What is the square root of

Four water tanks can hold a total of 432.4 gallons of water. On average, how much water can one tank hold? How much water is in

andreyandreev [35.5K]

On average one tank holds 108 gallons because 432.4 divided by 4 is 108.1. One half full tank would hold about 54 gallons (54.05 to be exact) because half of 108.1 gallons (a full tank) is 54.05 gallons.

3 0

3 years ago

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A science museum has a spherical model of the earth with a diameter of 6.5 m. What is the volume of the model? Use 3.14 for and

natka813 [3]

radius = diameter/2

radius = 6.5/2 = $\frac{13}{4}$ m

<span>volume </span> $= \frac{4}{3}$ x $\pi$ x (radius)³

$= \frac{4}{3}$ x $\pi$ x $( \frac{13}{4})^3$

$= \frac{4}{3}$ x $\pi$ x $\frac{2197}{64}$

$= \frac{2197}{64}$

= 144 cubic meters

6 0

3 years ago

A sample of 100 workers located in Atlanta has an average daily work time of 6.5 hours with a standard deviation of 0.5 hours. A

Readme [11.4K]

Answer:

$t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398$

$df = n_1 +n_2 -2= 100+110-2= 208$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{208}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

$\bar X_{1}=6.5$ represent the sample mean for Atlanta

$\bar X_{2}=6.7$ represent the sample mean for Chicago

$s_{1}=0.5$ represent the sample deviation for Atlanta

$s_{2}=0.7$ represent the sample standard deviation for Chicago

$n_{1}=100$ sample size for the group Atlanta

$n_{2}=110$ sample size for the group Chicago

t would represent the statistic (variable of interest)

$\alpha=0.01$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the meanfor atlanta is different from the mean of Chicago, the system of hypothesis would be:

Null hypothesis: $\mu_{1}=\mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-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 value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398$

What is the p-value for this hypothesis test?

The degrees of freedom are given by:

$df = n_1 +n_2 -2= 100+110-2= 208$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{208}$

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

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3 years ago

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The variables xx and yy vary directly. use the values to find the constant of proportionality, kk. then write an equation that r

Sergeu [11.5K]

Direct variation means that changes in x will result to changes in y. If x increase, y also increases and vice versa.

y = kx
k = y / x

y = 45 ; x = 40

k = 45/40
k = 1.125

y = 1.125x

y will increase by 1.125 interval of x.

5 0

3 years ago

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Write an expression for “Triple the sum of 33 and b”. *

IrinaK [193]

Answer:

99+3b

Step-by-step explanation:

The original equation would be 3(33+b), but simplifying it would get 99+3b.

8 0

2 years ago