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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?

Answers

Answer 1

Answer:

Answer:

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%

Answer 2

Answer:

Final answer:

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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Which of the following shows the extraneous solution to the logarithmic equation x = -16
x = -4
x = 4
x = 16

Answers

Answer:

The correct answer option is x = 4.

Step-by-step explanation:

We are given the following logarithmic equation and we are to determine whether which of the given options shows its extraneous solution:

$log _ 7 ( 3 x ^ 3 + x ) - log _ 7 ( x ) = 2$

We can rewrite it as:

$log7[(3x^3+x)/(x) ]=2$

But we know that $log_7(49)=2$

So, $log7[(3x^3+x)/(x) ]=log_7(49)$

Cancelling the log to get:

$(3x^3+x)/(x) =49$

Further simplifying it to get:

$3x^2+1=49$

$3x^2=48$

$x^2=(48)/(3)$

$x^2=16$

x = 4

Answer:

The extraneous solution to the logarithmic equation is $x=-4$

Step-by-step explanation:

We have the equation:

$Log_(7) (3x^3+x)-Log_7(x)=2$

By properties of logarithms:

$LogA-LogB=Log((A)/(B))$

So, with the equation we have:

$Log_(7) ((3x^3+x))/(x)=2$

$Log_(7)( (3x^3+x)/(x))=2\nLog_(7)( (3x^3)/(x)+(x)/(x))=2\nLog_(7)( (3x^3)/(x)+1)=2\nLog_(7)(3x^2+1)=2$

This logarithm base is 7 and this equation is equal to 2, the number 7 passes as the base on the other side of the equation and the two as an exponent, after that we just to find x:

$7^2=(3x^2+1)\n49=3x^2+1\n49-1=3x^2\n(48)/(3) =x^2\n16=x^2$

Now, we can find x with square root

$16=x^2\n√(16) =√(x^2) \nx_1=4\nx_2=-4$

This equation has two answers because it is a quadratic equation, so with this logic the strange solution is -4

The label on William's muffin said that one serving provided 11 grams of protein, which is 22% of the recommended dailyamount. What is the total recommended daily amount of protein?

Answers

Answer: 50 grams

Step-by-step explanation:

11=0.22 a

A =50

Twenty air-conditioning units have been brought in for service. Twelve of them have broken compressors, and eight have broken fans. Seven units are chosen at random to be worked on. What is the probability that three of them have broken fans

Answers

Answer: 0.3576

Step-by-step explanation:

Let the probability that the units that have broken fans from the seven units chosen at random be x.

The probability that three of them have broken fans will be 0.3576. Check the attachment for details

Given: Z2 and Z4 are vertical angles.
Prove: Z2 = Z4

Answers

Step-by-step explanation:

we know about vertical angels that are equal

so <2=<4

(in fact they are congruent angles)

we found those only from the definition of vertical angles.

Final answer:

In geometry, vertical angles (like Z2 and Z4) formed by two intersecting lines are always equal. Therefore, if Z2 and Z4 are defined as vertical angles, they are equal in measurement. This is a fundamental concept of geometry.

Explanation:

In the field of Geometry, vertical angles are always congruent, which means they have the same measure in degrees. When you have two intersecting lines, they create vertical angles that are across from one another. Therefore, if Z2 and Z4 are defined as vertical angles, they must be equal in measurement.

Here is an explicit step-by-step explanation:

In the given, we have two intersecting lines that form Z2 and Z4.
By the properties of vertical angles, we know that angles positioned opposite each other (like Z2 and Z4) are equal.
Therefore, we can conclude that Z2 = Z4.

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Twenty-one less than a number is seven. What is the number?
3
14.
28
147

Answers

Answer: the answer will be 28

Step-by-step explanation:

First you have to add 21+7 which equals to 28 and that's how I got my answer.

Please mark me brainiiest.

Answer:

Step-by-step explanation:

add 7 + 21

HELP!!!!!In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.

What is the average number of siblings for this group? Enter your answer as a decimal, rounded to the nearest tenth,
_______

Answers

The average number of siblings for the group is 1.3.

We must compute the total number of siblings and divide it by the total number of children in the group to determine the average number of siblings for the group.

There are a total of: siblings in the bunch.

3 + 8 + 9 = 20 (1 sibling times 3 children) + (2 siblings times 4 children) + (3 siblings times 3 children)

The total number of kids in the group is: 5 + 3 + 4 + 3 = 15

As a result, the group as a whole has an average of:

20/15 = 1.33 (rounded to the nearest tenth) (rounded to the nearest tenth)

So, the group as a whole has 1.3 siblings on average.

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