You are to take multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (randomly select one of the five answers) on each question. Let x represent the number of correct responses on the test (a) What kind of probability distribution does x have? normal distribution uniform distribution geometric distribution binomial distribution (b) What is your expected score on the exam? (Hint: Your expected score is the mean value of the x distribution:)_______
(c) Calculate the variance and standard deviation of X Variance_____
standard deviation ______
(d) Based on your answers to parts (b) and (c), is it likely that you would score over 50 on this exam? Explain the reasoning behind your answer:
A score of 50 is z =__________________ standard deviations above the mean therefore it___________ not likely that you would score over 50 on this exam;,

The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.

Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

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To find the product, we need to first factor the numerators and denominators of both fractions:

x^2 + 9x + 20 = (x + 5)(x + 4)

x^2 - x - 12 = (x - 4)(x + 3)

x^2 + 3x - 4 = (x + 4)(x - 1)

Substituting these into the expression, we get:

[(x + 5)(x + 4)/(x + 3)] * [(x - 4)(x + 3)/(x + 4)(x - 1)]

Now, we can simplify the product by cancelling out common factors:

[(x + 5) * 1/(x - 1)] * [(x - 4) * 1/1]

= (x + 5)(x - 4)/(x - 1)

So the product in simplest form is (x + 5)(x - 4)/(x - 1).

However, there is a restriction on the variable because the expression involves division by (x + 3), (x - 1), and (x - 4). Therefore, x cannot be equal to -3, 1, or 4, since these values would make the denominators zero and the expression undefined.

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For all values of x the function is decreasing function because as x increases the value of the function decreases.

One of the core ideas of calculus is the derivative, which shows how quickly a function is changing at any given moment. It offers a means of determining the slope of a curve at a certain location, which may be used to address a variety of issues in physics, engineering, economics, and social sciences. The derivative may be used to predict the behaviour of physical systems, discover the maximum and lowest values of a function, and improve a process or system.

From the given table we observe that as x increases the value of the function decreases.

That is for all values of x the function is decreasing function.

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The length of the diagonal is 8√2 ft.

If the side of the square is 8 ft, then the diagonal will form a right triangle with legs of length 8 ft. We can use the Pythagorean theorem to find the length of the diagonal (hypotenuse).

Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

In this case, we have:

a = 8 ft (one leg)

b = 8 ft (the other leg)

c = ? (the hypotenuse)

Using the Pythagorean theorem, we have:

c² = a² + b²

c² = 8² + 8²

c² =  64 + 64

c² = 128

c = √128

c = 8√2 ft

Therefore, the length of the diagonal is 8√2 ft.

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It would take the three of them about 6 hours to paint the four rooms.

Let t represent the time that it would take all three of them to paint one room.

It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room.

Therefore:

(1/6 + 1/4 + 1/8)t = 1

(2/3)t = 1

t = 1.5 hours

It would take all of them 1.5 hours each to paint one room.

For 4 rooms:

Total time = 1.5 hours * 4 = 6 hours

It would take the three of them about 6 hours to paint the four rooms.

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The required probability is obtained as:

(a) P(X^2 < 1) = 0.8413.

(b) P(X^2 + Y^2 < 1) = 0.7854.

(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:

P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))

Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:

P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))

Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.

(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.

We can use polar coordinates to express X and Y as:

X = Rcosθ

Y = Rsinθ

where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).

Therefore, we can find P(X^2 + Y^2 < 1) as:

P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))

Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:

P(R^2 < 1) = 0.7854

Therefore, P(X^2 + Y^2 < 1) = 0.7854.

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From the given jar, the probability that both are red marbles is 15/171.

Suppose a jar contains 6 red marbles and 13 blue marbles.

If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.

Let's first find out the total number of marbles in the jar:

Total number of marbles in the jar = 6 + 13 = 19

Since we need to find the probability of picking out two red marbles, we need to calculate the total number of ways we can pick 2 marbles from 19:

n(S) = (¹⁹C₂)

we need to calculate the total number of ways to pick out two red marbles from 6:

n(E) = (⁶C₂)

We can use the formula for probability:

[tex]P(picking two red marbles) = \frac{n(E) }{n(S)} \\ = \frac{6C2 }{19C2} \\= \frac{15}{171}[/tex]

So, the probability of both marbles being red is 15/171. This fraction cannot be reduced any further.

