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Allushta [10]
3 years ago
6

Determine whether the following number is an integer. 692 A. yes B. no

Mathematics
2 answers:
dsp733 years ago
8 0
A. Yes it is an integer
kirill115 [55]3 years ago
4 0
Yes as it has no decimal place
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Mai put $4,250 in the bank for a rate of 4% simple interest per year. After
Nataly [62]

Answer:

4760

Step-by-step explanation:

Simple interest formula:

PV(1+it)

4250(1+.04*3)=4760

8 0
3 years ago
The sum of the ages of Berma, her mother Rinna and her father Erwin is 80. Two years from now, Rinna’s age will be 13 less than
jekas [21]

Answer: Berma is 5 years old

Rinna is 38 years old

Erwin is 37 years old

Step-by-step explanation:

Let x represent Berma's age

Let y represent Rinna's age

Let z represent Erwin's age

Since the sum of their ages is 80,

x + y + z = 80 - - - - - - -1

Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that

y +2 = [ (z+2) + 2(x+2) ] - 13

y +2 = z + 2 + 2x + 4 - 13

2x - y + z = 13 + 2 - 4 -2

2x - y + z = 9 - - - - - - -2

Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that

15(x - 3) = (y - 3) - 5

15x - 45 = y - 3 - 5

15x - y = - 8 + 45

15x - y = 37 - - - - - - - -3

From equation 3, y = 15x - 37

Substituting y = 15x - 37 into equation 1 and equation 2, it becomes

x + 15x - 37 + z = 80

16x + z = 80 + 37 = 117 - - - - - - 4

2x - 15x + 37 + z = 9

-13x + 2 = -28 - - - - - - - - -5

subtracting equation 5 from equation 4,

29x = 145

x = 145/29 = 5

y = 15x - 37

y = 15×5 -37

y = 38

Substituting x= 5 and y = 38 into equation 1, it becomes

5 + 38 + z = 80

z = 80 - 43

z = 37

6 0
3 years ago
Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample
fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

37% of the company's orders come from first-time customers.

This means that p = 0.37

A random sample of 225 orders will be used to estimate the proportion of first-time-customers.

This means that n = 225

Mean and standard deviation:

\mu = p = 0.37

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{225}} = 0.0322

What is the probability that the sample proportion is between 0.26 and 0.38?

This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.

X = 0.38

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

By the Central Limit Theorem

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

Z = \frac{0.38 - 0.37}{0.0322}

Z = 0.31

Z = 0.31 has a pvalue of 0.6217

X = 0.26

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

Z = \frac{0.26 - 0.37}{0.0322}

Z = -3.42

Z = -3.42 has a pvalue of 0.0003

0.6217 - 0.0003 = 0.6214

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

5 0
2 years ago
Which represents r in terms of A and S?
ladessa [460]

Answer:

r=\frac{6\sqrt{10AS}}{S\sqrt{\pi }}

Step-by-step explanation:

Given the formula;

A=\frac{\pi r^2S}{360}

We want to solve the given formula for r.

Multiply both sides by \frac{360}{\pi S}

A\times \frac{360}{\pi S}=\frac{\pi r^2S}{360} \times \frac{360}{\pi S}

A\times \frac{360}{\pi S}=r^2

Take square root of both sides

r=\sqrt{\frac{360A}{\pi S}}

r=\frac{\sqrt{360A}}{\sqrt{\pi S}}

r=\frac{\sqrt{360A}}{\sqrt{\pi }\sqrt{S}}

r=\frac{\sqrt{360A}\times \sqrt{S}}{\sqrt{\pi }\sqrt{S} \times \sqrt{S}}

r=\frac{\sqrt{360AS}}{S\sqrt{\pi }}

r=\frac{6\sqrt{10AS}}{S\sqrt{\pi }}

5 0
3 years ago
Find the slope between (6,-9) and (-2,8).
Zina [86]

Answer:

-17/8

Step-by-step explanation:

8-(-9)=17

-2-6=-8

17/-8

3 0
3 years ago
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