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3 years ago

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4. A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diame

ter equal to the sphere diameter.
How high is the cylinder?
O A. 8 mm
OB. 14 mm
O C. 16 mm
O D. 18 mm

1 answer:

Ludmilka [50]3 years ago

3 0

Answer: The answer is A, 8 mm.

Step-by-step explanation:

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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.

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4 years ago

is the statement below always, sometimes or never true. Gi at least 2 examples to support your reasoning. The lcm of two numbers

ASHA 777 [7]

The statement is not always true.
For Example...
The LCM of 6 and 8 is not the product of the two numbers
6*8= 48
48 is not the LEAST common multiple
Multiples of 6 are...
6,12,18,24,30,36,42,48...
Multiples of 8 are....
8,16,24,32,40,48...
The least common multiple is 24 not 48 even though they are both common multiples.

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4 years ago

Two cities, A and B, are mapped on the coordinate plane. How far apart are they from each other?

kiruha [24]

I can’t help because I can’t see the coordinate plane.

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2 years ago

Solve the equation by completing the square: <br> 3x^2 – 9x = -6

AVprozaik [17]

So my step one would be to add the six over and get 3x squared -9x+6=0, then divide by 3 to get x squared-3x+2=0. The next step is seeing what two numbers multiply to 2 but also add to negative three. The two numbers are -1 and -2. So then you are going to make two equations, one being x-1=0 and the other being x-2=0. Solve both to get X=1 and X=2, check your answers in the original equation. Hope this helps!

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