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dusya [7]
3 years ago
5

A 110 point final exam is

Mathematics
2 answers:
statuscvo [17]3 years ago
4 0

Answer:

There are 45 2-point questions and 5 4-point questions

Step-by-step explanation:

NeX [460]3 years ago
4 0

Answer: The two point questions are 45, while the four point questions are 5.

Step-by-step explanation: We shall start by assigning letters to the unknown variables. Let the first type of question be called a and the second type of question be called b.

If the final exam is made up of 50 questions, that means

a + b = 50

Also if some questions are two points while others are four points and the total score for all of them is 110 points, then

2a + 4b = 110

(That is, we assume that a is the two point question and b is the four point question, so total score equals 110)

We now have a pair of simultaneous equations

a + b = 50 ————(1)

2a + 4b = 110 ——-(2)

From equation (1), we shall make a the subject of the equation,

hence let a = 50 - b

Substitute for the value of a in equation (2)

2a + 4b = 110

2(50 - b) + 4b = 110

100 - 2b + 4b = 110

By collecting like terms we now have

4b - 2b = 110 - 100

2b = 10

Divide both sides of the equation by 2

b = 5

Now substitute for the value of b into equation (1)

a + b = 50

a + 5 = 50

Subtract 5 from both sides of the equation

a = 45.

Therefore the two point questions are 45, while the four point questions are 5

**A quick check would show the following results ; 2(45) + 4(5) = 90 + 20 = 110.**

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16. A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours
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Answer:

a) 23.11% probability of making exactly four sales.

b) 1.38% probability of making no sales.

c) 16.78% probability of making exactly two sales.

d) The mean number of sales in the two-hour period is 3.6.

Step-by-step explanation:

For each phone call, there are only two possible outcomes. Either a sale is made, or it is not. The probability of a sale being made in a call is independent from other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours, find:

Six calls per hour, 2 hours. So

n = 2*6 = 12

Sale on 30% of these calls, so p = 0.3

a. The probability of making exactly four sales.

This is P(X = 4).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{12,4}.(0.3)^{4}.(0.7)^{8} = 0.2311

23.11% probability of making exactly four sales.

b. The probability of making no sales.

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138

1.38% probability of making no sales.

c. The probability of making exactly two sales.

This is P(X = 2).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678

16.78% probability of making exactly two sales.

d. The mean number of sales in the two-hour period.

The mean of the binomia distribution is

E(X) = np

So

E(X) = 12*0.3 = 3.6

The mean number of sales in the two-hour period is 3.6.

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Median:it is the middlemost observation of data arraged in increasing or decreasing order of values

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