Which of the following is the value of a when the function f(x) = 3|x| written in the standard form of an absolute value function?
–1
–3
1
3

Simplify

22 - (-24)

Swap since they are both negatives.

22-(-24) =

22+(24)

22+24

= 46

Which now add in the negative 32 to the problem

46 + (-32)

Recreate the problem to make it more simple:

46 - 32

  = 14

The probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.

Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. It is used to quantify uncertainty and make predictions based on incomplete information. In general, probability is defined as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur.

The basic concept of probability is based on the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 or 0.5, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

We can use the central limit theorem to approximate the distribution of the sample mean, assuming that the sample size is large enough. Since the sample size is n=36, we can assume that the sample mean has a normal distribution with mean μ=6.1 and standard deviation σ/√n=0.6/√36=0.1.

Let X be the sample mean sleeping time per night. Then we need to find the probability P(X > 6), which can be transformed into a standard normal distribution using the formula:

Z = (X - μ) / (σ/√n)

where Z is the standard normal variable.

Substituting the given values, we get:

Z = (6 - 6.1) / (0.1) = -1

Now we need to find the probability that Z is greater than -1. Using a standard normal distribution table or calculator, we can find that the probability is approximately 0.8413.

Therefore, the probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.

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The missing polynomial is 40 - 4x - 12x²

The missing polynomial is solved by comparing the polynomials as done below

? - (20 - 4x - 5x²) = 20 - 7x²

? =  20 - 7x² + (20 - 4x - 5x²)

comparing the terms

constant terms: 20 + 20 = 40

x terms : -4x

x² terms : -7x² - 5x² = -12x²

This can be combined as 40 - 4x - 12x²

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There are approximately 819 children who weigh between 40 kilograms and 55 kilograms.

What is Standard deviation ?

Standard deviation is a measure of the spread or dispersion of a set of data from its mean. It is calculated as the square root of the variance.

To solve this problem, we can use the properties of a normal distribution, assuming that the weights of the children follow a normal distribution.

We know that the mean weight of 1000 children is 50 kilograms and the standard deviation is 5 kilograms. This means that the weights of the children are distributed around the mean with a spread of 5 kilograms.

We want to find the number of children who weigh between 40 kilograms and 55 kilograms. To do this, we can standardize the values using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can use the following formula to standardize the values:

z = (x - μ) ÷  σ

where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.

For x = 40 kilograms:

z = (40 - 50) ÷  5 = -2

For x = 55 kilograms:

z = (55 - 50) ÷ 5 = 1

Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -2 and z = 1. This area represents the proportion of children who weigh between 40 kilograms and 55 kilograms.

Using a standard normal distribution table or calculator, we find that the area under the curve between z = -2 and z = 1 is approximately 0.8186.

Therefore, the number of children who weigh between 40 kilograms and 55 kilograms is:

0.8186 * 1000 = 818.6 children

Since we can't have a fraction of a child, we round this number to the nearest whole number, which is 819 children.

Therefore,  there are approximately 819 children who weigh between 40 kilograms and 55 kilograms.

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Mr Leonard will receive a discount of £45.84 on his oil purchase.

We must first determine the entire amount of oil Mr. Leonard intends to buy in order to determine the discount he will receive.

There are currently 450 liters in the tank, which has a capacity of 1200 liters. Therefore, Mr. Leonard needs to buy an extra 750 liters (1200 - 450 = 750).

The total cost of the oil before the discount must then be determined.

With a litre costing 81.5p, the price for 750 liters of oil would be:

750 liters x 81.5 pence per liter = £611.25.

We must multiply the entire cost of the oil by the discount rate (7.5 percent, or 0.075), in order to determine the discount:

£611.25 x 0.075 = £45.84

Therefore, Mr Leonard will receive a discount of £45.84 on his oil purchase.

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The total amount of oil that can be added to the tank is 1200 liters, and there are already 450 liters in the tank. Therefore, the tank can hold an additional 750 liters of oil.

Mr. Leonard will get a discount of [tex]£45.84[/tex] on this purchase.

The price of oil is 81.5p per litre. So, the cost of 750 liters of oil would be:

[tex]750 * 81.5p = £ 611.25[/tex]

As Mr. Leonard is a loyal customer and gets a discount of 7.5% on the price of oil, he will get a discount of:

[tex]7.5% of £611.25 = £45.84[/tex]

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Answer:

D

Step-by-step explanation:

If you flip the X and Y axis you get the same answer

You could shade in the faces of the prism or add labels to identify different parts of the drawing.

What is Pentagonal ?

"Pentagonal" is an adjective that describes something that has five sides or angles. In geometry, a pentagon is a two-dimensional shape with five straight sides and five angles.

To draw a pentagonal prism, you'll need to follow these steps:

Draw identical pentagonal bases: Start by drawing two identical pentagons. Make sure they have the same size and shape. You can use a ruler and a protractor to help you draw the lines.

Draw five vertical lines: Connect each vertex of one pentagon to its corresponding vertex on the other pentagon using straight lines. These lines should be perpendicular to the base and have the same length. You should end up with five evenly spaced vertical lines.

Change any hidden lines to dashed lines: Identify any lines that won't be visible in the final drawing and change them to dashed lines. This will help to make the drawing easier to read and understand.

Add any additional details: Once you've completed the basic shape of the pentagonal prism, you can add any additional details or shading to make the drawing more realistic or interesting.

Therefore,  You could shade in the faces of the prism or add labels to identify different parts of the drawing.

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Thus, the parking space is longer than length of the truck by 42 inches.

The same attribute is expressed using a unit conversion, but in a different measurement equivalent. For instance, time can always be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or another type of measurement unit instead of miles.

Using conversion factors, existing units, and or the fact that a unit of measure cancels out another unit of measure, a unit cancellation table is created.

Given data:

Length of the parking space = 60 feet

Length of truck = 6 yard.

Convert yards in feet

1 yard = 3 feet

Multiply both side by 6.

6*1 yard = 6*3 feet

6 yard = 18 feet

Difference = 60 - 18 = 42 feet.

The parking space is longer than length of the truck by 42 inches.

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Answer: Choice A

Step-by-step explanation:

M= slope

B= y-intercept

Answer:

First, we need to find the quadratic function that models the given table. We know that a quadratic function has the form: y = ax^2 + bx + c where a, b, and c are constants to be determined. To find these constants, we need to use the values in the table. When x = -5, y = 0, we get: 0 = a(-5)^2 + b(-5) + c 0 = 25a - 5b + c When x = -3, y = 12, we get: 12 = a(-3)^2 + b(-3) + c 12 = 9a - 3b + c When x = -1, y = 12, we get: 12 = a(-1)^2 + b(-1) + c 12 = a - b

Step-by-step explanation:

F'(x) = f(x + h)² - 5(x + h) + 3 - (x² - 5x + 3)

---------------------------------------------------

h

F'(x) = x² + 2xh + h² - 5x - 5h + 3 - x² + 5x - 3

--------------------------------------------------------

h

F'(x) = 2xh + h² - 5h

-----------------------

h

F'(x) = h(2x + h - 5)

----------------------

h

F'(x) = 2x + h - 5

Lim

h---0

= 2x + 0 - 5

= 2x - 5

1) The cost of both bands would be equal for 100 students. 2) the fixed cost for the caterer is $150 and the rate per student served is $3. 3) Ticket Price = $4.75 4) you can afford a maximum of 3 bouquets of roses.

Let x be the total number of students in Part 1A.

Band A costs $500.

Band B costs $350 plus $1.50 times.

Part B: By graphing the equations, we can determine the location where the price of the two bands is equal.

