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statuscvo [17]
3 years ago
12

Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor

k together they can do the entire prospectus in five hours. How long will it take each of them working alone to repair the prospectus? Round answers to the nearest 10th of an hour
Mathematics
1 answer:
Dahasolnce [82]3 years ago
3 0

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

<u>Solution:</u>

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is \frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }

If they work together they can do the entire prospectus in five hours

\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}

On cross-multiplication we get,

\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}

\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}

On cross multiplication ,we get

\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}

<em><u>using quadratic formula:-</u></em>

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

x=\frac{12 \pm \sqrt{144-40}}{2}

\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

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The play director spent 190 190190 hours preparing for a play. That time included attending 35 3535 rehearsals that took varying
sineoko [7]

Answer:

The equation 35x+93\frac{3}{4}=190 gives average time spent on 35 rehearsals.

Step-by-step explanation:

Please consider the complete question.

The play director spent 190 hours preparing for a play. That time included attending 35 rehearsals that took varying amounts of time and spending 93\frac{3}{4} hours on other responsibilities related to the play. What question does the equation 35x+93\frac{3}{4}=190 help answer?    

Since time spent on each rehearsal is 35 hours, so time spent on 35 rehearsals would be 35x.

93\frac{3}{4} hours is time spent on other responsibilities related to play. The sum of these times equals to total time spent on preparing the play.

Now let us solve our equation step by step.

35x+\frac{375}{4}=190

35x=190-\frac{375}{4}

35x=\frac{760}{4}-\frac{375}{4}

35x=\frac{760-375}{4}

35x=\frac{385}{4}

35x=96.25

Time spent on 35 rehearsals is 96.25 hours and we are told that each rehearsal took different amount of time. Dividing 96.25 by 35 we will get average time spent on each rehearsal.

Therefore, equation 35x+93\frac{3}{4}=190 gives average time spent on 35 rehearsals.

8 0
3 years ago
Please help me in answers 6 and 8
Ivenika [448]
For #6

x + y = -10
x - y = 2

First solve for y in one of the equations

x - y = 2
-y = 2 - x
y = -2 + x
y = x - 2

Now substitute into one of the equations and solve for x

x + y = -10
x + x - 2 = -10
2x - 2 = -10
2x = -8
x = -4
3 0
3 years ago
. Let X and Y be random variables of possible percent returns (0%, 10%,
bazaltina [42]

(a) The marginal distribution of <em>X</em> is

Pr(<em>X</em> = <em>x</em>) = ∑ Pr(<em>X</em> = <em>x</em>, <em>Y</em> = <em>y</em>)

… = 0.0625 + 0.0625 + 0.0625 + 0.0625

… = 0.25

That is, the first equality follows from the law of total probability, with the sum taken over <em>y</em> from {0, 5, 10, 15}. Each probability Pr(<em>X</em> = <em>x</em>, <em>Y</em> = <em>y</em>) is given in the table to be 0.0625.

Similarly, the marginal distribution of <em>Y</em> is

Pr(<em>Y</em> = <em>y</em>) = 0.25

(b) Yes, they're independent because

Pr(<em>X</em> = <em>x</em>, <em>Y</em> = <em>y</em>) = 0.0625,

and

Pr(<em>X</em> = <em>x</em>) Pr(<em>Y</em> = <em>y</em>) = 0.25 • 0.25 = 0.0625.

(c) The mean of <em>X</em> is

E[<em>X</em>] = ∑ <em>x</em> Pr(<em>X</em> = <em>x</em>)

… = 0.25 ∑ <em>x</em>

<em>… </em>= 0.25 (0 + 5 + 10 + 15)

… = 7.5

and you would find the same mean for <em>Y</em>,

E[<em>Y</em>] = 7.5

The variance of <em>X</em> is

V[<em>X</em>] = E[<em>X</em>^2] - E[<em>X</em>]^2

… = (∑ <em>x</em>^2 Pr(<em>X</em> = <em>x</em>)) - 7.5^2

… = 0.25 (∑ <em>x</em>^2) - 56.25

… = 0.25 (0^2 + 5^2 + 10^2 + 15^2) - 56.25

… = 31.25

and similarly,

V[<em>Y</em>] = 31.25

(each sum is taken with <em>x</em> and <em>y</em> from {0, 5, 10, 15})

7 0
3 years ago
Solve for p. <br><br> i = prt<br><br> p = i-rt<br> p = i/(rt)<br> p = (rt)/i
Debora [2.8K]

Answer:

<h2>p = (rt)/i</h2>

Step-by-step explanation:

i=prt\to prt=i\qquad\text{divide both sides by}\ rt\neq0\\\\\dfrac{prt}{rt}=\dfrac{i}{rt}\\\\p=\dfrac{i}{rt}

5 0
3 years ago
Calculate the value of y
Reika [66]
157 degrees ... set 4x-5 = x+16 then solve, you should get x=7, plug in 7 for one of the equations and you'll get 23. subtract 23 from 180 and get 157. hope that helped :)
4 0
3 years ago
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