Decompose each of the numbers 72, 204, 1800, and 42336 as products of their prime factors. (4)

Answer:

[tex]P = 56\sqrt2[/tex]

Step-by-step explanation:

We can find the perimeter of a square given its diagonal by modeling the square as two congruent right triangles and using the Pythagorean Theorem to solve for the square's side lengths.

The Pythagorean Theorem states that...

[tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are the right triangles legs, and [tex]c[/tex] is its hypotenuse.

However, since we are working with a square, we know that the right triangles' legs are congruent. Thus, the theorem becomes:

[tex]a^2 + a^2 = c^2[/tex]

[tex]2 \cdot a^2 = c^2[/tex]

Using this formula, we can solve for the square's side lengths, inputting the given hypotenuse length of 28.

[tex]2 \cdot a^2 = 28^2[/tex]

↓ simplify the exponent

[tex]2 \cdot a^2 = 784[/tex]

↓ divide both sides by 2

[tex]a^2 = 392[/tex]

↓ take the square root of both sides

[tex]a = \sqrt{392}[/tex]

↓ simplify the square root

[tex]a = \sqrt{2^3 \cdot 7^2}[/tex]

[tex]a = (2\cdot 7)\sqrt{2}[/tex]

[tex]a=14\sqrt2[/tex]

Finally, we can multiply the side length by 4 to get the square's perimeter (since a square has 4 sides).

[tex]P = 4 \cdot a[/tex]

[tex]P = 4 \cdot 14\sqrt2[/tex]

[tex]\boxed{P = 56\sqrt2}[/tex]

[tex]\boxed{P \approx 79.2}[/tex]

45% of the burgers served were well-done.

What is percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

To find the percentage of well-done burgers, we need to divide the number of well-done burgers by the total number of burgers served and then multiply by 100 to get the percentage.

Total number of burgers served = 9 well-done + 11 medium = 20

Percentage of well-done burgers = (9/20) x 100% = 45%

Therefore, 45% of the burgers served were well-done.

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The Angie and Mandy’s current age are 22 and 44 years respectively.

Angie is x years old.

Mandy = 22 + x

After 2 years:

22 + x = 2x

Solving linear equation:

22 = 2x - x

22 = x (Angie’s current age)

Mandy’s current age.

x + 22 = 22 + 22

x = 44

Thus, the Angie and Mandy’s current age are 22 and 44 years respectively.

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Answer:

C. The mass of a basketball

Step-by-step explanation:

C. The mass of a basketball is typically measured in kilograms.

A. You would measure the mass of a butterfly in milligrams or grams.

B. The capacity of a bottle is measured in milliliters or liters.

D. The length of a river is measured in meters or kilometers.

Answer:

The answer to your problem is, C. The mass of a basketball

Step-by-step explanation:

First of all, if you want to measure heavy items then you could do it in kilograms for example:

Cup filled with water ( lb )

Gallon tank ( kg )

Since basketball or heavy ( depends how much pressure is put it there ) and you cannot really " weigh " a river.

The heaviest option from the option choices A, B, & C.

Option C, is the heaviest

Thus the answer to your problem is, C. The mass of a basketball

Answer:

Step-by-step explanation:

1

Answer:

$850

Step-by-step explanation:

If you make $34,000 per year, then you make $2833.33 per month.

[tex]\frac{34000}{12} = 2833.333[/tex]

30% of your monthly income would go towards housing (every month)

(2833.33)(0.3) = $850

Answer:

Square Plot

Step-by-step explanation:

Let us compare the Area of both plots

Rectangular Plot :  L X B = 45 x 25 = 1125 M^2
Square Plot : S X S = 35 x 35 = 1225 M^2

Area of Square Plot > Area of Rectangular Plot

Therefore he should prefer the Square Plot as it has more area.

Hope it helps.

For any real number x, x > 5 implies that x ≥ 5 is the true statement.

For any real number x, x > 5 implies that x ≥ 5 is the true statement. This can be expressed with the following inequality:

x > 5 implies x ≥ 5

This means that if x is greater than 5, then x must be greater than or equal to 5. We can demonstrate this with an example calculation. Let x = 6.

6 > 5

We can see that 6 is greater than 5, so the inequality is true.

6 ≥ 5

We can see that 6 is also greater than or equal to 5, so the inequality is also true. Therefore, for any real number x, x > 5 implies that x ≥ 5.