$500 = $350 + $1.50x \s$150 = $1.50x \sx = 100

As a result, the price for both bands for 100 students would be the same.

Part 2: Let's solve for the fixed cost and rate per student served using the information provided:

50f + 50r = $450

150f + 150r = $1050

When we deduct the first equation from the second, we obtain:

100f + 100r = $600

F plus R equals $6 when we divide by 100.

The result of replacing the value of f in the first equation is:

50($6 - r) + 50r = $450

$300 - 50r + 50r = $450 \sr = $3

As a result, the caterer's fixed fee is $150, and the cost each student served is $3.

Part 3: For 100 pupils, Band A would cost $500, and Band B would cost $350 plus $1.50 (100) for a total of $500.

Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:

Total Price = Band Fee + Caterer Fee

Expense in total is $500 plus ($150 + $3(100)).

Final price: $950

Total Cost / Number of Students x Ticket Price equals $9.50

Band A would cost $500 for 200 pupils, and Band B would cost $350 + $1.50 (200) = $650.

Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:

Total Price = Band Fee + Caterer Fee

Expense in total is $500 plus ($150 + $3(200)).

Final price: $950

Total Cost / Number of Students x Ticket Price is $4.75

Let d be the total number of daisy bouquets and r be the total number of rose bouquets in part 4A.

[tex]25d + 35r \leq $500[/tex]

B. You would have spent $375 if you purchased 15 bouquets of daisies at a cost of 15 ($25).

When we deduct this from the overall budget, we get:

$500 - $375 = $125

The result of dividing by the price of one bunch of roses is: $125/$35 3.57.

Thus, you can buy no more than three rose bouquets.

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The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.

Circumference is the distance around the edge of a closed curve or a circle. It is the length of the boundary of a circular object or shape. In other words, it is the total length of the circular shape.

We can use trigonometry to determine the rotation's angle. The rider's height above the ground is equal to the ferris wheel's radius plus the distance travelled around its circle. Let's call the angle of rotation we're trying to find θ.

The distance traveled along the circumference of the wheel can be calculated as follows:

distance = θ/360 * 2πr

where r is the radius of the wheel. Substituting the given values, we get:

95 = 100 + θ/360 * 2π(100)

Simplifying the equation:

θ/360 = (95-100)/(2π(100))

θ/360 = -0.007957747

θ = -2.8661 degrees or 357.1339 degrees

So there are two possible answers: The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.

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The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear function.

A linear function is one whose graph on a Cartesian plane is a straight line. The line is always straight even though it can travel in any direction.

Given table:

x        y

-2      -7

-1       -4

0      -1

1         2

2        5

Plot the coordinates on graph:

(-2, -7), (-1, -4),(0,-1),(1,2),(2,5)

The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear.

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Complete question:

Explain, if the given table shows linear or non linear function?

x        y

-2      -7

-1       -4

-0      -1

1         2

2        5

Answer:2000

Step-by-step explanation:

Dana has 1500 yellow beads when Dana had an equal number of red beads and yellow beads.

Dana had an equal number of red beads and yellow beads, so let's say she had x red beads and x yellow beads.

After using 500 red beads to make necklaces, she was left with x - 500 red beads.

Since she now had 3 times as many yellow beads as red beads, she had a total of 3 * (x - 500) = 3x - 1500 yellow beads.

We know that the total number of yellow beads is x, so we can set the two expressions equal to each other:

x = 3x - 1500

Solving for x, we get:

2x = 1500

x = 750

Therefore, Dana had x = 750 yellow beads.

Since she now has 3 times as many yellow beads as red beads, she has a total of 3 * 750 = 1500 yellow beads.

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Answer:

Since the legs of figure 2 are twice as long as those of figure 1, the scale factor to produce figure 1 from figure 2 would be 1/2. This means that every length in figure 1 is half the length of the corresponding length in figure 2.

Answer:

Option A. 1/2

Step-by-step explanation:

100 on the test!

