the time it takes a person to wash the dishes is uniformly distributed between 8 minutes and 17 minutes. what is the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes? round your answer accurate to two decimal places.

The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.

We can use the formula for calculating probabilities of combinations:

P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players

Total number of ways to choose 2 DVD players out of 6 is:

C(6,2) = 6! / ([2!] [4!]) = 15

Number of ways to choose 2 non-defective DVD players out of 4 is:

C(4,2) = 4! / ([2!] [2!]) = 6

Therefore, the probability that Cecil chooses 2 non-defective DVD players is:

P(not defective) = 6/15 = 2/5

So the value of P(not defective) is 2/5.

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The properties of a parallelogram indicates that the variables in the segments and angles are;

A parallelogram is a four sided figure with two pairs of sides that are parallel.

Whereby the figures are parallelogram, we get;

The length of the opposite sides are the same, therefore;

1. b + 1 = 2·b

1 = 2·b - b = b

1 = b

b = 1 (symmetric property)

3·a - 4 = a + 2

3·a - a = 4 + 2

2·a = 6

a = 6/2 = 3

a = 3

2. The opposite angles of a parallelogram are congruent, therefore;

(y + 10)° = (2·y - 40)°

10 + 40 = 2·y - y = y

50 = y

y = 50

The adjacent interior angles of a parallelogram are supplementary, therefore;

(4·x)° + (2·y - 40)° = 180°

(4·x)° + (2 × 50 - 40)° = 180°

(4·x)°  = 180° - (2 × 50 - 40)° = 60°

x = 60°/4 = 15°

x = 15

3. The diagonals of a parallelogram bisect each other, therefore;

y + 3 = 12

y = 12 - 3 = 9

y = 9

x - 3 = 15

x = 15 + 3 = 18

x = 18

4. The diagonals of a parallelogram bisect each other therefore;

x + 6 = 4·x

4·x = x + 6

4·x - x = 6

3·x = 6

x = 6/3 = 2

x = 2

5·y - 8 = 3·y + 1

5·y - 3·y = 1 + 8 = 9

2·y  = 9

y = 9/2 = 4.5

y = 4.5

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Answer: 9 miles

Step-by-step explanation: The speed of 12 miles per hour means that for every hour, Clare is 12 miles further from the starting point. 1 hour = 12 miles Since an hour is equivalent to 60 minutes, 60 mins = 12 miles We can divide both sides by 60 to find the distance travelled per minute. 1 min = 12 ÷60= 0.2 miles Multiply both sides by 45 to find the distance travelled in 45 minutes: 45 mins = 0.2(45)= 9 miles Given that the starting position is at zero, Clare's position is at 9 miles after 45 minutes.

the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.

There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.

The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:

Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)

Expected gain = 38/13 - 10/13 - 18/13

Expected gain = 10/13 ≈ 0.77

Therefore, the expected gain is $0.77, rounded to the nearest cent.

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The central limit theorem is a statistical theory that specifies the probability distribution of a sum or average of several random variables whose distribution is not known.

It is an important theorem since it is utilized to help forecast or estimate the behavior of a specific set of data.

This theorem holds that when you take repeated samples of the same size from a population with a finite standard deviation, the means of those samples will be normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Further more, the theorem indicates that the larger the sample size, the more closely the sample mean distribution will approximate a normal distribution.

This is why it is vital in the development and use of statistical quality control techniques, since they rely on correct assumptions about the population’s normality.

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The four uppercase letters of the alphabet in block style with rotational symmetry are H, I, O, and X. Rotational symmetry refers to the property of a figure or object that appears identical after being rotated around a central point by a certain angle.

In block style writing, letters are written with straight lines and sharp corners, creating a uniform and geometric appearance. H, I, O, and X are the only uppercase letters that have rotational symmetry and can be written in block style.

H has a rotational symmetry of 180 degrees, meaning it looks the same when rotated 180 degrees around its center point.

I has a rotational symmetry of 180 degrees as well, with the dot above the letter acting as its center point.

O has a rotational symmetry of 360 degrees, meaning it looks the same when rotated any number of degrees around its center point.

Lastly, X has a rotational symmetry of 180 degrees, with the intersection of the two lines acting as its center point.

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The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)

The formula for the division of line segments in the ratio m:n is

P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}

We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)

Thus, if the ratio is 2:5, we have:

U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}

U(x, y) = (84/7), (42/7)

U(x, y) = (12, 6)

Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.

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Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.

To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]

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Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ

The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:

[tex]Q = mcΔT[/tex]

Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).

Using the equation, the amount of heat produced can be calculated as follows:

Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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Implementing multiple types of technology and thereby precluding that the failure of one system will compromise the security of information is referred to as redundancy.

Explanation:

Redundancy is the term used to describe the use of multiple components in a system to ensure that the failure of one component does not lead to system failure. Redundancy is a method of protecting computer systems against damage and disruption caused by component failure.The use of redundancy in computer systems is usually targeted at increasing system availability and lowering the likelihood of data loss.

                                       Multiple types of technology may be employed to achieve redundancy in a computer system, such as mirroring data across multiple disks, deploying standby servers, using a hot backup server, and so on. Redundancy can be implemented in numerous ways to provide reliable service and protect against system failure.

