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Alina [70]
3 years ago
6

A cube has a volume of 343 cm3. What is the length of each side of the cube?

Mathematics
1 answer:
Anna [14]3 years ago
3 0
Volume of a cube=side³

Data:;
volume=343 cm³
Therefore:

343 cm³=side³
side=∛343 cm³=7 cm.

Answer: the lenght of each side of the cube is 7 cm.
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In the last 10 years, the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues,
REY [17]

Answer:

288750006

Step-by-step explanation:

<u>Growth rate:</u>

  • 1.12% or 1.0112 times

<u>Current population:</u>

  • 258,316,051

<u>Predicted population after 10 years:</u>

  • 258,316,051*(1.0112)^10 = 288,750,006.168≈ 288,750,006 rounded
4 0
3 years ago
Read 2 more answers
Suppose that a random sample of 10 newborns had an average weight of 7.25 pounds and sample standard deviation of 2 pounds. a. T
frosja888 [35]

Answer:

z=\frac{7.25-7.5}{\frac{1.4}{\sqrt{10}}}=-0.565  

p_v =P(Z  

a) If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true average is not significantly less than 7.5.  

b) \chi^2 =\frac{10-1}{1.96} 4 =18.367  

p_v =P(\chi^2 >18.367)=0.0311

If we compare the p value and the significance level provided we see that p_v >\alpha so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 1.96.

Step-by-step explanation:

Assuming this info: "Suppose birth weights follow a normal distribution with mean 7.5 pounds and standard deviation 1.4 pounds"

1) Data given and notation  

\bar X=7.25 represent the sample mean  

s=1.2 represent the sample standard deviation

\sigma=1.4 represent the population standard deviation

n=10 sample size  

\mu_o =7.5 represent the value that we want to test  

\alpha=0.05,0.01 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

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

2) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is less than 7.5, the system of hypothesis would be:  

Null hypothesis:\mu \geq 7.5  

Alternative hypothesis:\mu < 7.5  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

3) Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{7.25-7.5}{\frac{1.4}{\sqrt{10}}}=-0.565  

4)P-value  

Since is a left tailed test the p value would be:  

p_v =P(Z  

5) Conclusion  

Part a

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true average is not significantly less than 7.5.  

Part b

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

n=10 represent the sample size

\alpha=0.01 represent the confidence level  

s^2 =4 represent the sample variance obtained

\sigma^2_0 =1.96 represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance increase, so the system of hypothesis would be:

Null Hypothesis: \sigma^2 \leq 1.96

Alternative hypothesis: \sigma^2 >1.96

Calculate the statistic  

For this test we can use the following statistic:

\chi^2 =\frac{n-1}{\sigma^2_0} s^2

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

\chi^2 =\frac{10-1}{1.96} 4 =18.367

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 9. And since is a right tailed test the p value would be given by:

p_v =P(\chi^2 >18.367)=0.0311

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(18.367,9,TRUE)"

Conclusion

If we compare the p value and the significance level provided we see that p_v >\alpha so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 1.96.

4 0
3 years ago
The point slope form of the eqaution of the line that passes through (-5,-1) and (10, -7) is y+7= -2/5 (x - 10) what is the stan
stira [4]

Answer:

<h2>2x + 5y = -15</h2>

Step-by-step explanation:

The standard form of an equation of a line:

Ax+By=C

We have the equation in point-slope form:

y+7=-\dfrac{2}{5}(x-10)

Convert it to the standard form:

y+7=-\dfrac{2}{5}(x-10)     <em>multiply both sides by 5</em>

5y+35=-2(x-10)         <em>use the distributive property </em><em>a(b + c) = ab + ac</em>

5y+35=(-2)(x)+(-2)(-10)

5y+35=-2x+20          <em>subtract 35 from both sides</em>

5y=-2x-15            <em>add 2x to both sides</em>

2x+5y=-15

7 0
3 years ago
A cylinder has a circular base with a radius that measures 9 inches. Determine the diameter of the base of the cylinder. 3 inche
yarga [219]
It is 18 because the radius is half the diameter and 9 x 2 = 18.
4 0
3 years ago
Read 2 more answers
One side of a right triangle has a length of 12 feet. Which of the following could be lengths for the two other sides of the rig
Elodia [21]

Answer:

B

Step-by-step explanation:

Apply the Pythagorean Theorem to determine whether or not the given triplets represent right triangles or not:

I. 5 feet and 13 feet:  5^2 + 12^2 = 13^2 is TRUE

II.  9 ft and √63 ft:  9^2, 63, 12^2:  63 + 81 do add up to 144  TRUE

III.  2, 10, 12^2:  2 + 10 do NOT add up to 144.  FALSE

Answer B is correct

5 0
2 years ago
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