1. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the pair of triangles?

Answer:

9.47

Rounded to the nearest 0.01 or

the Hundredths Place.

Explanation

9.4725

You rounded to the nearest hundredths place. The 7 in the hundredths place rounds down to 7, or stays the same, because the digit to the right in the thousandths place is 2.

9.47

When the digit to the right is less than 5 we round toward 0.

9.4725 was rounded down toward zero to 9.47

Hope this helps!

Answer:

  tan(θ) = 2/3

Step-by-step explanation:

You want the tangent of the angle θ between the x-axis and the line connecting the origin to point (3, 2).

The tangent ratio is given by ...

  Tan = Opposite/Adjacent

In the attachment, you can see that the side opposite the angle of interest is the y-coordinate of the point. The side adjacent is the x-coordinate. That means ...

  tan(θ) = y/x

  tan(θ) = 2/3

__

Additional comment

In general, the tangent of the angle a line makes with the x-axis is the slope of the line. Your line has slope 2/3, and that is the tangent of the angle it makes with the x-axis.

The measure of angle ABD is 118 degree.

An equation is an expression that shows the relationship between two or more numbers and variables.

WE have been given that the angles are;

(3x +10)° and 2x

WE need to solve the value of x then we use the linear pair;

(3x +10)° + 2x = 180

Solving;

(3x +10)° + 2x = 180

5x + 10 = 180

5x = 180 - 10

5x = 170

x = 36

Angle ABD = (3x +10)° = 3(36) + 10

= 108 + 10

= 118

Hence, the measure of angle ABD is 118 degree.

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The value of x in the inverse variation is  x = 4

Inverse variation is express mathematically by; y = k/x

where,  y and x = variables

k = constant of variation

We solve for 'x' in the variation using standard form for inverse variation:

y = k/x

Given; y = 3, x = 24

We now use the given information to find k.

Step 1: Substitute the given in to equation y= k/x; to

3 =k/24

Cross multiply

k = 3 * 24

k = 72

Step 2; The inverse relation for is y = 72/x since we have gotten k=72

For y = 18, we get

18 = 72/x

Cross multiply

18x = 72

x = 72/18

X=4

Therefore, the value of  x = 4.

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Answer:

[tex]y=-\frac{1}{3}x +4[/tex]

Step-by-step explanation:

slope= 1-7/9- -9= -1/3

y-intercept: 7 = -1/3(-9)+b, b=4

Answer:

26

Step-by-step explanation:

18 + (6 - 2) x 2

18 + (4) x 2

18 + 8

= 26

The dimensions of the dumpster that will minimize its surface area are Length = 4.43 yds ,Width  = 2.215 yds and Height  = 2.956 yds

since l = 2w.

Now, the formula for a cube's surface area is;

S = 2lw + 2lh + 2wh.

Changing 2w to l yields;

S = 4wh + 4w² + 2wh.

S = 4w² + 6wh

in the meantime, the formula for a cube's volume is;

V = lwh

add 2w for l to receive;

V = 2w²h

h = V/2w²

In the SA equation, substitute V/2w² for h to get;

SA = 4w² + 6w(V/2w²)

SA = 4w² + 3V/w

V is stated to equal 29 yd3.

Thus;

S = 4w² + 87/w

Let's find the first derivative of S as we want to reduce the surface area;

S' = 8w - 87/w²

At S' = 0;

8w - 87/w² = 0

8w = 87/w²

w³ = 87/8

w = ∛(87/8)

w = 2.215 yds

L = 2 x 2.215= 4.43

since, l = 2w.

l = 4.43 yds

h = V/2w²;

h = 29/(2 × 2.215²)

h = 2.956 yds

Hence, The dimensions of the dumpster that will minimize its surface area is l = 4.43 yds, w = 2.215 yds and h = 2.956 yds

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Random sampling: It is a type of probability sampling in which the researcher randomly selects a subset of participates from the population.

Biased Sample: Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower and higher sampling probability than other.

The population generalized in this case, is almost random, the only problem here is that people that want to participate will participate so is likely that the sample is not totally randomized and that there is huge number of people that regularly exercises.

b) This case is less random than the previous , here all the people in the sample regularly do exercise and these people can choose is they prefer to work with a partner or not. So the sample is biased.