The value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.

What is mean?

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the IQR for the mean of 15 pumpkins, we need to first find the standard error of the mean, which can be calculated using the formula:

SEM = σ / sqrt

where SEM is the standard error of the mean, σ is the standard deviation, and n is the sample size.

Substituting the given values, we get:

SEM = 1.68 / sqrt(15) = 0.433

The interquartile range (IQR) for the mean can be calculated as:

IQR = 1.35 * SEM

where 1.35 is the multiplier for the IQR based on the normal distribution.

Substituting the value of SEM, we get:

IQR = 1.35 * 0.433 = 0.585

Rounding to the nearest thousandth, we get the final answer as:

IQR ≈ 0.585

Therefore, the value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.

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The 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.

Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.

The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.

To determine which is a better buy, we need to compare the cost per fl. oz. of detergent for both options.

For the first option, the cost is $3.99 for 25 fl. oz., so the cost per fl. oz. is:

Cost per fl. oz. = $3.99 / 25 fl. oz. ≈ $0.16/fl. oz.

For the second option, the cost is $6.99 for 90 fl. oz., so the cost per fl. oz. is:

Cost per fl. oz. = $6.99 / 90 fl. oz. ≈ $0.08/fl. oz.

Since the cost per fl. oz. is lower for the second option, it is a better buy. Therefore, the 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.

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The complete question is:

It cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?

By using the P-value method, we conclude that, fewer than half of Americans prefer to watch the news rather than read or listen to it.

What is p-value?

In statistics, the p-value is a probability value that measures the evidence against a null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the actual test statistic, assuming that the null hypothesis is true.

In this problem, we want to test the claim that fewer than half of Americans prefer to watch the news, based on a poll of 1075 Americans where 46.8% of the respondents said they prefer to watch the news.

Let p be the true proportion of Americans who prefer to watch the news. Then the null hypothesis is:

H0: p ≥ 0.5 (more than or equal to half of Americans prefer to watch the news)

The alternative hypothesis is:

Ha: p < 0.5 (fewer than half of Americans prefer to watch the news)

We will use the normal distribution as an approximation to the binomial distribution, since n = 1075 is large and the success-failure condition is satisfied. The expected number of respondents who prefer to watch the news is:

E = np = 1075 × 0.468 = 503.1

The standard deviation of the sampling distribution of p is:

σ = sqrt[(p(1-p))/n] = sqrt[(0.5×0.5)/1075] ≈ 0.015

We can now calculate the z-score for the sample proportion:

z = (x - E) / σ = (1075 × 0.468 - 503.1) / 0.015 ≈ -4.28

where x is the observed number of respondents who prefer to watch the news, which is 1075 × 0.468 ≈ 503.

The P-value for this test is the probability of getting a z-score less than or equal to -4.28 under the standard normal distribution. Using a standard normal table or calculator, we find that this probability is very close to 0. Therefore, the P-value is less than 0.10, the chosen significance level.

Since the P-value is less than the significance level, we reject the null hypothesis. We have sufficient evidence to conclude that fewer than half of Americans prefer to watch the news rather than read or listen to it.

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-1, -0.10, 0.15, 0.25

So, the answer is the way we do it

-1 , -0.1(or 0.10) , 0.15 , and 0.25

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The required value of x is approximately [tex]x = 257.25[/tex] cm.

The volume of cuboid A can be found by multiplying its length, width, and height:

[tex]$V_A = 6\text{ cm} \times 2\text{ cm} \times 5\text{ cm} = 60\text{ cm}^3$[/tex]

To find the volume of cuboid C, we can use the given information that the volume of A multiplied by 343/8 is equal to the volume of C:

[tex]$V_C = V_A \times \frac{343}{8} = 60\text{ cm}^3 \times \frac{343}{8} =2572.5[/tex]

Now, we can use the formula for the volume of a cuboid to find the length of C:

[tex]$V_C = \text{length} \times \text{width} \times \text{height}$[/tex]

[tex]$2572.5}\text{ cm}^3 = x\text{ cm} \times 2\text{ cm} \times 5\text{ cm}$[/tex]

[tex]{2572.5}\text{ cm}^3 = 10x\text{ cm}^3$[/tex]

[tex]x = 257.25[/tex]

Therefore, the value of x is approximately [tex]x = 257.25[/tex] cm.

