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MatroZZZ [7]
3 years ago
14

Evaluate the expression if m = 3. 3m^2 (SHOW YOUR WORK)

Mathematics
1 answer:
iragen [17]3 years ago
5 0

The value of given expression when m = 3 is 27

<h3><u>Solution:</u></h3>

Given expression is 3m^2

We have to evaluate the given expression for m = 3

To find for m is equal to 3, substitute m = 3 in given expression

From given expression,

\rightarrow 3m^2

Plug in m = 3 in above expression

\rightarrow 3(3)^2 ------ eqn 1

We know that,

a^2 can be expanded as,

a^2=a \times a

Applying this in eqn 1, we get

\rightarrow 3(3)^2=3 \times (3 \times 3)

Simplify the above expression

\rightarrow 3(3)^2=3 \times (3 \times 3) = 3 \times 9 = 27

Therefore, for m = 3 we get,

\rightarrow 3(3)^2=27

Thus value of given expression when m = 3 is found

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Nichole can play a video game where each round lasts 7/12 of an hour. She has scheduled 3 3/4 hours to play the game. How many r
Vladimir79 [104]

Answer:

6 3/7 of a round

Step-by-step explanation:

Total playing time hrs. ÷ each round = total rounds that can be played

3 3/4 = 15/4

15/4 ÷ 7/12

= 15/4 x 12/7

= 180/28

= 6 12/28

= 6 3/7 of a round

8 0
3 years ago
How many distinct set of three positive integers have a mean of 6, a medium of 7 no mode ?​
Natasha_Volkova [10]

Answer:

3 sets.

1 7 10

2 7 9

3 7 8.

Step-by-step explanation:

The sum must be 18 ( 3*6)  and 7  is the middle number ( the median).

So the first and last numbers must add up to 11  with the first number less than 7.  As there is no mode no number can be repeated.

So one set is 3 7 8    (the first number can't be 4 as the last number would have to be 7)

Others are 2 7 9,

1 7 10.

8 0
3 years ago
John inherited $25,000 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. Af
Lena [83]

Answer:

Step-by-step explanation:

Understand

Let :

x = The amount of money invested in the money market account.  

y = The amount of money invested in municipal bonds.  

z = The amount of money invested in a mutual fund.  

The total investment is represented as:

x + y + z = $25,000

The interest earned can be represented as:

0.06x + 0.07y + 0.08z = $1,620

The amount invested in municipal bonds and mutual funds can be represented as:

y - z = $6,000

Process

The system of three equations can now be solved either by substitution, elimination, or with matrices.  Any process appropriately applied will supply a correct answer.  For this example, let's solve the problem by using matrices.

Solving with Matrices

The process of using matrices is essentially a shortcut for the process of elimination. Each row of the matrix represents an equation, and each column represents coefficients of one of the variables.  

Step 1:        Create a three-row by four-column matrix using coefficients and the constant of each equation.

The vertical lines in the matrix stands for the equal signs between both sides of each equation. The first column contains the coefficients of x; the second column contains the coefficients of y; the third column contains the coefficients of z; the last column contains the constants.  

We want to convert the original matrix to the following matrix.

because you can then read the matrix as x = a, y = b, and z = c.

Step 2:        We work with column 1 first. The number 1 is already in cell 11(Row 1- Col 1).  

Add -0.06 times Row 1 to Row 2 to form a new Row 2.

-0.06 [Row 1] + [Row 2] = [New Row 2]

Step 3:        We will now work with column 1. We want 1 in Cell 22, and we achieve this by multiplying Row 2 by 100.

100[Row 2] = [New Row 2]

Step 4:        Let's now manipulate the matrix so that there are zeros in Cell 12 and Cell 32. We do this by adding Row 2 to Row 1 and Row 3 to Row 2. That gives us a new Row 1 and a new Row 3.

- [Row 2] + [Row 1] = [New Row 1]

- [Row 2] + [Row 3] = [New Row 3]

Step 5:        Let's now manipulate the matrix so that there is a 1 in Cell 33. We do this by multiplying Row 3 by -1.

-1 [Row 3] = [New Row 3]

Step 6:        Let's now manipulate the matrix so that there are zeros in Cell 13 and Cell 23. We do this by adding Row 3 to Row 1 for a new Row 1 and adding -2 times Row 3 to Row 2 for a new Row 3.  

1[Row 3] + [Row 1] = [New Row 1]

-2[Row 3] + [Row 2] = [New Row 2]

Solution

You can now read the answers off the matrix:

x = $15,000 in the money market

y = $8,000 in municipal bonds

z = $2,000 in a mutual fund

6 0
3 years ago
The temperature is at -2 F at 6A.M. During the next three hours, the temperature increases to 15F. What is the temperature at 9A
egoroff_w [7]

Answer:

Temperature at 9 A.M =  13° F

Step-by-step explanation:

Given:

Temperature at 6 A.M = - 2° F

Temperature increases in 3 hours =  15° F

Find:

Temperature at 9 A.M

Computation:

Temperature at 9 A.M = Temperature at 6 A.M + Temperature increases in 3 hours

Temperature at 9 A.M =  - 2° F + 15° F

Temperature at 9 A.M =  13° F

6 0
3 years ago
1) 17, 29, 32, 9, 30, 14, 8, 39, 11, 32, 23<br> Minimum :<br> Maximum:<br> Q1:<br> Q2:<br> Q3:
Lisa [10]

Answer:

Minimum: 8

Maximum: 39

Q1: 11

Q2: 23

Q3: 32

Step-by-step explanation:

Set the numbers into numerical order

8 9 11 14 17 23 29 30 32 32 39

Then separate into quarters

[8 9 11] [14 17 23] [29 30 32] 32 39

6 0
3 years ago
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