A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 volt, and the manufacturer wishes to test volts against volts, using units. In your intermediate calculations, use z-scores rounded to two decimal places (e.g. 98.76).
(a) The acceptance region is_____. Find the value of a.
(b) Find the power of the test for detecting a true mean output voltage of 5.1 volts.

Answer:

0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2

Three weeks, so [tex]\mu = 2*3 = 6[/tex]

Calculate the probability that fewer than four tornadoes occur in a three-week period.

This is:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025[/tex]

[tex]P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149[/tex]

[tex]P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446[/tex]

[tex]P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512[/tex]

0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.

Answer:

The price elasticity of demand is -10

Step-by-step explanation:

Given

[tex]p_1,p_2 = 50,40[/tex]

[tex]q_1,q_2 = 400,500[/tex]

Solving (a): The coefficient of price elasticity of demand (k)

This is calculated as:

[tex]k = \frac{\triangle q}{\triangle p}[/tex]

So, we have:

[tex]k = \frac{500 - 400}{40 - 50}[/tex]

[tex]k = \frac{100}{-10}[/tex]

[tex]k = -10[/tex]

Because |k| > 0, then we can conclude that the company made a wise decision.

Answer:

2/5

Step-by-step explanation:

There are a total of 4+3+2+1=10 marbles in the bag. Since there is an equal chance of drawing any marble from the bag, the chances of drawing a red marble is equal to the number of red marbles divided by the total number of marbles.

What we're given:

Therefore, the probability of drawing a red marble is:

[tex]\frac{4}{10}=\boxed{\frac{2}{5}}[/tex]

Answer: Most probably

Step-by-step explanation:

Answer:

Inconsistent system

Step-by-step explanation:

Given

The attached graph

Required

The type of system

When two lines are parallel, it means they have the same slope and as such, the system has no solution.

Equations with the same slope are:

[tex]y = 2x + 6[/tex]

[tex]y = 2x- 8[/tex]

Both have a slope of 2

Such system are referred to inconsistent system.

Hence, (c) is correct.

Answer:

1.  e. Convenience sampling is used because students are chosen due to convenience of location.

2. a. University students may not be representative of all people in their age group.

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.

Students sampled as they leave the build, which is convenience, in this case convenience of location, which means that the correct answer to question 1 is given by option e.

2. What potential sources of bias are present if any. Select all that apply.

Only members of one group are asked(university students), and this may not be representative of the rest of the population, which means that the correct answer to question 2 is given by option a.

Answer:

0.15866

Step-by-step explanation:

6-7/1

=-1

p(x>-1)=1-p(x<1)

=0.15866

Answer:

2nd Graph

Step-by-step explanation:

Bases off the graphs, you gave me, I assume your the equation is

[tex]f(x) = - 4(2) {}^{x} [/tex]

The parent equation of this function is

[tex]f(x) = b {}^{x} [/tex]

Let say x=0

Using the rules of exponets, the y value must be 1 so a critical point is

(0,1)

The function is multiplied by -4.

This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be

(0,-4).

The base 2 the function will get compressed by 1/2.

The best graph that represents this is the second graph

Answer:

the number of diagonals can be found by n *n minus 3 by 2

a) the number of all possible diagonals drawn for having 7 side = 14 diagonals

b) the number of all possible diagonals drawn for having 10 side=35 diagonals

Answer:

5.5inches

Step-by-step explanation:

1331/8=166.375

then length of a side is = cubic root of 166.375

=³√166.375

5.5

Answer:

2.5 inches per year

Step-by-step explanation:

We can deduce the rate of change by obtaining the slope or gradient of thw points given :

Gradient = Rise / Run.

Point A (2, 5) ; point B (4, 10)

x1 = 2 ; y1 = 5 ;x2 = 4 ; y2 = 10

Rise = y2 - y1 = 10 - 5 = 5

Run = x2 - x1 = 4 - 2 = 2

Rate of change = Gradient = 5 /2 = 2.5

Which is 2.5 inches per year

Answer: 2.5

Step-by-step explanation: Took the assignment on edge

She gets a 4% raise so her new pay is 100% + 4% of her previous pay.

104% = 1.04 as a decimal.

Divide her new pay by 1.04:

24,960 / 1.04 = 24,000

Her previous pay was $24,000

Answer:

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.

Step-by-step explanation:

I hope it helps

Answer:

The volume (density) of cement that will be needed to cover this hollow pipe is:

= 50,000 kg/m³

Step-by-step explanation:

Length of a cylindrical pipe = 5m

Width of the cylindrical pipe = 4m

Depth of the cylindrical pipe = 2.5m

The cubic meters of the cylindrical pipe = 5 * 4 * 2.5 = 50m³

1 cubic meter is equal to 1,000 kilogram

Therefore, the volume (density) of cement that will be needed to cover this hollow pipe is:

= 50 * 1,000

= 50,000 kg/m³

9514 1404 393

Answer:

  B. only (-2, 9)

Step-by-step explanation:

A graph of the equation makes it easy to see that (-2, 9) is a solution and (2, -9) is not.

You can try these values of x in the equation to see what the corresponding y-values are.

  y = -2{-2, 2} +5 = {4, -4} +5 = {9, 1}

Points on the line are (-2, 9) and (2, 1).

(2, -9) is not a solution.

