Determine the domain of the function graphed above.

Answer:

0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A carpet expert believes that 9% of Persian carpets are counterfeits.

This means that [tex]p = 0.09[/tex]

Sample of 686:

This means that [tex]n = 686[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{0.09*0.91}{686}} = 0.0109[/tex]

What is the probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%?

Proportion lower than 9% - 3% = 6% or higher than 9% + 3% = 12%. The normal distribution is symmetric, thus these probabilities are equal, so we can find one of them and multiply by 2.

Probability it is lower than 6%

p-value of Z when X = 0.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0109}[/tex]

[tex]Z = -2.75[/tex]

[tex]Z = -2.75[/tex] has a p-value of 0.0030

2*0.0030 = 0.0060

0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%

Answer:

7-i

Step-by-step explanation:

It is asking for the product of the given complex numbers.

Z1Z2 means Z1 times Z2

(1+i)(3-4i)

You can do the whole foil thing here since we are multiplying a pair of binomials. But all you are doing when you do that is multiplying every term in the first ( ) to every term in the second ( ).

1(3)+1(-4i)+i(3)+i(-4i)

Simplify each term. That is, perform the multiplication in each term:

3-4i+3i-4i^2

Combine like terms and also replace i^2 with (-1):

3-1i-4(-1)

Multiplication identity property used:

3-i+4

Combine like terms:

7-i

Answer:

(-6,-12)

Step-by-step explanation:

A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.

[tex] - 2 \times 3 = - 6[/tex]

[tex] - 4 \times 3 = - 12[/tex]

So our new coordinates is

(-6,-12)

Answer:

(-6,-12)

Step-by-step explanation:

A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.

So our new coordinates is

(-6,-12)

Step-by-step explanation:

Answer:

0.0756

Step-by-step explanation:

p(success), p = 70% = 0.7

Nunber of trials, n = 4

q = 1 - p = 1 - 0. 7 = 0.3

x = 1

The question meets the requirements of a binomial probability distribution :

P(x = x) = nCx * p^x * q^(n-x)

P(x = 1) = 4C1 * 0.7^1 * 0.3^(4-1)

P(x = 1) = 4C1 * 0.7 * 0.3^3

P(x = 1) = 4 * 0.7 * 0.027

P(x = 1) = 0.0756

Answer: 5 ft i think so

Use the Pythagorean theorem

Answer:

113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1

Answer:

3x + 2 - 5

3x - 3

x = 3 ÷ 3

x = 1

I hope this helped!

9514 1404 393

Answer:

  -16∛2

Step-by-step explanation:

It can be helpful to have some familiarity with the cubes of small integers. For example, ...

  2³ = 8

  6³ = 216

With this in mind you recognize the expression as ...

  3∛((-6)³(2)) +∛((2³)(2))

  = 3(-6)∛2 +2∛2

  = (-18 +2)∛2

  = -16∛2

Answer:

305°

Step-by-step explanation:

The bearing in the reverse direction is 180° plus the bearing in the forward direction, that is

bearing of B from A = 180° + 125° = 305°

Answer:

A. (–2, 4), one, three

Step-by-step explanation:

For a linear equation:

y = a*x + b

the point-slope form is:

(y - y₁) = m*(x - x₁)

Where we know that this line has the slope m, and passes through the point (x₁, y₁)

In this case, the equation:

(y + 2) = –1/3(x – 4)

is already in the point-slope form.

here we have:

y₁ = -2

x₁ = 4

then the point is (-2, 4)

m = -(1/3)

m = -1/3 means that when we move 3 units to the right, we need to move one unit down. (or the inverse, we can move one unit down and 3 to the right)

So, to complete the statement we have:

plot the point (-2, 4),  move one unit down, and three units over to find the next point on the line.

The correct option is A.

Answer:

hope this will help you a lot

Answer:

check the attachment

Step-by-step explanation:

2x - y = - 4

- y = - 4 - 2x

y = 2x + 4

slope of the line = 2 with y - intercept 4

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Answer:

  Tk 173.25

Step-by-step explanation:

The firm will break even if its cost is equal to its revenue. That is, the price of each item sold must equal the cost of producing it. To cover the fixed cost, a share of it must be added to each of the items sold. Then the break-even price for 80 items is ...

  price = variable cost + share of fixed cost

  price = Tk 60.75 +9000/80 = Tk 60.75 +112.50 = Tk 173.25

Answer:

I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line

Answer:

0.9936 = 99.36% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

Step-by-step explanation:

For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Assume that there is a 8​% rate of disk drive failure in a year.

