Select the correct answer. A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. Given: Transversal t passes through parallel lines r and s. Prove: ∠3 ≅ ∠6 ∠4 ≅ ∠5 Statement Reason 1. r || s given 2. ∠3 ≅ ∠7 ∠4 ≅ ∠8 For parallel lines cut by a transversal, corresponding angles are congruent. 3. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7 Reason: Congruent Supplements Theorem B. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180° Reason: Linear Pair Theorem C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem

The best way to represents the change in the vertices of rectangle ABCD to rectangle A'B'C'D' in the attached graph is given by :

option A. (x, y ) → (2x, 2y).

From the attached graph we have,

Coordinates of rectangle ABCD are :

Coordinate of vertex A ( -3, -2 )

Coordinate of  vertex  B ( -3,  2 )

Coordinate of  vertex  C ( 3, 2 )

Coordinate of  vertex  D ( 3, -2 )

And coordinates of A'B'C'D' are:

Coordinate of  vertex  A' ( -6, -4 )

Coordinate of  vertex  B' ( -6, 4 )

Coordinate of  vertex  C' ( 6, 4 )

Coordinate of  vertex D' ( 6, -4 )

Coordinate of rectangle ABCD gets dilated by the scale factor of :

Scale factor of 'x' coordinate  = -6 / -3

                                                 = 2

Scale factor of 'y' coordinate  = -4 / -2

                                                 = 2

Change in the vertices of rectangle ABCD to A'B'C'D' is given by :

( x , y ) → ( 2x , 2y )

Therefore, the vertices of rectangle ABCD changed to A'B'C'D' is equal to option A. ( x , y ) → ( 2x , 2y ).

The above question is incomplete, the complete question is:

Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?

A) (x, y ) → (2x, 2y)

B) (x, y ) → (1. 5x, 1. 5y)

C) (x, y ) → (3x, 3y)

D) (x, y ) → (4x, 4y)

Graph is attached.

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Answer:

A

Step-by-step explanation:

The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)

The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.

Kathy is organizing her desktop, which measures 22 inches by 4 feet. To calculate the area of Kathy’s desktop, we can use the formula for area, which is length multiplied by width. In this case, the length is 4 feet and the width is 22 inches. To make the measurements easier to work with, we can convert the length into inches. There are 12 inches in a foot, so 4 feet is equal to 48 inches. Now, the length of Kathy’s desktop is 48 inches and the width is 22 inches. To calculate the area, we multiply the length (48 inches) by the width (22 inches). The area of Kathy’s desktop is 1,056 square inches.

To further explain the concept of area, it is the amount of two-dimensional space that a shape takes up. It is measured in square units, such as square inches, square feet, or square yards. To calculate the area of any shape, you need to know its length and width. To calculate the area of a rectangle, you multiply the length by the width. The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.

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a) The Equation is  7.65x + 50 = 149.45.

b) The customer used the car for 13 hours.

c)  If the car used for 2 days i.e., 48 hours then the amount will be $471.12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given that;

Members of a car sharing program pay a fee of $50 per month plus $7.65 for every hour they use a car.

And, a members bill was $149.45 last month.

a) Let number of hours for the customer use a car last month = x

So, 7.65x + 50 = 149.45

7.65x = 149.45 - 50

7.65x = 99.45

x = 13

b) The customer used the car for 13 hours.

c) If the car used for 2 days i.e., 48 hours

= 7.65x + 50

= 7.65(48)+ 50

= 471.2

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Answer:

160 pounds of algae

Step-by-step explanation:

10 times 2 is 20   ( first 5 hours )

20 times 2 is 40  (10 hours)

40 times 2 is 80 (15 hours)

80 times 2 is 160 ( 20 hours)

there would be 160 pounds of algae

A)  The mean of 2018 scores: μ₂₀₁₈ = 75

 The mean of 2019 scores: μ₂₀₁₉ = 75

 The standard deviation of 2018 scores: s₂₀₁₈ = 2.07

 The standard deviation of 2019 scores: s₂₀₁₉ = 5.26

B) The primary difference is that variation is higher in the 2018 season than the 2019 season.

A)

We know that the mean is nothing but the sum of all scores divided by the number of scores.

