Find the equation of the linear function represented by the table below in
slope-intercept form.
X
-2
1
4
7
y
6
-6
-18
-30

-First question:

To calculate the number of liters, the number of roofs must be multiplied by the amount of waterproofing used for each roof.

To multiply the fractions, transform the mixed fractions to improper:

[tex]\begin{gathered} \sf1 \frac{1}{4} \times 4 = \\ \\ \sf \frac{4 \times 1 + 1}{4} \times \frac{4}{1} = \\ \\ \sf \frac{4 + 1}{4} \times \frac{4}{1} = \\ \\ \sf\frac{5}{4} \times \frac{4}{1} = \\ \\ \sf \frac {5 \times 4}{4 \times 1} = \\ \\ \boxed{ \sf \frac{ \red{20}}{ \red4}} = \sf \blue5\end{gathered}[/tex]

So you need five liters of waterproofing to get the job done.

-Second question:

To calculate the number of liters; It must be subtracted from the number of liters you need in total, which you already had or had:

[tex]\begin{gathered} \sf5 - 2 \frac{1}{4} = \\ \\ \sf \frac{5}{1} - \frac{4 \times 2 + 1}{4} = \\ \\ \sf\frac {5}{1} - \frac{8 + 1}{4} = \\ \\ \sf \frac{5}{1} - \frac{9}{4} = \\ \\ \sf\frac{4 \div 1 \times 5 - 4 \div 4 \times 9}{4} = \\ \\ \sf \frac{20 - 9}{4} = \\ \\ \boxed{ \sf \frac{11}{4}} = \boxed{ \sf \blue2 \: \: \blue{\sf\frac{3 }{4} }}\end{gathered}[/tex]

So, you need two whole and three quarter liters of waterproofing.

Based on the information given the constant of variation is 11.67.

What is the rate of change?

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time

by using this formula

Constant of variation = Amount earned/Time

Where:

Amount earned=$175

Time=15 hours

Let's plug in the formula

Constant of variation=$175/15

Constant of variation=11.66

Constant of variation=11.67 (Approximately)

Hence, the constant of variation is 11.67.

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Tan A + Cot A = 2 Cosec 2A.

It is a simple TRIGNOMETRY question, which is directly based on their formulas.

In this question we have one side of formula either LHS or RHS and we have to find other,

Tan A + Cot A

we know Tan A = sin A /Cos A  and Cot A = cos A / sin A

So by putting this in place of  Tan A + Cot A we get,

⇒ (sin A / cos A) + (cos A / sin A)

⇒ (sin∧2 A + cos∧2 A) / cos A sin A

⇒1/ cos A sin A

⇒2/2cos A sin A

⇒ 2/Sin 2A

⇒ 2 Cosec 2A

Hence, the question is simplified.

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Answer:

1/14

Step-by-step explanation:

If 7 people equally share 1/2 a pan of macaroni and cheese, each person will get 1/2 / 7 = 1/14 of the pan.

To find the fraction of the pan that each person gets in terms of the whole pan, we can multiply the fraction 1/14 by the denominator of the fraction representing the whole pan. If the whole pan is represented by 1 pan, the fraction representing each person's share would be 1/14 * 1 = 1/14 of a pan.

So, each person would get 1/14 of a pan of macaroni and cheese.

Answer: 1/14

Step-by-step explanation:

1/2 / 7 = 1/14≅ 0.07142857

There are 523 units did she produced.

What is paycheck?

Traditionally, an employer would issue a paper document known as a paycheck—also spelled pay cheque, pay check, or pay cheque—to pay an employee for services rendered.

Businesses pay their employees for their work through paychecks. Bi-weekly and semi-monthly delivery schedules are the most typical ones, though this can change depending on the employer's preferences and any applicable state laws and regulations.

Given that:

Piecework pay = $465.47

Price per unit = 89 cents = $0.89

Number of units=$x

Let,

Total piecework pay = Price per unit x number of items sold

                   $465.47 = 0.89 x x

                               x = 523

Hence, there are 523 units did she produced.

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Step-by-step explanation:

y = 3.52x

This equation states that the total amount paid, y, is equal to 3.52 multiplied by the number of pounds of potatoes, x.

D is the midpoint of AC, and E is the midpoint of BC, hence the value of x for the given problem will be 9 units.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.

