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3 years ago

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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2sin^(-2490)+tan 1410

givi [52]

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7 0

4 years ago

The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4. Suppose 64 golfers play

Vilka [71]

Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .