Evaluate. (1/4)^-2 - (5^0×2)×1^-1

To solve the equation mn + 7p = 8 for p, subtract mn from both sides to get 7p = 8 - mn, then divide by 7 to isolate p, resulting in p = (8 - mn) / 7.

To solve the equation mn + 7p = 8 for p, we need to isolate p on one side of the equation. We can do this by performing the following steps:

Now, the variable p is isolated, and the equation shows p in terms of m and n.

The provided reference solution and the graphing technique are not directly applicable to this algebra problem, as they pertain to different cases with specific contexts such as elasticity and supply-demand curves. For the actual question at hand, we focused exclusively on algebraic manipulation to find the value of p.

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

in this problem we have

[tex]A(-1,-7)\ B(1,5)[/tex]

substitute the values in the formula

[tex]m=\frac{5+7}{1+1}[/tex]

[tex]m=\frac{12}{2}[/tex]

[tex]m=6[/tex]

therefore

the answer is

the slope of the line is [tex]6[/tex]

To find the greatest number of pens or pencils that Louis can place in each bag, we need to find the greatest common divisor (GCD) of 45 and 75. Using the Euclidean algorithm, the GCD is determined to be 15.

In order to find the greatest number of pens or pencils that Louis can place in each bag, we need to find the greatest common divisor (GCD) of the given numbers, 45 and 75. The GCD represents the largest number that can evenly divide both 45 and 75.

We can find the GCD by using the Euclidean algorithm. Starting with the larger number (75), we divide it by the smaller number (45) and find the remainder (30). Then, we divide the divisor (45) by the remainder (30) and find the new remainder (15). We continue this process until we reach a remainder of 0. The last non-zero remainder (15) is the GCD of 45 and 75.

Therefore, the greatest number of pens or pencils that Louis can place in each bag is 15.

Final answer:

A 66-kg person contains approximately 39.6 kilograms of water, considering that the human body is comprised of about 60% water.

Explanation:

To estimate how many kilograms of water is in a 66-kg person, biology and a general understanding of the human body composition are required. The human body is comprised of approximately 60% water. Thus, to calculate the mass of water in a 66-kg person, the following calculation is performed:

Water mass = Total body mass x Percentage of water in the body

Water mass = 66 kg x 0.60

Water mass = 39.6 kg

Therefore, a 66-kg person contains approximately 39.6 kilograms of water.

Yes, the total price pay is proportional to the number of tickets.

In mathematics, proportionality indicates that two quantities or variables are related in a linear manner.

Since you never plan to buy the popcorn but only the movie ticket, therefore we can definitely say that there is a direct correlation between the total price and the number of tickets bought.

Since, 1 ticket = $10.50

So,

The proportion equation is:

P = 10.50 t

where P is the total price and t is the number of tickets

Hence,  the total price pay is proportional to the number of tickets.

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Let

x-----> the original price of the calculator

y-----> the original price of the binder

we know that

[tex]15\%= \frac{15}{100}=0.15[/tex]

[tex](x+y)(1-0.15)=107.27[/tex]

[tex](x+y)(0.85)=107.27[/tex] -----> equation A

[tex]y=6.20[/tex] -----> equation B

substitute the value of y in the equation A and solve for x

[tex](x+6.20)(0.85)=107.27[/tex]

[tex](x+6.20)=(107.27/0.85)[/tex]

[tex]x=(107.27/0.85)-6.20[/tex]

[tex]x=126.20-6.20[/tex]

[tex]x=\$120[/tex]

therefore

the answer is

the original price of the calculator is [tex]\$120[/tex]

Your Answer Will be

c=16d+18

GradPoint Answer

The value of p for the for given absolute value inequality |6p + 3|>15 lies in between - 3 and 2.

An absolute value inequality is an expression with absolute functions as well as inequality signs.

According to the given question.

We have an absolute value inequality |6p + 3| > 15

The above inequality can be written as

[tex]-15 < 6p+3 < 15[/tex]

⇒ [tex]-15-3 < 6p < 15-3[/tex]

⇒[tex]-18 < 6p < 12[/tex]

⇒[tex]\frac{-18}{6} < p < \frac{12}{6}[/tex]

⇒[tex]-3 < p < 2[/tex]

⇒ p ∈ (-3, 2)

Hence, the value of p for the given absolute value inequality |6p + 3|>15 lies in between - 3 and 2.