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Answer:

they bought 8 candy bars and 8 + 4 = 12 packs of gum.

Step-by-step explanation:

Let's use algebra to solve this problem:

Let x be the number of candy bars they bought.

Then, the number of packs of gum they bought is x + 4.

The total cost of the candy bars is 60x cents.

The total cost of the packs of gum is 85(x + 4) cents.

We know that they spent $15.00, which is 1500 cents, so we can write an equation:

60x + 85(x + 4) = 1500

Simplifying the equation, we get:

145x + 340 = 1500

145x = 1160

x = 8

Therefore, they bought 8 candy bars and 8 + 4 = 12 packs of gum

Answer: 22

Step-by-step explanation:

The number of the gum is 13 and the number of the candy will be 22.

What is linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.

They spent $26.38 total and bought 35 items total.

Let x be the number of the gum and y be the number of the candy.

Then the equation will be

x + y = 35 ...1

0.54x + 0.88y = 26.38 ...2

By solving the equations 1 and 2, then we have

x = 13 and y = 22

Then the number of the gum is 13 and the number of the candy will be 22.

Answer:

the answer is d

Step-by-step explanation:

before the increase the range is three with the lowest number being four and the highest 7

where as after the increase the lowest value is 5 and the highest nine giving us a range of four

four minis three is one therefore the range increases by one mile

Answer: D: The range will increase by 1 mile.

Step-by-step explanation:

The current range is solved by doing the highest number minus the lowest number, so 7-4. The current range would therefore be 3.

The miles on Monday and Tuesday have been increased by 1 mile, from 4 miles to 5 miles.

The miles on Friday, Saturday and Sunday have been increased by 2 miles, from 7 miles to 9 miles.

You subtract the new values: 9 miles - 5 miles = 4 miles

And subtract your new values from your old range: 4 miles - 3 miles = 1 mile

The range would therefore increase by 1 mile.

Answer

a=24

Step-by-step explanation:

12 times 24 equals 288 plus 14 equals 302

If we take multiple samples of the same size and calculate their means, 90% of the resulting sample which is 69.3 means will fall within 9.02 units of the true population mean for standard deviation.

The following formula must be used to determine the margin of error for a 90% confidence interval for the population mean ():

Margin of error =  [tex]z * (/n)[/tex].

where is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution with a 90% confidence level.

The matching z-value is 1.645 because a 90% confidence interval is what we are looking for. Thus, the margin of error can be determined as follows:

Margin of error: (50 / 77) / 1.645 = 9.02

This indicates that 90% of the sample means obtained when calculating the means of several samples of equal size will be within 9.02 units of the actual population mean.

It is significant to remember that the margin of error lowers with sample size and rises with confidence level. A bigger sample size in this situation would lead to a smaller margin of error, whereas a greater confidence level would lead to a larger margin of error.

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A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice. So, B is the right answer.

The American Society of Home Inspectors is known as ASHI. It is a non-profit company with its main office in Des Plaines, Illinois, and it was established in 1976.

ASHI's major objective is to advance professionalism in the home inspection industry by establishing and upholding high standards for its members. Home inspectors can get education, training, and certification from ASHI. Members are also obliged to abide by the organisation's Code of Ethics and Standards of Practice. The minimal requirements for a house inspection are outlined in the Standards of Practice, along with the inspector's obligations to the client.

A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice.

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Answer:

Step-by-step explanation:

compliment of an event A is probability of not happening A

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