The product means multiplication.
An expression does not have an equal sign.
83 * x
83x
Answer: 83x
In this current scenario,
Probability of passing, p = 65% = 0.65
Then,
Probability of not passing, q = 1-p = 1-0.65 = 0.35
Part (a): When 15 people are tested
(i) Number of people expected to pass
This is 65% of the 15 people tested. That is,
Number of people expected to pass = 0.65*15 = 9.75. This is rounded downwards as upward rounding will violate the 65% criteria.
Therefore,
Number of people expected to pass = 9 people.
(ii) Probability that 11 people are expected to pass the test
p(x=11) = [15Cx]*p^x*q^(15-x) = [15C11]*0.65^11*0.35^(15-11) = 0.1792 ≈ 17.92%
Part (b): Teenager determined to pass the test no matter how many times
(i) Probability that he passes the test the third time
This means that he will fail the first and second time. That is,
Probability pf passing the third time = q*q*p = 0.35*0.35*0.65 = 0.079625 = 7.9625%
(ii) Number of trials it takes to pass
This is a case of mathematical expected, E, that it takes before first occurrence of success. Normally,
E = 1/p
Substituting;
E = 1/0.65 = 1.54 ≈ 2
Therefore, at least two trials will be required.
Answer:
Step-by-step explanation:
Commission received on selling each storm window 
of the selling price of each storm window
Commission received on selling each door 
of the selling price of each door
Amount earned on selling storm windows = $5,400
Amount earned on selling doors = $28,790
Commission received on selling storm windows 
Commission received on selling doors 
Therefore,
Total commission received 
Answer:
1.) x = 110
So for 3 to become 15 it would have to be multiplied by 5 because 3 x 5 = 15. And if I multiply the numerator by anything I always have to do the same to the denominator. So I multiply 22 x 5 = x. x = 110
2.) x = 72
For 16 to become 2 it has to be divided by 8 because 16 ÷ 8 = 2. And I have to do the same to the numerator of course, so i have to find x ÷ 8 = 9. I know the answer by memory, but for some it's easier to rewrite this as 9 × 8 = x. x=72
3.) c = 24
For 5 to become 40 it must be multiplied by 8 because 5 × 8 = 40. I have to multiply 8 by the numerator as well and 3 × 8 = 24. c = 24
6x^2 + 23x - 4 = 0
factorising:-
(6x - 1)(x + 4 ) = 0
x = 1/6 , - 4
