A box of 15 cookies costs $9dollar sign, 9. What is the cost for 1 cookie?

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\stackrel{\textit{"y" varies directly as "x"}}{y = kx}\qquad \textit{we also know that} \begin{cases} y = 540\\ x = 10 \end{cases}\implies 540=k(10) \\\\\\ \cfrac{540}{10}=k\implies 54=k~\hfill \boxed{y=54x} \\\\\\ \textit{when y = 1080, what is "x"?}\qquad 1080=540x\implies \cfrac{1080}{540}=x\implies 2=x[/tex]

The value of x when y = 1080 for the condition when its given that y varies directly as x and that y = 540 when x = 10, is found to be x = 20

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For this case, it is specified that y varies directly as x.

That means

[tex]y \propto x\\or\\y = kx[/tex]

At x = 10, y is 540. Putting these values in the equation y = kx as they're related, we get:

[tex]540 = k \times 10\\\\\text{Dividing both the sides by 10}\\\\\dfrac{540}{10} = k\\\\k = 54[/tex]

Thus, the relationship between x and y is: y = 54x

Now, when y = 1080, we get:

[tex]1080 = 54x\\\\\text{Dividing both the sides by 54}\\\\\dfrac{1080}{54} = x\\\\x = 20[/tex]

Thus, the value of x when y = 1080 for this condition is when x = 20.

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The sales receipt for the purchase includes the sales tax

The sales tax is calculated as:

Percentage sales tax * (Sum of Items subjected to tax) =  Sales tax.

So, we have:

T * (3 + 0.5) =  0.21

Evaluate the sum

T * (3.5) =  0.21

Divide both sides by 3.5

T =  6%

Hence, the sales tax is 6%

The price (p) at the top is calculated using:

p = 13 - 3 - 2 - 0.5

Evaluate the difference

p = 7.5

Hence, the price at the top is $7.50

60% of the original price (P) is p.

So, we have:

60% * P = p

Substitute 7.5 for p

60% * P = 7.5

Divide both sides by 60%

P = 12.5

Hence, the original price at the top is $12.50

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Answer:

The slope is 5/7.

Step-by-step explanation:

Use a slope formula.

Slope:

[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

y₂ = (17)

y₁ = (7)

x₂ = (18)

x₁ = (4)

Rewrite the problem down.

[tex]\sf{\dfrac{17-7}{18-4}=\dfrac{10}{14}={\dfrac{10\div2}{14\div2}=\boxed{\sf{\dfrac{5}{7}}}[/tex]

Therefore, the slope is 5/7.

I hope this helps! Let me know if my answer is wrong or not.

Answer:

5/7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(17-7)/(18-4)

m=10/14

simplify

m=5/7

Eigenvalues are the special set of scalar values which is associated with the set of linear equations in matrix equations.

Your information is incomplete. Therefore, an overview will be given. An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.

The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in thesame direction or opposite direction to X.

Since the zero vector 0 has no direction, 0 is never allowed to be an eigenvector.

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An eigenvector of a linear transformation and eigenvectors of a system

Ax = Bx can be determined where B is an eigenvalue of A.

An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.

The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in the same direction or opposite direction to X.

The basic equation is

Ax = Bx

here B is an eigenvalue of A.

Since the zero vector has no direction, zero is never allowed to be an eigenvector.

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The area of the sector that has a central angle of 120 degrees and radius of 8 units is 64π / 3 units²

The area of a sector is defined as follows:

area = ∅ / 360 × πr²

where

Therefore,

r = 8

∅ = 120°

Hence,

area of the sector = 120 / 360 × π × 8²

area of the sector = 1 / 3 × π × 64

area of the sector = 64π / 3 units²

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Answer:

X = 6

Step-by-step explanation:

Hope this helped!!

maybe mark brainiest

The two inequalities that represents the constraints for the art studio classes per week are:

x + 1.5y = 40

35(x + y)  > 1,000

Here are inequalities signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

= means equal to

The inequality that represents the total hoursthe art studio is open would be an equal to sign. This is because the store is open for a maximum of 40 hours.

The inequality that represents the total earnings would be represented with a greater than sign because the studio earns more than $1000 weekly.

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Answer:

6 1/4

Step-by-step explanation:

3+2=5

2+3

1/2+3/4= ----------------------------------------------------

4

=5/4

=1 1/4

5+ 1 1/4

=6 1/4

Answer:

Circumference = 7.68 cm

Area = 113.04 cm²

Step-by-step explanation:

First, let us find the radius of the given circle.

d = 2r

r = d / 2

r = 12 / 2

r = 6 cm

And now, let us find the circumference of the circle using the below formula.

C = 2 π r

C = 2 × 3.14 × 6

C = 37.68 cm

And now let us find the area of the circle using the below formula.

A = π r²

A = 3.14 × 6 × 6

A = 113.04 cm²

Step-by-step explanation:

there are in total 21 marbles.

5 black, 6 blue = 11 black or blue marbles.

so, the probability of pulling a black or blue marbles is as always desired possible outcomes / total possible outcomes = 11/21

Based on the speed Alyssa used to get to London and the speed back to Boston, the average speed was 540 mph.

The average speed that Alyssa was going can be found by the formula:

= (Initial speed + Final speed) / 2

Solving gives:

= (480 + 600) / 2

= 1,080 / 2

= 540 mph

In conclusion, Alyssa's average speed was 540 mph.