In method 01 we can conclude that the result apply to the whole population , whole in method 02 we can't conclude that just because the sample is biased.

Method 01: - Recruit volunteers who are willing to participate. Randomly assign each participate to exercise with a training partner or exercise alone.

So there are people who wants to participate but people don't necessarily do exercise normally day to day life. People also can't choose to work out in a team or alone.

Method 02:  Select a random sample of people from all the people who exercise at a community fitness center. ask each person in the sample whether they use a training partner, and use the response to create the two groups.

The members in the sample are people who exercises regularly and we ask them if they work alone or with a partner then, we create two groups. so this is more biased sample.

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The diagram which represents Mason's ratio of made throws and missed throws in the story is option A.

The following are answers to like terms collected respectively

The following expressions are equivalent

If Mason made 20 free throws

Equate missed throws ratio made throws

2 : 5 = x : 20

2/5 = x/20

cross product

2 × 20 = 5 × x

40 = 5x

divide both sides by 5

x = 40/5

x = 8

Total free throws Mason attempted = Number of throws Mason missed + Number of throws Mason made

= 8 + 20

= 28 free throws

If Jennifer made 16 bracelet with neon

Equate neon made bracelet ratio pastel made bracelet

4 : 3 = 16 : x

4/3 = 16/x

cross product

4 × x = 3 × 16

4x = 48

divide both sides by 4

x = 48/4

x = 12

Combine the like terms

4d + 5d

= 9d

8r + 6 + 9r - 3

= 8r + 9r + 6 - 3

= 17r + 3

6r - r + 4

= 5r + 4

Determine if the following expressions are equivalent

3 + 4 = 2 + 5

7 = 7

4(2 + x) = 8 + 4x

8 + 4x = 8 + 4x

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The car B was 10 miles east of Car A.

A function is a formula, rule, or law that specifies how one variable (the independent variable) and another variable are related. The linear equation is of the form Ax+By+C=0.

Where A and B are the coefficient and C is the constant.

Speed of car A = 45 miles per hour and the direction of car A is East.

The distance of car B from Johnstown after 2 hours is 100 miles, east

The distance of car B from Johnstown is given on the graph.

So , the initial distance of car A from Johnstown will be,

= 100 - 2 × 45

=100 - 90

= 10 miles

As seen from the graph, the initial distance, east, of car B from Johnstown is 20 miles.

So, the difference between the cars will be 20-10= 10 miles that means car B was 10 miles east of Car A.

Therefore, the car B was 10 miles east of Car A.

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Answer:

He gets $7.50 per cap

Step-by-step explanation:

I took the test

Answer:

$17.50

Step-by-step explanation:

Answer: Real and Rational

Step-by-step explanation:

2/3 is a fraction. ALL numbers are are considered real numbers. Rational numbers are typically fractions and decimals.

Answer:d

Step-by-step explanation:

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

Given,

Number of smokers; Sample size, n = 40

Mean of the sample, μ = 172.5

Standard deviation, σ = 119.5

We have to find the 90% confidence interval estimate of the mean cotinine level of all smokers.

Here,

The confidence interval is given as;-

x − E < μ < x + E

E is the margin of error.

Margin of error,

E = zα/₂ σ/√n

E = 1.644854 119.5/√40

E = 31.07887

Then,

The confidence interval is;

x − E < μ < x + E

141.4211 < μ < 203.5789

That is,

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

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Answer:

5. 1/2 & 3 , 6. 2 & 5

Step-by-step explanation:

5.

slope = 2

m = y2 - y1 / x2 - x1

m = 13-3/5-0

m = 10/5 or 2

y-intercept = 3

(0,3)

6.

slope = 1/2

m = y2 - y1 / x2 - x1

m = 6-5/2-0

m = 1/2

y-intercept = 5

(0,5)

The inequality that can be used to find the number of gigabytes used is 52.50+5g<75 and the value of g should be less than 4.5.

According to the question,

We have the following information:

Gabriel pays a flat cost of $52.50 per month and $5 per gigabyte. He wants to keep his bill under $75.

Now, the number of gigabytes used are represented by g.

