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2 years ago

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For every 3 boys in the class there are 5 girls. If there are 36 boys in gym class, How many girls are there in the gym class ?

how many total students are in that gym class?

1 answer:

SVEN [57.7K]2 years ago

7 0

Answer:

60

Step-by-step explanation:

I divided 36 by 3 got 12 then mutiplyed 12 by 5

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Write an equation for each sentence then solve. The sum of two consecutive even numbers is thirty-four. What are the numbers? I

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<h3 /><h3>▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄</h3><h3>Required Solution :</h3>

Let the first even number be 'x' & the second even number be (x + 2)

<u>According to the Question</u>,

⇒x + (x + 2) = 34

⇒x + x + 2 = 34

⇒2x + 2 = 34

⇒2x = 34 - 2

⇒2x = 32

⇒x = 32/2

⇒x = 16

⇒First even number = x = 16

⇒Second even number = (x + 2) = 16 + 2 = 18

<u>∴</u><u> </u><u>The t</u><u>wo consecutive even n</u><u>u</u><u>m</u><u>b</u><u>e</u><u>r</u><u>s</u><u> are 16 & 18</u> ...!

<h3>Verefication : </h3>

As, In our Question it was given that "The sum of two consecutive even numbers is thirty-four". So, as we got our two consecutive even numbers as 16 & 18 ... By this, we can say that these both even numbers should be equals to 34, i.e., 16 + 18 = 34. Hence, The equation which we formed is correct ...!

<h3>▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄</h3>

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Identify the three similar triangles in the figure. Be sure to name the vertices in the correct order

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2 years ago

Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a math

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Answer: $\frac{8}{3}\times \sqrt{\frac{2}{5}}$

Step-by-step explanation:

Given two upward facing parabolas with equations

$y=6x^2 & y=x^2+2$

The two intersect at

$6x^2=x^2+2$

$5x^2=2$

$x^2$ = $\frac{2}{5}$

x= $\pm \sqrt{\frac{2}{5}}$

area enclosed by them is given by

A= $\int_{-\sqrt{\frac{2}{5}}}^{\sqrt{\frac{2}{5}}}\left [ \left ( x^2+2\right )-\left ( 6x^2\right ) \right ]dx$

A= $\int_{\sqrt{-\frac{2}{5}}}^{\sqrt{\frac{2}{5}}}\left ( 2-5x^2\right )dx$

A= $4\left [ \sqrt{\frac{2}{5}} \right ]-\frac{5}{3}\left [ \left ( \frac{2}{5}\right )^\frac{3}{2}-\left ( -\frac{2}{5}\right )^\frac{3}{2} \right ]$

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3 years ago

A restaurant chain has two locations in a medium-sized town and, believing that it has oversaturated the market for its food, is

scoray [572]

Answer:

Yes, since the test statistic value is greater than the critical value.

Step-by-step explanation:

Data given and notation

$\bar X_{1}=360000$ represent the mean for the downtown restaurant

$\bar X_{2}=340000$ represent the mean for the freeway restaurant

$s_{1}=50000$ represent the sample standard deviation for downtown

$s_{2}=40000$ represent the sample standard deviation for the freeway

$n_{1}=36$ sample size for the downtown restaurant

$n_{2}=36$ sample size for the freeway restaurant

t would represent the statistic (variable of interest)

$\alpha=0.05$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the true mean of revenue for downtown is higher than for freeway restaurant, the system of hypothesis would be:

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

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

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.

Determine the critical value.

Based on the significance level $\alpha=0.05$ and $\alpha/2=0.025$ we can find the critical values from the t distribution dith degrees of freedom df=36+36-2=55+88-2=70, we are looking for values that accumulates 0.025 of the area on the right tail on the t distribution.

For this case the value is $t_{1-\alpha/2}=1.66$

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:

$t=\frac{360000-340000}{\sqrt{\frac{50000^2}{36}+\frac{40000^2}{36}}}}=1.874$

What is the p-value for this hypothesis test?

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

$p_v =P(t_{70}>1.874)=0.033$

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 reject the null hypothesis, and the true mean for the downtown revenue restaurant seems higher than the true mean revenue for the freeway restaurant.

The best option would be:

Yes, since the test statistic value is greater than the critical value.

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2 years ago