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oksano4ka [1.4K]
3 years ago
6

Suppose you have 20 coins that total $3.00. Some coins are nickels and some are quarters. Which of the following pairs of equati

ons would you use to find out how many of each coin you have?
Mathematics
1 answer:
kap26 [50]3 years ago
5 0

Answer:

Step-by-step explanation:

n + q = 20

.05n + .25q = 3.00

5n + 25q = 300

 n + q = 20

5n + 25q = 300

-5n - 5q = -100

20q = 200

q = 10 quarters

n + 10 = 20

n = 10 nickels

(10 nickels, 10 quarters)

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The local cable company charges $90 per month for basic and $12 per month for each additional premium cable channel.The function
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Answer:

2 additional premium channels

Step-by-step explanation:

Using the given function, we substitute c(x) = 114 and solve for x:

114 =90 + 12x

Subtract 90 from both sides:

24=12x

Divide both sides by 12:

2=x

So you have ordered 2 additional premium channels.

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3 years ago
The hypotenuse of a 30°-60°-90°
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The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b.
denis-greek [22]
\mathrm{gcd}(a,b)=9\implies9\mid a\text{ and }9\mid b\implies9\mid a+b

which means there is some integer k for which a+b=9k.


Because 9\mid a and 9\mid b, there are integers n_1,n_2 such that a=9n_1 and b=9n_2, and


\mathrm{lcm}(a,b)=\mathrm{lcm}(9n_1,9n_2)=9\mathrm{lcm}(n_1,n_2)=378\implies\mathrm{lcm}(n_1,n_2)=42

We have 42=2\cdot3\cdot7, which means there are four possible choices of n_1,n_2:

1, 42
2, 21
3, 14
6, 7

which is to say there are also four corresponding choices for a,b:

9, 378
18, 189
27, 126
54, 63

whose sums are:

387
207
153
117

So the least possible value of a+b is 117.
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Alan averages 10 hits out of 25 shots at the target. What is the chance that he will hit his next two attempts?
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