a homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
write an expression to find the area of the fenced region.

Answer:

2 d.p = 41.87

Step-by-step explanation:

41.86/632

check whether its below or above 5 then round it to the nearest number

2 d.p = 41.87

Answer: 41.87

Step-by-step explanation:

41.86632 to 2 dp is 41.87

Centriod!

A centroid is also known as the centre of gravity.

Hope this answers your question!

Answer: centroid

Step-by-step explanation:

The least possible value of n, where the product of 180 and the positive integer n is a perfect cubic number is 150.

so, by the question,

n×180 is a perfect cube

on the prime factorization of 180, we get

180 = 2²×3²×5

so the number should be

n = 2 × 3 × 5² =150

when we multiply both of them we get

180×n = (2²×3²×5)×(2 × 3 × 5²)

          = (2³×3³×5³)

          =(2×3×5)³

          =(30)³

          =27000

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Answer:

839.369863

(Might need to round it depending on what the question requests)

Step-by-step explanation:

Step 1: I divided $61,274 by 73.

Step 2: I multiplied 839.369863 by 73, and I got 61,274.

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

If it asks to explain say this:

"I divided the amount of money spent by the total amount of laptops bought, and i got 839.369863, To make sure it can be multiplied by 73 to get $61,274, I multiplied 839.369863 by 73 to get $61,274."

Answer:

4.76

Step-by-step explanation:

had this on a test today!

The Little Monsters of Beast Academy completed 15 problems during the math meet in March.

The issue is a simultaneous equation involving two equations and two unknowns.

These are the equations that are created:

Let the quantity of questions that the students at the Beast Academy have answered in

The Little Monsters of Beast Academy successfully completed $frac1/5$ of the problems in the November = y/5

In Math Meet. they resolved $frac23$ = 2x/3 problems i

Hence:

y/5 + 2x/3 = 12

x + y = 30

When the equation is solved,

x = y = 15

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The final price of the comic book after it is marked up is $5.79.

Since we have given that

Cost of a comic book including tax = $ 3.99

According to the question, it is given that it is marked up 45%,

=3.99 × (100+45)÷100

=3.99 × 145/100

=399 × 1.45

=5.79

Hence, the final price of the comic book after it is marked up is $5.79.

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The fraction of a mile that Evan has to hike and the fraction he has hiked, gives the completed statement as follows;

[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex]. So the difference is closest to [tex]\frac{1}{2}[/tex]

A fraction is a representation of the part of a whole of an item or collection of items. The distance Evan's hiking trail of [tex]\frac{5}{6}[/tex] miles is a fraction of a mile.

The length of the trail = [tex]\frac{5}{6}[/tex] mile

The distance Evan has hiked = [tex]\frac{2}{5}[/tex] mile

The distance Evan has left to hike is given by the difference between the length of the trail and the distance Evan has hiked as follows;

Distance remaining = [tex]\frac{5}{6} -\frac{2}{5} = \frac{13}{30}[/tex]

Representing the numbers in decimal form, we have;

[tex]\dfrac{5}{6} = 0.8\overline 3[/tex]

The value of [tex]\frac{5}{6}[/tex] is close to 1

[tex]\dfrac{2}{5} = 0.4[/tex]

The value of [tex]\frac{2}{5}[/tex] is closest to 0.5

[tex]\dfrac{13}{30} = 0.4\overline 3[/tex]

The difference between [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{5}[/tex], which is [tex]\frac{13}{30}[/tex] is therefore closest to [tex]\frac{1}{2}[/tex]

The completed statement is therefore;

[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex] so the difference is closest to [tex]\frac{1}{2}[/tex]

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Answer: B. ≤

Step-by-step explanation:

≤

The total volume of both cubed boxes, combined, is of:

612 cubic inches.

The volume of a cube of side length s is given by the side length s cubed, as shown by the formula presented as follows:

V = s³.

In this problem, the boxes are given as follows:

The volume of the box with side length 8 inches is given as follows:

V = 8³ = 512 cubic inches.

(measure is in inches, hence the cubed measure is in cubic inches).

The total volume is given by the sum of the volumes of the two boxes, hence:

Total volume = 512 cubic inches + 100 cubic inches = 612 cubic inches.

The image showing the cubes is given at the end of the answer.

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The length of each desk when the width of each of the desks is 30 inches is A. 24 inches.

From the information, Randy and two of his friends have rectangular desks of the exact same size and the sum of the perimeters of the 3 desks is 324 inches.

