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Ilia_Sergeevich [38]
3 years ago
11

Cherries cost $5 for 2 pounds and $7.50 for 3 pounds. Question: a. What is the cost per pound? b. Is it constant? c. If you were

to graph this situation, would you put weight or cost on the x-axis? Which one would you put on the y-axis? d. Plot the two points described. e. How much would 5 pounds of cherries cost? What did you do to solve this problem?
Mathematics
1 answer:
Fittoniya [83]3 years ago
8 0
A. 1 pound of cherries costs 2.50

B. Yes it is constant

C. I believe that you would put cost on the y and lbs on the x
E. 5 lbs of cherries = 2.50 x 5 = $12.50

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Riley is saving up to buy a new television. She needs a total of $1,049.77. Riley has saved $200.79 already and earns $77.18 per
Xelga [282]

11 weeks are required for Riley to work to save enough money to buy the new television

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

Given that Riley needs a total of $1,049.77

Riley has saved $200.79 already and earns $77.18 per week at her job

To find: Number of weeks Riley need to work to save enough money to buy the new television

Remaining amount needed = $1,049.77 -  $200.79

Remaining amount needed = $ 848.98

Let "n" be the number of weeks Riley need to work to save enough money to buy the new television

Also she earns $77.18 per week at her job

1 week ⇒ $ 77.18

"n" weeks ⇒ $ 848.98

Therefore, by cross multiplication,

n \times 77.18 = 1 \times 848.98\\\\n = \frac{848.98}{77.18}\\\\n = 11

Therefore 11 weeks are required for her to work to save enough money to buy the new television

<h3><u>Method 2:</u></h3>

<em>Total amount = amount already saved + ($77.18 per week at her job)("n" weeks)</em>

1,049.77 = 200.79 + (77.18)(n)

1049.77 - 200.79 = 77.18n

848.98 = 77.18n

n = \frac{848.98}{77.18}

n = 11

Therefore 11 weeks are required for her to work to save enough money to buy the new television

5 0
3 years ago
A 26-inch pice of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third pie
Arisa [49]

your answer will be 2 inch for the first piece 4 inch for the second piece 20 inch for the last piece

6 0
3 years ago
7) PG &amp; E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many
BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>
5 0
2 years ago
0.75h + 3 = 12 <br> What's the answer?
kykrilka [37]

Answer:

h = 12

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

0.75h + 3 = 12

<u>Step 2: Solve for </u><em><u>h</u></em>

  1. Subtract 3 on both sides:                    0.75h = 9
  2. Divide 0.75 on both sides:                  h = 12

<u>Step 3: Check</u>

<em>Plug in h into the original equation to verify it's a solution.</em>

  1. Substitute in <em>h</em>:                    0.75(12) + 3 = 12
  2. Multiply:                               9 + 3 = 12
  3. Add:                                     12 = 12

Here we see that 12 does indeed equal 12.

∴ h = 12 is a solution of the equation.

5 0
3 years ago
Read 2 more answers
2. Carl pays $79.99 for a Disney Plus subscription every year. Because Carl
tensa zangetsu [6.8K]

Answer:

12.33

Step-by-step explanation:]

450-80=370/30=12.33

7 0
2 years ago
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