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inna [77]
3 years ago
12

Find the values of x and y.

Mathematics
1 answer:
eimsori [14]3 years ago
3 0

Answer:

The answers are

x=12

y=60

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Add them up:
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Divide it by the total:
5335 / (62 + 87 + 21) = 31.38
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C. 11/100

Step-by-step explanation:

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x is directly proportional to y and inversely proportional to z. if x= 1/2 when y = 3/4 and z=2/3, find x when y= 7/8 and z = 7/
ipn [44]

Answer:

1/2

Step-by-step explanation:

x is directly proportional to y (this means y will go on top because of the directly part) and inversely proportional to z (this means z will go on bottom due to the inversely part).

There is a constant k such that:

x=k \cdot \frac{y}{z}.

Contant means it will never change.  It will not care what (x,y,z) you use, it will remain the same.

We will use the first point to find k and then that k will still be there no matter what (x,y,z) they give you.

We have (1/2 , 3/4 , 2/3) is on our graph of the equation:

x=k \cdot \frac{y}{z}.

Insert the numbers:

\frac{1}{2}=k \cdot \frac{\frac{3}{4}}{\frac{2}{3}}

Multiply both sides by \frac{2}{3}:

\frac{1}{2}\cdot \frac{2}{3}=k \cdot \frac{3}{4}

Simplify left hand side:

\frac{1}{3}=k \cdot \frac{3}{4}

Multiply both sides by 4:

\frac{4}{3}=k \cdot 3

Multiply both sides by 1/3  (or you can say divide by 3):

\frac{4}{9}=k

So k=4/9 no matter the (x,y,z).

x=\frac{4}{9} \cdot \frac{y}{z}

We are asked to find x given y=7/8 and z=7/9.

Input these numbers:

x=\frac{4}{9} \cdot \frac{\frac{7}{8}}{\frac{7}{9}}

Change the division to multiplication:

x=\frac{4}{9} \cdot \frac{7}{8} \cdot \frac{9}{7}

I see a 7 on top and bottom that I can cancel:

x=\frac{4}{9} \cdot \frac{1}{8} \cdot \frac{9}{1}

I see a 9 on top and bottom that I can cancel:

x=\frac{4}{1} \cdot \frac{1}{8} \cdot \frac{1}{1}

Let's go ahead and multiply and reduce more later if we can.

Multiply straight across on top.

Multiply straight across on bottom.

x=\frac{4}{8}

Divide top and bottom by 4:

x=\frac{1}{2}

4 0
3 years ago
Pat Statsdud is taking an economics course. Pat's exam strategy is to rely on luck for the next exam. The exam consists of 20 mu
Delicious77 [7]

Answer:

0.01386 or 1.386%

Step-by-step explanation:

Each question has a binomial distribution with probability of success p =0.25 (1 correct answer out of four alternatives).

The probability of 'k' successes in n trials is given by:

P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}

Pat will pass the exam if x ≥ 10. The probability that Pat will pass is:

P(pass)=P(x=10)+P(x=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)+P(x=17)+P(x=18)+P(x=19)+P(x=20)

The probability for each number of success is:

P(x=10)=\frac{20!}{(20-10)!10!}*0.25^{10}*0.75^{10}=0.0099\\\\P(x=11)= \frac{20!}{(20-11)!11!}*0.25^{11}*0.75^{9}=0.0030\\\\P(x=12)=\frac{20!}{(20-12)!12!}*0.25^{12}*0.75^{8}=0.00075\\\\P(x=13)=\frac{20!}{(20-13)!13!}*0.25^{13}*0.75^{7}=0.00015\\\\P(x=14)=\frac{20!}{(20-14)!14!}*0.25^{14}*0.75^{6}=0.0000257\\\\P(x=15)=\frac{20!}{(20-15)!15!}*0.25^{15}*0.75^{5}=3.426*10^{-6}\\\\

P(x=16)=\frac{20!}{(20-16)!16!}*0.25^{16}*0.75^{4}=3.569*10^{-7}\\\\P(x=17)=\frac{20!}{(20-17)!17!}*0.25^{17}*0.75^{3}=2.799*10^{-8}\\\\P(x=18)=\frac{20!}{(20-18)!18!}*0.25^{18}*0.75^{2}=1.555*10^{-9}\\\\P(x=19)=\frac{20!}{(20-19)!19!}*0.25^{19}*0.75^{1}=5.457*10^{-11}\\\\P(x=20)=\frac{20!}{(20-20)!20!}*0.25^{20}*0.75^{0}=9.095*10^{-13}\\\\

The probability that Pat will pass his exam is:

P(pass)=0.01386

4 0
3 years ago
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Vinil7 [7]
B. 96 cubic inches.
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3 years ago
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