The perimeter for each desk will be:

= 324 / 3

= 108

The perimeter is calculated as:

= 2(length + width)

This will be

2(length + width) = 108

2(length + 30) = 108

2l + 60 = 108

Collect like terms

2l = 108 - 60

2l = 48

Divide

l = 48/2

l = 24

The length is 24 inches.

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The required minimum sample size is 2875

Given that,

A government organization wanted to determine how many drivers between the ages of 16 and 24 had recently engaged in an accident. The agency wanted to make the estimate with a 90% confidence level and within one percentage point.

From the standard normal table, the z-critical value at 90% confidence is 1.65.

The information represent E = 0.01, p = 0.12 and z. =1.65 for finding sample size.

n = (Zc / E )² x P(1-P)

  = (1.65 2x0.12(1 - 0.12)0.01

  = 2874.96 ~ 2875

Hence, 2875 is the necessary number of samples, minimum.

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The solutions of the equation x^2 - 6x + d = 0 are both integers and d is a prime number is 5.

From the information, the solution of the equation x^2-6x+d=0 are integers

To find d, the numbers which can be added or subtracted to get -6 is needed which when multiplied will give a prime number

In this case - 5- 1 = -6

And when multiplied (-5×-1) will give +5 which is a prime number.

Therefore, x^2-6x+5=0

This illustrates that d is 5.

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Each motorcycle travel a distance of 240 miles for the faster motorcycle and 120 miles for the slower motorcycle.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = time it took the faster motorcycle to travel

If the faster motorcycle travels 1 hr longer than the slower motorcycle, then the slower motorcycle travels x - 1 hours.

The product of the rate of speed and time is equal to the distance.

Hence, the distance traveled by the faster motorcycle is 80x, while the distance traveled by the slower motorcycle is 60(x - 1).

If the faster motorcycle travels twice the distance of the slower motorcycle, then the distance traveled by the slower motorcycle is 80x/2.

60(x - 1) = 80x/2

Simplify and solve for x.

60(x - 1) = 80x/2

60x - 60 = 40x

20x = 60

x = 3

distance traveled by the faster motorcycle = 80x = 80(3) = 240 miles

distance traveled by the slower motorcycle = 80x/2 = (80)(3)/2 = 120 miles

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By secant line formula, the missing value of the point S is equal to 4.

Two line segments are parallel if and only if both line segments have the same slope. Slopes can be determined by secant line formula, defined below:

m = Δy / Δx

Where:

Then, the missing value of the variable y in the point S is:

(- 4 - 3) / (8 - 1) = (y - 9) / (7 - 2)

- 7 / 7 = (y - 9) / 5

- 1 = (y - 9) / 5

- 5 = y - 9

y = 4

The missing value of the variable y is 4.

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The probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013

The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.

An element that is below the mean is indicated by a z-score that is less than 0.

An element bigger than the mean is indicated by a z-score greater than 0.

An element that is equal to the mean is represented by a z-score of 0.

P(Z > a) = 1-P(Z<a)

Let's say we want to know, for instance, the likelihood that a z-score will be higher than 3.00.

We learn from the table, that

P(Z < 3.00) = 0.9987.

Therefore,

P(Z > 3.00) = 1 - P(Z < 3.00)

= 1 - 0.9987

= 0.0013.

Therefore, the probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013

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A six-sided die is rolled, with the potential results being 1, 2, 3, 4, or 6. Gender and illness status are examples of categorical random variable data. A, B, AB, or O correspond to a person's blood type. A voter's potential choice for a political party, e.

Hence, the example is . the color of a piece of meat

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Answer: C Undefined

Step-by-step explanation:

A vertical line never moves left and right, so the run is 0. Because the quotient of a number divided by 0 is undefined, the slope of a vertical line is always undefined.

The slope is positive

D.Positive

The correct statement regarding whether the graph is a one-to-one function is:

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

An one-to-one function is a function in which each output is related to only one input, that is, there are no horizontally aligned points.

These horizontally aligned points happen when an horizontal line is traced on the graph of the function, and crosses the function more than once.

From the graph of the function given by the image at the end of the answer, it can be seen that this line would cross the function twice for values of y between 0 and 2, hence the correct option is:

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

The problem asks for the correct statement regarding the function given on the image at the end of the answer.

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The cost of each bottle of water is equal to the cost of each bag of chips.

The expression:

The expression is defined as a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)

Here it is given that 4 bottles, 2 bags of chips, and a fruit salad.

The price of a fruit salad is $5.

The expression given is:

4x + 2x + 5

To find the relation between the price of a bottle and a bag of chips, we have:

Price of bottles = 4x/4 = x

Price of bag of chips = 2x/ 2 = x

Therefore we get that the cost of each bottle and each bag of chips is the same.

