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3 years ago

Use decimals to answer the question what is 6% of 225

Mathematics

2 answers:

ElenaW [278]3 years ago

8 0

Answer:

13.5

Step-by-step explanation:

(Are you meaning this as the answer is a decimal?)

3/50 * 225/1

Cross-cancel 50 and 225 by cancelling out 25.

3/2 * 9/1

Rewrite this so it is a single fraction.

(3 * 9)/2

Multiply 3 by 9 to get 27.

27/2

Divide 27 by 2 to get 13.5.

13.5

6% of 225 is 13.5.

Taya2010 [7]3 years ago

3 0

The answer for 6 percent of 225 is 13.5

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Sindrei [870]

Answer:

Step-by-step explanation:

to solve this problem we can use the Pythagorean theorem

UT and TL are the legs, while LU is the hypotenuse

We have to find LU so we can proceed like this

x^2 + (x+1)^2 = LU^2

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$\sqrt{2x^2+2x+1}$

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2 years ago

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RideAnS [48]

Answer:

P(X<1200) is 0.8212

Step-by-step explanation:

Test statistic (z) = (X - mean)/sd

X is score of a tester = 1200

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sd = 322

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The cumulative area of the test statistic is the probability that X<1200. The cumulative area is 0.8212.

Therefore, P(X<1200) = 0.8212

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3 years ago

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Which expression is equivalent to the expression below?

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Step-by-step explanation:

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Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly samp

aleksklad [387]

Answer:

95.44% probability the resulting sample proportion is within .04 of the true proportion.

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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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.

For the sampling distribution of the sample proportion in sample of size n, the mean is $\mu = p$ and the standard deviation is $s = \sqrt{\frac{p(1-p)}{n}}$

In this question:

$p = 0.2, n = 400$

$\mu = 0.2, s = \sqrt{\frac{0.2*0.8}{400}} = 0.02$

How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?

This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16.

X = 0.24

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By the Central Limit Theorem

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

$Z = \frac{0.24 - 0.2}{0.02}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

X = 0.16

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

$Z = \frac{0.16 - 0.2}{0.02}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

95.44% probability the resulting sample proportion is within .04 of the true proportion.

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3 years ago

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vitfil [10]

Answer:

a) The minimum head breadth that will fit the clientele = 4.105 inches to 3d.p = 4.1 inches to 1 d.p

b) The maximum head breadth that will fit the clientele = 8.905 inches to 3 d.p = 8.9 inches to 1 d.p

Step-by-step explanation:

This is normal distribution problem.

A normal distribution has all the data points symmetrically distributed around the mean in a bell shape.

For this question, mean = xbar = 6.1 inches

Standard deviation = σ = 1 inch

And we want to find the lowermost 2.3% and uppermost 2.3% of the data distribution.

The minimum head breadth that will fit the clientele has a z-score with probability of 2.3% = 0.023

Let that z-score be z'

That is, P(z ≤ z') = 0.023

Using the table to obtain the value of z'

z' = - 1.995

P(z ≤ - 1.995) = 0.023

But z-score is for any value, x, is that value minus the mean then divided by the standard deviation.

z' = (x - xbar)/σ

- 1.995 = (x - 6.1)/1

x = -1.995 + 6.1 = 4.105 inches

The maximum head breadth that will fit the clientele has a z-score with probability of 2.3% also = 0.023

Let that z-score be z''

That is, P(z ≥ z'') = 0.023

Using the table to obtain the value of z''

P(z ≥ z") = P(z ≤ -z")

- z'' = - 1.995

z" = 1.995

P(z ≥ 1.995) = 0.023

But z-score is for any value, x, is that value minus the mean then divided by the standard deviation.

z'' = (x - xbar)/σ

1.995 = (x - 6.1)/1

x = 1.995 + 6.1 = 8.905 inches

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3 years ago