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4 years ago

7

A test has twenty questions worth 100 points. The test consists of x true-false questions worth 4 points each and y multiple cho

ice questions worth 8 points each. How many of each type of question are on the test?

2 answers:

kvv77 [185]4 years ago

7 0

Answer:

Number of true-false questions =15

Number of multiple choice questions =5

Step-by-step explanation:

Number of true-false questions = $x$

Number of multiple choice questions = $y$

Total number of question = $x+y=20$

Points for true-false questions = 4

Total points for true-false questions = $4\times x =4x$

Points for multiple choice questions = 8

Total points for multiple choice questions = $8\times y =8y$

Total points of the test = $4x+8y=100$

We have 2 equations now:

(1) $x+y=20$

(2) $4x+8y=100$

We need to solve the 2 equations to find $x$ and $y$ .

Dividing equation 2 by 4.

$\frac{4x+8y}{4}=\frac{100}{4}$

(2a) $x+2y=25$

Multiplying equation (2a) with (-1)

$-1(x+2y)=25\times (-1)$

(2b) $-x-2y=-25$

Adding equation (2a) with equation (1).

$x+y=20$

$-x-2y=-25$

$-y=-5$

$y=5$ [ Divided both sides by -1]

Substituting value of $y$ in equation (1).

$x+5=20$

Subtracting both sides by 5.

$x+5-5=20-5$

$x=15$

∴ $x=15 \ and\ y=5$

Number of true-false questions =15

Number of multiple choice questions =5

sasho [114]4 years ago

3 0

Answer:

1: 15

2: 5

Step-by-step explanation:

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If f(x)= <br><img src="https://tex.z-dn.net/?f=x%20-%20%7Bx%7D%5E%7B2%7D%20" id="TexFormula1" title="x - {x}^{2} " alt="x - {x}^

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Answer:

f(2+h)=-(h+2/3)^2+1/4

f(x+h)=-(x+h-1/2)^2+1/4

Step-by-step explanation:

1. f(2+h)=(2+h)-(2+h)^2=2+h-4-4h-h^2=-h^2-3h-2=-(h^2+3h+2)

=-(h+2/3)^2+1/4

2. Let (x+h)=a, then rewrite the equation into f(a)=a-a^2.

a-a^2=-(a^2-a)=-[(a-1/2)^2-1/4]=-(a-1/2)^2+1/4.

Insert a=x+h, f(x+h)=-(x+h-1/2)^2+1/4

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3 years ago

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Answer:

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Step-by-step explanation:

(a)

Using combination formula, nCr where n is the total sample and r is the limitation hence 7 combination 5.

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Using the normal distribution, it is found that there is a 0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.

In a <em>normal distribution</em> with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

For n instances of a normal variable, the mean is $n\mu$ and the standard error is $s = \sigma\sqrt{n}$

In this problem:

Mean of $0.47, standard deviation $0.15, hence $\mu = 0.47, \sigma = 0.15$

30 instances, hence $n\mu = 30(0.47) = 14.1, s = 0.15\sqrt{30} = 0.8216$

The probability is <u>1 subtracted by the p-value of Z when X = 15</u>, hence:

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

Considering the n instances:

$Z = \frac{X - n\mu}{s}$

$Z = \frac{15 - 14.1}{0.8216}$

$Z = 1.1$

$Z = 1.1$ has a p-value of 0.8643.

1 - 0.8643 = 0.1357.

0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.

A similar problem is given at brainly.com/question/25769446

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