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Two parallel lines are cut by a transversal.

1/2
3/4
5/6
7/8

If the measure of 2 is 75°, what is the measure of 5?

A.) 180°
B.) 75°
C.) 105°
D.) 90°

Answer:

40/7

Step-by-step explanation:

3 3/7 divided 4 4/5+1 1/7 * 4 3/8

3 3/7 = 24/7

4 4/5 = 24/5

1 1/7 = 8/7

4 3/8 = 35/8

So, our equation is

24/7 divided 24/5 + 8/7 · 35/8

120/168 + 8/7 · 35/8

120/168 + 280/56

120/168 + 840/168

960/168

240/42

120/21

40/7

It will take the pump 80 minutes to fill the tank completely.

We can find the time to fill the tank by subtracting the current amount of the tank (3/8 of its capacity) from its total capacity. Then, dividing that amount by the flow rate of the pump (which is 1/16 of its capacity per minute).

The calculation is given as:

Remaining amount to fill = Total capacity - Current amount = 1 - 3/8 = 5/8

Time to fill completely = Remaining amount ÷ Flow rate = 5/8 ÷ (1/16) = 80 minutes

So, it will take the pump 80 minutes to fill the tank completely.

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____ The given question is incorrect, the correct question is given below:

If a pump fills a tank in 16 minutes and the tank currently has 3/8 of its capacity, then we can calculate how many minutes it will take to fill the tank completely.

The piece of information which would have to be marked on the triangle to show congruence by the HL theorem is ac = dc which is denoted as option C.

It states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.'

In triangle  ABC and triangle EDC, hypotenuses of triangles are AB and DE respectively.To use HL hypotenuse and one leg of triangles must be equal which means that :

AB = DE (hypotenuse)

AC = DC  (leg)

This means that the additional information  which  will allow you to prove the triangles congruent by the HL Theorem is AC = DC.

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The full question is:

What additional information will allow you to prove the triangles congruent by the HL Theorem?

choices

A = E

bce= 90

ac = dc

ac=bd

The cost of the event at Skate Fest can be represented as 200 + 3x. The cost of the event at Roller Rama can be represented as 5x.

The cost of the event at Skate Fest can be represented by the mathematical expression 200 + 3x, where x is the number of students attending the event. This represents the fixed fee of $200 plus an additional $3 for each skater.

The cost of the event at Roller Rama can be represented by the mathematical expression 5x, where x is the number of students attending the event. This represents $5 per skater.

By comparing these two expressions, the director can determine which skating rink is more cost-effective based on the number of students attending the event.

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Answer:

20 - (6 + b)

Step-by-step explanation:

ur mom

The number increase by a percentage of 76.29 over the given period of time.

To calculate the percent increase, we need to find the difference between the two values and divide that by the original value, then multiply by 100 to express the answer as a percentage:

If in 1995, a total of 945477 graduating seniors took the exam, and in 2012, the number of graduating seniors taking the ACT exam was 1666809, then the percent increase from 1995 to 2012 is:

(1666809 - 945477) / 945477 = 0.7629 x 100 = 76.29%

Therefore, the number of graduating seniors taking the ACT exam increased by 76.29% between 1995 and 2012.

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Answer:212

Step-by-step explanation:

$2000 - $200 = $1800

$1800/$8.50 = 211.76 round up to 212

Answer:

The answer is 24%

Step-by-step explanation:

Your welcome have a nice day!

The data given has: a) A strong correlation, b) A positive correlation

Correlation is a statistical measure that expresses the extent to which two variables are linearly related, meaning they change together at a constant rate.

We have ordered pairs in the data as:

x             y

1             2

2            3

3            8

4            10

5            26

6            38

7            46

8            50

9            68

Plotting the graph (attached)

Clearly, on plotting the scatter plot on the basis of table of values, we see that the relation is a strong correlation since we can find a relationship between variable x and y.

i.e. the points will lie above or below the curve  which is formed by connecting some points of the scatter plot and are not scattered away.

Hence, the data above has: A strong correlation.

Also, the graph is a positive correlation since with the increasing value of x the y-value also increases.

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Answer:

1. 62.8

2. 3.14

Step-by-step explanation:

It is important to note that the circumference formula is pi times 2 times radius. Radius for bigger circle is 10 so its circumference would be 62.8 (3.14 times 2 times 10) where was the radius for small circle is 31.4 (3.14 times 2 times 5) so subtract 31.4 from 62.8 and you get your answer.

The quadratic function from the given graph is g(x)= -1/2 x². Therefore, option A is the correct answer.

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

The given function is f(x)=x².

