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3 years ago

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Mathematics

1 answer:

Shtirlitz [24]3 years ago

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LETTER =c 62.3
Sorry if it’s wrong

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A cash box contains $74 made up of quarters, half-dollars, and one-dollar

Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

$0.25q+0.50h+1.00d=74$

$\displaystyle{h=\frac{3}{5}d+1}$

$q=4(d+h)$

Then, substitute q in the first equation with the expression from the third equation:

$0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74$

Next, substitute h in that equation with the expression from the second equation:

$\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}$

$2d+0.9d+1.5=74\\2.9d+1.5=74$

Solve for d, the number of one-dollar coins:

$2.9d+1.5=74\\2.9d=72.5\\d=25$

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{h=\frac{3}{5}(25)+1}$

$h=15+1\\h=16$

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

$q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164$

Then, verify that the coins total $74:

$0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}$

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{16=\frac{3}{5}(25)+1}$

$16 = 15 + 1\\16 = 16\\\text{Check.}$

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

$q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}$

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3 years ago

What number is 20% of 40?

VladimirAG [237]

Answer:

It would be 8

Step-by-step explanation:

20% of 40 is 8

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Anelle subtracts –4 from a number. The result is 2. What is the number? –6 –2 2 6

Lynna [10]

Answer:

the answer is 2. so it is 2

Step-by-step explanation:

2 ➕ 2 is 4

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16=5y/3 HELLLPPP PLSSSS

Lunna [17]

Answer:

y = 9.6

Step-by-step explanation:

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The number of flaws per square yard in a type of carpet material varies with mean 1.4 flaws per square yard and standard deviati

oksian1 [2.3K]

According to the Central Limit Theorem, the distribution of the sample means is approximately normal, with the mean equal to the population mean (1.4 flaws per square yard) and standard deviation given by:
$\frac{\sigma}{ \sqrt{n} }=\frac{1.2}{ \sqrt{178} }=0.09$
The z-score for 1.5 flaws per square yard is:
$z=\frac{1.5-1.4}{0.09}=1.11$
The cumulative probability for a z-score of 1.11 is 0.8665. Therefore the probability that the mean number of flaws exceeds 1.5 per square yard is
1 - 0.8665 = 0.1335.

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