The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a

mean diameter of 22 mm and a standard deviation of 2. 5 mm. After they are picked and washed, tomatoes with a

diameter of at most 15 mm or at least 30 mm are rejected and not sold. What proportion of such tomatoes are

rejected?

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O 0. 0033

O 0. 0201

O 0. 9799

O 0. 9967

Yes, the walls form a right angle.

To determine if the walls form a right angle, we can use the Pythagorean theorem. The question states that a wall 12 feet long makes a corner with a wall that is 14 feet long, and the other ends of the walls are about 18.44 feet apart.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, let's consider the 12-foot and 14-foot walls as the two shorter sides, and the 18.44-foot distance as the potential hypotenuse.

Step 1: Calculate the square of the lengths of the 12-foot and 14-foot walls.

12² = 144

14² = 196

Step 2: Calculate the sum of the squares of these two sides.

144 + 196 = 340

Step 3: Calculate the square of the length of the 18.44-foot distance.

18.44² ≈ 339.95

Since 339.95 is very close to 340, we can conclude that the walls form a right angle.

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According to the information, we can infer that the dimension of each shape is A are 8 x 8.5 x 2, B are 8 x 2 x 10, olume of 401.9 cubic inches,  height of 2 inches and a radius of 4 inches.

For shape A, the height of the rectangular prism is equal to the length of the paper (8 inches) and the width is equal to one-fourth of the width of the paper (2 inches). Therefore, the dimensions of shape A are 8 x 8.5 x 2.

For shape B, the height of the rectangular prism is equal to one-fourth of the length of the paper (2 inches) and the width is equal to the width of the paper (8 inches). Therefore, the dimensions of shape B are 8 x 2 x 10.

For shape C, the height of the cylinder is equal to the length of the paper (8 inches) and the radius of the circle top is equal to one-half of the width of the paper (4 inches). Therefore, the dimensions of shape C are a height of 8 inches and a radius of 4 inches, giving a volume of 401.9 cubic inches (rounded to one decimal place).

For shape D, the height of the cylinder is equal to one-fourth of the length of the paper (2 inches) and the radius of the circle top is equal to one-half of the width of the paper (4 inches). Therefore, the dimensions of shape D are a height of 2 inches and a radius of 4 inches, giving a volume of 100.5 cubic inches (rounded to one decimal place).

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it will cost Vince $5,175 to get new carpet installed, assuming the area to be covered is 500 square feet.

To calculate the cost for Vince to get new carpet installed, we need to add up the cost of the carpet, padding, labor, and hauling away the old carpet.

Let's assume that the area to be covered is 500 square feet. Then, the cost for each component can be calculated as follows:

Cost of carpet = $8/sq ft * 500 sq ft = $4,000

Cost of carpet padding = $0.30/sq ft * 500 sq ft = $150

Cost of labor = $0.75/sq ft * 500 sq ft = $375

Cost of hauling away old carpet = $1.30/sq ft * 500 sq ft = $650

Total cost = Cost of carpet + Cost of carpet padding + Cost of labor + Cost of hauling away old carpet

= $4,000 + $150 + $375 + $650

= $5,175.

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A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C. preconditions. These elements help provide a clear understanding of how a system should interact with its users and the expected outcomes.

A document can be defined as a form of information that might be useful to a user or set of users1. It can be either digital or nondigital1. Different methods are used to store digital and non-digital documents

There are different types of documents such as job descriptions2, and project descriptions. and technical descriptions5.

A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C.

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A z-score is a statistical measurement that indicates how many standard deviations an individual value is from the mean - True.

The mean from the value of interest and dividing the result by the standard deviation.

This standardized score provides a way to compare values from different data sets or populations.

For example, if a student's score on a test is 80 and the mean score for the class is 70 with a standard deviation of 5, the student's z-score would be 2.

This means that the student's score is two standard deviations above the class mean. This information can be useful in understanding the student's performance relative to their peers.

Z-scores can also be used to identify outliers or extreme values in a data set. Values with a z-score greater than 3 or less than -3 are considered to be outliers and may warrant further investigation.

