I came up with 7 hours and 15 minutes but that is not one of the answer choices?

C) 1/2 is the value of P(A)

Independent events are events in probability and statistics that have no effect on each other and are not related to each other in any way, so the outcome of one event does not affect the outcome of the other event.

let the value of P(A) be x and the value of P(B) be y  given A and B are independent events

so P(A∩B) = P(A) * P(B)

=> x*y=1/6 ---(i)

now P(⁻A) = 1 - P(A) , P(B) = 1 - P(⁻B)

so P( ⁻A  ∩ ⁻B ) = (1-x)*(1-y)

=> 1 -x - y +xy = 1/3

=> x +y  =1+1/6-1/3

=> x + y = 5/6  ----(ii)

x - y = √(x+y)²-4xy

=> √(5/6)² - 4*1/6

=> √25/36 - 4/6

=> √(25-24)/36

=> √1/36

=> 1/6

so x-y = 1/6 ---(iii)

adding equation (ii) and (iii) we get

2x = 1

=> x = 1/2

so P(A)  = 1/2

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Complete question :

If A and B are independent events of random experiment such that P(A∩B)=1/6 and P( ⁻A  ∩ ⁻B )=1/3, then P(A)=?

a. 1/4b. 1/5c. 1/2s. 2/3

The linear speed of the vehicle In miles per hour is 19.04 miles per hour

Angular speed is the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes. In the figure, this displacement is represented by the angle θ between a line on one body and a line on the other.

The relationship between angular and linear speed is v = wr

where w= angular speed

v = linear speed

and r is the radius

1 inch = 1.578×10^-5

r = 32/2 = 16 inches = 16×1.578×10^-5

= 25.25×10^-5 = 2.5×10^-4miles

1 revolution = 2π = 6.28

800 revolution = 6.28× 800 = 5024

1 minutes = 1/60

800rev/minutes = 5024×60= 301440 rad/hour

v = wr

v = 301440 × 1.578 × 10^-5 = 4.76 miles per hour

therefore the linear speed of the car is 4.76miles/ hour × 4 = 19.04 miles per hour

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The dealerships will each have sold 23 cars in 1 day.

The first step is to form a linear equation that represents the number of cars that are sold by the dealerships. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of a linear equation that represents the total cars sold by the dealership is:

Total cars sold = cars already sold + (number of cars sold per day x number of days)

Total cars sold by Clarksville Cars= 15 + (8 x d)

= 15 + 8d

Total cars sold by Robinson's Autos = 13 + (10 x d)

= 13 + 10d

When the two dealerships are tied, the two above functions would be equal:

13 + 10d= 15 + 8d

In order to determine the value of d, take the following steps:

Combine and add similar terms:

10d - 8d = 15 - 13

2d = 2

Divide both sides of the equation by 2

d = 2 / 2

w = 1 week

Number of cars that would have been sold by each dealership =

13 + 10(1)

13 + 10 = 23 cars

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The height, in feet above the ground, is 26 feet

(Achieved Peak Value - Attained Lowest Value)/2

The lowest number = is 5 if the ride starts at the bottom of the Ferris wheel, which keeps you 5 feet above the ground.

Charlie will be 47 feet off the ground at the apex, or 5 feet off the ground plus the diameter of the wheel.

Amount = a = (47-5)/2 = 21.

(2/period) = b. You can just plug in the period from the question since you will already have located it.

(Peak value + Lowest value)/2 = for d = midline.

(47+5)/2 = 52/2 = 26

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The graph of "square root of 13" is 3.61 is seen below.

So, the graph of "square root of 13" = 3.61 is seen below.

As a result, the quotient obtained using the aforementioned division approach, or roughly 13 = 3.605, is the necessary square root of 13.

Plotting the number "square root of 13" on the number line is necessary.

since we are aware,

13 has a square root of 3.61.

In other words, we must write 3.61 on the number line.

Since 3.61 is between 3 and 4, it tends to lean more toward 4.

So, the graph of "square root of 13" = 3.61 is seen below.

The graph of "square root of 13" is 3.61 is seen below.

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The decision between one sided and two sided alternative hypothesis is based on the statement of the null hypothesis and the alternative hypothesis appropriate for the context of the problem.

The hypothesis test is used to check if the observed data is consistent with the expected data or not. To do this, a null hypothesis and an alternative hypothesis are formulated. The decision between one sided and two sided alternative hypothesis is based on the statement of the null hypothesis and the alternative hypothesis appropriate for the context of the problem. The one-sided alternative hypothesis is used when the researcher is mainly interested in testing whether the population mean is either greater than or less than a given value. On the other hand, the two-sided alternative hypothesis is used when the researcher is mainly interested in testing whether the population mean is either different from or not different from a given value. The level of significance chosen for the test should be determined before the decision is made between one sided and two sided alternatives.

