so that the proportion of computers that use the new operating system can be estimated with a 99% CI and a margin of error no greater than 4%.

The confidence interval for the population proportion is:

p' ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

$Z_{1-\alpha /2}= Z_{0.995}= 2.586$

a) In this item there is no known value for the sample proportion (p') when something like this happens, you have to assume the "worst-case scenario" that is, that the proportion of success and failure of the trial are the same, i.e. p'=q'=0.5

The margin of error of the interval is:

d= $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

$\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p)}{n} }$

$(\frac{d}{Z_{1-\alpha /2}})^2 = \frac{p'(1-p')}{n}$

$n * (\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')$

$n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2$

$n=[0.5(1-0.5)]*(\frac{2.586}{0.04} )^2= 1044.9056$

n= 1045 computers

b) This time there is a known value for the sample proportion: p'= 0.88, using the same confidence level and required margin of error:

$n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2$

$n= [0.88*0.12]*(\frac{{2.586}}{0.04})^2= 441.3681$

n= 442 computers

c) The additional information in part b affected the required sample size, it was drastically decreased in comparison with the sample size calculated in a).

I hope it helps!

4 0

4 years ago

If 1 m is approximately 3.28 feet how many meters are in 20 feet

icang [17]

Answer:

20 feet = 6.096 meters

Step-by-step explanation:

Formula for an approximate result, divide the length value by 3.281

8 0

3 years ago

Given f(x)= -4x-10 and f(x)=10. find x

yulyashka [42]

Answer:

x = - 5

Step-by-step explanation:

Given

f(x) = - 4x - 10 and f(x) = 10, the equate right sides, that is

- 4x - 10 = 10 ( add 10 to both sides )

- 4x = 20 ( divide both sides by - 4 )

x = - 5

4 0

3 years ago

Which of the following pairs of numbers contain like fractions?

saveliy_v [14]

Like fractions are fractions that have the same denominator. In option D, both denominators are 7. Therefore, they are like fractions.

7 0

4 years ago

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