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3 years ago

Pleaaaaaaase help me!! :)

Mathematics

1 answer:

Paul [167]3 years ago

5 0

Hello there, and thank you for posting your question here on brainly.

Short answer: 25.48 x 10^4

Why?

This equation has a few steps. Simplify the brackets. (2.8 x 10^-2)*(9.1 x 10^6) --> 2.8 x 10^-2 * 9.1 x 10^6 Simplify. (or multiply the two decimals) 2.8 x 10^-2 * 9.1 x 10^6 --> 25.48 x 10^-2 x 10^6 Use the product rule. (the formula is x^y x^z = x^ y+z) 25.48 x 10^-2 x 10^6 --> 25.48 x 10^4

Hope this helped you! ♥

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When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

sergiy2304 [10]

Answer:

(a) P(X=3) = 0.093

(b) P(X≤3) = 0.966

(c) P(X≥4) = 0.034

(d) P(1≤X≤3) = 0.688

(e) The probability that none of the 25 boards is defective is 0.277.

(f) The expected value and standard deviation of X is 1.25 and 1.089 respectively.

Step-by-step explanation:

We are given that when circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.

Let X = the number of defective boards in a random sample of size, n = 25

So, X ∼ Bin(25,0.05)

The probability distribution for the binomial distribution is given by;

$P(X=r)= \binom{n}{r} \times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,......$

where, n = number of trials (samples) taken = 25

r = number of success

p = probability of success which in our question is percentage

of defectivs, i.e. 5%

(a) P(X = 3) = $\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $2300 \times 0.05^{3}\times 0.95^{22}$

= 0.093

(b) P(X $\leq$ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}+\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $1 \times 1 \times 0.95^{25}+25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.966

(c) P(X $\geq$ 4) = 1 - P(X < 4) = 1 - P(X $\leq$ 3)

= 1 - 0.966

= 0.034

(d) P(1 ≤ X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.688

(e) The probability that none of the 25 boards is defective is given by = P(X = 0)

P(X = 0) = $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}$

= $1 \times 1\times 0.95^{25}$

= 0.277

(f) The expected value of X is given by;

E(X) = $n \times p$

= $25 \times 0.05$ = 1.25

The standard deviation of X is given by;

S.D.(X) = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{25 \times 0.05 \times (1-0.05)}$

= 1.089

8 0

3 years ago

Jacob is a teacher. He made 75 cookies to give to his students on the first day of school. He gave 2 cookies to each student who

Lisa [10]

Answer:

See explanation

Step-by-step explanation:

Jacob has 75 cookies.

He gave 2 cookies to each student.

Complete the table:

$\begin{array}{cc}\text{Number of student arrived}&\text{Number of cookies left}\\1&75-2=73\\2&73-2=71\\3&71-2=69\\...&...\end{array}$

Let n be the number of students. After nth student arrived Jacob had left

$g(n)=75-2n$

cookies.

This is an arithmetic sequence with

$g_1=g(1)=73\\ \\d=-2$

Thus,

$g_{n}=g_{n-1}-2\\ \\g(n)=g(n-1)-2$

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colin has an ice cube tray with 12 identical compartments. Each compartment is a prism that is 4 cm. long, 3 cm. wide, and 3 cm.

a_sh-v [17]

Volume = length x width x height
V = 4 x 3 x 3
4 x 3 = 12
V = 12 x 3
V = 36 cubic cm.
1 cubic cm. = 1 ml.
36 cubic cm. x 12 compartments = 432 cubic cm.
432 cubic cm. = 432 cubic ml.

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3 years ago

Select each figure that appears to be a rectangle. You must select all that apply.

Archy [21]

Answer:

Step-by-step explanation:

i Believe its A. B. And D. But i could be wrong

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2 years ago

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Carlos dropped the phone he had received for his birthday and broke the screen. He knows he has to pay for the replacement himse

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Answer:

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Step-by-step explanation:

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