Here,

Since these are similar triangle,

BE=EC

BC=BE+EC

BC=2BE

6/(3x-15)=1/2

12=3x-15

3x=27

x=9

The value of x for the given problem where D is the Midpoint of AC and E is the midpoint of BC will be 9 units.

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The number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Eliza has = 14 + 7x

x is the number of weeks

For Sahana:

y - 8.40 = (16.80-8.40)/(2-1)[x - 1]

y = 8.4x - 8.4 + 8.4

y = 8.4x

14 + 7x = 8.4x

x = 10 hours

Thus, the number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.

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Answer:

78.8

Step-by-step explanation:

It is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.

If a contradiction is rational, then log3(7) = a/b for some a,b∈R .

In which, b≠0 will be true.

As a result, 7 = 3ᵃ/ᵇ according to the definition of logarithms.

7 = 1*7 is unique according to the unique factorization theorem.

Thus, it is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.

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The answer is the Theoretical probability is higher than the Experimental probability.      

Experimental probability:

The basis for experimental probability is what actually happens. It is dependent on the outcomes of several tests or experiments.

It is calculated by repeatedly recreating the event, recording the outcomes, and then converting the outcomes into a ratio or decimals.

Experimental probability =  No of times event occurs/ No of trials

Theoretical Probability:

Theoretical probability is derived from a theory or what is predicted to occur. It is based on information and math.

It is determined by dividing the total number of outcomes by the proportion of favorable results. Either convert it to decimal form or leave it as a ratio or fraction.

Theoretical probability = No of favorable outcomes/ No of outcomes

Here we have

Tami rolled a die 20 times

14 times it landed on an even number;

6 times it landed on an odd number.  

The die rolled for an odd number

As we a die will have 6 faces

Number of odd numbers = 3       [i.e 1, 3, 5 ]                    

Number of even numbers = 3    [ i.e 2, 4, 6 ]

⇒ Theoretical probability = 3/ 6 × 100 = 50%

The die is rolled 20 times, 6 times it landed on an odd number.

⇒ Experimental probability =  6 / 20 = 30%

As we can see,

The theoretical probability is higher than the Experimental probability.

Therefore,

The answer is the Theoretical probability is higher than the Experimental probability.  

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If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The perimeter of the triangle is determined by adding together all of its sides.

The triangles ΔPQR and ΔSTU are congruent triangles. Then we have

PR = SU

3y - 2 = y + 4

3y - y = 2 + 4

2y = 6

y = 3

Then the value of the side PR is given as,

PR = 3(3) - 2

PR = 9 - 2

PR = 7 feet

Then the perimeter of the triangle ΔPQR is calculated as,

P = 4 + 6 + 7

P = 17 feet

If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.

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You will find 5 rare trading cards if you bought 110 packs of trading cards

Given that:

The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one twenty-second times x.

Thus, we can the equation as:

y = (1/22)x

To determine the number of rare trading cards if you bought 110 packs of trading cards, substitute x = 110 into the equation:

y = 1/22 × 110

y = 5

Therefore, you will find 5 rare trading cards if you bought 110 packs of trading cards

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Answer:

Step-by-step explanation:

y = the number of rare trading cards found

x = the number of packs of trading cards

1/22 = the probability of finding a rare card per pack

Equation

y = 1/22(x)

y = 1/22(110)

y = 110/22

y = 5

There is a chance of finding 5 rare cards in 110 packs of trading cards.

Answer:

4

Step-by-step explanation:

20% = 40

10% = 20

100% = 200

200 * .02 = 4

The value of 2% of that number is,

⇒ 4

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

20% of a number is 40.

Let the number = x

Hence, We get;

⇒ 20% of x = 40

⇒ 20/100 × x = 40

⇒ 1/5 × x = 40

⇒ x = 200

Thus, The value of 2% of that number is,

⇒ 2% of 200

⇒ 2/100 x 200

⇒ 4

Thus, The value of 2% of that number is,

⇒ 4

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Answer:

TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)

Step-by-step explanation:

They ask you "elect any expressions that could represent the total number of tadpoles that you and your friend can catch.​"

then you need the SUM of both.

TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)

Step-by-step explanation:

you can find it by using the arc formula?

