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3 years ago

Question 6 of 6

Mathematics

1 answer:

Bezzdna [24]3 years ago

6 0

$\huge \boxed { \sf \: Answer}$

We have to use the formula:

$(ab) ^{n} = {a}^{n} {b}^{n}$

So,

$(5 \times 9) ^{12} \\ = {5}^{12} . 9^{12}$

Also, it will be

$45^{12}$

Hope you could understand.

If you have any query, feel free to ask.

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the sum of three and a number is added to twenty four I need to translate each verbal expression in to a algebraic expression

Ede4ka [16]

Answer:

(3+x)+24

Step-by-step explanation:

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3 years ago

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Qualification exams for becoming a state-certified welding inspector are based on multiple-choice tests. As in any multiple-choi

erik [133]

Answer:

(a) The probability distribution of the random variable X is Binomial.

(b) The mean and standard deviation of the 25-question test are 5 and 2 respectively.

Step-by-step explanation:

The random variable X is defined as the number of correct answers given by a person who is guessing each answer on a 25-question exam.

There are five possible answer for every question.

This implies that the probability of getting a correct answer is:

P (X) = 0.20.

There are a total of n = 25 questions.

Every answer is independent of the others.

(a)

The random variable X has finite number of independent trials (i.e. 25 questions). There are only two outcomes for each trial, i.e. Success = correct answer and Failure = wrong answer. Each trial has the same probability of success (, i.e. P (X) = 0.25).

Thus, the probability distribution of the random variable X is Binomial with parameters n = 25 and p = 0.20.

(b)

Compute the mean of the random variable X as follows:

$E(X)=np\\=25\times 0.20\\=5$

Compute the standard deviation of the random variable X as follows:

$SD(X)=\sqrt{np(1-p)}\\=\sqrt{25\times 0.20\times (1-0.20)}\\=2$

Thus, the mean and standard deviation of the 25-question test are 5 and 2 respectively.

(c)

The sample is large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 5

2. n(1 - p) ≥ 5

Check the conditions as follows:

$np=25\times 0.20=5=5\\\\n(1-p)=25\times (1-0.20)=20>5$

Thus, a Normal approximation to binomial can be applied.

So, $X\sim N(5, 2^{2})$

It is provided that the minimum passing score foe the test is such that only 1% of students who are guessing will pass the test.

That is P (X < x) = 0.01.

⇒ P (Z < z) = 0.01

The value of z is -2.33.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\\\-2.33=\frac{x-5}{2}\\\\x=5-(2.33\times 2)\\\\x=0.34$

Thus, the value of x is 0.34.

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4 years ago

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elena-s [515]

Answer:

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3 years ago

The line through (1, 7) and (-6,7) in point-slope form

Natasha2012 [34]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 1 &,& 7~) 
% (c,d)
&&(~ -6 &,& 7~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{7-7}{-6-1}\implies \cfrac{0}{-7}\implies 0
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-7=0(x-1)$

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3 years ago

Helppppp Meeeeee !!!!!!!!!

Natali [406]

Answer:

a) draw the triangle using the graph points

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c) translation

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e) write down the coordinates

Step-by-step explanation:

The x-3 in translation tells you to move 3 squares to the left along the x axis in translation and y-1 tells you to move down one on the y axis.

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4 years ago