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liubo4ka [24]
3 years ago
6

A multiple-choice test has 30 questions and each one has five possible answers, of which only one is correct. If all answers wer

e guesses, find the probability of getting exactly four correct answers.
Mathematics
1 answer:
kumpel [21]3 years ago
5 0

Answer: the probability is 0.13

Step-by-step explanation:

First, each question has 5 options and only one is correct.

Then, selecting at random, the probability of getting a correct answer is equal to:

p = 1/5 = 0.20 (and the probability of getting it incorrect is p = 4/5 = 0.80)

Now, if out of 30 questions, we got 4 correct and 26 incorrect, the probability for a given combination is;

p = (0.20^4)*(0.80^26)

But we also need to multiply this by the total number of combinations.

This is we have 30 questions in total, and we can select 4 of them that will be the correct ones.

Now, if we have N objects in total, the number of different combinations of K elements out of those N elements is

C = \frac{N!}{(N-K)!*K!}

In this case, N = 30 and K = 4.

C = \frac{30!}{(30 -4)!*4!} = \frac{30*29*28*27}{4*3*2}  = 27,405

Then the probability of getting exactly 4 correct answers is:

P = (0.20^4)*(0.80^26)*27,405 = 0.13

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Algebra I: Quadratics
sertanlavr [38]
The answer id 12 meters.divide -2x^2+20x+48 by 2 to get x alone and then umbrella
3 0
3 years ago
(3-4i)(6i+7)-(2-3i)
Sergeu [11.5K]

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)}  \\  \displaystyle \large{[18i + 21  - 24 {i}^{2}  - 28i]- (2 - 3i)}

Now combine like terms.

\displaystyle \large{[ - 10i+ 21  - 24 {i}^{2} ]- (2 - 3i)}

<u>I</u><u>m</u><u>a</u><u>g</u><u>i</u><u>n</u><u>a</u><u>r</u><u>y</u><u> </u><u>U</u><u>n</u><u>i</u><u>t</u>

\displaystyle \large{i =   \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2}  =   - 1 }

Therefore:-

\displaystyle \large{[ - 10i+ 21  - 24  ( - 1) ]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 21   + 24]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

\displaystyle \large{- 10i+ 45 -  (2 - 3i)}  \\   \displaystyle \large{- 10i+ 45 -  2 + 3i}

Combine like terms.

\displaystyle \large{43 - 7i}

5 0
2 years ago
<img src="https://tex.z-dn.net/?f=%28fog%29%28%20-%205%29" id="TexFormula1" title="(fog)( - 5)" alt="(fog)( - 5)" align="absmidd
Xelga [282]
That should be the answer

8 0
3 years ago
Which inequality correctly compares Two-fifths, Six-sevenths, Five-eighths, and 1?
Ronch [10]

Answer:

<u>2/5 < 5/8 < 6/7 < 1 </u>

   <u>OR</u>    

<u>1 > 6/7 > 5/8 > 2/5</u>

Step-by-step explanation:

It is required to compare Two-fifths, Six-sevenths, Five-eighths, and 1

Two-fifths = 2/5

Six-sevenths = 6/7

Five-eighths = 5/8

So, the given numbers are: 2/5, 6/7, 5/8, and 1

We need to make the numbers in order from the least to the greatest or from the greatest to the least

The easy method is convert the rational numbers to decimal numbers

So,

2/5 = 0.4

6/7 ≈ 0.857

5/8 = 0.625

1 = 1

So, the numbers form the least to the greatest are:

0.4 , 0.625 , 0.857 , 1

So,

2/5 , 5/8 , 6/7 , 1

The inequality correctly compares the numbers are:

<u>2/5 < 5/8 < 6/7 < 1</u>

Or can be written from the greatest to the least as:

<u>1 > 6/7 > 5/8 > 2/5 </u>

6 0
3 years ago
Two pounds of bananas cost $1.16 what would be the cost of 5pounds s of bananas
ivann1987 [24]
If 2 lb of bananas cost $1.16, then each pound costs $0.58.

0.58 * 5 = 2.9

So 5 lb of bananas will cost $2.90.

Hope this helps!
6 0
3 years ago
Read 2 more answers
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