Answer:

p=24/528

Step-by-step explanation:

4+2p=10(53p-2)

4+2p=530p-20

24+2p=530p

24=528p

24/528=p

The answer to Question based on Conversion of Units is 1008gm

What is Conversion OF Units?

It is a method to convert units from one version from another.

Solution:

Here in this Question we must know the conversion that 1 ounce is nearly equal to 28gms

Hence if Doreen Schmidt needs to prepare 36 ounces of 11% solution he needs to have exact measurement of chemicals

Hence we can say must have that 36 ounces of chemicals to make that

Hence by unit conversion 36 multiplied by 28 which comes out to be 1008gm of chemical he needs to have

to make 11% solution

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The length of rectangle is 20cm and width is 12cm.

Let the length is x cm and width is y cm.

then perimeter 2(x+y) =64 cm

=> x+y = 64/2 = 32

=> x + y = 32 .............(1)

and according to question twice the width is 4cm more than length so,

2y = x + 4

=> 2y -x = 4 .............(2)

now we add these two equation to find the value of x and y.

3y = 36

=> y = 12

now put the value of y on any equation to find value of x ,

x +12 = 32

=> x = 32 -12 = 20

so, the length of rectangle is 20cm and width is 12cm.

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Answer: C) $83.25

Step-by-step explanation: First you multiply 124 by whatever amount equivocates to 10,323 then multiply 1 by that same amount and you get the answer, 124 x 83.25 = 10,323, and 1 x 83.25 = 83.25

Answer:

  (a)  √8

Step-by-step explanation:

You want to know the radical equivalent to 2^(3/2).

The relationship of indices to radicals is ...

  [tex]\large{\sqrt[n]{a^m}}={a^{\frac{m}{n}}[/tex]

The given expression can be rewritten as ...

  [tex]2^{\frac{3}{2}}=\sqrt[2]{2^3}=\boxed{\sqrt[2]{8}}[/tex]

__

Additional comment

When the index of the radical is 2, it is usually left off. The radical can be simplified by removing the perfect square factor.

  [tex]\sqrt[2]{8}=\sqrt{8}=2\sqrt{2}[/tex]

The expected payoff from the raffle is given as follows:

$3.

The payoff is modeled by a discrete distribution, hence the expected payoff is the expected value of the said discrete distribution.

There are 500 tickets in the raffle, hence the probabilities are given as follows:

The expected value of a discrete distribution is calculated as the sum of all outcomes multiplied by it's respective probability, hence:

E(X) = 560 x 1/500 + 490 x 1/500 + 270 x 1/500 + 180 x 1/500 + 0 x 496/500 = $3.

(all the outcomes and their probabilities are taken from the distribution built in this problem).

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Answer: r > 30

Step-by-step explanation:

Answer:

idek

Step-by-step explanation:

Answer:

1.42 liters is the correct answer

The length of the diagonal of a square with a perimeter of 56 is 14√2.

A diagonal is the longest line that divides a plane shape into two equal parts.

To calculate the length of the diagonal of the square, first we need to find the length of the square using the perimeter formula.

Formula:

Where:

From the question,

Given:

Substitute the value into equation 1 and solve for a

Finally to find the length of the diagonal of the square, we use the formula below

Where:

Substitute into equation 2

Hence, the length of the diagonal is 14√2.

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Answer:

qfewwqeffwqfefewqwqreg

Step-by-step explanation:

1 meter and 59 centimeters.

The longest side in a right triangle is called the hypotenuse. In other terms, the hypotenuse is the side that faces the right angle.

theorem of Pythagoras

[tex]a^{2} +b^{2} = c^{2}[/tex]

A is a right triangle's side.

B is the right triangle's side.

c = hypotenuse

Think of a right triangle where the height and distance are the legs and the hypotenuse is the rope.

We are aware that:

cos(45°) =x/10

cos(30°) =y/10,

where x represents the distance between the ship and the dock at low tides and y represents the distance during high tides.

We are searching for the y-x distance difference (since it will be farther away during high tides).

Using the previous equations:

x=cos(45°) and y=cos(30°)

Hence:

y - x = 10(cos(30°) - cos(45°))

Hence, the exact value of the distance is 10(cos30° - cos45°)

Using a calculator, this is approximately 1.59 meters.

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