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Papessa [141]
3 years ago
8

Mr. Williams can grade 50 essays in 7 hours. His assistant, Mr. Wilfred, can do the same job in 14 hours. His other assistant, M

s. Stealth, can grade 25 essays in 6 hours. How long will it take them to grade 200 essays if all three work together?
Mathematics
1 answer:
Elza [17]3 years ago
5 0

Answer:

13.44 or 13 11/25 hours

Step-by-step explanation:

First use this format: number of essays/hours

- they are asking if all three work together, how many hours would it take, so this means addition:

50/7 + 50/14 + 25/6 = 200/x

Second, solve:

- least common multiple: 42

300/42 + 150/42 + 175/6 = 200/x

625/42 = 200/x

- cross-multiply

625x = 8,400

x = 336/25 = 13 11/25 = 13.44 (any one of these answers would work)

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What is the slope of a line whose equation is 4x – 6y = 12?
Black_prince [1.1K]
4x - 6y = 12
6y = 4x - 12
y = 4/6x - 12/6
y = 2/3x -2

Answer : Slope = 2/3
3 0
3 years ago
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-X + 8 + 3x = x-6<br> Help
Alexeev081 [22]
The answer would be, x = -14
8 0
3 years ago
Read 2 more answers
Two positive, consecutive, odd integers have a product of 143. set up an equation to then solve for the integers.
mixer [17]

Answer:

Step-by-step explanation:

Let (2n-1) and (2n+1) be the consecutive, odd numbers.

(2n-1)(2n+1) = 143

4n² - 1 = 143

4n² = 144

n² = 36

n = 6

2n-1 = 11

2n+1 = 13

The numbers are 11 and 13.

6 0
2 years ago
The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, Sout
mafiozo [28]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: The number of emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina for 50 days.

a)

In the first column, you have the possible number of emergency calls made, in the second column, you have the observed absolute frequency (fi) for each value of the variable.

To establish the probability distribution you have to calculate the relative frequency (hi) for each value of X.

The formula for the relative frequency is

hi= fi*n where i= 0, 1, 2, 3, 4

X₁= 0

f₁= 8

h₁= 8/50= 0.16

X₂= 1

f₂= 10

h₂= 0.20

X₃= 2

f₃= 22

h₃= 22/50= 0.44

X₄= 3

f₄= 9

h₄= 9/50= 0.18

X₅= 4

f₅= 1

h₅= 1/50= 0.02

(See attachment)

b)

The variable of interest is a cuantitative discrete variable, so this is an example of a driscrete distribution.

Discrete variables are numerical and take certain numbers within its range of definition, contrary to the continuous variables that can take any value within the range of definition of the variable.

Another example of a discrete variable is "the money", If the variable is "I have at most 10 dollars in my wallet", the range of definition goes from 0 dollars to 10 dollars.

c) To calculate the mean when the data is arranged in a frequency table you have to use the following formula:

X[bar]= ∑Xihi= (0*0.16)+(1*0.2)+(2*0.44)+(3*0.18)+(4*0.02)= 1.7

This means that they expect an average of 1.7 calls per day.

d) The formula for the standard deviation is:

S=\sqrt{\frac{1}{n-1}[sumX^2fi-\frac{(sumXfi)^2}{n} ] }

∑X²fi= (0²*8)+(1²*10)+(2²*22)+(3²*9)+(4²*1)=  195

∑Xfi= (0*8)+(1*10)+(2*22)+(3*9)+(4*1)= 85

S=\sqrt{\frac{1}{49}[195-\frac{(85)^2}{50} ] }= 1.015

I hope this helps!

3 0
3 years ago
Which of the following are solutions to 2x2 – 8x - 90? Select all that apply.
Bond [772]

Answer:

x=-5, x=9

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

2x^{2} -8x-90  

equate to zero

2x^{2} -8x-90=0  

so

2=-1\\b=-8\\c=-90

substitute in the formula

x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}

x=\frac{8\pm\sqrt{784}} {4}

x=\frac{8\pm28} {4}

x=\frac{8+28} {4}=9

x=\frac{8-28} {4}=-5

therefore

The solutions are x=-5, x=9

6 0
2 years ago
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