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The PC is initially worth $3,340.

Given that a computer loses half of its worth after six years, and assuming that value is $835, we must determine the device's original value.

What does the term "starting value" mean?

The starting output value is the initial value.

Let's say that computer's starting value is x.

As a result, after four years,

It is X/2 for the fourth year.

It is X/2 for the fifth year.

It's X/4 in the sixth year.

We stated that the PC will be worth $835 after six years. Hence, we may express it as,

X/4 = $835

X=4( $835)

X= $3,340

Hence, the initial value of the computer is $3,340.

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It will take approximately 8.5 years to triple the population and approximately 10 years to quadruple the population.

Given that the population of a community is known to increase at a rate proportional to the number of people present at time t, and an initial population p0 has doubled in 5 years.

To calculate:

How long will it take to triple?

How long will it take to quadruple?

Let p be the population of a community at any time t. According to the given information, the population p is proportional to the number of people present at time t. Therefore, we have p ∝ p_0 …… (1)

where p_0 is the initial population of the community. It is given that the initial population p_0 has doubled in 5 years.

So, we have 2p_0 = p_0e^(rt) 2 = e^(5r)

Taking natural logarithm on both sides, ln 2 = ln e^(5r) = 5rln 2/5 = r …… (2)

Using equation (1) and (2), we can write population p asp = p_0e^(rt) = p_0e^(ln2/5 t) = p_0 2^(t/5)

Now, we have to find for how many years (t) we need to wait until the population of the community triples, i.e.

3p_0 = p_0 2^(t/5) 3 = 2^(t/5)

Taking logarithm (with base 2) on both sides,

log_2 3 = log_2 2^(t/5)log_2 3 = (t/5)log_2 2t = 5 log_2 3t ≈ 8.5 (Rounded to one decimal place)

Therefore, it will take approximately 8.5 years to triple the population.

Now, we need to find for how many years (t) we need to wait until the population of the community quadruples, i.e. 4p_0 = p_0 2^(t/5) 4 = 2^(t/5)

Taking logarithm (with base 2) on both sides,

log_2 4 = log_2 2^(t/5)

log_2 4 = (t/5)log_2 2t = 5 log_2 4t ≈ 10 (Rounded to one decimal place)Therefore, it will take approximately 10 years to quadruple the population.

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Answer:

y = -3x - 2

Step-by-step explanation:

To write the equation 6x + 2y = -4 in slope-intercept form, we need to solve for y.

First, we can isolate the y-term by subtracting 6x from both sides:

6x + 2y = -4

2y = -6x - 4

Next, we can divide both sides by 2 to isolate y:

2y/2 = (-6x - 4)/2

y = -3x - 2

So the slope-intercept form of the equation 6x + 2y = -4 is y = -3x - 2.

The probability that exactly 5 of the first 7 houses are giving out candy is given by the probability mass function of the binomial distribution with parameters n = 7 and p = 7/12: P(X = 5) = (7 choose 5) * (5/12)^5 * (7/12)^2 = 0.1464, correct to four decimal places.

Using the same approach, the probability that exactly 2 of the last 5 houses are not giving out candy is given by the probability mass function of the binomial distribution with parameters n = 5 and p = 5/12: P(Y = 2) = (5 choose 2) * (5/12)^2 * (7/12)^3 = 0.2818, correct to four decimal places.

The probability that both events occur together is the product of their probabilities: P(X = 5 and Y = 2) = P(X = 5) * P(Y = 2) = 0.1464 * 0.2818 = 0.0413, correct to four decimal places.

Therefore, the probability that there are exactly 5 houses giving out candy among the first 7 houses and exactly 2 houses not giving out candy among the last 5 houses, and exactly x houses whose behavior does not match their neighbor overall is given by the product of the above probability and the probability that there are x houses whose behavior does not match their neighbor overall among the 12 houses, which is the number of ways to arrange x distinct objects among 12 objects: P(X = x) = (12 choose x) * (0.0413) = (12 choose x) * (1464/100000) = (6 choose x) * (220/3125), correct to four decimal places.

