# Suppose 8 quarts of a solution that is 45% anti-freeze is mixed with 12 quarts of a solution that is 33% anti-freeze. How many quarts of antifreeze are in the resulting measures? What percentage of the resulting mixture is anti-freeze?

7.56 quarts of antifreeze in the resulting mixture, and 37.8% of the resulting mixture is antifreeze.

Step-by-step explanation:

8 * .45= 3.6 quarts antifreeze

12 * .33= 3.96 quarts antifreeze

3.6 + 3.96= 7.56 quarts of antifreeze in the resulting mixture

7.56 quarts/ 20 quarts (12 + 8) * 100= 37.8%

In the combined solution, there are 7.56 quarts of anti-freeze, which equals 37.8% of the total solution.

### Explanation:

To solve this problem, we first need to calculate how many quarts of anti-freeze are in each solution, then add them together.

First, we have 8 quarts of a solution that is 45% anti-freeze. To find how many quarts of the solution is anti-freeze, we multiply the total amount by the percentage: 8 quarts * 0.45 = 3.6 quarts anti-freeze.

Next, we have 12 quarts of a solution that is 33% anti-freeze. Doing the same calculation as before, 12 quarts * 0.33 = 3.96 quarts anti-freeze.

Now, to find the total quarts of anti-freeze in the combined solution, we simply add the two amounts together: 3.6 quarts + 3.96 quarts = 7.56 quarts.

The total amount of solution is 8 quarts (from the first solution) + 12 quarts (from the second) = 20 quarts.

To find the percent of anti-freeze in the final solution, we divide the total amount of anti-freeze by the total amount of solution: (7.56 quarts / 20 quarts) * 100 = 37.8%. Therefore, the resulting mixture is 37.8% anti-freeze.

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## Related Questions

How do you find the answer to this?

D)  {-1}

Step-by-step explanation:

A rational expression is "not defined" when its denominator is zero. Hence to find values of x that make the expression "not defined," you solve the equation ...

denominator = 0

2x +2 = 0 . . . . . . put the actual denominator into the equation

x + 1 = 0 . . . . . divide by 2

x = -1 . . . . . . . . subtract 1

The expression is "not defined" for x in the set {-1}.

What is the pattern in the values as the exponents increase?

as the exponents increase, the value is multiplied by 2

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned (BusinessWeek, January 1 5, 2007). A Houston department store sampled 80 items sold in January and found that 12 of the items were returned.Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store.

Using the sample proportion, it is found that the point estimate is of 0.15 = 15%.

### What is a sample proportion?

A sample proportion is given by the number of desired outcomes divided by the number of total outcomes. It can also serve as the point estimate for the population proportion.

In this problem, 12 out of the 80 items sold were returned, hence:

12/80 = 0.15 = 15%.

The point estimate is of 0.15 = 15%.

More can be learned about point estimates at brainly.com/question/24651197

a)

b)

And the 95% confidence interval would be given (0.072;0.228).

c) For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.

Step-by-step explanation:

Assumign the following question for the problem:

a. Construct a point estimate of the proportion of items returned for the population of  sales transactions at the Houston store.

For this case the best estimate for the true proportion is given by the sample proportion:

b. Construct a 95% confidence interval for the porportion of returns at the Houston store.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval would be given by this formula

For the 95% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.

And replacing into the confidence interval formula we got:

And the 95% confidence interval would be given (0.072;0.228).

c. Is the proportion of returns at the Houston store significantly different from the returns  for the nation as a whole? Provide statistical support for your answer.

For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.

The observation which occurs most frequently in a sample is the mean

Step-by-step explanation:

Mode- the value that appears most often in a set of data.

Median- the middle number in a list of numbers ordered from lowest to highest.

Mean- the total of all the values, divided by the number of values.

Range- the difference between the lowest value and the highest value.

mode

Step-by-step explanation:

Find the number of distinct triangles with a=11, b=17, and A=23°A. 0
B. 1
C. 2
D. cannot be determined

The answer would be C, 2

Using the diagram below, what is the measure of ZE?