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2 years ago

William has 32 coins that are all either quarters or dimes. The coins have a value of $5.00. How many dimes does William have?

Mathematics

1 answer:

Arte-miy333 [17]2 years ago

5 0

Answer:

Step-by-step explanation:

d + q = 32

.10d + .25q = 5.00

d + q = 32

10d + 25q = 500

-10d - 10q = -320

10d + 25q = 500

15q = 180

q= 12 quarters

d + 12 = 32

d = 20 dimes

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Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the followin

svp [43]

Answer:

a) 1+2+3+4+...+396+397+398+399=79800

b) 1+2+3+4+...+546+547+548+549=150975

c) 2+4+6+8+...+72+74+76+78=1560

Step-by-step explanation:

We know that a summation formula for the first n natural numbers:

1+2+3+...+(n-2)+(n-1)+n=\frac{n(n+1)}{2}

We use the formula, we get

a) 1+2+3+4+...+396+397+398+399=\frac{399·(399+1)}{2}=\frac{399· 400}{2}=399· 200=79800

b) 1+2+3+4+...+546+547+548+549=\frac{549·(549+1)}{2}=\frac{549· 550}{2}=549· 275=150975

c)2+4+6+8+...+72+74+76+78=S / ( :2)

1+2+3+4+...+36+37+38+39=S/2

\frac{39·(39+1)}{2}=S/2

\frac{39·40}{2}=S/2

39·40=S

1560=S

Therefore, we get

2+4+6+8+...+72+74+76+78=1560

5 0

2 years ago

A cement bridge post is 24 inches square and 15 feet 9 inches in length. If the cement weighs 145 pounds per cubic foot, how muc

lisov135 [29]

Answer:

The answer is option (C), One cement bridge post weighs 9,135 pounds

Step-by-step explanation:

Step 1: Get the total volume of a cement bridge post

The cement bridge post is in the shape of a cuboid, therefor the volume of the cement bridge post can be expressed as;

Volume of cement bridge post=Base area×Length

where;

Base area=(24^2) inches square

1 foot=12 inches

Convert 24 inches to foot=24/12=2^2=4 feet²

Length=15 feet and 9 inches

1 foot=12 inches

Convert 9 inches to foot=9/12=0.75 feet

Total length=(15+0.75)=15.75 feet

replacing;

Volume of cement bridge post=(4×15.75)=63 cubic feet

Volume of cement bridge post=63 cubic feet

Step 2: Get the total weight of the cement bridge post

Total weight of the cement bridge post=Weight per cubic foot×total volume of the cement bridge post

where;

Weight per cubic foot=145 pounds per cubic foot

Total volume of the cement bridge post=63 cubic feet

replacing;

Total weight of the cement bridge post=(145×63)=9,135 pounds

One cement bridge post weighs 9,135 pounds

8 0

2 years ago

22 customers are eating dinner at an Italian restaurant. Of the 22 customers, 18 order pizza, 10 order a salad, and 8 order pizz

Ne4ueva [31]

Answer:

Step-by-step explanation:

P(A) = 18/22

P(B) = 10/22

P(A and B) = 8/22

P(A or B) = 18/22 * 10/22 = 0.37

4 0

2 years ago

Chris tried to rewrite the expression \left( 4^{-2} \cdot 4^{-3} \right)^{3}(4

crimeas [40]

We have been given an expression $\left( 4^{-2} \cdot 4^{-3} \right)^{3}$ . We have been given steps how Chris tried to solve the given expression. We are asked to choose the correct option about Chris's work.

Let us simplify our given expression.

Using exponent property, $a^m\cdot a^n=a^{m+n}$ , we cab rewrite our given expression as:

$\left( 4^{-2+(-3)} \right)^{3}$

$\left( 4^{-5} \right)^{3}$

Now we will use exponent property $(a^m)^n=a^{m\cdot n}$ to further simplify our expression.

$\left( 4^{-5} \right)^{3}= 4^{-5\cdot 3}$

$\left( 4^{-5} \right)^{3}= 4^{-15}$

Therefore, Chris made mistake in step 2.

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2 years ago

How is a calculation of net worth different from a day-to-day or month-to-month tallying of expenses?

alina1380 [7]

The difference in tallying of expenses from a day to day and month to month is the consistency. in a day to day basis it is consistent the time for a day is 24 hrs it will not change, so you will really know why the expenses goes up or down/ unlike for a month to month it is inconsistent,, some months have 30, 31 or 28 days in a month.

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2 years ago