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Answer:

The population of China: 1.381 × 10^9=13.81 × 10^8

The population of the United States: 3.23 × 10^8

Total: 13.81 × 10^8 + 3.23 × 10^8 = (13.81 + 3.23) × 10^8 = 17.04 × 10^8

= 1.704 × 10^9

Step-by-step explanation:

The number of people living in both countries is an illustration of addition operation.

About [tex]\mathbf{17.04 \times 10^8}[/tex] people live in both countries

From the question, we have the following highlights

[tex]\mathbf{China = 1.381 \times 10^9}[/tex]

[tex]\mathbf{US = 3.23 \times 10^8}[/tex]

So, the population living in both countries is:

[tex]\mathbf{Total = China + US}[/tex]

Substitute known values

[tex]\mathbf{Total = 1.381 \times 10^9 + 3.23 \times 10^8}[/tex]

Factor out 10

[tex]\mathbf{Total = 1.381 \times 10 \times 10^8 + 3.23 \times 10^8}[/tex]

[tex]\mathbf{Total = 13.81 \times 10^8 + 3.23 \times 10^8}[/tex]

Factor out 10^8

[tex]\mathbf{Total = (13.81 + 3.23 )\times 10^8}[/tex]

[tex]\mathbf{Total = 17.04 \times 10^8}[/tex]

Hence, about [tex]\mathbf{17.04 \times 10^8}[/tex] people live in both countries

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A music teaching system that is used to engage students more in music practice. The music teacher needs a ladder system to teach high notes to students.

Therefore, the music teacher needs a ladder system to teach high notes to students.

Learn more about the Musical Ladder System:

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To make 6 dozen cookies, you will need 2 1/2 cups of flour.

To find out how many cups of flour are needed to make 6 dozen cookies, we can set up a proportion:

1 2/3 cups / 4 dozen cookies = x cups / 6 dozen cookies

Cross multiplying, we get:

4 dozen cookies * x cups = 1 2/3 cups * 6 dozen cookies

Simplifying, we find that x cups = (1 2/3 cups * 6 dozen cookies) / 4 dozen cookies

Therefore, x cups = 2 1/2 cups

Final answer:

To make 6 dozen cookies, you would need 2.5 cups of flour.

Explanation:

To find out how many cups of flour are needed to make 6 dozen cookies, we can set up a proportion using the given information. We know that 1 2/3 cups of flour are needed to make 4 dozen cookies. So we can set up the proportion:

1 2/3 cups / 4 dozen = x cups / 6 dozen

To solve for x, we can cross multiply and then divide:

(1 2/3 cups) * (6 dozen) = (4 dozen) * x cups

(5/3) * (6) = (4) * x

30/3 = 4x

10 = 4x

x = 10/4 = 2.5

Therefore, you would need 2.5 cups of flour to make 6 dozen cookies.

The equation of the line will be y = ( 2 / 3 )x -2. The correct option is B.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Given that the line in the image has the points ( 3, 0 ) and ( 0,-2). The equation of the line will be calculated by finding the slope and the y-intercept of the line.

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2 - 0 )/ ( 0 - 3 )

Slope = ( 2 / 3 )

y = mx + c

-2 = m 9 0 ) + c

c = - 2

The equation of the line will be written as:-

y = mx + c

y = ( 2 / 3 )x - 2

Therefore, the equation of the line will be y = ( 2 / 3 )x -2. The correct option is B.

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Trey can expect to make approximately 30 out of 75 free throw shots based on his previous success rate of 12 out of 30 shots.