In summary, a z-score is a valuable tool in statistical analysis that measures how many standard deviations a value is from the mean. It provides a standardized way to compare values across different data sets and can help identify outliers or extreme values.

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Answer:x+2

Step-by-step explanation:

If the  domain is{ -12,-7,0,4,12} and range is {0,1,2} then the function is  {(4, 1), (-7, 0), (12, 2), (0, 0), (-12, 1)}

The domain of a function is the set of values that we are allowed to plug into our function.

This set is the x values in a function such as f(x).

The range of a function is the set of values that the function assumes

domain is{ -12,-7,0,4,12} range is {0,1,2}

The function that has the given domain and range is:

{(4, 1), (-7, 0), (12, 2), (0, 0), (-12, 1)}

Therefore, the function is {(4, 1), (-7, 0), (12, 2), (0, 0), (-12, 1)}

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Which function has the following domain and range?

Domain: {-12, - 7, 0, 4, 12}

Range: {0, 1, 2}

O {(-12, 12), (0, 2)}

O {(4, 1), (-7, 0), (12, 2), (0, 0), ( − 12, 1)}

O {(-12, 0), ( – 7, 1), (0, 2), ( – 4, 5), (3, -1)}

O {(0,4), (2, 12), (1, -7), (0, - 12), (1, 0)}

The volume of the bookshelf is 1/4 cubic units.

The amount of space a three-dimensional object occupies is measured by its volume.

A cubic unit, such as a cubic foot, cubic metre, or cubic metre is typically used to express it.

An object's volume can be calculated by figuring out how much space is contained within its boundaries. Depending on the shape of the object, different mathematical formulas can be used to accomplish this.

To calculate the volume of the bookshelf, we need to add the volumes of the two cubes together.

The length of one side cubed determines a cube's volume.

Since each cube has a side of (1/2), the volume of each cube can be calculated as:

(1/2)³ = 1/8

To get the total volume of the bookshelf, we can add the volumes of the two cubes:

1/8 x 2 = 1/4

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The volume of  the solid is 761.97 in².

The mistake the student made is that the student did not subtract the square of the radius of the inner hollow cylinder  from the square of the radius of the main cylinder.

The volume of the solid can be found by adding the volume of hollow cylinder and the volume of the cone. That is:

Volume of solid = volume of hollow cylinder + volume of the cone

Volume of solid = π(R²-r²)H + 1/3πR²h

where R = 8/2 = 4 in, r = 2 in, H = 18 in and h = 5 in

Volume of solid = [3.14 * (4²-2²) * 18] + [1/3 * 3.14 * 4² * 5]

Volume of solid = 678.24 + 83.73

Volume of solid = 761.97 in²

The mistake the student made is that the student did not subtract the square of the radius of the inner hollow cylinder  from the square of the radius of the main cylinder.

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The quadratic equation in the given graph is:

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

How to write the quadratic.

Look at the vertex, is it at (1, 4), then we can write the general quadratic equation in the vertex form (with a leading coefficient a) as follows:

y = a(x - 1)^2 + 4

Now the function passes through (0, 1) then we can replace these values in the equation above to get.

1 = a(0 - 1)^2 + 4

1 = a + 4

1 - 4 = a

-3  =a

The quadratic equation is:

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

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In the number 425.871, the digit with the greatest value is 4 because it is in the hundreds place, representing a value of 400.

In the number 425.871, each digit has a position and a value based on where it's located in the number. The position starting from the right of the decimal point we call the tenths, hundredths, and thousandths place, respectively. Similarly, the position to the left of the decimal point is called the ones, tens, hundreds place, etc., respectively. In this case, the digit with the greatest value is the one in the hundreds place, which is 4. This is because it represents 400, which is greater than any other individual digit's value in the number 425.871.

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With a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.

To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have electrical/environmental problems, we need to have a sample of data on this issue. Let's assume that we have a random sample of 100 homes, and 20 of them were found to have electrical/environmental problems.