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The APR on the loan, given the amount you are to pay in interest every day, can be found to be 190. 54 %

To calculate the APR (Annual Percentage Rate) for this loan, we need to know the total interest paid over the course of a year, as a percentage of the loan amount.

First, we need to determine the total interest paid over the course of one year. Since the interest rate is $3.98 per day, we can multiply that by the number of days in a year (365) to get the total interest paid per year:

$3.98 x 365 = $1, 452.70

The APR would therefore be :

= ( 1, 452. 70 - 500 ) / 500

= 1. 9054

= 190. 54 %

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The cost per square inch of the apple pie is $ 0.16.

Given that,

The diameter of the pie = 10 in

The radius of the pie = 10/2

                             = 5 inches.

Area of the pie = [tex]\pi r^{2}[/tex]

                         =  3.14 × 5²

                         = 3.14 × 25

                          = 78.5 in²

The cost of the apple pie = $ 12.85.

Therefore, the cost per square inch of the pie = 12.85 ÷ 78.5

                                                                             = $ 0.16.

Hence, the cost per square inch of the apple pie is $ 0.16.

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The perimeter of DEFG will be 2(√10+√17).

The cοοrdinate system that is mοst frequently emplοyed in three-dimensiοnal systems is called spherical cοοrdinates οf the system, represented as (r,Ф,∅ ).

The surface area in three dimensiοns is calculated using the spherical cοοrdinate system. Radial distance, pοlar angles, and azimuthal angle are the three numbers that these cοοrdinates indicate. Additiοnally knοwn as spherical pοlar cοοrdinates.

A 2-dimensiοnal graph with an x-axis and a y-axis is given.

A parallelοgram DEFG is drawn οn it with cο-οrdinates (2,1), (3,4), (7, 5) and (6,2) respectively.

Sο the perimeter will be DE = √10

DG=√17

EF = √17

FG=√10

Sο the perimeter will be 2(√10+√17).

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Answer:

3

Step-by-step explanation:

slope of the line, m = (y2 - y1 ) / ( x2 - x1 )

= (-19 + 10 ) / (-7 + 4)

= -9 / -3

= 3

The waste sites in State Y in the year 2000 was 21.

Let n be the number of hazardous waste sites in State Y.

Based on the problem statement, we have

2n - 8 = 34

So, we have

2n = 42

Divide

n = 21

Hence, the waste sites in State Y in the year 2000 was 21.

Given that

6x + 1.6 = 58

Apply the subtraction property

6x = 56.4

Apply the division property

x = 9.4

Hence, the solution to the equation is x = 9.4

Here, we have the bar diagram

Adding the terms in the bar, we have

n + n + n + 8 = 53

3n + 8 = 53

Apply the subtraction property

3n = 45

Apply the division property

n = 15

Hence, the bar equation is 3n + 8 = 53

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Answer:

Part A:

To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:

Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)

Simplifying the expression by combining like terms, we get:

Side 1 + Side 2 = 2x^2 + 1

Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.

Part B:

To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:

5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]

Simplifying the expression by distributing the negative sign, and then combining like terms, we get:

5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4

Simplifying further by combining like terms, we get:

5x^3 - 4x^2 + 11x - 4

Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.

Answer:

A) 5x^3 - 4x^2 + 3x - 4

Step-by-step explanation:

Answer:

A) 5x^3 - 4x^2 + 3x - 4

Step-by-step explanation:

Part A:

To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:

Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)

Simplifying the expression by combining like terms, we get:

Side 1 + Side 2 = 2x^2 + 1

Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.

Part B:

To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:

5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]

Simplifying the expression by distributing the negative sign, and then combining like terms, we get:

5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4

Simplifying further by combining like terms, we get:

5x^3 - 4x^2 + 11x - 4

Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.

Answer:

A) 5x^3 - 4x^2 + 3x - 4

Answer:

8 meters

Step-by-step explanation:

their formation creates a triangle

Shelby to Dillon =15

Shelby to Patty =17

Dillon to Patty =?

a^2 + 15^2 = 17^2

a^2 + 225 = 289

a^2 = 64

a = 8

From the given information provided, she has 14.50 dollars money left to spend on gift C.