To find how many free throws Trey might make out of 75 attempts, we use the proportion of his successful shots in the initial 30 attempts. Trey made 12 out of 30 shots, which is a success rate of  [tex]\( \frac{12}{30} = \frac{2}{5} \).[/tex] We can expect him to maintain this rate over 75 shots:

[tex]\[ \text{Expected shots made} = \left( \frac{2}{5} \right) \times 75 = \frac{2 \times 75}{5} = 30 \][/tex]

Therefore, Trey can expect to make approximately 30 free throws out of 75 attempts. This estimation assumes his skill level and shooting conditions remain consistent throughout the attempts.

This calculation is a basic projection and doesn't account for potential variations in Trey's performance. Factors such as fatigue, practice, and pressure can influence his actual performance. However, it provides a reasonable estimate based on his past performance.

Using this estimate, coaches or analysts can make rough predictions about Trey's potential scoring contribution from free throws in a game or practice session, helping them plan strategies accordingly.

The commutative property of addition allows us to rearrange the order of terms without changing the sum. Demonstrating this property makes simplifying expressions easier by rearranging terms.

The commutative property of addition states that changing the order of the numbers being added does not change the sum. In the expression (-3 + i) + (18 + 5i), we can demonstrate the use of the commutative property in the first step by rearranging the terms as (-3 + 18) + (i + 5i).

Simplifying further, we get 15 + 6i as the result after applying the commutative property of addition.

Answer:

The table shows the number of badges earned, based on the number of boxes of cards sold.

Let b(x) represents the number of badges earned and x represents the  number of boxes of cards sold.

Given that:

[tex]b(20) = 3[/tex]

here, x = 20 number of boxes of cards sold

and

b(20) represents the number of badges earned or we can say that the number of badges earned is 3.

Therefore, b(20) = 3 mean in terms of the problem is that you sell 20 boxes you will get 3 badges

Final answer:

The median is the best measure of center for the teacher to use to evaluate the overall performance of the class on a test when the data set includes an outlier.

Explanation:

The most appropriate measure of center for the teacher to use in this situation is the median. This is because the median is the best measurement when a data set contains outliers or extreme values that could significantly skew the mean. Since the dataset contains a student score that is significantly lower due to not following instructions, the median would provide a more accurate idea of how the class as a whole performed, as it is less affected by this outlier. On the other hand, the mode might not be as informative if most of the scores are unique, and the mean would be substantially affected by the low score. The range is a measure of spread, not center, and therefore not suitable for determining the average performance.

this is the correct answer

Answer:

statement A, C, D, are true.

Step-by-step explanation:

We check all the statements by the rule of 72 to find which statement about doubling an investment are true.

Formula we use = [tex]\frac{72}{R}[/tex]  R = Rate of interest

Statement A :

An investment of $5,000 will double in 6 years at an annual compound interest rate of 12%.

 [tex]\frac{72}{12}[/tex] = 6 years

It will take 6 years to double the investment. This statement is true.

Statement B :

An investment of $1000 will double at an annual compound interest rate of 18% in 6 years.

[tex]\frac{72}{18}[/tex] = 4 years

It will take 4 years to double the investment. This statement is not true.

Statement C:

An investment of $350 will double in 9 years at a compound interest rate of 8%.

[tex]\frac{72}{8}[/tex] = 9 years

It will take 9 years to double the investment. This statement is true.

Statement D :

An investment of $2000 will double at a simple interest rate of 5% in 20 years.

Formula for Simple interest = (PRT)

                                           I  = (2000 × 0.05 × 20) = $2000

So the amount will be 4000 in 20 years. This statement is true.

Statement E :

An investment of  $700 will double in 12 years at a simple interest rate of 6%

Interest = ( 700 × 0.06 × 12 ) = $504

Amount after 12 years 700 + 504 = $1204. This statement is not true.

Answer: Shakira bowled 4 games.

Step-by-step explanation:

Hi, the total cost for Shakira (21) is equal to the multiplication of the price of each game of bowl  (4.75) and the number of games bowled (g), plus the cost of the shoes rental (3).

3 + 4.75 g = 21

Solving for g:

4.75 g = 21-3

4.75 g = 18

g= 18/4.75

g = 3.78 = 4 games (rounded)

Feel free to ask for more if needed or if you did not understand something.

add the 2 sets of numbers

-5 +-7 = -12

-3 +-1 = -4

 Answer is B