Thus the mean for 2018 scores is:

μ₂₀₁₈ = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8

μ₂₀₁₈ = 75

Similarly the mean for 2019 scores is:

μ₂₀₁₉ = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8

μ₂₀₁₉ = 75

We know that the formula for the standard deviation is:

[tex]s=\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1} }[/tex]

where s sample standard deviation

n the size of the sample

[tex]x_i[/tex] each value from the sample

[tex]\bar{x}[/tex] the sample mean

Using this formula, the standard deviation for 2018 scores is:

s₂₀₁₈ = [tex]\frac{\sqrt{ (73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 +(74-75)^2 + (76-75)^2} }{7}[/tex]

s₂₀₁₈ = 2.07

And the standard deviation for 2019 scores is:

s₂₀₁₉ = [tex]\frac{\sqrt{ (70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 +(70-75)^2 + (78-75)^2} }{7}[/tex]

s₂₀₁₉ = 5.26

B)

We cwn observe that both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.

Thus, the variation in scores was higher in 2019.

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Find the complete question below.

After 3 years the rate of simple interest charged at this to Chloe bank is  7%

We can start by using the formula for simple interest:

Simple Interest = Principal * Rate * Time

where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.

Plugging in the given values, we get:

168 = 800 * Rate * 3

Solving for the rate, we get:

Rate = 168 / (800 * 3) = 0.07

Hence,

The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.

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The value of sin (θ/2) in the trigonometry is π/9

Information given in the problem

tan θ = 7/8,

where

0 < θ <  π/2

solving for θ, from tan θ = 7/8

tan θ = 7/8

θ = arc tan (7/8)

θ = 0.7188 radians

soling for sin (θ/2)

= sin (θ/2)

= sin (0.7188/2)

= 0.3517 approximately π / 9

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If The total revenue earned (in dollars) from selling the books is given by the function R-32. 80N.The equation relating the profit P (in dollars) to the number of books N is P = 16.85N - 750.

The profit made by the company is the difference between the total revenue earned and the total production cost, so we can write:

P = R - C

Substituting the expressions for R and C, we get:

P = 32.80N - (15.95N + 750)

Simplifying the right-hand side, we get:

P = 16.85N - 750

This equation shows that the profit made by the company is a linear function of the number of books printed. The slope of the line is the revenue per book (32.80 dollars), minus the cost per book (15.95 dollars), which is 16.85 dollars.

The intercept of the line is the fixed cost for editing (750 dollars). The equation can be used to estimate the profit for any given number of books printed, and to determine the break-even point, which is the number of books that need to be sold to cover the total production cost.

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By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.

Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.

Here, μ = 2.61 , σ = 0.41

Using the empirical rule :

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

2.61 − 0.41 = 2.2

2.61 + 0.41 = 3.02

The range of numbers is 2.2 to 3.02

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

2.61 − 2(0.41) = 1.79

2.61 + 2(0.41) = 3.43

The range of numbers is 1.79 to 3.43

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

2.61 − 3(0.41) = 1.38

2.61+3(0.41) = 3.84

The range of numbers is 1.38 to 3.84.

Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.  

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Answer:

A.  9.4 mi

Step-by-step explanation:

Sketch a right triangle with legs of 8 and 5.  Shortest distance back to the starting point is the hypotenuse (h) of the triangle:

h² = 8² + 5² = 89

h = √89 = 9.43 mi

According to the information, the area of the parallelogram plotted from the points would be: 36 cm²

To find the area of the parallelogram we must divide the parallelogram into a quadrilateral section and another triangular section and find the area of these segments.

According to the above, we can infer that the area of the quadrilateral zone would be

On the other hand, the area of the triangular section would be:

Additionally, we must multiply the area of the triangular segment by two because there are two triangular sections in the parallelogram. Finally we have to add the area of the quadrilateral and triangle segments to get the total area.

Note: This question is incomplete. Here is the complete information:

TASK

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The linear regression of the data is given as follows:

y = 25.1x + 150.4.

The estimate for the year in which the profit would reach $482,000 is of:

2019.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for this problem are given as follows:

(0, 147), (1, 167), (2, 209), (3, 239), (4, 250), (5, 267).

Hence the equation is of:

y = 25.1x + 150.4.

The estimate for the year in which the profit would reach $482,000 is x years after 2006, when y = 482, hence:

482 = 25.1x + 150.4.

x = (482 - 150.4)/25.1

x = 13.

2006 + 13 = 2019 -> year.

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Answer: $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.

Explanation:

To find out the total cost of raising a child in a household with an annual income of $64,000, we can plug in x = 64,000 into the equation y = 1.55x + 110,419:

y = 1.55x + 110,419

y = 1.55 * 64,000 + 110,419

y = 101,600 + 110,419

y = $212,019

So, it would approximately cost $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.

The number of solutions of the system of equations is given as follows:

D. Infinitely many solutions.

The system of equations is defined as follows:

The second equation was obtained multiplying the first equation by 3, meaning that the two equations are multiples, and thus the system of equations has an infinity number of solutions and the correct option is given by option D.

