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2 years ago

Which number is equivalent to 2^−5⋅ 3 ⋅ 2^2 ⋅ 3^3? A. 648 B. 216 C. 81/8 D. 27/8

1 answer:

3 0

$2^{-5} \cdot 3 \cdot 2^2 \cdot 3^3\\\\=2^{-5 +2} \cdot 3^{1+3}\\\\=2^{-3} \cdot 3^4\\\\=\dfrac{3^4}{2^3}\\\\=\dfrac{81}{8}\\\\\\\text{So, the answer is C.}$

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Cottage cheese is being sold in different size containers. The sizes and prices are given below: 4 - 5 ounce containers for $5.

Karolina [17]

Division is the process of finding the number of times a number is multiplied by itself. The 16-ounce container is the better buy.

<h3>What is Division?</h3>

The division is the process of finding the number of times a number is multiplied by itself.

The prices of the different size containers are given to us,

4-5 ounce containers for $5. 00

1-12 ounce container for $3. 24

1-16 ounce container for $4. 19

Now, find the cost of the cheese per ounce when we buy the minimum cheese and when we but the maximum amount of cheese.

1. For the first Container, 4-5 ounce containers for $5.00

If we buy 4 ounces of cheese, then the cost of each ounce of cheese will be $1.25 for each ounce, while if we buy the maximum amount of cheese therefore 5 ounces for $5 then the cost of each ounce of cheese will be $1.

2. For, the second container, 1-12 ounce container for $3.24

If we buy 1 ounce of cheese, then the cost of each ounce of cheese will be $3.24 for each ounce, while if we buy the maximum amount of cheese therefore 5 ounces for $5 then the cost of each ounce of cheese will be $0.27.

3. For, the third container, 1-16 ounce container for $4.19.

If we buy 1 ounce of cheese, then the cost of each ounce of cheese will be $4.19 for each ounce, while if we buy the maximum amount of cheese therefore 16 ounces for $4.19 then the cost of each ounce of cheese will be $0.26.

Thus, if we buy the maximum amount of cheese from each of the boxes, the third box will be the cheapest.

Hence, The 16-ounce container is the better buy.

Learn more about Division:

brainly.com/question/369266

3 0

2 years ago

2.Solve the system using substitution.

Lena [83]

2x+2y=38
y=x+3

First you would substitute the y for x+3
2x+2(x+3)=38

You would multiply the 2 by the x+3
2x+2x+6=38

Add the 2x and the 2x
4x+6=38

Subtract the 6 on both sides
4x=32

Divide the 4 on both sides
x=8

Now substitute the x in the second problum for 8
y=8+3

Add the 8 and the 3 to solve for y
y=11

Your answers
x=8
y=11
the correct answer would be A:(8,11)

3 0

2 years ago

State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A firm makes

Sedbober [7]

Answer:

Maximum profit at (3,0) is $27.

Step-by-step explanation:

Let quantity of products A=x

Quantity of products B=y

Product A takes time on machine L=2 hours

Product A takes time on machine M=2 hours

Product B takes time on machineL= 4 hours

Product B takes time on machine M=3 hours

Machine L can used total time= 8hours

Machine M can used total time= 6hours

Profit on product A= $9

Profit on product B=$7

According to question

Objective function Z= $9x+7y$

Constraints:

$2x+3y\leq 6$

$2x+4y\leq 8$

Where $x\geq 0, y\geq 0$

I equation $2x+3y\leq 6$

I equation in inequality change into equality we get

$2x+3y=6$

Put x=0 then we get

y=2

If we put y=0 then we get

x= 3

Therefore , we get two points A (0,2) and B (3,0) and plot the graph for equation I

Now put x=0 and y=0 in I equation in inequality

Then we get $0\leq 6$

Hence, this equation is true then shaded regoin is below the line .

Similarly , for II equation

First change inequality equation into equality equation

we get $2x+4y=8$

Put x= 0 then we get

y=2

Put y=0 Then we get

x=4

Therefore, we get two points C(0,2)a nd D(4,0) and plot the graph for equation II

Point A and C are same

Put x=0 and y=0 in the in inequality equation II then we get

$0\leq 8$

Hence, this equation is true .Therefore, the shaded region is below the line.

By graph we can see both line intersect at the points A(0,2)

The feasible region is AOBA and bounded.

To find the value of objective function on points

A (0,2), O(0,0) and B(3,0)

Put A(0,2)

Z= $9\times 0+7\times 2=14$

At point O(0,0)

Z=0

At point B(3,0)

Z= $9\times3+7\times0=27$

Hence maximum value of z= 27 at point B(3,0)

Therefore, the maximum profit is $27.

6 0

3 years ago

it costs $36.75 for 3 tickets to visit the science center. it costs $51 for 4 tickets to visit the zoo. which attraction will co

lord [1]

Find the cost for one ticket for the science center.

36.75 ÷ 3 = 12.25

Multiply the product with 12 to get the cost of 12 tickets.

12.25 × 12 = 147

Find the cost of 1 zoo ticket.

51 ÷ 4 = 12.75

Find the cost of 12 tickets by multiplying the product and 12

12.75 × 12 = $153

12 Science Center Tickets cost $147

12 zoo tickets cost $153

The <u><em>Zoo</em></u> costs more than the Science Center.

To find out how much more the Zoo costed, subtract 147 from 153.

153 - 147 = 6

The zoo only costs <u><em>$6 </em></u>more for 12 students.

So, you're answers are Zoo and $6

5 0

3 years ago

Read 2 more answers

Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need

Archy [21]

Method 1:

$\begin{array}{ccc}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}\\\\1\dfrac{1}{2}=\dfrac{3}{2}\ \text{cup of corn}&-&x\ \text{cup of water}\end{array}\qquad\text{cross multiply}\\\\\\\dfrac{1}{4}\cdot x=\dfrac{3}{2}\cdot\dfrac{1}{2}\\\\\dfrac{1}{4}x=\dfrac{3}{4}\qquad\text{multiply both sides by 4}\\\\\boxed{x=3}$

<h3>Answer: Henry will need 3 cups of water.</h3>

Method 2:

$\begin{matrix}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}&|\text{multiply both sides by 2}\\\\\dfrac{1}{2}\ \text{cup of corn}&-&1\ \text{cup of water}&|\text{multiply both sides by 2}\\\\1\ \text{cup of corn}&-&2\ \text{cup of water}&|\end{matrix}$

$\begin{matrix}\left(\dfrac{1}{2}+1\right)\ \text{cups of corn}&-&(1+2)\ \text{cups of water}\\\\1\dfrac{1}{2}\ \text{cups of corn}&-&3\ \text{cups of water}\end{matrix}$

<h3>Answer: Henry will need 3 cups of water.</h3>

5 0

3 years ago

Read 2 more answers