Which relationship between x and y in the equation shows a proportional relationship?

A. y = 4x + 2

B. y = 8x

C. y = x - 2

D. y = x/2 + 2

Answer:    Number of sand bags are 105

Step-by-step explanation:

Alright, lets get started.

The diameter of pool is given as : [tex]20 \ \text{feet}[/tex]

The radius of pool will be : [tex]r=\frac{20}{2}=10[/tex]

So the area of the pool will be:

Area = [tex]\pi r^2[/tex]

Area = [tex]\pi *10^2[/tex]

Area = [tex]100 \pi[/tex]

Area = [tex]314.16[/tex]

3 square feet is covered by 1 sand bag, so

314.16 square feet will be covered by : [tex]\frac{314.16}{3}[/tex]

So, no of sand bag = [tex]104.7[/tex]

Rounding off to nearest number

Number of sand bags are 105  :   Answer

Hope it will help :)

The student will need 105 bags of sand.

The student asked about the necessary quantity of sand bags required to cover an area for an above ground pool. First, we need to calculate the area of the pool's base. Since the pool is circular with a diameter of 20 feet, we can use the formula for the area of a circle, which is A = [tex](\pi d^2)/4,[/tex] where d is the diameter.

The area A works out to [tex]\(A = \pi \times (20 feet)^2 / 4 = \pi \times 400 / 4 = \pi \times 100)[/tex] square feet. Assuming [tex]\pi[/tex] is approximately 3.14, the area is about 314 square feet.

Since one bag of sand covers 3 square feet, we divide the total area by the coverage area per bag: 314 square feet / 3 square feet per bag. This calculation gives us approximately 104.67 bags. Since we can't have a fraction of a bag, we need to round up to the nearest whole number. The student would therefore need 105 bags of sand to cover the area of the pool evenly.

Answer:

  102 1/3

Step-by-step explanation:

To find the 6th term, add the common difference to the 5th term:

  103 + (-6 2/3) = 102 1/3

The equation of the horizontal asymptote of the graph of the function y = 1/(x + 5) - 4 is y = -4.

To determine the equation of the horizontal asymptote of the given rational function y = \frac{1}{x + 5} - 4, we need to analyze the behavior of the function as x approaches infinity.

For rational functions, if the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis, which is y = 0.

However, if there is a constant being subtracted from the fraction, as in this case, the horizontal asymptote is shifted vertically by that constant.

Since the degree of the numerator (0, as the numerator is 1 which is constant) is less than the degree of the denominator (1, since x is to the first power), and we subtract 4 from the fraction, the horizontal asymptote is y = -4.

No. Because -2 has two outputs. To be a function  each input have to  have one output. I.E

2,3  4,5  6,7  8,9 are functions.

Answer:

Step-by-step explanation:

Percent increase/decrease has a formula:

[tex]\frac{orig-sale}{orig}*100=%inc/dec[/tex]

For us, this looks like:

[tex]\frac{400-350}{400}*100[/tex]

which simplifies to

[tex]\frac{50}{400}*100[/tex]

which is 12.5%

Answer:

[tex]V=1,185.6\ in^3[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BL[/tex]

where

B is the area of the triangular face

L is the length of the prism

we have that

[tex]B=\frac{1}{2}(b)(h)[/tex]

substitute the given values

[tex]B=\frac{1}{2}(12)(10.4)=62.4\ in^2[/tex]

[tex]L=19\ in[/tex]

substitute in the formula of volume

[tex]V=62.4(19)=1,185.6\ in^3[/tex]

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

we know that

In a parallelogram opposite sides are parallel and congruent

In this problem

AB and CD are opposite sides

so

AB=CD

substitute the given values

[tex]6x-10=3x+5[/tex]

solve for x

[tex]6x-3x=10+5[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Answer:

the tens place is going down one number each time

Step-by-step explanation:

To find the pattern of the data set we can subtract the 1st term to the 2nd term.

788 - 778 = 10

Now, multiply the 2nd term to the 3rd term to check.

778 - 768 = 10

Thus, the rule of the pattern is 10.

Best of Luck!

Answer:

y=-70x+350

Step-by-step explanation:

Since x is the number of years since 1995, this means that at 1995, x=0. This also means that in 2000, x=5. The values of the stuffed animals were 350 in 1995 and 0 in 2000. The formula for slope is rise over run, so we can find the answer using this mathematical expression: y2-y1/x2-x1. Plugging in our values, we get 0-350/5-0 which simplifies into -350/5. This further simplifies into -70. Our slope is -70. The definition of y-intercept is the value of y when x=0. We know that x=0 at 1995 and the value for the stuffed animals was 350 at that time. This tells us that the y-intercept is 350. Slope-intercept form is y=mx+b, so plugging in our information, we get y=-70x+350.

