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2 years ago

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Susan has 4 times as many quarters as dimes and 16 less dimes than nickels. If she has $13.45 in coins. How many of each coin do

es she have?
Help pls

1 answer:

Maslowich2 years ago

4 0

Using a system of equations, it is found that Susan had 44 quarters, 11 dimes and 27 nickels.

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

We are going to use:

x as the number of quarters.
y as the number of dimes.
z as the number of nickels.

A <em>quarter </em>is worth $0.25. A <em>dime </em>is worth $0.1, and a <em>nickel </em>is worth $0.05. Total of $13.45, then:

$0.25x + 0.1y + 0.05z = 13.45$

4 times as many <u>quarters as dimes</u>, thus:

$x = 4y \rightarrow y = 0.25x$

16 less <u>dimes than nickels</u>, thus:

$z = y + 16 = 0.25x + 16$

Replacing in the first equation, we find x:

$0.25x + 0.1y + 0.05z = 13.45$

$0.25x + 0.1(0.25x) + 0.05(0.25x + 16) = 13.45$

$0.2875x = 12.65$

$x = \frac{12.65}{0.2875}$

$x = 44$

Now, with x, we find y and z:

$y = 0.25x = 0.25(44) = 11$

$z = y + 16 = 11 + 16 = 27$

Susan had 44 quarters, 11 dimes and 27 nickels.

A similar problem is given at brainly.com/question/24342899

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The price of an item yesterday was 135 . Today, the price fell to 54. Find the percentage decrease.

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Answer:

60%

Step-by-step explanation:

135-60%=54

so therefore the price fell to 54 and was 60% off!

Hope this helped!

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3 years ago

Read 2 more answers

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal prob

Novay_Z [31]

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that $\mu = 36, \sigma = 5.5$

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that $n = 9$ . So

$s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333$

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{38 - 36}{1.8333}$

$Z = 1.09$

$Z = 1.09$ has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{34.5 - 36}{1.8333}$

$Z = -0.82$

$Z = -0.82$ has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

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3 years ago

Need help on these asap please

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9.6958 rounded to the nearest hundredth is 9.70
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2 years ago

5. Kamala worked for 7 1/2 h. She spent 2/3 of the time on her computer. How long was she on her computer?

Lina20 [59]

Answer:

5 hrs

Step-by-step explanation:

7 1/2 hours equates to 450 minutes total

2/3 of 450 = 300 total minutes

turning the minutes back into hours, 300 / 60 = <u>5</u>

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2 years ago

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a famer has 120 feet of fencing with whcih to enclose two adjacent rectangular pens as shown. what dimeensions should be used th

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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

or, y = 2x (40 - 4/3 x)

or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height = 40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

To learn more about area visit:

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6 0

1 year ago