To calculate the lower confidence bound, we can use the formula:

Lower bound = p - zα/2 * sqrt(p * (1-p) / n)

where:

p = proportion of homes in the sample that have electrical/environmental problems = 20/100 = 0.2

zα/2 = z-score for the given confidence level of 99% = 2.576 (obtained from a standard normal distribution table or calculator)

n = sample size = 100

Plugging in these values, we get:

Lower bound = 0.2 - 2.576 * sqrt(0.2 * 0.8 / 100) = 0.083

Therefore, with a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.

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This means we can be 99% confident that the true percentage of all homes with electrical/environmental problems is

at least 17.5%.

To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have

electrical/environmental problems, you would need a sample of homes and the number of homes in the sample that

have such problems. Using this information, you could calculate the sample proportion (p-hat) of homes with

electrical/environmental problems.

Then, using a formula or calculator, you could find the lower confidence bound by subtracting the margin of error (ME)

from the sample proportion.

The margin of error can be calculated using the sample proportion, sample size, and the chosen confidence level (in

this case, 99%).

For example, if the sample proportion is 0.25 and the sample size is 100, the margin of error would be 0.075 and the

lower confidence bound would be 0.175 (0.25 - 0.075).

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The volume of the candle is,⇒ V = 31.4 in³.What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.Given that;A candle in the shape of a cylinder has the dimensions shown, in inches.And, Diameter of candle = 5 in.Height of candle = 8 in.We know that;Volume of cylinder = πr²hHence, We get;The volume of the candle is,⇒ V = 3.14 × (5/2)² × 8⇒ V = 3.14 × 10⇒ V = 31.4 in³.Thus, The volume of the candle is,⇒ V = 31.4 in³.

If your business starts with 3% awareness and grows awareness by 5% per week (compounded), how long will it take to reach 75% awareness is b) 66 weeks

Compound growth denotes the procedure of generating profits not only on the investment's principal amount, but also on the accumulated interest.

It is essentially reallocating its earnings where the investor's interest is integrated with the beginning sum, while additional interest is contingent on this amplified amount.

The purposeful act of compounding can yield noteworthy accomplishments over time, since interest earned from pre-existing income inflates drastically in value due to accruing interest outlays, and hence boosts the final outcome substantially and rapidly- resulting in exponential growth of the given input.

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If "water-sprinkler" sends out water 21 feet in any direction in circular pattern, then the area formed by water pattern is 1384.74 feet².

If the sprinkler can spray water out 21 feet in any direction, then the radius of the circular pattern formed by the water is 21 feet.

The formula for area of circular pattern is : A = πr², where 'r" is = radius of the circle.

Substituting the radius of circular pattern as 21 feet,

We get,

⇒A = πr² = 3.14 × 21 × 21 = 1384.74 ft².

Therefore, the area formed by the water pattern is 1384.74 square feet.

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Step-by-step explanation:

Put '16' where 'x' is and compute

3/4 ( 16 ) + 7 = f(16) = 19

The true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.

In hypothesis testing, the power of a test refers to the probability of correctly rejecting a false null hypothesis.

To calculate the power of a test, we need to know the significance level of the test, the sample size, the effect size, and the variance of the population.

Additionally, we need to know the specific hypothesis being tested, as the decision rule and power calculation depend on the null and alternative hypotheses.

A hypothesis test for the population mean amount of mercury in a certain type of fish.

Test whether the mean amount of mercury is different from 11.5 micrograms per ounce, using a two-tailed test at a significance level of 0.05.

If the sample size is 100, the effect size is 0.5, and the population variance is 4, then the power of the test is approximately 0.7629.

This means that if the true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.

The hypothesis test, it is impossible to calculate the power.

It is essential to know the specific hypothesis being tested, as well as the details of the test, such as the sample size, effect size, and variance.

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The money in the account will be $252.

For simple interest, use the formula:

I = Prt

where I stands for interest earned, P for principle (amount paid in the beginning), r for yearly interest rate (in decimal form), and t for the time in years.

P equals $200, r equals 0.052, and t equals 5. With these values entered into the formula, we obtain:

I = Prt = ($200)(0.052)(5) = $52

The account will thus have $52 in interest after 5 years. After five years, we add the interest to the principal to determine the account's total balance:

Total = $200 + $52 = $252

Therefore, after five years, the account will have $252.