So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]

Two disks are used:

This means that [tex]n = 2[/tex]

What is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive?

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]

0.9936 = 99.36% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

Answer:

0.25

Step-by-step explanation:

Given that :

Charity raffle price = $1000

Amount of ticket sold = 4000

Only one winner is to be selected ;

Point ticket buyer is expected to break even :

Probability of winning = 1 / number of ticket sold = 1 / 4000 = 0.00025

P(winning) * raffle price = 0.00025 * 1000 = 0.25

Answer:

11 half years

Step-by-step explanation:

The formula for compound interest is

A = P(1+r/n)^(nt), with r representing the interest rate, n being the number of times interest is applied over the time period, and t being the amount of time periods.

If we make the time period a half year (so interest is compounded once per time period), n=2. Then, our interest rate is 7%, or 0.07 (to convert from percent to decimal, simply divide by 100). Our starting amount is 500, and we want it to double, making it 1000. Our formula is thus

1000 = 500 (1+0.07)^(t)

divide both sides by 500

2 = (1+0.07)^(t)

2 = (1.07)^(t)

Using logarithms, we can say that

[tex]log_{1.07} 2 = t[/tex]

and using a calculator, we get

10.24 = t

Since interest is only compounded once per time period, though, we have to round up to make sure it doubles, so t = 11

Answer:

I think C

Step-by-step explanation:

Sorry if its wrong

Answer:

The slope of the green line is 3

Step-by-step explanation:

The lines are perpendicular, so the slopes are negative inverses

-1/(-1/3)

3

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Answer:

  4

Step-by-step explanation:

The function definition tells you its domain is ...

  -6 < x ≤ 4

Values -7, -6, and 5 are not in this domain.

Of the listed values, only 4 is in the domain.

Answer:

hope it helps much

Answer:

[tex]{19}C_1=19[/tex]

Step-by-step explanation:

We need to find the value of [tex]{19}C_1[/tex].

C stands for combination.

The formula of combination is as follows :

[tex]nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Here,

n = 19 and r = 1

So,

[tex]nC_r=\dfrac{19!}{1!(19-1)!}\\\\nC_r=\dfrac{19!}{1!\times 18!}\\\\nC_r=\dfrac{19\times 18!}{1!\times 18!}\\\\nC_r=19[/tex]

So, the value of [tex]{19}C_1[/tex] is 19.

Answer:

Your answer will be 19C1 =19

Answer:

No, the sum of all the probabilities is not equal to 1.

Step-by-step explanation:

Given

[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} & {P(x)} & {0.001} & {0.007} & {0.033} & {0.059} \ \end{array}[/tex]

Required

Determine if the given parameter is a probability distribution

For a probability distribution to exist, the following must be true;

[tex]\sum P(x)=1[/tex]

So, we have:

[tex]\sum P(x) = 0.001 + 0.007 + 0.033 + 0.059[/tex]

[tex]\sum P(x) = 0.1[/tex]

Hence, it is not a probability distribution because the sum of all probabilities is not 1

9514 1404 393

Answer:

  y = x^2 +10x -9

Step-by-step explanation:

Quadratic regression generally requires the use of "technology" to aid in finding the equation of the curve of best fit. Use the technology you've been introduced to.

__

When only a few data points are provided, I prefer to use the Desmos graphing calculator. It shows the equation to be ...

  y = x^2 +10x -9

Answer: 1/50, or 0.02

Step-by-step explanation:

I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.

Answer:

answer is 1 2 3 and 4 respectively of given match the following

Answer:

The answer is 40 chocolates in the box in total

Answer:

45.9

Step-by-step explanation:

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Answer:

  3/4

Step-by-step explanation:

It might be easier to start by expressing the ratios with AD as the denominator.

  AD/AC = 2/1   ⇒   AC/AD = 1/2

  AD/AB = 3/1   ⇒   AB/AD = 1/3

From the latter, we have ...

  (AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD

Then the desired ratio is ...

  AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)

  AC/BD = 3/4

Answer:

3/8.

Step-by-step explanation:

First convert days to hours:

2 days = 2 * 24 = 48 hours.

The greatest common factor of 18 and 48 = 6 so the required fraction is

18/48

= (18/6) / (48/6)

= 3/8.