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Kris currently has $190 and wants to have at least $1,625 by the end of the summer. To find out how much money she needs to earn each weekend we need to subtract the money she already has from the money she wants to have and divide that by the number of weekends.

$1,625 - $190 = $1,435

$1,435 ÷ 8 = $179.38

So, Kris needs to earn at least $179.38 each weekend to reach her goal.

Answer choice C. Kris needs to earn at least $179.38 each weekend to meet her goal. is the best interpretation of the solution in the context of the problem.

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

What is the Linear equation?

An algebraic equation with only a constant and a first-order (linear) term is said to be linear if it has the formula y = mx + b, where m is the slope and b is the y-intercept. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

y = mx + c

where m denotes the slope.

The y-intercept is represented by the constant c. (Where x is zero)

In our instance, y-intercept equals 60.

The line's equation will therefore be:

y = mx + 60

y = mx + 60

There are given the line's coordinates (4, 90). These considerations will thus satisfy the equation.

90 = 4*m + 60

4.m = 30 m = 7.5 m = 7.5 y = 7.5x + 60 y = 7.5 * 6 + 60 y = 45 + 60 y = 105 is

y = 7.5x + 60.

If Adam's study for 6 hours then his score would be

y = 7.5x + 60.

y = 7.5(6) + 60

y = 105

Hence,

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

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a) The information not required in the tax computation is; the amount of the bill

b) The total bill is calculated as; $12.65

A percentage is defined as a number or ratio that is expressed as a fraction of 100.

The parameters are that a restaurant customer left ​$1.65 as a tip, the tax was 4 % and the tip was 15​% of the after tax cost. Thus;

Let the bill after the tax plus tip will be a and the bill after tax be b,

Therefore,

a = b + $1.65

Since $1.65 = 15% of b, then we have;

b = 1.65*100/15

b = 11

a = 11 + 1.65

a = 12.65

Hence, the total cost after the tip = $12.65

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The probability of rolling an even number on an unfair die is 0.65, which means that if you roll the die multiple times, the proportion of times that you roll an even number will be close to 0.65.

So, the probability of rolling an even number is closest to option c) 0.65

A die is a cube with numbers on each face that are used in games or gambling. A fair die is a die that is equally likely to land on any of its faces, meaning that each face has a probability of 1/6 of being the face that lands up. An unfair die is a die that does not have an equal probability of landing on each face. It means that the probability of landing on each face is not the same.

In the given scenario, it is said that the probability of rolling an even number on an unfair die is 0.65. This means that if you roll the die multiple times, the proportion of times that you roll an even number will be close to 0.65. It means that the die is not fair, and it is more likely to roll an even number.

Therefore, the probability of rolling an even number is closest to 0.65, it is the probability of rolling an even number on an unfair die.

--The question is incomplete, answering to the question below--

"The probability of rolling an even number on an unfair die is 0.65 which of the following is closest to the probability that an even number

a. 0.35

b. 0.40

c. 0.65

d. 0.70"

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Answer:4x+3

Step-by-step explanation:

Given the following in the question if:

Volume of the box= 4x3+19x2+12z

Height of the box= x

width of the box =?

we have to find the width of the box, so as we know that

box is in the shape of cuboid, so

Volume of the cuboid = length * width * height

4x3+9x2+12x   =   x+4* width * x

width = 4x3+9x2+2x/x2+4x

we have to use long division method for this algebraic expression to divide and find width of the box.

we get width= 4x+3

Hence, the width of the box which in the shape of cuboid is 4x+3

The Equation For calculating the paver area is

Length(m) x width(m) = area(m²).

Concrete, natural stone, clay brick, or even porcelain can be used to make pavers. They are typically little fragments of varying sizes. Homeowners can choose from a variety of hues, patterns, and textures.

Divide your space into squares or rectangles and multiply the length by the width to find the square metres of paved surface. The total square metres should be included. There are about 38 pavers per square metre, although this varies depending on how many cuts are made and what laying pattern is used. Additionally, you must account for waste.

The area to be paved and the paver selected will determine how many pavers are required.

Determine the area that will be paved in square metres.

Equation : Length(m) x width(m) = area(m²).

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A. The unit cost of the product follows a normal distribution with an expected value of ETB 305 and a standard deviation of ETB 5.

