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If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct.

ad-work [718]

Answer:

Probability = 0.190

Step-by-step explanation:

Given:

Number of questions, 'n' = 20

Each question has four choices.

Let event of choosing correct answer be success and its probability be represented by 'p'.

Therefore, event of choosing wrong answer is failure and its probability be represented by 'q'.

Now, probability of success is choosing one correct answer out of 4 options. So, $p=\frac{1}{4}=0.25$

Now, 'p' and 'q' are complements of each other. Therefore,

$q=1-p=1-0.25=0.75$

Now, we need 4 successes. Therefore, $x=4$

Using Bernoulli's theorem to find 'x' successes from 'n' questions, we get:

$P(x)=_{x}^{n}\textrm{C}p^xq^{n-x}$

Plug in 4 for 'x', 20 for 'n', 0.25 for 'p' and 0.75 for 'q'. Solve.

$P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{20-4}\\P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{16}\\P(4)=4845\times (0.25)^4\times (0.65)^{16}\\\\P(4)=0.1896\approx0.190$

Therefore, the probability of getting 4 correct answers out of 20 questions is 0.190.

6 0

3 years ago

Eric's average income for the four months of the year 1450 point to $5 what must be his average income for the remaining eight m

Zielflug [23.3K]

Answer:

$2668.63

Step-by-step explanation:

If the average of 4 months is $5

Meaning the total sum for 4 months

4×5 =$20

If the average for the year was $1780.75

It means the total sum for a year is;

$1780.75×12 =$21369

This means the money received for the remaining 8 months is;

$21369-$20=$21349

Hence the average income for the remaining 8months is ;

The total amount for 8 months / 8;

$21349/8= $2668.625

$2668.63

8 0

3 years ago

Chase consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Chase's body

PIT_PIT [208]

Answer:

(a) The 5-hour decay factor is 0.5042.

(b) The 1-hour decay factor is 0.8720.

(c) The amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

Step-by-step explanation:

The amount of caffeine in Chase's body decreases exponentially.

The 10-hour decay factor for the number of mg of caffeine is 0.2542.

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

(a)

Compute the 5-hour decay factor as follows:

$5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042$

Thus, the 5-hour decay factor is 0.5042.

(b)

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

Thus, the 1-hour decay factor is 0.8720.

(c)

The equation to compute the amount of caffeine in Chase's body is:

A = Initial amount × (0.8720)<em>ⁿ</em>

It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.

Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:

$A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112$

Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

4 0

3 years ago

If the point (2, -10) lies on the graph of a direct variation, which represents the direct variation equation?

Zanzabum

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{2},\stackrel{y}{-10})~~ \textit{we know } \begin{cases} x=2\\ y=-10 \end{cases}\implies -10=k2\implies \cfrac{-10}{2}=k\implies -5=k \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-5x~\hfill$

8 0

3 years ago

steve measured the length of his room and found it to be 9 feet and 6 inches. The width of his room was 11 feet exacly. What is

Art [367]

Length: 114 in.
Width: 132 in.

For length, you have 9 feet and 6 inches. Meaning that if you would want to get the length of his room in inches, you would have to multiply 9 with 12 and add 6.

It's the same thing for the width.

If you need more help comment below!

4 0

4 years ago