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Answer:

Step-by-step explanation:

(4x - 5)(4x + 5) Option 1

16x^2 + 20x - 20x - 25

Answer: a=7.6

Step-by-step explanation:

solve for angle C:

[tex]\frac{sinc}{5} =\frac{sin120}{11}[/tex]

[tex]11sinc=5sin120[/tex]

[tex]C=23.2[/tex]

solve for A:

=180-(120+23.2)

=36.8

solve for a:

Using the law of sines

[tex]\frac{sin120}{11} =\frac{sin36.8}{a}[/tex]

[tex]asin120=11sin36.8[/tex]

[tex]a=7.6[/tex]

Answer:

For me it's C.

Step-by-step explanation:

the third one if you would like me to explain tell me.

The solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.

Given that the equation  [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex]

To find all the solutions to the equation  [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] ,  solve for x by isolating the cosine term and then applying the inverse cosine function.

Here are the steps to solve the equation:

Add [tex]\sqrt{30}[/tex] to both sides:

[tex]2cos(x) = \sqrt{30}[/tex]

Divide both sides by 2:

[tex]cos(x) = \sqrt{30} / 2[/tex]

Find the inverse cosine ([tex]cos^{-1}[/tex]) of both sides:

[tex]x = cos^{-1}(\sqrt{30} / 2)[/tex]

To determine the values of x in the interval [tex][0, 2\pi)[/tex] that satisfy the equation.

Evaluate [tex]cos^{-1}(\sqrt{30} / 2)[/tex] to find its approximate value.

[tex]cos^{-1}(\sqrt{30} / 2) = 0.5514[/tex] radians

Since the cosine function has a periodicity of [tex]2\pi[/tex], we can find other solutions by adding multiples of [tex]2\pi[/tex] to the initial solution.

So, the solutions in the interval  [tex][0, 2\pi)[/tex] are:

x ≈ 0.5514 radians

x ≈ [tex]0.5514 + 2\pi[/tex]

x ≈ [tex]0.5514 + 4\pi[/tex]

...

To simplify, express the solutions as:

x ≈ [tex]0.5514 + 2n\pi[/tex]

where n is an integer.

Therefore, the solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.

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Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.

What is average ?

Average, also known as mean, is a statistical measure that represents the central value of a dataset. It is calculated by adding up all the values in the dataset and dividing by the total number of values. The average can be used to provide a general idea of the value of the dataset and to compare different datasets. There are different types of averages, including arithmetic mean, geometric mean, and median.

According to the question:
To find out how many cars Martin will have to wash each month on average, we need to first find out how many weeks there are in a year:

52 weeks/year

Then we can use this information to calculate how many cars Martin will have to wash each week:

1,200 cars/year ÷ 52 weeks/year = 23.08 cars/week

Since Martin cannot wash a fraction of a car, he will have to round up to 24 cars/week.

Finally, we can calculate how many cars Martin will have to wash each month on average:

24 cars/week x 4 weeks/month = 96 cars/month

Therefore, Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.

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The correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The y-intercept of a line of fit is the value of y when x equals 0. In the context of this problem, the y-intercept represents the amount of diet soda that the machine starts with when it is filled.

Since the y-intercept of the line of fit is −5.1, this means that the machine starts with 5.1 ounces of diet soda.

This is a reasonable value, as it is unlikely that the machine would be completely empty when it is filled.

It's important to note that the slope of the line of fit is also relevant in this context.

The slope represents the rate at which the amount of diet soda in the machine decreases over time. However, the question only asked for the y-intercept.

Hence, the correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

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Answer:

First, we can factor out 5x²y²z from each term:

15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)

So the fully factorized expression is:

5x²y²z(3y+5xz+7z)

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

__________________

hope it helps ⸙

Answer:

x = 17/4, or 4.25

The x-intercept is (4.25, 0)

Step-by-step explanation:

We can get the intercepts by isolating x and y.

4x - 3y = 17

Subtract 4x from both sides.

-3y = -4x + 17

Divide both sides by -3.

y = 4/3x - 17/3

Input 0 for x.

y = -17/3

The y-intercept is (0, -17/3)

4x - 3y = 17

Add 3y to both sides.

4x = 3y + 17

Divide both sides by 4.

x = 3/4y + 17/4

Input 0 for y.

Julie hourly rate of pay from the given different rates of the day with total earning of $612 is equal to $12per hour.

Total number of hours Julie works in a week is equal to,

On Sunday = 10 hours

On Monday = 10 hours

On Tuesday = 7 hours

On Wednesday = 10 hours

On Thursday = 7 hours

On Friday = 7 hours

On Saturday = 0 hours

Total hours worked in whole week is

= 10 + 10 + 7 + 10 + 7 + 7 + 0

= 51 hours

Total money earned by Julie in whole week = $612

Hourly rate of pay = Weekly earnings / Total hours worked

Substitute the value we have,

⇒ Hourly rate of pay = $612 / 51 hours

⇒ Hourly rate of pay = $12 per hour

Therefore, Julie's hourly rate of pay is $12 per hour.

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The above question is incomplete , the complete question is:

Julie works Sunday, Monday, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612. What is Julie's hourly rate of pay, in dollars?

Answer:

1-

a. 19

b. -8

2-

a. -31

b. 0

c. -10.7

d. -3/7

e. 4

3-

a. -5

b. -60

c. 0

d. -1/4

4. -13/2

5. -85/18

6.  -5/12

7. -11

8. 16/11

9. -20/27

10.  26/11

11. -55/9

Step-by-step explanation:

why did i do this