B. The expected value of the unit cost of the product is ETB 305 and the variance is ETB 25.

In order to calculate the standard deviation, follow the following steps:

1. Calculate the mean (average) of your data set.

2. For each data point, subtract the mean and square the result (the squared difference).

3. Sum all of the squared differences.

4. Divide the sum by the number of data points. This gives you the variance.

5. Take the square root of the variance to get the standard deviation.

Therefore, the correct answer is as given above

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Answer:

240

Step-by-step explanation:

C. 240

The expected value is calculated by taking the total sample size (300) and multiplying it by the hypothesized proportion of graduates who have full-time employment within 6 months of graduation (80%).

Expected value = 300 x (80/100) = 240

To create a third-degree polynomial model for the velocity data of the space shuttle Endeavour we need to use a graphing calculator or computer.

1. Enter the velocity data into the graphing calculator or computer.

2. Select the "Polynomial Regression" option.

3. Choose the degree of the polynomial (third degree).

4. Enter the polynomial regression equation displayed.

5. Select the "Graph" option to view the polynomial model.

A third-degree polynomial model can be used to accurately represent data points. To create a third-degree polynomial model for the velocity data of the space shuttle Endeavour, we need to use a graphing calculator or computer. First, we enter the velocity data into the graphing calculator or computer. Then we select the "Polynomial Regression" option and choose the degree of the polynomial (third degree). This will generate the polynomial regression equation which can then be entered. Finally, we select the "Graph" option to view the polynomial model. This will show us a graph of the velocity data points with the third-degree polynomial fitted to the points. This can be used to accurately predict the velocity of the shuttle Endeavour throughout its mission STS-49.

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The probability that the first item is not the first to be delivered is 0.6667

Let's call the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.

Therefore, the probability that one of the other two items arrives first is

1/3 + 1/3 = 2/3.

The probability that the first item is not the first to be delivered is

1 - 2/3 = 1/3

Evaluate

1 - 2/3 = 0.6667

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The equations are 100x + 80y = 25600 and 50x + 160y = 18200.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Let x be the cost of a quail and y be the cost of a rabbit bought by the business lady.

Given that a business lady bought 100 quails and 80 rabbits for sh 25600.

100x + 80y = 25600

If she bought twice as many rabbits, number of rabbits = 80 × 2 = 160.

If she bought half as many quails, number of quails = 100/2 = 50

The equation is then,

50x + 160y = 25600 - 7400

50x + 160y = 18200

Hence the equations formed here at two situations are 100x + 80y = 25600 and 50x + 160y = 18200.

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Over the past few months, Brody has eaten 3 glazed donuts and 6 other donuts. we expect 1 to be glaized

Generally, Based on the data provided, it seems that Brody has eaten 3 glazed donuts out of a total of

3 + 6 = 9 donuts.

This means that 3/9, or approximately 1/3, of the donuts Brody has eaten are glazed.

So, if Brody eats 3 more donuts, we would expect 1/3 of them to be glazed,

or 3*(1/3)=1.

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As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

Circled portion of the shaded partition is 7/4 of the total.

Take 1/2's reciprocal and switch the sign to multiply. 7/4 * 1/2 = 3 1/2

As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .

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Answer:

[tex]y = \frac{1}{3} x - 4[/tex]

[tex]\it y=ax+b\\ \\ x=0 \Rightarrow y=-4 \Rightarrow b=-4 \Rightarrow y=ax-4\\ \\ x=3 \Rightarrow y=-3 \Rightarrow a\cdot3-4=-3\bigg|_{+4}\Rightarrow a\cdot3=1 \bigg|_{:3}\Rightarrow a=\dfrac{1}{3} \\ \\ Therefore, the\ equation\ of\ this \ line\ is: \ \ y=\dfrac{1}{3}x-4[/tex]

Sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.

What is Sampling variation?

The term "sampling variance" describes how much a sample estimate (a statistic) is likely to fluctuate from sample to sample due to the unique nature of each sample.

Sample Sizes and Variability are the factors which lead to sampling variation. As and when the sample size is changed i.e. either increased or decreased, the variability of samples fluctuates.

Since, Sam runs a large chain of car repair shops, this means he has large number of employees.

But his sample size is only of 10 employees whom he asks about their billable hours from which he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company.

Since, sampling variation is greatly affected by the sample size and variability, therefore it will have more impact on confidence interval.

Hence, sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.

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Since the options are missing in the question, here are the options from which answer is to be chosen

The parent function for f(x) = -1/2√x+4 can be transformed in a variety of ways to create new functions.

