Taylor buys 2 gallons of milk for $5.50. What is the cost per gallon

UNO [17]

Ok so we know that student tickets cost $5, and adult tickets cost $8. We also know that the total no. of tickets sold was 150.

Let's make the amount of student tickets sold be S, and the no. of adult tickets sold be A.

We know that tickets sales amounted to $1,020, so:
8A + 5S = 1020
And:
A + S = 150. Multiply this by 5;
5A + 5S = 750

When you subtract the two equations;
(8A+5S) - (5A+5S) = 1020-750
So 3A = 270
A = 90
So 90 adult tickets were sold.
S = 150 - 90
= 60
So 60 student tickets were sold (although you don't need this as part of your answer)

Hope this helped

4 0

3 years ago

A number z, when rounded to the nearest whole, is equal to 70. Find the upper and lower bound of x

rusak2 [61]

Answer:

A quick way to calculate upper and lower bands is to halve the degree of accuracy specified, then add this to the rounded value for the upper bound and subtract it from the rounded value for the lower bound.

4 0

2 years ago

Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to

attashe74 [19]

Answer:

a) Null hypothesis: $\mu \leq 30.2$

Alternative hypothesis: $\mu > 30.2$

b) $X \sim N(\mu=32.12, \sigma=4.83)$

And the distribution for the random sample is given by:

$\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)$

c) $t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81$

$p_v =P(t_{(49)}>2.81)=0.0035$

d) If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.

e) The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation

$\bar X=32.12$ represent the sample mean

$s=4.83$ represent the sample standard deviation

$n=50$ sample size

$\mu_o =30.2$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

a. Define the parameter and state the hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 30.2 mpg, the system of hypothesis would be:

Null hypothesis: $\mu \leq 30.2$

Alternative hypothesis: $\mu > 30.2$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

b. Define the sampling distribution (mean and standard deviation).

Let X the random variable who represent the variable of interest. And we know that the distribution for X is:

$X \sim N(\mu=32.12, \sigma=4.83)$

And the distribution for the random sample is given by:

$\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)$

c. Perform the test and calculate P-value

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=50-1=49$

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

$p_v =P(t_{(49)}>2.81)=0.0035$

d. State your conclusion.

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.

e. Explain what the p-value means in this context.

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

6 0

3 years ago

The Garcia family started the day with 2 gallons of milk. They drank 111 quart of milk for breakfast and 3 pints for lunch.

irina1246 [14]

3 pints

There are 8 pints of milk in 1 gallon. There is also 4 quarts in 1 gallon. So each quart is 2 pints.
After breakfast they had 3 quarts of the original gallon left since 4 - 1 = 3.
3 quarts is the same as 6 pints. They drank 3 pints at lunch. This means 6 - 3 = 3. After lunch, there were 3 pints left.

6 0

3 years ago

The bar diagram represents 24 hours in one day and shows a mark at 30%If you sleep 30% of the day, how many hours do you sleep?

horrorfan [7]

Let:

100%---------------->24h

30%------------------>xh

Using cross multiplication:

$\begin{gathered} \frac{100}{30}=\frac{24}{x} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=\frac{30\cdot24}{100} \\ x=\frac{720}{100}=7.2h \end{gathered}$

8 0

1 year ago