Every day a school bus driver passes the same traffic light twice, once before school and once after. Each time he passes the light, he records If it is red, green, or yellow.
Here is a summary of the data he got after 200 days.

Traffic light before school Traffic light after school Number of day
red red 25
red green 21
red yellow 17
green red 16
green green 31
green yellow 27
yellow red 22
yellow green 28
yellow yellow 13

Suppose the driver will continue recording the colors for 150 more days.
In how many of these 150 days will the light be red exactly once? Use the data to make a prediction.

a. Acceleration of the system (a) = 6.125 m/s^2

b. The tension in the rope (T) = 110.25

What is the definition of acceleration ?

Acceleration  defines that the rate at which velocity changes with time, in terms of both speed and direction.

For 30 kg mass

m . g - T = m . a

30 x 9.8  - T = 30. a   ⇒  (1)

For 10 kg mass

T - m base 2 g Sin θ = m base 2 a

T - 10 x 9.8 Sin 30° = 10 x a         ⇒  (2)

a. Adding equation (1) and (2)

    294 - 49 = 30 a + 10 a

    245 = 40 a

     a = 245/40

     a = 6.125 m/s^2

  Therefore, acceleration = 6.125 m/s^2

b. Sub a value in equation (1) we get,

    T = 110.25

   Therefore , tension in the role = 110.25

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Answer:

1.42 liters is the correct answer

Keith live 480 miles far way from the mountains.

The distance between two locations is represented by the length of the line linking them. If the two points are on the same horizontal or vertical line, subtracting the various coordinates will show how far apart they are.

Consider the provided information.

Keith drove to the mountains last weekend. The trip took 12 hours because of the high traffic on the way there.

Let the distance is D and average rate or speed is x miles.

Distance = speed × time

Substitute the respective values.

D = x  * 12

D= 12x

When Keith drove home, there was no traffic and the trip only took  

hours. The average rate was  8 miles per hour faster on the trip home,

The average rate or speed during return is x+20 miles.

Substitute the respective values in the above formula.

D = (x+20) ×8

D= 8x+160

Equate both the equations.

8x+160 = 12x

4x= 160

x=160/4

=40

Substitute the value of x in D= 12x

D=12(40)

D= 480

Hence, Keith live 480 miles far way from the mountains.

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Answer:

2. C

3. BCEF

4. C

Step-by-step explanation:

2. In a function, the x value cannot have two y values (for example: if the points are (1,2) and (1,3) then that is not a function).

In this question, none of the x values repeat with multiple y values, so it is a function. the answer is C.

It is not D, because not all straight lines are functions. If the straight line is vertical, then there is only one x value and it has infinitely many values for y. So, not all straight lines are necessarily functions.

3. Range is the y values. The points are (3,4), (-2,3), (7,1), (2, 1/2)

Here, the y values are 4, 3, 1, and 1/2

Choices B,C,E,F are the answers.

4. If the domain is x[tex]\geq[/tex]0, then 0 is the lowest we can plug into x.

y=2(0)+6

y=6

So, the answer is C. y[tex]\geq[/tex]6

You were on the right track :)

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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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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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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Answer: You would have eaten 31/32 of the pizza.

Step-by-step explanation:

1/2 + 1/2^2+1/2^3+1/2^4+1/2^5 =

1/2(1-(1/2)^5)/1-1/2 =

1-1/32=

31/32

good question.

The measure of [tex]\angle 1[/tex] is [tex]60^{\circ}[/tex] because it is related to one of the angles of the triangle by the alternate interior angles theorem.

The measure of [tex]\angle 2[/tex] is [tex]120^{\circ}[/tex] because it is adjacent to one of the angles in the triangle.

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

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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Step-by-step explanation:

you can find it by using the arc formula?

The linear regression equation in this problem is given as follows:

y = 4.774x + 39.474.

Then the estimates are given as follows:

a) x = 3 hours: 53.8.

b) x = 4.5 hours: 61.

c) x = 13 hours: 101.5.

d) x = 1.5 hours: 46.6

The linear regression equation is obtained inserting the points of the table into a linear regression calculator.

From the table in this problem, the points are given as follows:

(0,39), (1,45), (2,52), (4, 49), (5, 61), (5,72).

Inserting these points into a calculator, the equation is given as follows:

y = 4.774x + 39.474.

Then the estimates are obtained with the numeric values, as follows:

a) x = 3 hours: y = 4.774(3) + 39.474 = 53.8.

b) x = 4.5 hours: y = 4.774(4.5) + 39.474 = 61.

c) x = 13 hours: y = 4.774(13) + 39.474 = 101.5.

d) x = 1.5 hours: y = 4.774(1.5) + 39.474 = 46.6.

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Answer:

78.8

Step-by-step explanation:

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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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)

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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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.

Answer:

idek

Step-by-step explanation:

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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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:1235160000 beats

Step-by-step explanation:

There are 525600 minutes in a year

47*525600= 24703200

24703200*50= 1235160000

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:

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

The second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.

What is PPG Statistics?

First, calculate the PPG earned by the current leader of the season.

The total points earned by the current leader amount to 2112 and he had participated in a total of 77 games.

The following formula can be used to determine the PPG earned by the current leader per game,

PPG = Total Points / Total Games

[tex]\implies PPG=\frac{2112}{77}\\ \implies PPG = 27.42[/tex]  -----(1)

Now, calculate the PPG of the player who is ranked in the second place for the season.

The total number of points earned by the second place player is 2020 and he played a total of 74 games.

The second place player earned the following points per game,

PPG = Total Points / Total Games

[tex]\implies PPG=\frac{2020}{74}\\ \implies PPG = 27.29[/tex]  ---(2)

The difference in score with the leading team can be found by subtracting (2) from (1),

[tex]\implies 27.42-27.29=0.13[/tex]

So, to be the leading player, the second place player must obtain a lead of 0.14 points per game in the next three games if the current player plays no more games.

In such a situation, the total PPG of the player should be 27.43 and the number of games to be played is 3.

So, the number of points required to take lead can be calculated as,

PPG = Total Points / Total Games

[tex]\implies 27.43=P/3[/tex]

So, the Total Points required, [tex]P=27.43 \times 3 =82.29[/tex]

And, the PPG required by the second place player to score in each of the next three games is calculated as,

[tex]\frac{0.14}{3}=0.0467[/tex]

Therefore, the second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.

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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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