Shifting:

f(x) = -1/2√x+4 + c, where c is the amount of the shift on the y-axis

Reflecting:

f(x) = -1/2√-x+4, where the negative sign reflects the graph across the y-axis

Stretching:

f(x) = k(-1/2√x+4), where k is the amount of the stretch on the y-axis.

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Answer:

The cost of the wings per dollar is 18/15 = 1.2 wings per dollar.

Answer:

1.2

Step-by-step explanation:

Answer:

  A, B, C, D

Step-by-step explanation:

You want to know which of these equations have exactly one solution:

An equation in a single variable will have one solution if the variable terms on either side of the equal sign have different coefficients.

  A: coefficients are -13 and +13; one solution (x=25/26)

  B: coefficients are 12 and 13; one solution (x=0)

  C: coefficients are -13 and +13; one solution (x=-1/26)

  D: coefficients are 12 and 13; one solution (x=24)

All of the given equations have exactly one solution.

When rolling a pair of dice, there are 36 possible outcomes, each representing a unique combination of the numbers on the two dice.

Event A: "at least one die is a 3" is not mutually exclusive with Event B: "at least one die is a 6" or Event C: "the sum is 11"

Event A and Event B are mutually exclusive because when one of the die is a 6, the other die cannot be a 3 and vice versa.

Event A and Event C are not mutually exclusive because there are some outcomes where at least one die is a 3 and the sum is 11. For example (3,8), (4,7) and (6,5) are all outcomes where at least one die is 3 and the sum is 11.

Event B and Event C are not mutually exclusive because there are outcomes where at least one die is a 6 and the sum is 11. For example (5,6) and (6,5) are both outcomes where at least one die is a 6 and the sum is 11.

So, in conclusion, Event A and Event B are mutually exclusive, but Event A and Event C and Event B and Event C are not mutually exclusive.

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A person can see a distance of approximately 32.9 miles on a clear day from a height of 1461 feet above the given planet.

d = 2 √(hR)

We can use the formula d = 2 √(hR) to calculate the distance d to the horizon that a person can see on a clear day from a 1461 feet above the given planet.

First, we need to convert the height of 1461 feet to miles. We can use the conversion factor of 1 mile = 5280 feet. Therefore, the height h = 1461/5280 ≈ 0.2772 miles.

Next, we need to find the radius of the planet. The radius of the planet is given as 3900 miles.

Finally, we can substitute h = 0.2772 miles and R = 3900 miles into the formula d = 2 √(hR).

d = 2 √(0.2772*3900) = 2 √(1083.08) ≈ 32.9 miles

Therefore, a person can see a distance of approximately 32.9 miles on a clear day from a height of 1461 feet above the given planet.

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The center of the circle is (3 , -2) and the radius is 4 then the equation of circle is (x)² + (y)²-6x+4y = 3

What is a circle?

The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle is,

( x - h )² + ( y - k )² = r²

(x-3)² + (y+2)² = 16

(x)² + (y)²-6x+9 +4y+4 = 16

(x)² + (y)²-6x+4y = 3

Compare the equations and find the center and radius,

Center = ( h,k) = ( 3, -2)

Radius = r = 4

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The best-hitting team can be calculated by finding the mean of each team's hitting percentages. To do this, add the ten numbers for each team and divide by 10.

Team 1: (0.345 + 0.254 + 0.278 + 0.331 + 0.267 + 0.465 + 0.189 + 0.312 + 0.365 + 0.287) / 10 = 0.3125

Team 2: (0.243 + 0.378 + 0.312 + 0.298 + 0.287 + 0.387 + 0.301 + 0.412 + 0.254 + 0.342) / 10 = 0.3267

Team 2 has the highest mean, so it is the best-hitting team.

In this example, it was determined that Team 2 was the best-hitting team by finding the mean of each team's hitting percentages. The mean of Team 1's hitting percentages was 0.3125, and the mean of Team 2's hitting percentages was 0.3267. Since Team 2 had the highest mean, it was determined to be the best-hitting team.

The best-hitting team can be calculated by finding the mean of each team's hitting percentages. To do this, add the ten numbers for each team and divide by 10.

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Using the normal distribution and the central limit theorem, considering that this is a sample proportion, as we are dealing with percentages, it is found that there is a 0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.

Normal Probability Distribution

In a normal distribution with mean  and standard deviation , the z-score of a measure X

It 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, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean  and standard deviation .

In this problem:

55% of the registered voters are Democrats, hence .

A sample of size 100 is taken, hence

The mean and the standard deviation of the sampling distribution of sample proportions

The probability of getting less than 50% Democrats in a random sample of size 100 is the p-value of Z when X = 0.5, hence:

By the Central Limit Theorem

has a p-value of 0.1562.

0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.

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