The system of equations is defined as follows:

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Answer:

atq= let no.be x and y

x= 4y-3.......(1)

x-2y=7....(2)

subtracting both eqn

x-x+2y=4y-3-7

2y=4y-10

-2y= -10

y=5 ........second no.

first no...x=7+2y=7+10=17.......first no.

Step-by-step explanation:

Answer:

i think this the answer

Step-by-step explanation:

26×14=ans

20×14+6×14=the same answer

10×26+4×26=same answer

It is a biased sample.

What is meant by a random sample?

Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.

A random sample is one in which each individual, thing, or event has an equal chance of being chosen. Compared to other types of samples, a random sample has a higher likelihood of being representative of the total population. A skewed sample is one that does not fairly represent the population as a whole.

Here Dorthy considered only the first 20 people and not the whole population so this is not a random sample and it is a biased sample.

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The length of B'C' after the translation of the original object is; B'C' = 3 units

Translation in transformation is simply defined as the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

Now, from the attached image, we see that;

AB = 7 units

BC = 3 units

CD = 4 units

DA = 5 units

Now, by virtue of the definition of translation, it means that the translated object will retain the same dimensions. Thus;

B'C' = 3 units

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Susan predicts that private school pupils will perform better than the general populace. The best description for this type of test is a right-tailed test.

In this scenario, Susan is testing the hypothesis that the mean score of the students of the private school is greater than 572, which is the mean score of the general population. This type of test, where the alternative hypothesis is "greater than" a specified value, is known as a right-tailed test or a one-tailed test (since the test is only considering one direction of deviation from the null hypothesis).

So the correct answer is d) a right-tailed test or a one-tailed test.

The complete question is:-

Susan hypothesizes that the students of a private school will score higher than the general population. Susan records a sample mean equal to 578 and states the hypothesis as μ= 572 vs μ>572. Select the best description for this type of test. a.) lower-tailed test b.) left-tailed test c.) two-tailed test d.) right-tailed test.

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The sum of the 10th terms of the geometric progression is 1023

The sum of the terms of a geometric progression (GP) is a formula used to find the total of a series of numbers that are increasing or decreasing by a common ratio. A geometric progression is a sequence of numbers such that the ratio of any two consecutive terms is constant.

The formula for the sum of the n terms of a geometric progression with first term a and common ratio r is given by:

Sₙ = a(rⁿ - 1) / r - 1

where:

a is the first term of the progression

r is the common ratio

n is the number of terms in the progression

In the problem given;

a = 1, n = 10, r = 2

Using the formula above;

Sₙ = a(rⁿ - 1) / r - 1

Substituting the values into the formula

S₁₀ = 1(2¹⁰ - 1) / 2 - 1

S₁₀ = 1023

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The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.

Then the area of the rhombus is given as,

A = (Product of diagonal of rhombus) / 2

A = (8 x 6) / 2

A = 48 / 2

A = 24 square centimeters

The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

The diagram is shown below.

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The solution set to the inequality is w > 3

From the question, we have the following parameters that can be used in our computation:

w+ 4<4 (w - 2)

Open the bracket

So, we have the following representation

w+ 4 < 4w - 8

Evaluate the like terms

So, we have the following representation

12 < 3w

Divide by 3

4 < w

So, we have

w > 4

See attachment for number line

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The expression equivalent to  -2x +3+ 7y + 4x -5 is 2x+7y-2.

What exactly are expressions?

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.

Now,

Given expression is   -2x +3+ 7y + 4x -5

writing same terms together

=4x-2x+7y+3-5

=2x+7y-2

hence,

             The expression equivalent to  -2x +3+ 7y + 4x -5 is 2x+7y-2.

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Answer:

Step-by-step explanation:

Let's call the length of the winning jump "w".

Sarah's best jump is 12% more than her first jump, which was 4.25m. So her best jump was 4.25m * 1.12 = 4.77m.

However, her best jump is 15% lower than the winning jump, so we can set up an equation to solve for w:

4.77m * 1.15 = w

Solving for w:

w = 4.77m * 1.15 = 5.51m

So the winning jump was 5.51m.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer: Y would be 4

If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.

The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the quadrilateral be represented as ABCD

Now , the coordinates of ABCD is given as

A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )

Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin

Substituting the values in the equation , we get

A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )

On simplifying the equation , we get

The coordinates of A' is = A' ( -2 , 4 )

The coordinates of B' is = B' ( 4 , 4 )

The coordinates of C' is = C' ( 6 , -2 )

The coordinates of D' is = D' ( 0 , -2 )

Hence , the dilated figure is solved

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