The length of the enclosure for the pancake tortoise must be greater than the height. The volume of the enclosure is expressed in terms of the width, w.
w^3+6w^2-40w
Factor the expression, then match the factors to the dimensions they represent.

Let's break down the information given: "Three times the square of a number is greater than a second number." This can be represented as 3x^2 > y, where x is the first number and y is the second number.

"The square of the second number increased by 6 is greater than the first number." This can be represented as y^2 + 6 > x. Combining these two inequalities, we have: 3x^2 > y (Equation 1). y^2 + 6 > x (Equation 2).  Therefore, the system of inequalities that represents these criteria is: { 3x^2 > y, y^2 + 6 > x }

Three times the square of a number is greater than a second number. The square of the second number increased by 6 is greater than the first number. The system of inequalities that represents these criteria is: { 3x^2 > y, y^2 + 6 > x }

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The order top 2% of test takers must score at least 684 or higher on the test to get an interview with Bill Gates.

In order to be in the top 2% of test takers on a test with a mean of 500 and a standard deviation of 100, a test taker must score at least 684 or higher. This means that the test taker must be at least two standard deviations above the mean in order to be considered for an interview with Bill Gates. It is important to note that a score of 684 or higher is only the minimum requirement. Test takers may need to score even higher if they wish to have a better chance of getting the interview. Furthermore, even if the test taker scores 684 or higher, there is still no guarantee that they will get the interview as other factors such as the number of test takers and the quality of their application can also play a role.

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1. Absolute maximum: f(x) = 37.6/7
  Absolute minimum: f(x) = 37.6/7

2. y is increasing on: No intervals
   y is decreasing on: (-∞, +∞)

To find the absolute extrema of the constant function f(x) = 37.6/7 on the interval (-6, -3), we should first understand that since it is a constant function, its value will not change for any x in the given interval. Therefore, f(x) = 37.6/7 for all x in the interval.

Absolute maximum: f(x) = 37.6/7
Absolute minimum: f(x) = 37.6/7

For the function y = r - 48x + 3, to find the intervals where it is increasing and decreasing, we need to find its first derivative with respect to x. Then, we analyze the sign of the derivative to determine the intervals.

Step 1: Differentiate the function with respect to x.
dy/dx = -48

Step 2: Analyze the sign of the derivative.
Since dy/dx = -48 is negative for all values of x, the function is decreasing everywhere.

y is increasing on: No intervals
y is decreasing on: (-∞, +∞)

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

Below are some authorial techniques that can be used to create mystery, tension, or surprise in literature.

Order of events: The order in which events are presented can create a sense of mystery or suspense.

Pacing: The pace of a story can also be used to create suspense. A slow-paced story can build tension by allowing the reader to dwell on the details of a situation, while a fast-paced story can create excitement and surprise by keeping the reader guessing what will happen next.

Structure: The structure of a story can also be used to create mystery, tension, or surprise. For example, a story that is told in flashback can create a sense of mystery by revealing information about the past that is relevant to the present.

Time manipulation: The manipulation of time can also be used to create suspense.

Language: The language that an author uses can also be used to create mystery, tension, or surprise. For example, an author might use vague or ambiguous language to create a sense of mystery, or use strong language to create a sense of tension or surprise.

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Answer:

24

Step-by-step explanation:

Here is the full question used in answering this question :

Francine wants to find a total of 2/3 cup of blueberries and 5/8 cup of raspberries what is the least common denominator of the fractions

Least common denominator of fractions is the smallest number that can divide both the denominator of 2/3 and the denominator of 5/8. The denominators here are 3 and 8

The least common denominator = 3 x 8 = 24

If the sample size were n=48, the margin of error would be larger.  Part 1 of 2: Margin of error is used to measure the accuracy level of the population parameter based on the given sample statistic.

It is the range of values above and below the point estimate, which is the sample mean and represents the interval within which the true population mean is likely to lie at a certain level of confidence.

The formula to calculate margin of error is:

Margin of error (ME) = z*(σ/√n)

Where, z is the z-score representing the level of confidenceσ is the standard deviation of the population n is the sample size From the given information, Sample size,

n = 61

Standard deviation, σ = 6

Confidence level, 99%

The z-score for 99% confidence level can be found by using the formula as shown below:

z = inv Norm(1-(α/2))

=  inv Norm(1-(0.01/2))

= inv Norm(0.995)

≈ 2.576Substituting the values into the formula of the margin of error,

Margin of error (ME) = z*(σ/√n) = 2.576*(6/√61) = 1.967 ≈ 1.967

So, the margin of error for a 99% confidence interval for μ is 1.967.

Part 2 of 2: If the sample size were n = 48, the margin of error will be larger because of a lower sample size. As the sample size decreases, the accuracy level decreases, resulting in the wider range of possible values to represent the population parameter with the same level of confidence. This leads to a larger margin of error. The formula for margin of error shows that the sample size is in the denominator. So, as the sample size decreases, the denominator gets smaller and hence the value of margin of error increases.  