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Answer:

Matt used diameter of the ball instead of Radius

Step-by-step explanation:

The volume of a sphere is given as:

⇒ Matt made an error in his calculation by failing to covert the value of the diameter given to Radius.

⇒ By dividing the diameter by 2 = 15 / 2 = 7.5, we obtain the Radius, which is what Billy did in her own calculation.

Answer:

m = 41/6

Step-by-step explanation:

Convert everything into improper fractions with a denominator of 6.

Answer:

Step-by-step explanation:

In order to solve this problem, you need to add their similar elements together.

First, add similar to elements.

[tex]\sf{a+a=\boxed{\sf{2a}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

The difference in the volume of bedroom door in the house taken the length and width into consideration will be 120 inches³.

It should be noted that the volume of a door is simply gotten by multiplying the length by width.

Let's assume that the width is 20 inches. Therefore, the difference will be:

= (36 × 20) - (30 × 20)

= 720 - 600

= 120 inches³

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Answer:

When the actual temperature is -14 degrees Celsius, the wind chill equivalent temperature would be -22.2 degrees Celsius.

When the actual temperature is 3 degrees Celsius, the wind chill equivalent temperature would be 0.6 degrees Celsius.

Step-by-step explanation:

There is a + 1.2 pattern going right.  So each time you increase the actual temperature by 1, you increase the wind chill equivalent temperature by 1.2

Answer:

This question is asking for you to determine if the tables represent linear functions, functions in y=mx+b form, and to find the equation for the line.

If something is a linear function, each of the input values will have it's own corresponding y value, therefore c cannot be linear, as -1 and 1 both have 10 as the output.

I hope this helps, but if you need more clarification, please tell me in the comments!

Step-by-step explanation:

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Answer:

Explanation:

make x the subject in equation 2,

5x + y = -3

y = -3 - 5x __ equation 2

using substitution method,

-4x + 3(-3 - 5x) = 29

-4x -9 -15x = 29

-19x = 38

x = -2

Find y,

y = -3 - 5x

y = -3 - 5(-2)

y = 7

Answer:

t=-\frac{20}{11}

Step-by-step explanation:

Answer:

yeh

Step-by-step explanation:

1 gallons = 4 quarts

4,8,20,28

quarts= 2 pints

1,3,6,16

1 pint= 2 cups

2,6,5,18

Answer:

[tex]\frac{5}{6}:1[/tex]

Step-by-step explanation:

[tex]10:12[/tex] divide both sides of this ratio by 12 to give a ratio in the form [tex]n:1[/tex]

[tex]\frac{10}{12}:1[/tex] which simplifies to [tex]\frac{5}{6}:1[/tex]

The number of rectangular prism container that would be set on the shelf is: 4.

Volume of rectangular prism = length × width ×height

Given the following:

Find the length of one rectangular prism using the volume formula since volume for one prism = 45 in.³

45 = length × 9

length = 5 in.

Each rectangular prism container is 5 in. long, therefore, the number of the containers that can be set on the shelf that is 24 in. long, if the 4.5 in by 2 in. face touches each other = 24/5 = 4.8.

The fifth container won't fit in. Therefore, the number of rectangular prism container that would be set on the shelf is: 4.

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Answer:

add the 1.94+0.56 to get 2.5 liter

Step-by-step explanation:

wow, he drank almost 2 liters of milk more or less in one turn ? he might spend quite some time in the bathroom ...

anyway, x = original amount of milk.

x - 1.94 = 0.56 now we add 1.94 to both sides

x = 2.5 L

The surface area of a cuboid is the area of all the six faces of a cuboid. The Paint that is required to paint 3 boxes is 13 pints.

The surface area of a cuboid is the area of all the six faces of a cuboid. It is given by the formula,

[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]

As it is given the dimensions of the storage box are a length of 8 feet, a width of 5 1/2 feet(5.5 feet), and a height of 4 1/2 feet(4.5 feet). Therefore, the surface area of the box can be written as,

[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]

[tex]\rm \text{Surface area of the box}= 2[(8\times 5.5)+(5.5\times 4.5)+(8 \times 4.5)] = 209.5\ ft^2[/tex]

As it is given that the surface area that can be covered with a pint of paint is 50 square feet, therefore, the paint that will be required to paint 209 square feet is,

[tex]\text{Paint Required} = \dfrac{\text{Total area that is needed to be paint}}{\text{Area covered in a pint of paint}}[/tex]

[tex]\rm \text{Paint Required} = \dfrac{209.5}{50} = 4.19\ pints[/tex]

Now, we know that the surface area of the box is 209 square feet, while the paint required to paint a complete box is 4.19, therefore, the paint that will be required to paint 3 boxes will be,

[tex]\text{Paint required to paint 3 boxes} = 3 \times 4.19 = 12.57 \approx 13[/tex]

Hence, the Paint that is required to paint 3 boxes is 13 pints.

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The new length of the enlarged figure will 18 cm.

A scale factor is a number which scales, or multiplies, the original figure by some quantity.

We have the equation for the scale factor.

Y=Cx

C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.

As the given length is 4.5 cm, so with a scale factor of 4, the length of the enlarged figure will be

[tex]Y=4.5\times4=18\ cm[/tex]

Therefore, the new length of the enlarged figure will 18 cm.

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