To find out how much money is left for gift C, we first need to add up the amounts spent on gift A and gift B:

8 9/10 dollars + 6 3/5 dollars = (8 + 6) + (9/10 + 3/5) dollars

= 14 + (9/10 + 6/10) dollars

= 14 + 15/10 dollars

= 15 5/10 dollars

= 15.50 dollars

So the total amount spent on gift A and gift B is 15.50 dollars. To find out how much money is left for gift C, we need to subtract this amount from the total amount she has to spend:

30 dollars - 15.50 dollars = 14.50 dollars

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The probability of a random student scoring 84 or more if the maximum score is 95 is approximately 0.1179 or 11.79%.

To find the percentage of students scoring 84 or more, first we need to calculate the z-score using the formula:z = (X - μ) / σwhere X = 84, μ = 72, and σ = 15.2z = (84 - 72) / 15.2z = 0.7895Using a standard normal table or a calculator, we can find the percentage of students scoring 84 or more as:percentage = 1 - P(Z < 0.7895)percentage ≈ 21.4%Therefore, approximately 21.4% of students will score 84 or more on the test.b) To find the probability of a random student scoring 84 or more if the maximum score is 95, we need to first calculate the z-score using the same formula as before:z = (X - μ) / σwhere X = 84, μ = 72, and σ = 15.2z = (84 - 72) / 15.2z = 0.7895Then, we need to convert this z-score to a new z-score based on the maximum score of 95. Using the formula:z = (X - μ) / (max score - μ)σwhere X = 84, μ = 72, σ = 15.2, and max score = 95z = (84 - 72) / (95 - 72)z ≈ 1.19Using a standard normal table or a calculator, we can find the probability of a student scoring 84 or more as:P(Z > 1.19)P(Z > 1.19) ≈ 0.1179Therefore, the probability of a random student scoring 84 or more if the maximum score is 95 is approximately 0.1179 or 11.79%.

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You need to add 225mL of the 75% alcohol solution to obtain the desired 30% alcohol solution.

To find the amount of 75% alcohol solution needed to obtain a 30% alcohol solution, we must use the formula for dilution:

M1V1 = M2V2

Where M1 is the concentration of the initial solution, V1 is the volume of the initial solution, M2 is the desired concentration, and V2 is the desired volume.

In this case, M1 is 5%, V1 is 675mL, M2 is 30%, and V2 is unknown.

We can rearrange the equation to solve for V2, which is the volume of the 75% alcohol solution needed:

V2 = (M1V1) / M2

V2 = (5% x 675mL) / 30%

V2 = 225mL

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so it shrunk by 19.3 - 18.1 = 1.2.

so if we take 19.3(origin amount) as the 100%, what's 1.2 off of it in percentage.

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 19.3 & 100\\ 1.2& x \end{array} \implies \cfrac{19.3}{1.2}~~=~~\cfrac{100}{x} \\\\\\ 19.3x=120\implies x=\cfrac{120}{19.3}\implies x\approx 6.22[/tex]

recommendations

When answering questions on Brainly, you should always strive to be factually accurate, professional, and friendly. Your answer should be concise and not provide extraneous amounts of detail. You should not ignore any typos or irrelevant parts of the question, and provide a step-by-step explanation in your answer.The objective of the task is to analyze a multidimensional cube and provide recommendations for improving the profit. The cube that you will be analyzing is AdventureWorks. The methodology that will be followed is to analyze a cube built from the AdventureWorks Data Warehouse.The cube was built using Microsoft's SQL Server Analysis Services (SSAS). You will play the role of AdventureWorks management, and analyze the cube using Microsoft Excel. You will then make three recommendations for improving profitability.For analyzing the cube, you can use Excel's PIVOT table. It is recommended that you study the data first before analyzing. You can move the data to Tableau and analyze it that way, but it is not necessary.The deliverables of the task are two recommendations for improving the profitability of AdventureWorks along with the rationale of each recommendation. Additionally, you should include any and all cube views (i.e., reports or charts from Excel) that helped you arrive at your recommendations.

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effect size measure.

In the case of Dexter and Hughes (2011), the standardized mean difference is an unbiased version.What is an unbiased estimate?An unbiased estimate is a statistical term used to describe an estimate or forecast that has an equal chance of being too high or too low. In Dexter and Hughes (2011), the standardized mean difference is unbiased.A study's standardized mean difference is determined by dividing the difference between two means by their pooled standard deviation. It's used to compare two group means and is a standardized effect size measure.

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The probability of event Upper B 1 given event A is approximately 0.0134.