So, we will have the following inequality:

52.50+5g<75

Now, we will solve this inequality.

Subtracting 52.50 from both the side:

5g<75-52.50

5g<22.5

Dividing by 5 on both the sides:

g<22.5/5

g<4.5

Hence, the inequality that can be used to find the number of gigabytes used is 52.50+5g<75 and the value of g should be less than 4.5.

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it's 23% because 46 (ppl who do not like running but like swimming) divided by 200 (the total for everything) is 0.23 which is 23%

Answer:

Step-by-step explanation:

-19y=-13x -14 to y=-13/-19 - -14/-19

The relation that is a function is (d) the graph

The list of options represents the given parameter

As a general rule;

For a relation to be considered a function, the following must be true:

One x value must not point to several y values

Using the above as a guide, the ordered pair in (a), relation in (b) and table in (c) are not functions

This is because one x value must not point to several y values

However, there are unique values in the graph of (d)

Hence, (d) the graph is a function

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The value of variable in first figure will be;

⇒ x = 5

The value of variable in second figure will be;

⇒ y = 4

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

There are two figures is shown in figure.

Now,

In first figure;

By using definition of proportional as;

⇒ 4 / 2 = 6 / (x - 2)

Solve for x as;

⇒ 2 (x - 2) = 6

⇒ x - 2 = 3

⇒ x = 3 + 2

⇒ x = 5

Thus, The value of variable in first figure will be;

⇒ x = 5

In second figure;

By using definition of proportional as;

⇒ y / 6 = 12 / 9

Solve for y as;

⇒ y / 6 = 4 / 3

⇒ y = 4 x 6 / 3

⇒ y = 24 / 6

⇒ y = 4

Thus, The value of variable in second figure will be;

⇒ y = 4

Therefore, The value of variable in first figure will be;

⇒ x = 5

The value of variable in second figure will be;

⇒ y = 4

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Answer:

m∠5 = 91° (sorry if i got it wrong i tried my best)

The equation of each line in slope-intercept form are:

1. y = 3/4x + 4.

2. y = -x - 2

To express the equation of a line in slope-intercept form, y = mx + b, substitute the value of the slope (m) and the value of the y-intercept (b) into the equation.

1. Slope (m) = 3/4

y-intercept (b) = 4

Substitute m = 3/4 and b = 4 into the equation y = mx + b:

y = 3/4x + 4.

2. Slope (m) = -1

y-intercept (b) = -2

Substitute m = -1 and b = -2 into the equation y = mx + b:

y = -x - 2

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Answer: -4

Step-by-step explanation:

New York City will indeed pay two men $36 million for their wrongful conviction in the 1965 assassination of a civil rights activist.

How is the chronology so that New York City pays for the incident of wrongful conviction of two people for the alleged murder of a civil rights leader?

After carrying out further investigations into the lawsuits against 2 people, in particular Muhammad A. Aziz and Khalil Islam who were accused of the murder of the leader of civil rights activist, Malcolm X, it was found that the two defendants were victims of wrongful conviction. It was previously stated that the police appeared to be withholding evidence to weaken the charges leading to acquittal. However, in the end, the court gave an acquittal because it was known that Muhammad Aziz and Khalil Islam had been proven innocent. As a form of accountability, New York City is willing to pay 26 million dollars to the victims and an additional 10 million dollars from New York state.

In conclusion, the amount of money paid by New York City is a form of responsibility that has been approved for the wrongful conviction of Muhammad Aziz and Khalil Islam.

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These are  two ways to indicate how quickly this issue is evolving.

Given;

Jamel bought 2.5 pounds of hamburger meat at the shop for $7. What are the two possible methods to state the rate in this case?

Since he buys 2.5-pound hamburger meat on 7$;

The two ways to explain the rate of this situation is

(I) the amount of meat per $ is 2.5/7 = 5/14

(II) the cost of meat is 7/2.5 = 14/5 = 2.8 /pound

a) The maximum amount of hamburger meat that can be purchased by spending 1 dollar pounds of hamburger meat can be purchased by spending 1 dollar

b) The maximum cost of 1 pound of hamburger meat dollar Thus, 1 pound of hamburger meat costs 2.8 dollars

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