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kifflom [539]
3 years ago
14

The quotient of-54 and 9, subtracted from 8 times a number, is-18

Mathematics
1 answer:
AysviL [449]3 years ago
4 0
The number is:  " -3 " .
_____________________________________
Explanation:
_____________________________________
Let "x" be the "unknown number" for which we are to solve.

        8x − (-54/9) = -18 ;  Solve for "x" ; 

  →  8x  − (-6) = - 18 ;

  →  8x + 6 = - 18 ;

   Subtract "6" from each side of the equation:

  →  8x + 6 − 6  =  - 18 <span>− 6 ;

to get:   8x =  -24 ;

Divide EACH SIDE of the equation by "8" ; to isolate "x" on one side of the equation ; & to solve for "x" ; 

              8x / 8 = -24 / 8 ;

to get:   x = -3 .
________________________________
The number is:  " -3 " .
________________________________</span>
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Answer:

a) P(x<5)=0.

b) E(X)=15.

c) P(8<x<13)=0.3.

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We have the function:

f(x)=\left \{ {{\frac{1}{10},\, \, \, 10\leq x\leq 20 } \atop {0, \, \, \, \, \, \,  otherwise }} \right.

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P(x

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P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3

Therefore, the probability is P(8<x<13)=0.3.

d)  We calculate the probability that you will be late to each of the 9:30am classes next week:

P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6

You have 9:30am classes three times a week.  So, we get:

P=0.6^3=0.216

Therefore, the probability is P=0.216.

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P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1

Therefore, the probability is P=1.

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Step-by-step explanation:

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