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The complete question is:

Jalen bought 4 bottles of water, 2 bags of chips, and a fruit salad. the cost of the fruit salad was $5. this expression was used to represent the amount Jalen should pay. 4x +2x +5 based on the expression, the cost of each bottle of water is ______the cost of each bag of chips.

Answer:

105

Step-by-step explanation:

It will take 6 days for the sister to earn as much as the brother.

Two or more expressions with an equal sign are defined as an equation.

Given that, the sister earns $30 per day and pays a $60 license fee and the brother earns$20 per day.

The income of the sister in x days is:

30x - 60

The income of the brother in x days is:

20x

The income of the sister and the brother is equal when:

30x - 60 = 20x

30x - 20x = 60

10x = 60

x = 6

Hence, It will take 6 days for the sister to earn as much as the brother.

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The expression for the cost of each scarf is s/4.

According to the question,

We have the following information:

Let s be the total amount Heidi spent for scarves. each of the 4 scarves that she bought cost the same.

Now, the cost of 1 scarf can be easily found by dividing the total cost of the scarves by the number of scarves.

(If we would have to find the cost of 15 scarves then first we would have used division and then multiplication.)

So, we have the following expression:

4 scarves = s

Cost of one scarf = s/4

Hence, the expression for the cost of each scarf is s/4.

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The equation of the line is y=3x-2 where the slope is 3 and the y-intercept is -2.

A diagrammatic depiction of a set of facts is called a graph, chart, or diagram.

Graphs need to be accurate and effective in communicating information. They ought to be legible at different computer screen resolutions. Graphs should ideally be pleasing to the eye.

Please be aware that the terms graph, chart, and diagram can be imprecise and are sometimes used synonymously.

Graphs need to be accurate and effective in communicating information. They ought to be legible at different computer screen resolutions.

Given,

Slope m=3

y-intercept (c)=-2

The slope-intercept form is given as

y=mx +c

Therefore, y=3x-2

The equation of the line is y=3x-2 where the slope is 3 and the y-intercept is -2.

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The probability exactly two of the appeals were successful is 0.9536

We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012), and suppose ten first-round appeals have just been received by a Medicare appeals office.

This situation can be represented through Binomial distribution as;

[tex]P(X=r)={}^{n}C_{r}(p)^r(1-p)^r[/tex] where [tex]x=0,1,2,3.....[/tex]

where,  n = number of trials (samples) taken = 10

            r = number of success

            p = probability of success which in our question is % of first-round

                  appeals that were successful, i.e.; 40%

So, here X ~ Binom(n=10 , p=0.40

Probability that at least two of the appeals will be successful = P(X>=2)

   P(X >= 2) = 1 - P(X = 0) - P(X = 1)

                    = 1 - [tex]^{10}C_{0}(0.40)^0(1-0.40)^{10-0}-^{10}C_{1}(0.40)^1(1-0.40)^{10-1}[/tex]

                     = 1 - 0.00605 - 0.0403

                     = 0.9536

Hence, the probability exactly two of the appeals were successful is 0.9536

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The amount to be paid to the broker is 2167.025. Therefore option b is correct.

Percentage:

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, and none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Here we have to find the amount to pay to the broker.

The given values are:

Market rate = 86.681

The commission charges by broker = 2.5%

The broker has to pay = 86.681 × 2.5% × 1000

                                     = 86.681 × 2.5/100 × 1000

                                    = 86681 × 0.025

                                    = 2167.025

Therefore the amount paid to the broker is 2167.025.

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Answer:

B

I got it right

Step-by-step explanation:

An applicant needs 84.04 minutes to finish the test in order for 97 percent of them to pass.

An aptitude test is required of job candidates. Let's assume that the test's completion time has a mean of 69 minutes and a standard deviation of 8 minutes.

To get how much time an applicant should be given so that 97 percent of them will be able to complete the test.

Mean (μ) = 69

standard deviation (σ) =8

Hence, due to population standard deviation (σ) is known to use the normal distribution.

x_ Norm (μ,σ)

x_ Norm (69,8)

Therefore, x_ random variable that represents the time of applicant;

P(X<x) = 0.97

Corresponding to the left tail area of 0.97 lies in the z-table of z row of 1.8 and column 0.08.

P(z < 1.88) = 0.97

z < 1.88

(X - μ)/σ < 1.88

X < 1.88 (8) + 69

X < 84.04

The time taken by an applicant so that 97 percent of them will be able to complete the test is 84.04 minutes.

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