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Answer:

5. B) x = 7

6. D) 35°

7. C) 67°

8. A) 142°

Step-by-step explanation:

5. Inscribed angle of a semicircle is equal to 90°. Therefore,

16x - 22 = 90

Solve for x

16x - 22 + 22 = 90 + 22

16x = 112

16x/16 = 112/16

x = 7

6. Recall: inscribed angle = ½(intercepted arc)

3x - 1 = ½(8x - 26)

2(3x - 1) = 8x - 26

6x - 2 = 8x - 26

Collect like terms

6x - 8x = 2 - 26

-2x = -24

-2x/-2 = -24/-2

x = 12

m<LMN = 3x - 1

Plug in the value of x

m<LMN = 3(12) - 1 = 36 - 1

m<LMN = 35°

7. Recall: inscribed angle = ½(intercepted arc)

Therefore,

4x + 28 = ½(11x - 1)

2(4x + 28) = 11x - 1

8x + 56 = 11x - 1

Collect like terms

8x - 11x = -56 - 1

-3x = -57

-3x/-3 = -57/-3

x = 19

Arc BC = 360° - (Arc AC + Arc AB) (Full circle)

Substitute

Arc BC = 360 - (11x - 1 + 85)

Plug in the value of x

Arc BC = 360 - (11*19 - 1 + 85)

Arc BC = 360 - (209 - 1 + 85)

Arc BC = 360 - 293

Arc BC = 67°

8. Inscribed angles intercepted by the same arc are equal. Therefore,

8x - 41 = 5x + 1

Collect like terms

8x - 5x = 41 + 1

3x = 42

3x/3 = 42/3

x = 14

5x + 1 = ½(arc PS) => inscribed angle = ½ of intercepted arc

2(5x + 1) = arc PS

Plug in the value of x

2(5*14 + 1) = arc PS

2(70 + 1) = arc PS

2(71) = Arc PS

Arc PS = 142°

Answer:

189 diagonals have 21 sides.

it is called hectogan take care

Answer:

Katherine is not correct. To square a number, you multiply it by itself. 6 squared is 36, and 3 squared is 9. Neither of these are between 20 and 30.

Step-by-step explanation:

Step-by-step explanation:

The numbers between the squares are the possible answers.

For example, 2/3 ÷ 3/4 is either 1/2 or 8/9.

2/3 ÷ 3/4

2/3 × 4/3

8/9

The answer is 8/9, so you'll move up to the next square.

The expression that will give the correct lateral surface area of the rectangular prism = (14.5 + 14.5 + 7 + 7)(8.6)

The lateral surface of an object is for all the sides of the object, excluding its base and top (when they exist). The lateral surface area is defined as the area of the lateral surface. This is different from the total surface area, which is the lateral surface area together with the areas of the base and top.

The lateral surface area is given by the formula here as:

(LSA) = 2(l + w)h

Given the following:

l = 14.5

w = 7

h = 8.6

Thus:

Lateral surface area of the prism = 2(l + w)h = 2(14.5 + 7)8.6

Lateral surface area of the prism = (14.5 + 14.5 + 7 + 7)(8.6)

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Answer:

-1/2

Step-by-step explanation:

3/2 x 5/3 ÷ (-2+7)

=> 3/2 x 5/3 ÷ (-5)

=> 3/2 x 5/3 x (-1/5)

=> -1/2

Answer: expression 3

Step-by-step explanation:

Answer: Expression #2 is correct

Step-by-step explanation:

The problem gives you the values of x and y you just have to work the problem.

Expression 2 shows x + y x 7

So basically take the value of x (3) and y (5) and add them together

3 + 5 = 8

then take the product and multiply it by 7

8 x 7 = 56

Step-by-step explanation:

y = x + 8

x = 2 ==> y = 10

x = 0 ==> y = 8

x = 4 ==> y = 12

Follow my account^^

Answer:

2

Step-by-step explanation:

1+1 = 2

So the answer is 2

hope this helps

If each child consumed the same quantity, then each would need to drink (63)x(4/n) of a gallon.

The US fluid ounce is equal to 1/128 of a US gallon since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint. The US gallon is accepted to be equivalent to around 3.785 L or 231 in inches, but the Imperial gallon is accepted to be equal to 4.54609 L. The liter is the unit of volume used by the great majority of people in the world. a volume measurement equal to eight pints.

An imperial gallon (Britain, Canada) is exactly 4.54609 liters. (US) 3.785 liters or around 231 cubic inches for liquids (a "U.S. liquid gallon")

Here gallon of lemonade to share = 63

let each children has 1 gallon of lemonade

so gallon=63

so portion =63/1

Formula = gallon to share x (4 parts of gallon shape / number of gallon)

which means if each one have n gallon then portion = (63)x(4/n)

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Each child would need to eat 63*4/n of a gallon if they all consumed the same amount.

Since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint, one US fluid ounce is equivalent to 1/128 of a US gallon. The Imperial gallon is acknowledged to be equal to 4.54609 L, but the US gallon is accepted to be about 3.785 L or 231 in. The vast majority of people in the world measure volume in litres. a volume that is eight pints in size.