Answer:

B

Step-by-step explanation:

I know it is B. I know it because I put b in and I got it right on khan academy

Answer:

a. The mean is 3, the variance is 2.25 and the standard deviation is 1.5.

b. 0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.

c. 0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.

d. 0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two

e. Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they own stocks, or they do not. The probability of a person owning stocks is independent of any other person, 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.

One in four people in the US owns individual stocks.

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

You randomly select 12 people and ask them if they own individual stocks.

This means that [tex]n = 12[/tex]

a. Find the mean, variance, and standard deviation of the resulting probability distribution.

The mean of the binomial distribution is:

[tex]E(X) = np[/tex]

So

[tex]E(X) = 12(0.25) = 3[/tex]

The variance is:

[tex]V(X) = np(1-p)[/tex]

So

[tex]V(X) = 12(0.25)(0.75) = 2.25[/tex]

Standard deviation is the square root of the variance, so:

[tex]\sqrt{V(X)} = \sqrt{2.25} = 1.5[/tex]

The mean is 3, the variance is 2.25 and the standard deviation is 1.5.

b. Find the probability that the number of people who own individual stocks is exactly six.

This is P(X = 6). So

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

[tex]P(X = 6) = C_{12,6}.(0.25)^{6}.(0.75)^{6} = 0.0401[/tex]

0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.

c. Find probability that the number of people who say they own individual stocks is at least two.

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

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

[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]

[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0317 + 0.1267 = 0.1584[/tex]

0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.

d. Find the probability that the number of people who say they own individual stocks is at most two.

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

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

[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]

[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]

[tex]P(X = 2) = C_{12,2}.(0.25)^{2}.(0.75)^{10} = 0.2323[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0317 + 0.1267 + 0.2323 = 0.3907[/tex]

0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two.

e. Are the events in part c. and in part d. mutually exclusive

Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.

Answer:

D

Step-by-step explanation:

correct answer, thanks for 15 pts

Answer:

Option D is correct

Step-by-step explanation:

Hope it is helpful....

Answer:

1/3

Step-by-step explanation:

when you change the mixed numbers to improper fractions, you get 4/5 * 10/9 ÷ 8/3. you can flip the 8/3 to 3/8 and change the division sign to multiplication, because dividing by a fraction is the same as multiplying by its reciprocal. you can cancel some things and ultimately you get 1/3

There are 12 cards with a value ≤ 3 (3 between 1, 2, and 3, and multiply by 4 to count each suit). So the probability of drawing one of these cards and thus winning the game is 12/52 = 3/13.

The expected winnings for playing this game once are

3/13 × ($41) + 10/13 × (-$11) = $1

so after playing 877 times, you can expect to win a total of $877.

Answer:

$15,540

Step-by-step explanation:

I DONT KNOW IF ITS RIGHT THO BUT

9% = 1,800

Answer:

1) 5.2, and 4.94117647

2) Steph curry

Step-by-step explanation:

Answer:

2 < x < 6

Step-by-step explanation:

x/10

1/5 = 2/10

.6 = 6/10

2 < x < 6

Answer:

volume=length×width×height

v=15×20×20

v=6000

Answer:

x=−40

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x4−3x8=5

14x+−38x=5

(14x+−38x)=5(Combine Like Terms)

−18x=5

−18x=5

Step 2: Multiply both sides by 8/(-1).

(8−1)*(−18x)=(8−1)*(5)

x=−40

Answer:

x=−40

Hello!

x/4 - 3x/8 = 5

2x - 3x = 40

-x = 40

x = -40

Good luck! :)

Answer:

Amount left is 941.95 g.

Step-by-step explanation:

initial amount = 1000 g

time = 10 years

amount left =  980 grams

Now

[tex]980 = 1000 e^{-\lambda t}\\\\e^{\lambda\times 10}= 1.02\\\\10 \lambda = ln 1.02\\\\\lambda = 1.98\times10^{-3} per year[/tex]

time t = 20 years

Let the amount is N.

[tex]980 = 1000 e^{-\lambda t}\\\\e^{\lambda\times 10}= 1.02\\\\10 \lambda = ln 1.02\\\\\lambda = 1.98\times10^{-3} per year\\N = 980 e^{- 1.98\times 10^{-3}\times 20}\\\\ln N = ln 980 - 0.0396\\\\ln N = 6.88 - 0.0396 = 6.86\\\\N = 941.95 g[/tex]

Answer:

-9

Step-by-step explanation:

(f-g) (x) = 2x²-7x+24-5x²-5x+3

= -3x²-12x+27

(f-g) (2) = -3(2)²-12(2)+27

= -12-24+27

= -9

Answer:1

Step-by-step explanation:2

2

The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.

An absolute function is defined as a function which consists of an algebraic expression that is within absolute value symbols.

Here,

The standard form of the absolute value function is written by,

f(x) = a|x|

Given that,

f(x) = 3|x|

Comparing this with the standard form, we get,

a|x| = 3|x|

Therefore, a = 3

Hence,

The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.

To learn more about absolute function, click:

https://brainly.com/question/14364803

#SPJ7

Answer:

I think it would be 3/4

Step-by-step explanation:

Answer:

Please find the complete question and its solution in the attached file.

Step-by-step explanation:

Shortest had survived after 6741 hours [tex]2.5\%[/tex] of the lights burnt.

[tex]\to 0.15\% + 2.35\% = 2.50\%[/tex]