A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 22 cubic feet. A total of 21 boxes of paper were shipped with a combined volume of 342 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.

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.

According to the figure, I can safely assume that the 10 cm line and 15 cm line are parallel.

Thus, there are two similar triangles, one with the 10 cm bottom and 15 cm bottom, where one triangle is larger by a factor of 15/10 = 3/2

We know that the 8 cm line segment and y both join to create the side of the large triangle.

8cm + y = the side of the large triangle

Multiplying 8cm by 3/2 gives us 12, since we know the large triangle is 3/2 times larger than the smaller one.

8 + y = 12

y = 4 cm

Finding x is going to be a bit different. We know that the 6 cm line and x form the side of the larger triangle, which we know is 3/2 times larger than x.

x + 6cm = ?

The side of the larger triangle is 3/2x, thus

x + 6 = 3/2 x

Subtract both sides by x

6 = 1/2 x

Multiply both sides by 2

12 cm = x

Thus, y = 4 and x = 12.

Let me know if you need any clarifications, thanks!

Henry spent [tex]5\frac{1}{4}[/tex] hours on yard work.

Step-by-step explanation:

Given,

Time spent on cutting the grass = [tex]1\frac{1}{2}=\frac{3}{2}\ hours[/tex]

Time spent on pulling weeds = [tex]1\frac{3}{4}=\frac{7}{4}\ hours[/tex]

Time spent on sweeping and bagging = 2 hours

Total time spent = Time spent on cutting + Time spent on pulling + Time spent on sweeping

Total time spent = [tex]\frac{3}{2}+\frac{7}{4}+2[/tex]

Taking LCM

Total time spent = [tex]\frac{6+7+8}{4}=\frac{21}{4}[/tex]

Total time spent = [tex]5\frac{1}{4}[/tex] hours

Henry spent [tex]5\frac{1}{4}[/tex] hours on yard work.

Keywords: fraction, addition

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Answer:

Step-by-step explanation:

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:

dimeonsion 1 should be 3x13 dimension 2 should be 6x10 dimension 2 is what chris should choose

Step-by-step explanation:

ik this is from prodigy lol

Chris should create a rectangular rose garden with dimensions 8 meters in length and 8 meters in width to use all 32 meters of garden fencing.

To begin, let's assume the rectangular garden has a length (L) and a width (W). Since the garden is enclosed by fencing on all sides, the perimeter of the garden would be equal to the total length of the fencing, which is 32 meters.

Perimeter = 2L + 2W

Since we know the perimeter is 32 meters, we can set up the equation:

32 = 2L + 2W

To maximize the area of the garden, Chris needs to find the dimensions that will yield the largest possible area for a given perimeter. The area (A) of a rectangle can be calculated using the formula:

Area = L * W

Since we know the perimeter is 32 meters:

2L + 2W = 32

Solving for L:

2L = 32 - 2W

L = 16 - W

Now, substitute this value of L into the area equation:

Area = L * W

Area = (16 - W) * W

Expand the equation:

Area = 16W - W²

Now, this equation represents the area of the rectangular rose garden in terms of its width (W). To find the value of W that maximizes the area, we can take the derivative of the area equation with respect to W and set it equal to zero:

d(Area)/dW = 16 - 2W = 0

Solving for W:

2W = 16

W = 8 meters

Now that we have the width (W), we can find the length (L) using the previously derived equation:

L = 16 - W

L = 16 - 8

L = 8 meters

Therefore, to create a rectangular rose garden with 32 meters of fencing that utilizes all the available fencing, Chris should make the length and width of the garden 8 meters each.

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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:

3x-2

Step-by-step explanation:

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

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:

[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:

4

Step-by-step explanation:

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:

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:

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

Answer:

10

Step-by-step explanation:

okay so if he has 2 dogs and he feeds each dog 250 grams twice a day

if he buys a 10 kilo bag, how many days will it last?

so first off, convert the 250 grams into kilos. which is 0.25

0.25 × 4 = 1 kilo

4 is the amount of times he feeds the dogs.

so in reality, it should take 10 days.

The number of days will the bag last is 10 days.

Given that,

Based on the above information, the calculation is as follows:

Here first we have to convert the 250 grams into kilos so it should be 0.25

And, there is no of times the dog feed is 4

So, it should be 1 kilo

And, there is the purchase of 10 kilos

Therefore, we can conclude that The number of days will the bag last is 10 days.

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Answer:

The number is 8.

Step-by-step explanation:

4(x+(-3))-4=2x

4(x-3)-4=2x

4x-12-4=2x

4x-2x-16=0

2x-16=0

2x=0+16

2x=16

x=16/2

x=8

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:

Cost per ounce = $0.07 (7 cents per ounce)

Step-by-step explanation:

Each container is 7.8 ounces and there are 24 of them in a case.

Total weight in ounce of the case is:

7.8 * 24 = 187.2 ounces

It costs $12.99 for the case, which contains 187.2 ounces. We find the cost per ounce of yogurt by dividing the total cost by total ounces in the case.

12.99/187.2 = 0.0693

Rounded to nearest cent (2 decimal places), that would be:

Cost per ounce = $0.07 (7 cents per ounce)

The unit price of the Greek yogurt is $0.07 per ounce.

To calculate the unit price, we need to divide the total cost of the case by the total number of ounces in the case.

First, we determine the total number of ounces in the case by multiplying the number of containers by the ounces per container:

[tex]\[ 24 \text{ containers} \times 7.8 \text{ ounces per container} = 187.2 \text{ ounces} \][/tex]

Next, we divide the total cost of the case by the total number of ounces to find the cost per ounce:

[tex]\[ \frac{\$12.99}{187.2 \text{ ounces}} \approx \$0.0693 \text{ per ounce} \][/tex]

Finally, we round this to the nearest cent, which gives us:

[tex]\[ \$0.0693 \text{ per ounce} \approx \$0.07 \text{ per ounce} \][/tex]

Therefore, the unit price of the Greek yogurt, rounded to the nearest cent, is $0.07 per ounce.

Answer:

4

Step-by-step explanation:

Answer:

2*2 is 4 id4

Step-by-step explanation:

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

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:

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:

[tex]10[/tex]

Step-by-step explanation:

Combinations : When there are total [tex]n[/tex] choices and you have to choose [tex]k[/tex]of them (in any order)

                 The possible ways [tex]= \ ^n{c_{k}} = \frac{n!}{k!(n-k)!}[/tex]

Here total chances [tex]=5[/tex]

and we have to choose [tex]2[/tex]of them.

Possible ways[tex]=\ ^5{c_{2}}[/tex]

                             [tex]=&\frac{5!}{2!(5-2)!} = \frac{5!}{3! 2!} \\\\=&\frac{5 \times 4\times 3!}{3! 2!} = \frac{5 \times 4}{2} = 10[/tex]

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

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 d (-21/2 , 2)

Step-by-step explanation:

That's where the lines meet up

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:

[tex]A=61.8\ units^2[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of triangle ABC applying the law of sines is equal to

[tex]A=\frac{1}{2}(AC)(BC)sin(C)[/tex]

substitute the given values

[tex]A=\frac{1}{2}(10)(13)sin(72^o)[/tex]

[tex]A=61.8\ units^2[/tex]

Answer:

c) 61.8 square units

Step-by-step explanation:

just took the test

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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