In Britain and Canada, an imperial gallon equals precisely 4.54609 litres. 3.785 litres (US) or around 231 cubic inches (a "U.S. liquid")

Here, six thirty kids were sharing a gallon of lemonade.

each youngster should drink a gallon of lemonade.

Gallon = 63.

Hence part = 63/1

It indicates that the fraction is equal to 63*4/n if each has n gallons.

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Note: The complete question would be as bellow,

six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?

The domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as: (-∞, -49) U (-49, ∞)

In mathematics, the domain of a function is the set of all possible input values (usually represented by the variable x) for which the function is defined. It is the set of all values that can be substituted for the independent variable in a function to produce a valid output. The domain of a function is often restricted by the context in which it is being used, such as the type of problem or the natural limitations of the situation.

The given expression is (x-12)/(x+49).

The denominator of the expression is x + 49. The denominator cannot be equal to 0, as division by 0 is undefined. Therefore, x + 49 ≠ 0.

Solving for x, we get:

x ≠ -49

Therefore, the domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as:

(-∞, -49) U (-49, ∞)

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Answer:

12/5

Step-by-step explanation:

4/5 x 3 = (4 x 3)/5 = 12/5 (2 and 2 fifths)

Answer:

Simplified:

Step-by-step explanation:

Given equation:

Multiply ONLY the numerator with the whole number to get the answer:

Simplify:

Answer:

x= 6

Step-by-step explanation:

\(12x +4 = 10x+16 \\\)

You will subtract 10x from 12x and get 2x

\(2x + 4 = 16\)

Subtract 4 from 16 to get 12

\(2x = 12\)

You will then divide both sides by 2

\(\frac{2x}{2}\) = \(\frac{12}{2}\)

x= 6

The second one is hard to read but since ∠3 is 54° you should just start from there

Hope this helps

Answer:

x = 6

Step-by-step explanation:

The Answer for the first figure:

m<5 and m<7 are equal, since they are corresponding angles. So, that means;

m<5 = m<7

12x + 4 = 10x + 16

12x - 10x = 16 - 4

2x = 12

x = 6 (when both divided by 2)

The exact value of the letter D is three and three-tenths.

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

By observing the number line there are 10 subsections between two integers.

The letter D is in between two integers 3 and 4 so it can be from 3.1 to 3.9.

In between those ten subsections, the letter D is in the third subsection.

Therefore it is Three and three-tenths.

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Answer:

8-x=2

-x=2-8

-x=-6

x=6

if 8 is subtract from 6answer is 2

Answer:

Han has 9 books

Step-by-step explanation:

If diego has 27 comic books than that means that all you have to do is divide 27/3. then that equals to 9

The mean of this sample of car prices can be calculated by adding all the prices and dividing by the total number of dealers:

($35,700 x 2) + ($35,900 x 1) + ($36,200 x 3) + ($37,400 x 2) + ($37,900 x 2) = $326,500

$326,500 / 10 dealers = $32,650 (mean price)

To calculate the standard deviation, we first need to find the variance:

1. Subtract the mean from each individual price:

($35,700 - $32,650) = $3,050
($35,700 - $32,650) = $3,050
($35,900 - $32,650) = $3,250
($36,200 - $32,650) = $3,550
($36,200 - $32,650) = $3,550
($36,200 - $32,650) = $3,550
($37,400 - $32,650) = $4,750
($37,400 - $32,650) = $4,750
($37,900 - $32,650) = $5,250
($37,900 - $32,650) = $5,250

2. Square each of these differences:

$3,050^2 = $9,302,500
$3,050^2 = $9,302,500
$3,250^2 = $10,562,500
$3,550^2 = $12,602,500
$3,550^2 = $12,602,500
$3,550^2 = $12,602,500
$4,750^2 = $22,562,500
$4,750^2 = $22,562,500
$5,250^2 = $27,562,500
$5,250^2 = $27,562,500

3. Add up all of these squared differences:

$9,302,500 + $9,302,500 + $10,562,500 + $12,602,500 + $12,602,500 + $12,602,500 + $22,562,500 + $22,562,500 + $27,562,500 + $27,562,500 = $167,052,500

4. Divide the total by the number of dealers minus 1 (this is called the sample variance):

$167,052,500 / 9 = $18,561,388.89

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

√$18,561,388.89 = $4,307.17 (standard deviation)

So the mean price of this sample of car prices is $32,650 and the standard deviation is $4,307.17.

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Answer:

-6

Step-by-step explanation:

6 into -7 + 36

-42+36=-6

Answer:

Step-by-step explanation:

steps are stated below

step 1

6(-12+5)-3(-12)  equation

step 2

6(-12+5)-3(-12)  simplify the equation

(6)(-7)−(3)(-12)

-42-(3)(-12)

step 3

-42-(3)(-12)  times the number in the brackets

-42-(-36)

-6

Answer:

9/16

Step-by-step explanation:

Using the slope concept, it is found that the shelf should have a measure of 0 degrees relative to the floor.

In this problem, the shelf and the floor are parallel, hence they have the same slope, meaning that the difference of their angles is of 0 degrees, thus, the shelf should have a measure of 0 degrees relative to the floor.

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