The equation representing the data of Romi's stuffed animal inventory is y = -70x + 350

The given problem involves finding an equation in slope-intercept form to represent the data of Romi's stuffed animal inventory from 1995 to 2000. Let's first find the slope and y-intercept of the equation using the given data. We know that the inventory in 1995 was 350 and in 2000 was 0. We can use these two points to find the slope and y-intercept.

Slope (m) = (change in y)/(change in x) = (0 - 350)/(2000 - 1995) = -350/5 = -70

Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values

y = -70x + b

To find the value of b, we can substitute one of the given points into the equation. Let's use the point (0, 350).

350 = -70(0) + b

350 = b

Substituting the value of b back into the equation, we have the final equation:

y = -70x + 350

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Answer:

Step-by-step explanation:

Plug this into the quadratic formula.  It's the easiest and surest way to solve a quadratic.  

a = 2

b = 1

c = 2

Filling in the quadratic formula:

[tex]x=\frac{-1+/-\sqrt{1^2-4(2)(2)} }{2*2}[/tex]

which simplifies to

[tex]x=\frac{-1+/-\sqrt{-15} }{4}[/tex]

You can't have a negative under the square root sign (or ay even index radical, for that matter), so we will rewrite it as

[tex]x=\frac{-1+/-\sqrt{(-1)(15)} }{4}[/tex]

and since i-squared is equal to -1:

[tex]x=\frac{-1+/-\sqrt{15i^2} }{4}[/tex]

The only perfect square we can pull out of that square root is the i from the i-squared, so when we do that we get:

[tex]x=-\frac{1+/-\sqrt{15}i }{4}[/tex]

or you could put the i out front; it doesn't change the answer at all.  The third choice down is the one you want.

Answer:

[tex]210[/tex] £

Step-by-step explanation:

Let amount that abby gets[tex]=x[/tex]

Given that [tex]\frac{Amount\ of\ abby}{Amount\ of\ Ben} =\frac{2}{7}[/tex]

[tex]Amount\ of\ ben=\frac{7}{2}\times Amount\ of\ abby\\ =\frac{7}{2}\ x[/tex]

Amount of chole + amount of Danesh [tex]=1.5\times[/tex]of abby

                                                                      [tex]=1.5 \ x[/tex]

[tex]x +\frac{7}{2} \ x + 1.5 \ x =360\\\\6x=360\\\\x=\frac{360}{6}\\\\x=60[/tex]

[tex]Amount\ of\ Ben =\frac{7}{2}\ x = \frac{7}{2} \times 60\\\\=7\times 30\\\\=210[/tex]

The amount got by Ben =  £210

£360 is shared between Abby, Ben, Chloe and Denesh.

The ratio of the amount Abby gets to the amount that Ben gets is 2:7.

Chloe and Denesh get 1.5 times the amount Abby gets.

We have to work out the amount of money that Ben gets.

Let the amount  Abby gets = x ...........(1)

According to the given situation

[tex]\rm \dfrac{Amount\; got\; by\; Abby }{Amount \; got \; by \; Ben }= \dfrac{2}{7}[/tex]

[tex]\rm Amount \; got \; by \; Ben = (7/2) x......(2)[/tex]

[tex]\rm Amouut\; goy \; by\; Chole + Amount\; got \; by \; Denesh = 1.5 x........(3)[/tex]

The total amount = £360

From equation (1) (2) and (3) we get

[tex]\rm x + (7/2)x + 1.5x = 360\\x(1+3.5 +1.5) = 360\\x (6) = 360 \\x = 360/6= 60[/tex]

The amount got by Abby = £60

So  the amount got by Ben = 3.5 (60)  =  £210

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Step-by-step explanation:

4. 4+11=15

to find the length of The first piece

4/15*75=20

to find the length of the second one

11/15*75=55

5. 4+1=5

to find the length of the first one

4/5*180=144

to find the length of the second one

1/5*180=36

7. 5+7+8=20

to find the length of the first one

5/20*40=10

to find the length of the second one

7/20*40=14

to find the length of the third one

8/20*40=16

4. The lengths of the two pieces are 20 inches and 55 inches.

5. The measures of the two angles are 144 degrees and 36 degrees.

6. The measures of the angles are 36 degrees, 60 degrees, and 84 degrees.

7. The lengths of the sides are 10 inches, 14 inches, and 16 inches.

4: A string that is 75 inches long will be cut into two pieces in the ratio of 4:11. Find the lengths of the two pieces of string.

The total length of the string is 75 inches.

The ratio given is 4:11.

First, find the total parts in the ratio by adding the two numbers: [tex]4 + 11 = 15[/tex].

Now, to find the length of each piece:

5: The ratio of two supplementary angles is 4:1. Find the measures of the two angles.

Supplementary angles add up to 180 degrees.

The given ratio is 4:1.