Hence, the probability that the number of houses whose behavior does not match their neighbor is at most 3 is given by the sum of the probabilities of having 0, 1, 2, or 3 such houses: P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (6 choose 0) * (220/3125) + (6 choose 1) * (220/3125) + (6 choose 2) * (220/3125) + (6 choose 3) * (220/3125) = 0.7444, correct to four decimal places.

Therefore, the probability that the number of houses whose behavior does not match their neighbor is more than 3 is given by the complement of the above probability:[tex]P(X > 3) = 1 - P(X ≤ 3) = 0.2556\\[/tex], correct to four decimal places

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The base of the parallelogram is 18. 3 feet

From the information given, we have that;

Area = 280ft^2

height = 5x

Base = 6x

Note that he formula that is used for calculating the area of the parallelogram is represented with the equation;

Area = bh

Given that the parameters are;

Substituting the values of area, base and height.

280 = 5x × 6x

280 = 30x^2

Divide both sides by 30

x^2 = 280/30

Find the square root of both sides

x = √(280/30)

We have that the base = 6x

Substitute the value of x, we get;

Base = 6x = 6(√(280/30))

Base = 18.3ft

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Answer:

A diagonal of a rectangle is inclined to one side of the rectangle at 25º Angle between a side of the rectangle and its diagonal = 25º Consider x as the acute angle between diagonals

Step-by-step explanation:

According to the solving  the annual rate of depreciation is approximately 4.77%.

Annual percentage rate (APR) is the word used to define the annual interest that is generated by a payment that is due to investors or assessed to borrowers. The annual percentage rate, or APR, is a gauge of how much it actually costs to borrow cash over the duration of a loan or the income from an investment.

V = V0 * e[tex]^(^-^r^t^)[/tex]

where:

V0 is the initial value of the asset (in this case, $35,000)

V is the current value of the asset (in this case, $26,796.88)

r is the annual rate of depreciation (what we want to find)

t is the time elapsed (in years)

We know that the time elapsed is 2021 - 2014 = 7 years.

26,796.88 = 35,000 * e[tex]^(^-^7^r^)[/tex]

Dividing both sides by 35,000, we get:

0.766195 = e[tex]^(^-^7^r^)[/tex]

ln(0.766195) = -7r

Solving for "r", we get:

r = -ln(0.766195) / 7

r ≈ 0.0477

the annual rate of depreciation is approximately 4.77%.

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Answer:

The answer to your problem is, -3000

Step-by-step explanation:

:Write down the points through which the line passes through

:The line is passing through a point at (0, 80000) and (10, 50000)

Next, ( important )

Find the slope of the line

Since the line is passing through the point (0, 80000) and (10, 50000)

So the slope of the line:

= m

[tex]\frac{80,000 - 50,000}{0 - 10}[/tex]

= [tex]\frac{30,000 }{-10}[/tex]

= -3,000

Techniquelly the answer is, 30,000 but for more explanation here it is :)

Find the number that will complete the point-slope equation that models this scenario

The required point-slope equation that models this scenario is

[tex]y - y_{1} - m( x - x_{1} )[/tex]

y - 50,000 = -30,000 ( x - 10 )

Thus the answer to your problem is, - 3,000

Any questions? Write them down below \/

Answer:

Perpendicular

Step-by-step explanation:

Answer:

To solve the problem, we need to add 23 7/8 and 3 1/2 to find the final price.

First, we need to convert 3 1/2 to an improper fraction:

3 1/2 = (2 x 3) + 1/2 = 7/2

Next, we need to find a common denominator between 8 and 2:

8 = 8/1

2 = 2/1 x 4/4 = 8/4

Now we can add the two fractions:

23 7/8 + 3 1/2

= 23 14/16 + 3 8/16 (using 16 as the common denominator)

= 27 6/16

= 27 3/8

Therefore, the stock was priced at $27 3/8 at the end of trading.

Answer:

Step-by-step explanation:

First , we would add 10 + 4 = 14 then ,

using Pythagoras Theorem , a^2 + b^2 = c^2 to find out the hypotenuse so

10^2+4^2= 116

Finally , add the square root of 116 to 14 to get  

24.8 metres rounded to 1 decimal place.

