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2 years ago

Simplify: −6(1/4 x - 2/3 x + 5/6 x) A) -2 1/2 x B) -x C) 2x D) 3/4 x

Mathematics

1 answer:

horrorfan [7]2 years ago

5 0

Answer:

(-5 x)/2

Step-by-step explanation:

Simplify the following:

-6 (x/4 - (2 x)/3 + (5 x)/6)

Put each term in x/4 - (2 x)/3 + (5 x)/6 over the common denominator 12: x/4 - (2 x)/3 + (5 x)/6 = (3 x)/12 - (8 x)/12 + (10 x)/12:

-6(3 x)/12 - (8 x)/12 + (10 x)/12

(3 x)/12 - (8 x)/12 + (10 x)/12 = (3 x - 8 x + 10 x)/12:

-6(3 x - 8 x + 10 x)/12

The gcd of -6 and 12 is 6, so (-6 (3 x - 8 x + 10 x))/12 = ((6 (-1)) (3 x - 8 x + 10 x))/(6×2) = 6/6×(-(3 x - 8 x + 10 x))/2 = (-(3 x - 8 x + 10 x))/2:

(-1 (3 x - 8 x + 10 x))/2

3 x - 8 x + 10 x = 5 x:

Answer: (-5 x)/2

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Mario invests £2000 for 3 years at 5% per annum compound interest. Calculate the value of the investment at the end of 3 years.

Delicious77 [7]

Answer:

$2315.25

Step-by-step explanation:

Given data

Principal= £2000

Time= 3 years

Rate= 5%

The compound interest expression is

A= P(1+r)^t

substitute

A= 2000(1+0.05)^3

A= 2000(1.05)^3

A= 2000*1.157625

A= 2315.25

Hence the Amount is $2315.25

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2 years ago

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t

skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

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 establishes 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.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that $\mu = 273, \sigma = 100$

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 30, s = \frac{100}{\sqrt{30}}$

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}$

$Z = 0.88$

$Z = 0.88$ has a p-value of 0.8106

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}$

$Z = -0.88$

$Z = -0.88$ has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 50, s = \frac{100}{\sqrt{50}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}$

$Z = 1.13$

$Z = 1.13$ has a p-value of 0.8708

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}$

$Z = -1.13$

$Z = -1.13$ has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 100, s = \frac{100}{\sqrt{100}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}$

$Z = 1.6$

$Z = 1.6$ has a p-value of 0.9452

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}$

$Z = -1.6$

$Z = -1.6$ has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

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2 years ago

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3 years ago

A concrete slab 4 inches deep will be poured for the floor of greenhouse A. How many cubic feet of concretar are needed for the

Mars2501 [29]

This question is incomplete

Complete Question

Consider greenhouse A with floor dimensions w = 16 feet , l = 18 feet.

A concrete slab 4 inches deep will be poured for the floor of greenhouse A. How many cubic feet of concrete are needed for the floor?

Answer:

96 cubic feet

Step-by-step explanation:

The volume of the floor of the green house = Length × Width × Height

We convert the dimensions in feet to inches

1 foot = 12 inches

For width

1 foot = 12 inches

16 feet = x

Cross Multiply

x = 16 × 12 inches

x = 192 inches

For length

1 foot = 12 inches

18 feet = x

Cross Multiply

x = 18 × 12 inches

x = 216 inches

The height or depth = 4 inches deep

Hence,

Volume = 192 inches × 216 inches × 4 inches

= 165888 cubic inches

From cubic inches to cubic feet

1 cubic inches = 0.000578704 cubic foot

165888 cubic inches = x

Cross Multiply

x = 16588 × 0.000578704 cubic foot

x = 96 cubic feet

Therefore, 96 cubic feet of concrete is needed for the floor

8 0

3 years ago