Find the total parts in the ratio: [tex]4 + 1 = 5[/tex].

Now, calculate the measures of the angles:

6: The ratio of the measures of the angles in a triangle is 3:5:7. Find the measure of each angle.

The sum of the angles in a triangle is 180 degrees.

The given ratio is 3:5:7.

Total parts in the ratio: [tex]3 + 5 + 7 = 15[/tex].

Now, calculate each angle's measure:

7: The ratio of the measure of the sides of a triangle is 5:7:8 and its perimeter is 40 inches. Find the measure of each side.

The perimeter of the triangle is 40 inches.

The given ratio is 5:7:8.

Total parts in the ratio: [tex]5 + 7 + 8 = 20[/tex].

Now, calculate the length of each side:

Answer:

D

Step-by-step explanation:

Answer:

D. (sugar * frosting)/Flour

Step-by-step explanation:

Given that

The formula for sweetness of a cake is represented by S = sf/F

where the

sweetness of a cake is denoted with S

amount of sugar in a cake, with A

amount of frosting, with f

amount of flour with F.

To get the appropriate unit, all we need to do is to substitute the letter representation of each unit with the original word.

So,

S = sf/F becomes

S = (sugar * frosting)/Flour

We arrive at this by replacing s with sugar; f with frosting and F with Flour

Answer:

D

Step-by-step explanation: When you plug 3 into where x in the first equation and plug 2 in for y. When you do that you get 6-2<5, 6-2 is 4 and 4 is less than 5, so this makes this equation true. For the second equation you do the same. 3 goes into the x spot and 2 into the y, after doing this you get 3+2(2)>2, 3 times 4 is 12 and that is greater than 2, hich also means that equation is ture. So there you have both equations are ture and that is how you get your answer.

Answer:

the answer is a 18 because that would mean there are more red than any color in the bag

To make the probability of drawing a red marble 1/2 with the current bag of marbles, you would need to add 12 more red marbles.

To answer the question about how many additional red marbles must be added to the 18 marbles already in the bag so that the probability of randomly drawing a red marble is 1/2, we first need to understand how the probability of an event is calculated. Probability is calculated by dividing the number of ways an event can occur by the total number of outcomes. In this case, the event is drawing a red marble and the total number of outcomes is the total number of marbles in the bag.

Currently, there are 6 red marbles and 18 total marbles in the bag, so the probability of drawing a red marble is 6/18 = 1/3. We want this probability to increase to 1/2, so we need to add more red marbles. Let's represent the number of red marbles we need to add as x. To find x, we need to solve the following equation: (6 + x) / (18 + x) = 1/2.

Solving for x, we get x = 12. Therefore, you need to add 12 more red marbles to the bag to make the probability of drawing a red marble 1/2.

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Answer:

6

Step-by-step explanation:

5 times 4 is 20

20 divided by 10 is 2

2 plus 4 is 6

5 * 4 / 10 + 4

20 / 10 + 4

2 + 4

6

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The expected value of an insurance policy for the company is calculated by subtracting the expected costs (probability of accident * average payout) from the premium paid by the customer. In this case, the insurance company can expect to retain $185.20 from the annual premium after estimated payouts.

The subject of this question falls under the category of Mathematics, specifically in the field of probability and expected value. The expected value of an insurance policy is calculated as the product of the probability of an event (an accident in this case) and the corresponding payout, subtracted from the cost or premium of the policy. Here the insurance company estimates a 2.4% likelihood of an accident, which is a probability of 0.024, and the average payout being $2700.

First, determine the expected payout by the insurance company, which is computed by multiplying the probability of the event by the payout: 0.024 * $2700 = $64.80.

Then subtract this from the premium to calculate the company's expected value: $250 - $64.80 = $185.20.

This means, on average, the insurance company can expect to retain $185.20 from the annual premium after accounting for the estimated payouts from accidents.

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The expected value of this insurance policy for the company is approximately -$185.20.

Given information:

Likelihood of having an accident: 2.4% (expressed as a decimal, so (p = 0.024))

Average insurance payout: $2700

Annual premium charged: $250

The expected value ((E)) can be calculated as follows:

[tex][ E = (p \cdot \text{{Payout}}) - \text{{Premium}} ][/tex]

Substitute the given values: [ E = (0.024 x  2700) - 250 ]

Calculating: [ E = 64.8 - 250 = -185.2 ]

The expected value of this insurance policy for the company is approximately -$185.20.

Interpretation:

A negative expected value means that, on average, the insurance company is expected to lose money per policy sold.

In this case, the company charges a premium of $250 but expects to pay out an average of $2700 per accident. Therefore, the expected loss is $185.20 per policy.

Answer:

The answer is d (-21/2 , 2)

Step-by-step explanation:

That's where the lines meet up

Answer: -8

Step-by-step explanation: In this problem we're asked to add -3 + -5 so let's use a number line. A negative represents a move the left on the number line and a positive represents a move to the right on the number line.

