Ask question

Ask question

All categories

Aleksandr-060686 [28]

3 years ago

13

According to the annual Summer Vacation Survey conducted by Myvesta, a nonprofit consumer education organization, the average su

mmer vacation costs $2252. If $1650 of this amount is charged on a credit card, what percent of the vacation cost is charged?

1 answer:

AnnZ [28]3 years ago

4 0

Answer:

The answer is : 73.3% (to 1 decimal place)

Step-by-step explanation:

The question is asking us to convert the proportion of a certain amount into percentage, and this is done as shown below:

vacation cost = $2252

amount charged = $1650

%of vacation cost that was charged = X%

∴ X% of 2252 = 1650

$\frac{X}{100}$ × 2252 = 1652

$\frac{2252X}{100} =1650$

2252X = 165000 (dividing both sides by 2252)

$\frac{2252X}{2252}=\frac{165000}{2252}$

∴ X = 165000 ÷ 2252

X = 73.3%

You might be interested in

A study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. T

CaHeK987 [17]

Answer:

We need to conduct a hypothesis in order to check if the mean is higher than 75, the system of hypothesis are :

Null hypothesis: $\mu \leq 75$

Alternative hypothesis: $\mu > 75$

A. One-Tailed

$z=\frac{82.2-75}{\frac{10.4}{\sqrt{10}}}=2.189$

$p_v =P(z>2.189)=0.0143$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

We have the following data: 84 94 80 88 77 68 90 74 96 71

We can calculate the sample mean with the following formula:

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

And replacing we got:

$\bar X=82.2$ represent the sample mean

$\sigma=10.4$ represent the population standard deviation

$n=10$ sample size

$\mu_o =75$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 75, the system of hypothesis are :

Null hypothesis: $\mu \leq 75$

Alternative hypothesis: $\mu > 75$

A. One-Tailed

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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".

Calculate the statistic

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

$z=\frac{82.2-75}{\frac{10.4}{\sqrt{10}}}=2.189$

P-value

Since is a ONE-TAILED test the p value would given by:

$p_v =P(z>2.189)=0.0143$

Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

5 0

3 years ago

This is the two that go together, but are separate questions

ira [324]

Answers:

Option 1)

6a + 8s = 102

14a + 4s = 150

each adult ticket costs 9 dollars

===================================================

Explanation:

6 adult tickets and 8 student tickets bring in $102, so that means 6a+8s = 102

14 adult tickets and 4 students tickets bring in $150, so 14a+4s = 150

The system of equations is

$\begin{cases}6a+8s = 102\\14a+4s = 150\end{cases}$

If we multiply both sides of the second equation by -2, we get this updated system

$\begin{cases}6a+8s = 102\\-28a-8s = -300\end{cases}$

Add the equations straight down

6a+(-28a) = -22a

8s+(-8s) = 0s = 0 ... the 's' terms go away

102+(-300) = -198

So we end up with the equation -22a = -198 and that solves to a = 9 after dividing both sides by -22.

Each adult ticket costs $9

If you want the value of s, then

6a+8s = 102

6(9)+8s = 102

54 + 8s = 102

8s = 102-54

8s = 48

s = 48/8

s = 6

Meaning each student ticket costs $6

Or you could use the other equation

14a+4s = 150

14(9)+4s = 150

126+4s = 150

4s = 150-126

4s = 24

s = 24/4

s = 6

We get the same value of s

5 0

3 years ago

Alan works 6miles away from the apartment and rollerblades from his work place to the apartment at a constant rate of 7miles per

dimulka [17.4K]

Let the distance remaining after time t be x miles.

Distance traveled by Alan = (6-x) miles
Distance traveled by Soren = (8-x) miles

Time takes by the two is the same. Therefore,
(8-x)/12 = (6-x)/7 => 7(8-x) = 12(6-x) => 56-7x = 72-12x => 12x-7x = 72 -56 => 5x= 16 => x = 16/5 = 3.2 miles.

And then, time taken (t) = (8-3.2)/12 = (6-3.2)/7 = 0.4 hours

4 0

3 years ago

Read 2 more answers

race drivers must complete 200 laps in the Daytona 500. If Ricky Bobby only completed 57% of the race, how many laps did he comp

vlada-n [284]

We can set up a proportion to figure out how many laps out of 200 laps is 57% out of 100%

$\frac{x}{200} = \frac{57}{100}$

Cross multiply

$100x = 57(200)$

$x = \frac{57(200)}{100}$

$x = 2(57) = 114$

The answer is 114 laps.

4 0

3 years ago

Read 2 more answers

What percentage of 48 is 62?

Mila [183]

Answer:

129

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers