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NARA [144]
3 years ago
7

Please help (just tell me what i have to put in the blanks, i’ll give credit)

Mathematics
1 answer:
Misha Larkins [42]3 years ago
5 0

Answer:

a. earned: $292.50

b. total: $2,092.50

Step-by-step explanation:

A = 1800 [1 + (0.065 * 2.5)] = 2092.5

A = $2,092.50

To find the amount is earned, subtract the total with how much to started with

2,092 - 1,800 = 292.50

You might be interested in
What number is the highest and which is the lowest. 22.075, 25.125, 23.015, 25.085
Bess [88]
From lowest to highest

22.075, 23.015, 25.085, 25.125
7 0
3 years ago
Read 2 more answers
Working alone, Henry takes 3 hours less than Mary to clean the carpets in the entire office. Working together, they can clean th
Sati [7]

Answer:

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

Step-by-step explanation:

Assume that it takes Henry t hours to clean the carpets

∵ Henry takes 3 hours less than Mary to clean the carpets

∵ Henry takes t hours

- That means add 3 to t to find Mary time

∴ Mary takes t + 3 hours

∵ The rate of Henry is \frac{1}{t}

∵ The rate of Mary is \frac{1}{t+3}

∵ Working together, they can clean the carpets in 2 hours

- Add the two rates and equate the answer by \frac{1}{2} (their rate together)

∴ \frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}

Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side

∵ \frac{(1)(t+3)}{t(t+3)}+\frac{(1)t}{t(t+3)}=\frac{1}{2}

∴  \frac{(t+3)}{t(t+3)}+\frac{t}{t(t+3)}=\frac{1}{2}

- Add the two fractions in the left hand side

∴ \frac{t+3+t}{t(t+3)}=\frac{1}{2}

∴  \frac{2t+3}{t^{2}+3t}=\frac{1}{2}

Use the cross multiplication

∵ (t² + 3t)(1) = 2(2t + 3)

∴ t² + 3t = 4t + 6

- Subtract 4t from both sides

∴ t² - t = 6

- Subtract 6 from both sides

∴ t² - t - 6 = 0

- Factorize it into two factors

∴ (t - 3)(t + 2) = 0

Equate each factor by 0 to find t

∵ t - 3 = 0

- Add 3 to both sides

∴ t = 3

OR

∵ t + 2 = 0

- Subtract 2 from both sides

∴ t = -2 ⇒ reject this answer because there is no - ve time

∴ t = 3

∴ Henry would take 3 hours to clean the carpets alone

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

8 0
3 years ago
Simplify 4x + 8 + 2x - 7
Vikentia [17]

Answer:

6x+1

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
An example of an early application of statistics was in the year 1817. A study of chest circumference among a group of Scottish
otez555 [7]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is X: chest circumference of a Scottish man.

X≈N(μ;δ²)

μ= 40 inches

δ= 2 inches

The empirical rule states that

68% of the distribution lies within one standard deviation of the mean: μ±δ= 0.68

95% of the distribution lies within 2 standard deviations of the mean: μ±2δ= 0.95

99% of the distribution lies within 3 standard deviations of the mean: μ±3δ= 0.99

a)

The 58% that falls closest to the mean can also be referred to as the middle 58% of the distribution, assuming that both values are equally distant from the mean.

P(a≤X≤b)= 0.58

If 1-α= 0.58, then the remaining proportion α= 0.42 is divided in two equal tails α/2= 0.21.

The accumulated proportion until "a" is 0.21 and the accumulated proportion until "b" is 0.21 + 0.58= 0.79 (See attachment)

P(X≤a)= 0.21

P(X≤b)= 0.79

Using the standard normal distribution, you can find the corresponding values for the accumulated probabilities, then using the information of the original distribution:

P(Z≤zᵃ)= 0.21

zᵃ= -0.806

P(Z≤zᵇ)= 0.79

zᵇ= 0.806

Using the standard normal distribution Z= (X-μ)/δ you "transform" the values of Z to values of chest circumference (X):

zᵃ= (a-μ)/δ

zᵃ*δ= a-μ

a= (zᵃ*δ)+μ

a= (-0.806*2)+40= 38.388

and

zᵇ= (b-μ)/δ

zᵇ*δ= b-μ

b= (zᵇ*δ)+μ

b= (0.806*2)+40= 41.612

58% of the chest measurements will be within 38.388 and 41.612 inches.

b)

The measurements of the 2.5% men with the smallest chest measurements, can also be interpreted as the "bottom" 2.5% of the distribution, the value that separates the bottom 2.5% of the distribution from the 97.5%, symbolically:

P(X≤b)= 0.025 (See attachment)

Now you have to look under the standard normal distribution the value of z that accumulates 0.025 of the distribution:

P(Z≤zᵇ)= 0.025

zᵇ= -1.960

Now you reverse the standardization to find the value of chest circumference:

zᵇ= (b-μ)/δ

zᵇ*δ= b-μ

b= (zᵇ*δ)+μ

b= (-1.960*2)+40= 36.08

The chest measurement of the 2.5% smallest chest measurements is 36.08 inches.

c)

Using the empirical rule:

95% of the distribution lies within 2 standard deviations of the mean: μ±2δ= 0.95

(μ-2δ) ≤ Xc ≤ (μ+2δ)=0.95 ⇒ (40-4) ≤ Xc ≤ (40+4)= 0.95 ⇒ 36 ≤ Xc ≤ 44= 0.95

d)

The measurements of the 16% of the men with the largest chests in the population or the "top" 16% of the distribution:

P(X≥d)= 0.16

P(X≤d)= 1 - 0.16

P(X≤d)= 0.84

First, you look for the value that accumulates 0.84 of probability under the standard normal distribution:

P(Z≤zd)= 0.84

zd= 0.994

Now you reverse the standardization to find the value of chest circumference:

zd= (d-μ)/δ

zd*δ= d-μ

d= (zd*δ)+μ

d= (0.994*2)+40= 41.988

The measurements of the 16% of the men with larges chess are at least 41.988 inches.

I hope this helps!

8 0
3 years ago
Katelyn can complete 17 integer questions in one minute. Collin can also complete 17 integer questions in one minute. Which expr
BabaBlast [244]

Answer:

a: 17m + m

Step-by-step explanation:

Each one can answer 17 questions in 1 minute.

Each one can answer 17m questions in m minutes.

The total they can answer is 17m + 17m = 34m.

Every expression that is equal to 34m represents the amount they can both answer in the same number of minutes.

The expression we are looking for does not equal 34m.

a: 17m + m  = 18m

b: 34m  = 34m

c: 2(17m)  = 34m

d: 17m + 17m = 34m

Only choice a does not equal 34m.

Answer: a: 17m + m

5 0
3 years ago
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