So starting at 0, -3 tells us to move 3 units to the left along the number line. From there, -5 tells us to move 5 units further to left so you can see from the picture that we end up at -8.

This means that -3 + -5 is -8.

Answer:

-8

Step-by-step explanation:

you go 5 to the left of negitive 3 in the numberline

Step-by-step explanation:

Company A: y = 45x + 150

Company B: y = 50x + 125

let's use the number 5 for x as an example

45(5) + 150 = 375

50(5) + 125 = 375

So both companies charge the same amount of money for food truck permits

Final answer:

To compare the monthly food truck permit costs for two companies, we create linear equations for each company's total cost over time. Company A's cost CA is modeled by CA = 150 + 45x, and Company B's cost CB is modeled by CB = 125 + 50x, where x is the number of months. By analyzing these equations, we can determine which company is more cost-effective based on the duration of the permit usage.

Explanation:

To model the cost of food truck permits for the two companies over time, we need to create a system of linear equations representing the total cost for each company. Let x represent the number of months for which the permit is needed.

For Company A, which charges a one-time fee of $150 and $45 per month, the total cost CA after x months would be:

CA = 150 + 45x

For Company B, with a one-time fee of $125 and $50 per month, the total cost CB after x months would be:

CB = 125 + 50x

Each of these equations relates the total cost to the number of months the permit is held. From these equations, one can see that Company A has a larger initial fee but a lower monthly cost compared to Company B. The break-even point, where the costs of both companies are equal, can be found by setting the equations equal to each other and solving for x:

150 + 45x = 125 + 50x

The break-even point informs at what time period both companies would cost the same for the permits, which could help in making a decision between the two options based on how long you plan to keep the food truck.

Answer:

3x-2

Step-by-step explanation:

-2x-2+5x=-2x+5x-2=3x-2

Answer:

3 items are in B that are not in C

Step-by-step explanation:

a: only in a, not count those in b or c

b: only in b, not count those in a or c

c: only in c, not count those in a or b

A = a + b + c = 20

c = 7

a + b = 20 - 7 = 13

10 not in b, of course not in c ∴ a = 10

b = 13 -10 = 3

Answer:

x = 8

Step-by-step explanation:

If NO is parallel to KJ then the sides LK and LJ are in proportion, that is

[tex]\frac{KN}{NL}[/tex] = [tex]\frac{JO}{OL}[/tex], substitute values

[tex]\frac{x+2}{x-3}[/tex] = [tex]\frac{x}{x-4}[/tex] (cross- multiply )

x(x - 3) = (x + 2)(x - 4) ← expand factors on both sides

x² - 3x = x² - 2x - 8 ( subtract x² - 2x from both sides )

- x = - 8 ( multiply both sides by - 1 )

x = 8

Answer:

8

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

2.5 hours/3 hours

Step-by-step explanation:

If it takes the beginner 6 hours and experienced tinter 3 hours working together it should take roughly 2.5 hours to 3 hours because the time would be cut in half.

It will take them 2 hours to do the job together .

The tinter can tint a car in 3 hours . He does it at the rate of 1 / 3 per hour

A beginner needs 6 hours to do the same job. He does it at the rate of 1 / 6 per hour

For both of them to do the same job , the rate can be calculated below.

1 / 3 + 1 / 6 = 1 / 2 per hour

If they do the job at the rate of 1  / 2 per hour, how long will it take to complete 2 / 2 ?

2 / 1 = 2 hours

The time it will take them to do the job is 2 hours.

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Answer:

x=1, y=2. (1, 2).

Step-by-step explanation:

x-3y=-5

-3x+7y=11

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

x=3y+(-5)

x=3y-5

-3(3y-5)+7y=11

-9y+15+7y=11

-2y=11-15

-2y=-4

2y=4

y=4/2

y=2

x-3(2)=-5

x-6=-5

x=-5+6

x=1

Answer:

Yes

Step-by-step explanation:

Answer:

yes it is

Step-by-step explanation:

3.456 could be written as a fraction, that means it is a rational number because rational number is any number that could be written as a fraction.

3.456=3456/1000

Answer:

The value of  [tex]\frac{f}{g} (x)[/tex] is [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex]

Step-by-step explanation:

Given as :

f(x) = 4 x + 1

g(x) = x² - 5

Let the value of [tex]\frac{f}{g} (x)[/tex] = A

So, According to question

[tex]\frac{f}{g} (x)[/tex]  = [tex]\dfrac{f(x)}{g(x)}[/tex]

Or, A = [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex]

So, The value of  [tex]\frac{f}{g} (x)[/tex] = A =  [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex]

Hence, The value of  [tex]\frac{f}{g} (x)[/tex] is [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex] Answer