From the given figure, graph of f(x) is

Direction: Opens Up

Vertex: (0, 0)

Focus: (0, 1/4)

Axis of symmetry: x=0

Directrix: y= -1/4

Direction: Opens Up

Vertex: (0, 0)

Focus: (0, -1/2)

Axis of symmetry: x=0

Directrix: y=1/2

So, the function is g(x)= -1/2 x²

Therefore, option A is the correct answer.

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Answer:

Step-by-step explanation:

To find the standard deviation of the population, we first need to find the mean of the population.

Mean = (28 + 28 + 29 + 31 + 28 + 24) / 6 = 28

Next, we need to find the variance of the population.

Variance = [(28 - 28)^2 + (28 - 28)^2 + (29 - 28)^2 + (31 - 28)^2 + (28 - 28)^2 + (24 - 28)^2] / 6

Variance = (0 + 0 + 1 + 9 + 0 + 16) / 6 = 2.67

Finally, we can find the standard deviation of the population by taking the square root of the variance.

Standard deviation = sqrt(2.67) ≈ 1.63

Therefore, the standard deviation of the population is approximately 1.63 seconds.

the value of a will be 15 in equation 3 a plus b equals 54 when b equals 9.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, equation 3 a plus b equals 54 when b equals 9

In numerical form,

3a + b = 54

and b = 9

Comparing these equations

3a + 9 = 54

3a = 45

a = 15

Therefore, the value of a will be 15 in equation 3 a plus b equals 54 when b equals 9.

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The solution to equation is sinx.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

Given;

The equation cosine of the quantity x plus 3 times pi over 2

Using the expression for the cosine of a sum of angles:

cos(a + B): = cos a cos B - sin a sin ß

we have:

cos(x+3pi/2)

=cos(3pi/2)cosx- sin(3pi/2)sinx

=sinx

Therefore, the solution of trigonometric equation will be sinx

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The angle of elevation at which Luke shoots the squirt gun is 25.641°

A frequently used idea in relation to height and distance is the angle of elevation, particularly in trigonometry. It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Given that, the height of Luke is 6 ft .

the height of squirt gun from the ground is 30ft.

So, the height of squirt gun from the Luke's eye is 30-6 = 24 ft

The horizontal distance of Luke from Alex's building is 50 feet .

Let the angle of elevation is θ.

tan θ = the height of squirt gun from the Luke's eye / The horizontal distance of Luke from Alex's building

tan θ = 24/50

tan θ = 0.48

θ = tan⁻¹ 0.48

θ = 25.641°

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Answer: look at the image and better give me brainliest

Step-by-step explanation:

Just evaluate the line in the values of the point and check if the equation is true or not.

So let's say line l has an equaiton known:

y = a*x +b

To check if a point is on the line, just replace the values of the point on the line equation, if the equation is true, then that point belongs to the line, if don't, then the point does not belong to the line.

That is the only way to check that.

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Answer:

50%

Step-by-step explanation:

50% = 0.5

$90000 times 0.5 = $45000

So, 50% of $90000 is equal to $45000

Answer: 50%

Hope this helps :)

Step-by-step explanation:

45,000 / 90,000 = .5 (50 out of 100)

45 * 2 = 90

Answer:

When h(x)=0, x=4

Step-by-step explanation:

If: h(x)=-x+4

And: h(x)=0

—> We set the equation equal to 0

—>  -x+4=0

X=4

Answer:

              When h(x) = 0, x would equal 4.

Step-by-step explanation:

              Since we know the h(x) function is h(x) = -x + 4, when we're looking for a specific value for the function, we can replace the h(x) with the value we are setting the function equal to. In this case, 0 would replace h(x), and we would have a simple algebraic equation: -x + 4 = 0. Now we can solve for x, which will be equal to -x + 4 = 0 ⇒ -x = -4 ⇒ x = 4. Therefore, when h(x) equals 0, x would be equivalent to 4.

Have a great day! Feel free to let me know if you have any more questions :)

The diameter of the earth is 3.66 times larger than the diameter of the moon.

The mean radius of the earth is 6.37 x 10^6 meters,

Re = 6.37 x 10^6 meters

The mean radius of the moon is 1.74 x 10^6 meters.

Rm = 1.74 x 10^6 meters

To compare the size of the diameter,

D = De/Dm = 6.37 x 10^6 / 1.74 x 10^6

Diameter of the earth is 3.66 times larger than the diameter of the moon.

In geometry, a circle's diameter is any straight line segment whose centre is on the circle and whose ends are on the circle. The longest chord of the circle is another name for it. Either of the two approaches can be used to determine the diameter of a sphere.

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The angles m∠APE and m∠EPD are complementary angles and so the measure of angle m∠EPD is equal to 20° which makes option D correct.

In geometry, if two angles are said to be complementary, then the total of their sum is equal to 90°.

