Christina biked 36 miles in 6 hours. If she biked at a constant speed, how many miles did she ride in one hour?

71/3 - 21/4 (2 1/5 × 3/4) with working

RideAnS [48]

Answer:

15 1/240

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

2.06. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nucle

DaniilM [7]

Answer:

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=74$ represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$X_{2}=70$ represent the number of people suburban residents are in favor

$n_{1}=100$ sample 1 selected

$n_{2}=125$ sample 2 selected

$p_{1}=\frac{74}{100}=0.74$ represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$p_{2}=\frac{70}{125}=0.56$ represent the proportion of suburban residents are in favor

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

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

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 $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{74+70}{100+125}=0.64$

Calculate the statistic

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

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

Statistical decision

The significance level provided is $\alpha=0.05$ ,and we can calculate the p value for this test.

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

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

5 0

3 years ago

What is the height of a triangle with area 40 square inches and base 20 inches?

Andru [333]

A=1/2 bh
40=1/2•20h
80=20h
4=h

3 0

3 years ago

What value of g makes the equation true?

Ipatiy [6.2K]

(x+7)(x-4)
= x^2 + 7x - 4x - 28
= x^2 + 3x - 28

answer
g = 3

4 0

3 years ago

You throw a ball at a height of 6 feet above the

Alexandra [31]

Answer:

0.375 second and 3.5 second

Step-by-step explanation:

The position can be modeled by a quadratic function $\displaystyle{h=-16t^2+62t+6}$ . We are tasked to find the time when a ball reaches a height of 27 feet. Therefore, let h = 27:

$\displaystyle{27=-16t^2+62t+6}$

Solve for t:

$\displaystyle{27-6=-16t^2+62t}\\\\\displaystyle{21=-16t^2+62t}\\\\\displaystyle{16t^2-62t+21=0}$

Since the equation is quite complicated and more time-consuming to solve, i'll skip the factoring or quadratic part:

$\displaystyle{t=0.375, 3.5}$

After done solving the equation, you'll get t = 0.375 and 3.5 seconds. These solutions are valid since both are positive values and time can only be positive.

Hence, it'll take 0.375 and 3.5 seconds for a ball to reach 27 feet.

3 0

2 years ago