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2 years ago

Sophie is paid by the number of projects completed each month. Her monthly earnings are listed below. Based on Sophie's

Mathematics

1 answer:

Ivahew [28]2 years ago

7 0

Answer:

The June month salary is closest to her average monthly salary

The Sophie's average Monthly salary income = 3332.2

Step-by-step explanation:

Explanation:-

Given data Sophie's monthly earnings below

June $3,614

July $2,873

August $4,464

September $3,721

October $1,989

The mean or expected number

= ∑x/n

The Sophie's average Monthly salary income

= $\frac{3614+2873+4464+3721+1989}{5}$

= $\frac{16,661}{5}$

= 3332.2

The June month salary is closest to her average monthly salary

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Sam painted 3 pictures.ellie painted twice as many pictures as Sam how many pictures did they paint altogether

zepelin [54]

Sam painted 3
ellie painted 2x3, so she painted 6
6+3=9
together they painted 9 pictures

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2 years ago

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A city water department is proposing the construction of a new water pipe, as shown. the new pipe will be perpendicular to the o

vitfil [10]

I found a similar problem to your problem here, which is shown in the attached picture. So, from the picture, we have to find the equation for the red line. All we have to do is find two points of the line. That would be: Point 1(2,0) and Point 2(-2,3). The general equation would be:

y - y₁ = (y₂-y₁)/(x₂ - x₁) * (x - x₁)

Substituting the coordinates to the equation,

y - 0 = (3-0)/(-2 - 2) * (x - 2)
y = -3(x -2)/4
Rearranging,
4y = -3x + 6 or 4y + 3x = 6

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2 years ago

3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a pa

Artist 52 [7]

Answer:

0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 15000, p = 0.09$

$\mu = E(X) = np = 15000*0.09 = 1350$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05$

What is the probability that at least 1,500 will agree to respond

This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So

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

$Z = \frac{1499 - 1350}{35.05}$

$Z = 4.25$

$Z = 4.25$ has a pvalue of 1.

1 - 1 = 0

0% probability that at least 1,500 will agree to respond

6 0

2 years ago

The figure below shows a line graph and two shaded triangles that are similar:Which statement about the slope of the line is tru

zzz [600]

Here is something to keep in mind.
when there is a downward slope, the slope will ALWAYS have a negative slope. even if it is above the x-axis. negative slopes will tend to go from positive y-axis to negative y-axis
so personally would have to go with -4
because the x-axis is by 4 each time. and this slope is going downward.

your answer will be D

6 0

2 years ago

Read 2 more answers

"An ordinance requiring that a smoke detector be installed in all previously constructed houses has been in effect in a particul

Galina-37 [17]

Answer:

a) Probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 15) = 0.0173

b) Probability of not rejecting the claim when p = 0.7, P(X > 15) = 0.8106

when p = 0.6, P(X > 15) = 0.4246

c) Check Explanation

The error probabilities are evidently lower when 15 is replaced with 14 in the calculations.

Step-by-step explanation:

p is the true proportion of houses with smoke detectors and p = 0.80

The claim that 80% of houses have smoke detectors is rejected if in a sample of 25 houses, not more than 15 houses have smoke detectors.

If X is the number of homes with detectors among the 25 sampled

a) Probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 15)

This is a binomial distribution problem

A binomial experiment is one in which the probability of success doesn't change with every run or number of trials (probability that each house has a detector is 0.80)

It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure (we are sampling 25 houses with each of them either having or not having a detector)

The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 25 houses sampled

x = Number of successes required = less than or equal to 15

p = probability of success = probability that a house has smoke detectors = 0.80

q = probability of failure = probability that a house does NOT have smoke detectors = 1 - p = 1 - 0.80 = 0.20

P(X ≤ 15) = Sum of probabilities from P(X = 0) to P(X = 15) = 0.01733186954 = 0.01733

b) Probability of not rejecting the claim when p= 0.7 when p= 0.6

For us not to reject the claim, we need more than 15 houses with detectors, hence, th is probability = P(X > 15), but p = 0.7 and 0.6 respectively for this question.

n = total number of sample spaces = 25 houses sampled

x = Number of successes required = more than 15

p = probability that a house has smoke detectors = 0.70, then 0.60

q = probability of failure = probability that a house does NOT have smoke detectors = 1 - p = 1 - 0.70 = 0.30

And 1 - 0.60 = 0.40

P(X > 15) = sum of probabilities from P(X = 15) to P(X = 25)

When p = 0.70, P(X > 15) = 0.8105639765 = 0.8106

When p = 0.60, P(X > 15) = 0.42461701767 = 0.4246

c) How do the "error probabilities" of parts (a) and (b) change if the value 15 in the decision rule is replaced by 14.

The error probabilities include the probability of the claim being false.

When X = 15

(Error probability when p = 0.80) = 0.0173

when p = 0.70, error probability = P(X ≤ 15) = 1 - P(X > 15) = 1 - 0.8106 = 0.1894

when p = 0.60, error probability = 1 - 0.4246 = 0.5754

When X = 14

(Error probability when p = 0.80) = P(X ≤ 14) = 0.00555

when p = 0.70, error probability = P(X ≤ 14) = 0.0978

when p = 0.60, error probability = P(X ≤ 14) = 0.4142

The error probabilities are evidently lower when 15 is replaced with 14 in the calculations.

Hope this Helps!!!

6 0

2 years ago