What is the area of rectangle ABCD?

If a car averages 21.8 miles per gallon, how many miles will it travel on 16 gallons of gas?

asambeis [7]

Answer: 348.8 miles on 16 gallons of gas

Step-by-step explanation:

Make the following proportion:

$\frac{21.8 miles}{1 gallon}$ = $\frac{x miles}{16 gallons}$

Since the car consumes gas at the same rate and only the amount of gas is changed, these two fractions must be equivalent. If the rate at which the car consumes gas changes, it would be different.

Use basic algebraic skills and you should get 348.8 miles.

7 0

2 years ago

The following prices, in dollars, of 7.5-cubic-foot refrigerators were recorded from a random sample. 314 305 344 283 285 310 3

Mariana [72]

Answer:

$t=\frac{310.9-300}{\frac{31.09}{\sqrt{10}}}=1.109$

The degrees of freedom are given by:

$df=n-1=10-1=9$

And the p value would be given by:

$p_v =P(t_{9}>1.109)=0.148$

Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.

Step-by-step explanation:

Information given

314 305 344 283 285 310 383 285 300 300

We can calculate the sample mean and deviation with the following formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=310.9$ represent the sample mean

$s=31.09$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =300$ represent the value to test

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true mean is greater than 300, the system of hypothesis would be:

Null hypothesis: $\mu \leq 300$

Alternative hypothesis: $\mu > 300$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{310.9-300}{\frac{31.09}{\sqrt{10}}}=1.109$

The degrees of freedom are given by:

$df=n-1=10-1=9$

And the p value would be given by:

$p_v =P(t_{9}>1.109)=0.148$

Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.

6 0

3 years ago

The distance between port M and port N is 162m. A ship left port M with a speed of 45 mph. In 45 minutes another ship left port

matrenka [14]

Answer:

After 900 minutes

Step-by-step explanation:

when we convert the velocities of the ships into miles/ min we get

$45mph=45m/60min=0.75m/min$

$36mph=36m/60min=0.6m/min$

The equations determining the distances of the ships from the port M (set at x=0) are

$D_1=0.75t$ (for 45mph ship)

$D_2=162+0.6(t-45)$ (for 36mph ship)

The solution to these equation lie at t= 900 minutes; therefore the two ships will meet 900 minutes after the departure of the first ship.

8 0

3 years ago

Read 2 more answers

Solve. Justify your responses. a Given:a║b and c║d, m∠ 4=35° Find: m∠1, m∠2, and m∠3

STALIN [3.7K]

Answer:

m∠1 = 90°

m∠2 = 35°

m∠3 = 55°

Step-by-step explanation:

Find the diagram attached

From the diagram:

$m$

Given that <4 = 35°

$m$

The sum of the angle on a straight line at point A is 180°. Hence:

$90+m$

The sum of angle in the triangle ABC is 180°, hence;

$m$

7 0

2 years ago

If a positive integer that is not a multiple of 5 is divided by 5, what is the least possible remainder

solniwko [45]

I would say 1 would be the least possible remainder...

11/5 = 2 remainder 1
21/5 = 4 remainder 1
31/5 = 3 remainder 1

and since ur dealing with positive integers (whole numbers), 1 is gonna be the smallest

8 0

3 years ago