Answer:

Choice 2
∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

This is a good example of a problem that can be solved by POE(process of elimination)

First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°

The same applies for ∠3 and ∠4 (third choice)

The same applies for ∠1 and ∠4 (fourth choice)

That leaves choice 2

We can prove ∠1 ≅ ∠7 as follows:

∠1 ≅ ∠3 since they are vertically opposite angles

∠3 ≅ ∠7 since they are exterior angles

So ∠1 ≅ ∠7

By similar reasoning,
∠2 ≅ ∠8

So correct choice is Choice 2

The probability mass function of X( -3, -1, 1 ,3)  is P(X) 1/8 3/8 3/8 1/8.

A fair coin is flipped 3 times and the random variable X is defined as follows:

   X = 3 times the number of heads - 2 times the number of tails

To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.

The Possible outcomes are as shown:

   3 heads (X = 3)

   2 heads, 1 tail (X = 1)

   1 head, 2 tails (X = -1)

   3 tails (X = -3)

And the Probabilities are:

   P(X = 3) = 1/8

   P(X = 1) = 3/8

   P(X = -1) = 3/8

   P(X = -3) = 1/8

Therefore, the probability mass function of X is:

X( -3, -1, 1 ,3)  is  P(X) 1/8 3/8 3/8 1/8

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Answer:

The probability of drawing a black ball can be calculated using the following formula:

Probability of drawing a black ball = Number of black balls / Total number of balls

In this case, there are 5 black balls and 3 red balls, so the total number of balls in the bag is:

Total number of balls = 5 + 3 = 8

Therefore, the probability of drawing a black ball is:

Probability of drawing a black ball = 5/8

So, the answer is the probability of drawing a black ball from a bag containing 5 black and 3 red balls is 5/8.

Step-by-step explanation:

Answer:

Step-by-step explanation:

is 8,15,24

Answer:

A: -3/2

Step-by-step explanation:

-4x²-12x-9=0 First split the b value so that it equals a×c, or -4×-9

-4x²-6x-6x-9=0 Factor by grouping

(-2x-3)(2x+3)=0 Solve for x

x= -3/2

Answer:

6x + 7

Step-by-step explanation:

triangle has 3 sides right, which is 2x, 3x+5 and x+2

so basically you just have to add everything up since perimeter is just the total number of each sides combined

2x + (3x+5) + (x+2)

expand from the brackets

2x + 3x + 5 + x + 2

rearrange the numbers to avoid confusion

2x + 3x + x + 5 + 2

add everything up

6x + 7

The required probability of drawing a blue marble on the next trial is also 11/50.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.

Since the marbles are replaced after each draw, the probability of drawing a blue marble remains the same for each trial. Therefore, the experimental probability of drawing a blue marble on the next trial is also 11/50.

Expressed as a decimal, this is 0.22. Expressed as a percentage, it is 22%.

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Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000I=(

Step-by-step explanation:

Answer: [tex]1/3(x-1)[/tex]

Step-by-step explanation: In this case, factoring cannot be done at a large scale because there is no degree higher than one on both terms. However, you can factor out the gcf on both terms which is one-half to make the equation in factorized form.

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Answer:

Not sure what the expression actually is, but it is is either:

1.

[tex] \frac{1}{3x} - \frac{1}{3} [/tex]

Then:

[tex] \frac{1}{3x} - \frac{1}{3} = \frac{1}{3} ( \frac{1}{x} - 1)[/tex]

Or

2.

[tex] \frac{1}{3} x - \frac{1}{3} [/tex]

Then:

[tex] \frac{1}{3} x - \frac{1}{3} = \frac{1}{3} (x - 1)[/tex]

Answer:

Step-by-step explanation:

Tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.

A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.

We can express a 5% increase as a decimal by dividing 5 by 100, which gives 0.05. This means that the pοpulatiοn after οne year will be the current pοpulatiοn plus 5% οf the current pοpulatiοn. Mathematically, we can write:

Next year's pοpulatiοn = Current pοpulatiοn + 0.05 * Current pοpulatiοn

We can simplify this expressiοn by factοring οut the current pοpulatiοn:

Next year's pοpulatiοn = Current pοpulatiοn * (1 + 0.05)

Simplifying further, we can add 1 tο the decimal tο get:

Next year's pοpulatiοn = Current pοpulatiοn * 1.05

Therefοre, tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.

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