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3 years ago

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What is the lateral surface area of a cylindrical-shaped candle with a radius of 3 cm and a height of 15 cm? (Use 3.14 for .) A.

847.8 sq cm B. 45 sq cm C. 282.6 sq cm D. 339.12 sq cm

1 answer:

galben [10]3 years ago

5 0

I hope this helps you

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Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing i

Nina [5.8K]

Answer:

$z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358$

$p_v =2*P(Z>5.358) = 4.2x10^{-8}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.

Step-by-step explanation:

Data given and notation

$X_{1}=253$ represent the number with no defects in sample 1

$X_{2}=196$ represent the number with no defects in sample 1

$n_{1}=300$ sample 1

$n_{2}=300$ sample 2

$p_{1}=\frac{253}{300}=0.843$ represent the proportion of number with no defects in sample 1

$p_{2}=\frac{196}{300}=0.653$ represent the proportion of number with no defects in sample 2

z would represent the statistic (variable of interest)

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

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

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 $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{253+196}{300+300}=0.748$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

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

$z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>5.358) = 4.2x10^{-8}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=y%20-%20xy%20%2B%20x%20-%201" id="TexFormula1" title="y - xy + x - 1" alt="y - xy + x - 1" ali

nata0808 [166]

I believe it should be =(1-x) multiple by (y-1)
(1-x) x (y-1)

8 0

2 years ago

Read 2 more answers

suppose y varies directly with x and y=5 when x=20. Write a direct variation equation then find the value of x when y=3/2

jek_recluse [69]

X=k*Y
K*Y=X
K=X/Y
K=20/5
K=4

For Y=3/2
X=k*3/2
X=4*3/2
X=6

6 0

4 years ago

3. Are these ratios equivalent? 35:28 and 10:8 *

attashe74 [19]

Reduce each ratio to its minimum expression to find if they are equal.

35:28

$\begin{gathered} \frac{35}{28}=\frac{7\cdot5}{7\cdot4} \\ =\frac{5}{4} \end{gathered}$

10:8

$\begin{gathered} \frac{10}{8}=\frac{2\cdot5}{2\cdot4} \\ =\frac{5}{4} \end{gathered}$

Since both ratios reduce to 5:4, they are equivalent.

Another way to check a:b is equivalent to c:d, is that a*d = b*c

In this case, this will be true if 35 times 8 is equal to 10 times 28:

$\begin{gathered} 35\cdot8=280 \\ 10\cdot28=280 \end{gathered}$

Since both products are equal, then the ratios are equivalent.

4 0

1 year ago

Jason earns $78,000 per year. If he is paid weekly what is his weekly pay?

My name is Ann [436]

In one week he's made $1,500

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3 years ago

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