Gertrude sold 104 cars last year. There are 52 weeks in a year. What was the rate at which she sold cars?

The drain in your 45-gallon bathtub is partially clogged, but you need to take a shower. The shower head had a flow rate of 2.25

Helen [10]

Answer:

$Time = 1.978\ min$

Step-by-step explanation:

Given

$R_1 = 2.25\ gal/min$ --- Flow rate of the shower

$R_2 = 20.5\ gal/min$ --- Drain rate of the bathtub

$Size = 45gal$ -- Bathtub size

Required

Determine the maximum time of shower

First, we calculate the rate at which the bathtub fills.

$R_3 = R_1 + R_2$

$R_3 = 2.25 + 20.5$

$R_3 = 22.75gal/min$

The maximum time of shower is:

$Time = \frac{Size}{R_3}$

$Time = \frac{45gal}{22.75gal/min}$

$Time = 1.978\ min$

6 0

3 years ago

According to Nielsen Media Research. of all the U.S. households that owned at least one television set, 83% had two or more sets

Rudik [331]

Answer:

The proportion of U.S. households that owned two or more televisions is 83%.

Step-by-step explanation:

To determine whether the proportions of U.S. households that owned two or more televisions is less than 83% or not let us perform a hypothesis test for single proportion.

Assumptions:

The sample size (n) selected by the local cable company is 300 which is quite large. Then according to the Central limit theorem the sampling distribution of sample proportion follows a normal distribution with mean p and standard deviation $\sqrt{\frac{p(1-p)}{n} }$ .

Since the sampling distribution of sample proportions follows a normal distribution use the z-test for one proportion to perform the test.

The hypothesis is:

$H_{0}$ : The proportion of U.S. households that owned two or more televisions is 83%, i.e. $p=0.83$

$H_{1}$ :The proportion of U.S. households that owned two or more televisions is less than 83%, i.e. $p< 0.83$

Decision Rule:

At the level of significance α = 0.05 the critical region for a one-tailed z-test is:

$\\ Z\leq -1.645\\$

**Use the z table for the critical values.

So, if $\\ Z\leq -1.645\\$ the null hypothesis will be rejected.

Test statistic value:

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

Here $\hat{p}$ is the sample proportion.

Compute the value of $\hat{p}$ as follows:

$\hat{p}=\frac{X}{n} \\=\frac{240}{300}\\ =0.80$

Now compute the value of the test statistic as follows:

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\=\frac{0.80-0.83}{\sqrt{\frac{0.83*(1-0.83)}{300} } } \\=-1.383$

The test statistic is -1.383 which is more than -1.645.

Thus, the test statistic lies in the acceptance region.

Hence we fail to reject the null hypothesis.

Conclusion:

At 0.05 level of significance we fail to reject the null hypothesis stating that the proportion of U.S. households that owned two or more televisions is 83%.

6 0

3 years ago

I need an explanation (Picture provided)

Over [174]

Angles on a straight line add up to 180° so you do 180 take away 115 which gives you Y angle and then angles in a triangle add up to 180 so you do 45 add 65 and you get 110 which then u take away from 180 to get 70 answer D

5 0

3 years ago

PLS HELP

djyliett [7]

Answer:

Look at the unfolded cylinder down: it's consisted of a rectangle and 2 circles. so to find the surface area of the cylinder we should find the areas of the rectangle and the 2 circles.

1) A of 2 circles = 2(π $r^{2}$ ) = 2π $r^{2}$

2) A of rectangle = base x height (or length x width) = bh

but the if we fold the rectangle? what will happen?

the base will go around the circle, this means that the base is equal to the circle circumference, which is 2πr.

Therefore, A of rectangle = 2πrh

3) Surface area of cylinder = 2π $r^{2}$ + 2πrh

simplify more and take the common factor 2πr:

= 2πr (r+h)

4 0

3 years ago

Tickets for the theater are $5 for the balcony and $10 for the orchestra. If 600 tickets were sold and the total receipts were $

kherson [118]

5x+10y=4750
x+y=600

x=250
y=350

250 theater tickets
350 orchestra tickets

4 0

4 years ago