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A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of _12_ cell(s). Researchers would need to investigate _three__ main effect(s), _Three two-way interactions __ two-way interaction(s), and _ One three-way interaction__ three-way interaction(s) in this study.

a 2 x 2 x 3 within-groups factorial design, you have:
A total of 2 x 2 x 3 = 12 cells
Three main effects to investigate (one for each factor)
Three two-way interactions to investigate (AxB, AxC, and BxC)
4. One three-way interaction to investigate (AxBxC)
So, in this study, there are 12 cells, researchers would need to investigate 3 main effects, 3 two-way interactions, and 1 three-way interaction.

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The sum of the roots of x² - 9x + 8 is 9. The product of the roots of x² - 9x + 8 is 8.

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.

The expression x² - 9x + 8 can be factored as follows:

x² - 9x + 8 = (x - 1)(x - 8)

To check that this factorization is correct, you can expand the expression using the distributive property:

(x - 1)(x - 8) = x² - 8x - x + 8 = x² - 9x + 8

So the factorization is indeed correct.

The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -b/a, where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -9, and c = 8, so the sum of the roots is:

-sum of roots = -b/a = -(-9)/1 = 9

Therefore, the sum of the roots of x² - 9x + 8 is 9.

The product of the roots of the quadratic equation ax² + bx + c = 0 is given by c/a. In this case, c = 8 and a = 1, so the product of the roots is:

product of roots = c/a = 8/1 = 8

Therefore, the product of the roots of x² - 9x + 8 is 8.

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The volume of the cube is 1.82 in³

We know that the formula for the area of the cube, as a function of the volume, is:

A = 326*V^(2/3)

Solving that equation for V, we will get.

V = (A/326)^(3/2)

Then the volume of a cube whose surface area is A = 486 square inches is:

V = (486 in²/326)^(3/2)

V = 1.82 in³

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in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma

The correct answer is B.

N(x) = 40x + 12,500.

This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.

Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.

Based on the given information, the correct answer is B.

N(x) = 40x + 12,500
This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.

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The correct answer is B.N(x) = 40x + 12,500.

This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.

Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.

Based on the given information, the correct answer is B.

N(x) = 40x + 12,500

This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.

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It will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute

Assuming that the filling rate of the hose is constant, we can use the formula:

time = volume / rate

where time is the time taken to fill the hot tub, volume is the volume of the hot tub (440 gallons), and rate is the filling rate of the hose (4.6 gallons per minute).

Substituting the values, we get:

time = 440 / 4.6

which simplifies to:

time = 95.65 minutes

To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):

time = 95.65 / 60

which simplifies to:

time = 1.59 hours

Therefore, it will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute.

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It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.

To determine how many hours follow these steps:

First, we need to find out how many minutes it takes to fill the hot tub.

Divide the total volume of the hot tub (440 gallons) by the rate at which the hose fills (4.6 gallons per minute):

440 gallons ÷ 4.6 gallons/minute = 95.65 minutes

Now, we need to convert the minutes into hours.

Since there are 60 minutes in an hour, divide the minutes by 60:

95.65 minutes ÷ 60 minutes/hour = 1.594 hours

It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.

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Answer:

first one is 18 second one is 45

Step-by-step explanation:

add 18 and 45 to get 63

area is 63

Answer: f(8) = -208

Step-by-step explanation:

     To solve, we will substitute 8 into the equation for x.

Given:

     f(x) = -3x² - 2x

Substitute 8 for x:

     f(8) = -3(8)² - 2(8)

Square:

     f(8) = -3(64) - 2(8)

Multiply:

     f(8) = -192 - 16

Subtract:

     f(8) = -208

The number of hours that it will 2000-km flight would be = 2.5 hours.

The number of hours can be determined when a straight line is being drawn from the origin of the graph and allowing it to pass through most of the interceptions.

Therefore, form the graph, the amount of hours that it will take the 2000-km flight would be = 2.5 hours approximately.

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