To find P(Upper B 1|A) using Bayes' rule, we need to use the formula:

P(Upper B 1|A) = P(A|Upper B 1) × P(Upper B 1) / P(A)

To find P(A), we can use the law of total probability:

P(A) = P(A|Upper B 1) × P(Upper B 1) + P(A|Upper B 2) × P(Upper B 2) + P(A|Upper B 3) × P(Upper B 3)

Substituting the given values, we get:

P(A) = 0.6 × 0.05 + 0.5 × 0.4 + 0.4 × 0.55

P(A) = 0.029 + 0.2 + 0.22

P(A) = 0.449

Now, substituting the values of P(A|Upper B 1), P(Upper B 1), and P(A) into the Bayes' rule formula, we get:

P(Upper B 1|A) = (0.6 × 0.05) / 0.449

P(Upper B 1|A) = 0.006 / 0.449

P(Upper B 1|A) ≈ 0.0134

Therefore, the probability of event Upper B 1 given event A is approximately 0.0134.

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The given statemen is correct. The given hypothesis, μ = 55, is the null hypothesis, which is identified by the presence of the equality symbol.

The alternative hypothesis, Hଵ: μ ≠ 55, indicates that there is a difference between the population mean and the value specified in the null hypothesis. The symbol μ represents the population mean, which is the average of all the values in the population. In this case, the population from which the sample has been drawn is being referred to. Arithmetic mean is a mathematical term used to describe the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values in the set.

The formula for the arithmetic mean of a set of numbers is:

Arithmetic Mean = (sum of all values) / (total number of values)

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Answer:

5

Step-by-step explanation:

2(6+4) – 3(5)

= 12 + 8 - 15

= 20 - 15

= 5

So, the answer is 5

Based on the information in the table, we can infer that the graph would be as shown in the attached image.

To graph the information in the table we must analyze the information in the table. In this case we must take into account that to locate the fractions we can perform the division and convert it into a decimal number to locate them more easily on the number line.

In accordance with the above, we can establish that the height that is repeated the most times is 1 7/8 with a frequency of 4 times.

Note: This question is incomplete. Here is the complete information:

Attached image

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Trevor lifts a box to a height of 6 feet by turning the crank 10 times.

In mathematics, an equatiοn is a fοrmula that uses the equals sign (=) tο express hοw twο expressiοns are equal. In οther languages, the wοrd equatiοn and its cοgnates may have slightly different meanings. Fοr instance, in French, an equatiοn is defined as having οne οr mοre variables, while in English, an equatiοn is any prοperly fοrmed fοrmula that cοnsists οf twο expressiοns linked by the equals sign.

Using the equation y = 0.6x, we can calculate the height Trevor lifts a box by turning the crank 10 times:

y = 0.6x

y = 0.6(10)

y = 6

Therefore, Trevor lifts a box to a height of 6 feet by turning the crank 10 times.

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Answer:

(√122 - √10)/112.

Step-by-step explanation:

The average rate of change of a function f(x) over an interval [a, b] is given by:

average rate of change = (f(b) - f(a))/(b - a)

Here, we have f(x) = √x - 1, a = 10, and b = 122. So, the average rate of change of f(x) from x = 10 to x = 122 is:

(f(122) - f(10))/(122 - 10)

= (√122 - 1 - √10 + 1)/(112)

= (√122 - √10)/112

Therefore, the exact, fully simplified answer for the average rate of change of f(x) from x = 10 to x = 122 is (√122 - √10)/112.

To fully describe a triangular prism, you would need to provide the dimensions of its triangular bases (e.g. base length and height), the length of the prism, and the length and width of the rectangular faces. Thus, option C is correct.

To find the volume of filler material required to surround the triangular prism, we need to first calculate the volume of the box and the volume of the triangular prism.

The volume of the box is given by:

[tex]8[/tex] inches ×  [tex]13[/tex] inches ×  [tex]16[/tex] inches =  [tex]1,664[/tex] cubic inches

The volume of the triangular prism is given by:

[tex](1/2) × 8[/tex] inches ×  [tex]13[/tex] inches ×  [tex]16[/tex] inches = [tex]832[/tex] cubic inches

To completely fill the box, we need to add filler material with a volume equal to the difference between the volume of the box and the volume of the triangular prism, which is:

 cubic inches— [tex]832[/tex] cubic inches   [tex]= 832[/tex] cubic inches

Therefore, the [tex]832[/tex]  Cubic inches.

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