The angles m∠APE and m∠EPD are complementary angles so we evaluate for the angle m∠EPD as follows:

m∠APE + m∠EPD = 90°

70° + m∠EPD = 90°

m∠EPD = 90° - 70° {subtract 70° from both sides}

m∠EPD = 20°.

Therefore, the measure of angle m∠EPD is equal to 20°.

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Answer:

that answer should be wrong?

Answer:

-84

Step-by-step explanation:

To simplify the expression 20^2 - 22^2, we'll first square both 20 and 22:

20^2 = 20 * 20 = 400

22^2 = 22 * 22 = 484

Now, we can substitute these values back into the original expression:

400 - 484 = -84

So 20^2 - 22^2 = -84.

The missing values of Deviation of July is 289.17, August is 339.17, September is 14800.17, whereas, October, November and December are -65.83, 10690.17 and -480.83 respectively.

When determining the standard deviation: By combining the data points and dividing the result by the number of data points, you may determine the mean, or average, of the data points. Each data point's mean should be subtracted, and the results should then be squared.

Month               sales                          Average                           Deviation:

July                    $1,750                      1,460.83                                     289.17

August              $1,800                      1,460.83                                      339.17

September        $1,6251,                   1,460.83                                  14800.17

October            $1,395                      1,460.83                                      -65.83

November        $1, 2151                     1,460.83                                  10690.17

December           $980                      1,460.83                                   -480.83

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The race is 40 miles long, since there are two repair and two water stations evenly spaced between the start and finish lines, and the third water station is located 8 miles after the first repair station.

The race is 40 miles long because the start and finish lines are 20 miles apart, and there are evenly spaced water and repair stations between them. The figure indicates that the first repair station is located at the start line, and the second repair station is 20 miles after the start line. The first water station is located 8 miles after the first repair station, and the second water station is located 16 miles after the second repair station. Therefore, the third water station is located 8 miles after the first repair station. Since there are two repair and two water stations evenly spaced between the start and finish lines, the race is 40 miles long.

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Emma's total test score for the class is 156.5 out of 100.

We can calculate Emma's total score by considering the weight of each component of her grade and adding them up.

First, we can find the total score from the three tests:

(71 + 75 + 79) * 0.15 * 3 = 101.55

Next, we can find the score from the project:

85 * 0.10 = 8.5

Next, we can find the score from the final:

80 * 0.20 = 16

Finally, we can find the score from the homework:

87 * 0.35 = 30.45

The total score is the sum of all these components:

101.55 + 8.5 + 16 + 30.45 = 156.5

So, Emma's total score for the class is 156.5 out of 100.

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Answer:

Step-by-step explanation

the answer is

KN is 6 units long, AL is 6 units long, AR is 10 units long, and RG is 4 units long.

A line segment is a section of a straight line that is bounded by two different end points and contains every point on the line between them. The Euclidean distance between the ends of a line segment determines its length. A line segment has endpoints, but a line can be extended forever on both ends. A line segment is a section of a line that links two places known as the line's endpoints. It is possible to measure the distance between two places. Because line segments have a fixed length, they may be used to create the sides of any polygon.

Here,

They are equal in ratio.

4/8=x/12

x=6 units

4/8=3/y

y=6 units

4/8=5/z

z=10 units

4/8=2/p

p=4 units

The length of line segment KN is 6 units, AL is 6 units, AR is 10 units and  RG is 4 units.

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In linear equation, 80 cups of water will yonni need to replace all the water in the fish tank.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Now, as we know:

1 quart  = 0.25 gallons

⇒ 4 pints =  1  gallons

⇒ 8 pints =  2 gallons

Also, 1 pint  = 0.5 quart

⇒ 2 pints =  1 quarts

⇒ 8 pints =  4 quarts

⇒ 16 pints =  8 quarts

Again,  1 cup = 0.5 pint

⇒ 2 cup  = 1  pint

⇒ 32 cup  = 16  pints

so 16 * 5 = 80 cups

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Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

What is Distance?

Distance is defined as the space between two points in space.

To find out how far Jake will have traveled after 3 hours, we can use the formula:

distance = speed x time

where speed is the rate at which Jake is traveling and time is the duration of the travel. In this case, the speed is 12 mph and the time is 3 hours.

So, the distance traveled after 3 hours is:

distance = 12 mph x 3 hours = 36 miles

Therefore, Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

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The system of equations to find the number of each type of test is t + f = 28 and 2t + 4f = 100

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let t represent the number of 2 point questions and f represent the number of 4 point question.

Mr. Evans is giving a 28-question test, hence

t + f = 28      (1)

The entire test is worth 100 points., therefore:

2t + 4f = 100    (2)

From both equations:

t = 6, f = 22

The test had 6 number of 2 point questions and 22 number of 4 point question.

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