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valkas [14]
3 years ago
10

How many ways can change be made for a quarter using standard u.s. coins? (don't count "1 quarter" as making change for a quarte

r.)?
Mathematics
2 answers:
AveGali [126]3 years ago
5 0
25 pennies, 2 dimes and 5 pennies, 2 dimes and 1 nickel, 4 nickels.
neonofarm [45]3 years ago
4 0
There are 12 different ways to make change for a quarter without using a quarter itself.

A penny is worth 1 cent, a nickel is worth 5 cents, and a dime is worth 10 cents. With these values, the following combinations of coins will make change for a quarter, which is 25 cents:

Order: pennies, nickels, dimes

-
(1) 25 pennies

(2) 20 pennies, 1 nickel

(3) 15 pennies, 2 nickels
(4) 15 pennies, 1 dime

(5) 10 pennies, 3 nickels
(6) 10 pennies, 1 nickel, 1 dime

(7) 5 pennies, 4 nickels
(8) 5 pennies, 2 nickels, 1 dime
(9) 5 pennies, 2 dimes

(10) 5 nickels
(11) 3 nickels, 1 dime
(12) 1 nickel, 2 dimes

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A square has an area of 81 square inches. What is its perimeter?
disa [49]

Area of square = s^2 where, s is the side length of the square.

81=s^2

9=s

s must be positive since it is a side length, so the negative root of 81 is rejected.

Perimeter= 4s

Perimeter= 4(9)=36inches

7 0
2 years ago
Read 2 more answers
Find the general term of {a_n}
Assoli18 [71]

From the given recurrence, it follows that

a_{n+1} = 2a_n + 1 \\\\ a_{n+1} = 2(2a_{n-1} + 1) = 2^2a_{n-1} + 1 + 2 \\\\ a_{n+1} = 2^2(2a_{n-2}+1) + 1 + 2 = 2^3a_{n-2} + 1 + 2 + 2^2 \\\\ a_{n+1} = 2^3(2a_{n-3} + 1) + 1 + 2 + 2^2 = 2^4a_{n-3} + 1 + 2 + 2^2 + 2^3

and so on down to the first term,

a_{n+1} = 2^na_1 + \displaystyle \sum_{k=0}^{n-1}2^k

(Notice how the exponent on the 2 and the subscript of <em>a</em> in the first term add up to <em>n</em> + 1.)

Denote the remaining sum by <em>S</em> ; then

S = 1 + 2 + 2^2 + \cdots + 2^{n-1}

Multiply both sides by 2 :

2S = 2 + 2^2 + 2^3 + \cdots + 2^n

Subtract 2<em>S</em> from <em>S</em> to get

S - 2S = 1 - 2^n \implies S = 2^n - 1

So, we end up with

a_{n+1} = 4\cdot2^n + S \\\\ a_{n+1} = 2^2\cdot2^n + 2^n-1 \\\\ a_{n+1} = 2^{n+2} + 2^n - 1 \\\\\implies \boxed{a_n = 2^{n+1} + 2^{n-1} - 1}

5 0
3 years ago
EASY points here Solve for H; P=2L+2H
e-lub [12.9K]
P=2L+2H
First, isolate 2H:
2H=P-2L
Second, get a singular value of H (just H):
2H/2=(P-2L)/2

Final answer: 

H=\frac{P-2L}{2}
7 0
3 years ago
Read 2 more answers
The same number of people live on the islands Beautiful Sunrise and Gorgeous
aev [14]

Using the percentage concept, it is found that 75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.

<h3>What is a percentage?</h3>

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = \frac{a}{b} \times 100\%

In this problem, we have that:

  • We consider that the population of both Beautiful Sunrise and Gorgeous Sunset islands is of x.
  • There is a fiesta at Beautiful Sunrise, and a number a of people from Gorgeous Sunset are coming, hence, there will be x + a people at Beautiful Sunrise and x - a people t Gorgeous Sunset.

The percentage of people from Gorgeous Sunset is on Beautiful Sunrise now is:

P = \frac{a}{x} \times 100\%

Now the number of people on Beautiful Sunrise is seven times the number of people on Gorgeous Sunset, hence:

\frac{x + a}{x - a} = 7

We can find a <u>as a function of x</u> to find the percentage:

\frac{x + a}{x - a} = 7

7(x - a) = x + a

7x - 7a = x + a

8a = 6x

a = \frac{3x}{4}

Then, the percentage is:

P = \frac{a}{x} \times 100\%

P = \frac{\frac{3x}{4}}{x} \times 100\%

P = \frac{3}{4} \times 100\%

P = 75\%

75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.

You can learn more about the percentage concept at brainly.com/question/10491646

7 0
2 years ago
Read the following description of a relationship: Anne's shower uses 15 liters of water per minute. Let m represent the number o
ki77a [65]

Answer:

105

Step-by-step explanation:

m= minutes

Minutes*15= Whole water

m*15=w

7*15=105

3 0
3 years ago
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