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3 years ago

What is the volume of a cylinder with a radius of 3 feet and a height of 4 feet? Use 3.14 for pi. Enter your answer in the box.

2 answers:

8 0

The volume of a cylinder refers to the number of cubic units that will exactly fill a cylinder. The volume of a cylinder can be found or calculate by using the formula
V = πr²h, where r represents the radius of the figure.

In this exercise is given that the radius of a cylinder is 3 feet and the height is 4 feet, and it is asked to find its volume. In order to find the volume of the given cylinder, you should substitute the values for the radius and height into the previous mention formula.

V=πr²h
V=(3.14)(3 ft)²(4 ft)
V=(3.14)(9 ft²)(4 ft)
V=(3.14)(36 ft³)
V=113.04 ft³

The volume of the cylinder is 113.04 cubic feet.

natta225 [31]3 years ago

7 0

volume of a cylinder = V = πr²h, r = radius and h = height.

if r = 3 and h = 4, then V = π3²(4) => V = 36π => V ≈ 113.1.

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Two angles whose measures have a sum of 90° are called complementary angles. for exercises 28–30, x and y represent complementar

natulia [17]

28: x+y = 90
we substitute y with the given function 4x - 10
x + 4x - 10 = 905x -10 = 90 5x = 100= 100 ÷ 5x = 20, now you can substitute x in 4x - 10 =4(20) - 1080 - 10 = 70, which makes sense as 20º +70º = 90ºyour 2 angles are 20º and 70º
29: x + y = 90 x = 2y
Same thing we did above, substitute the given variable into the given equation
so, 2y + y = 90 = 3y=90, divide the 3 to both sides, y = 30, now substitue the y into your given x variable.x = 2(30)x= 60this makes sense as 60º + 30º do equal 90ºyour two angles are 60º and 30º30: x + y = 90 y = 2 (x - 15)ill do this one without explanation as you know what I am doing from the above examples. here is the work:
x + 2(x-15)=90 (simplify)
x+2x-30 = 903x-30=903x = 120x = 40now input to other equation2(40 - 15) = y (USE PEMDAS)2(25) = yy = 50
makes sense because 50º + 40º = 90ºyour two angles are 50º and 40º

6 0

4 years ago

At a large midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen

nasty-shy [4]

Answer:

B. Z=1.98

Step-by-step explanation:

1) Data given and notation

$X_{1}=20$ represent the number of sampled freshmen finished in the bottom third of their high school class in 1993

$X_{2}=10$ represent the number of sampled freshmen finished in the bottom third of their high school class in 1997

$n_{1}=100$ sample 1 selected

$n_{2}=100$ sample 2 selected

$p_{1}=\frac{20}{100}=0.20$ represent the proportion of sampled freshmen finished in the bottom third of their high school class in 1993

$p_{2}=\frac{10}{100}=0.0023$ represent the proportion ofsampled freshmen finished in the bottom third of their high school class in 1997

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion graduated in the bottom third of their high school class is higher for 1993 than 1997 , the system of hypothesis would be:

Null hypothesis: $p_{1} \leq p_{2}$

Alternative hypothesis: $p_{1} > p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{20+10}{100+100}=0.15$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.20-0.10}{\sqrt{0.15(1-0.15)(\frac{1}{100}+\frac{1}{100})}}=1.98$

4) Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =P(Z>1.98)=0.024$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion graduated in the bottom third of their high school classes in 1993 is not significant higher than the proportion in 1997.