Janine's family is designing a new garage. Use A  l  w to determine the area of the garage if the length l is 24 feet and the width w is 22 feet. Find the area A of the garage in square feet.

To prove the converse of the Vertical Angles Theorem, we need to show that if angles LDBC and LABE are congruent and points D, B, and E are on opposite sides of line AB, then they must be collinear.

Given: ∠LDBC ≅ ∠LABE

To Prove: D, B, and E are collinear

Proof:

1. Assume that points D, B, and E are not collinear.

2. Let BD intersect AE at point X.

3. Since D, B, and E are not collinear, then X is a point on line AB but not on line DE.

4. Consider triangle XDE and triangle XAB.

5. By the Alternate Interior Angles Theorem, ∠XAB ≅ ∠XDE (corresponding angles formed by transversal AB).

6. Since ∠LDBC ≅ ∠LABE (given), we have ∠LDBC ≅ ∠XAB and ∠LABE ≅ ∠XDE.

7. Therefore, ∠LDBC ≅ ∠XAB ≅ ∠XDE ≅ ∠LABE.

8. This implies that ∠XAB and ∠XDE are congruent vertical angles.

9. However, since X is not on line DE, this contradicts the Vertical Angles Theorem, which states that vertical angles are congruent.

10. Therefore, our assumption that D, B, and E are not collinear must be false.

11. Thus, D, B, and E must be collinear. Therefore, the converse of the Vertical Angles Theorem is proven, and we can conclude that if ∠LDBC ≅ ∠LABE and D, B, and E are on opposite sides of line AB, then D, B, and E are collinear.

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Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Describe four common ways in which individuals respond to perceived inequity are -

Equity, also known as shareholders' equity (or shareholders' equity for private companies), is the sum of money which would be handed back to a company ’s creditors if each of its assets have been liquidated and all of its debt was paid off in the event of liquidation.

Some key features regarding the equity are-

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Answer: The area of the larger square is 9 times the area of the smaller square.

Step-by-step explanation:

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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Answer:

CD = 12.81

Step-by-step explanation:

2 x CS = CA

2x4 = 8 = CA

10 = AD

\(CD = \sqrt{(CA^{2} +AD^{2}) }\)

\(CD = \sqrt{(8^{2}+10^{2} ) }\)

\(CD = \sqrt{(64+100) } \\CD= \sqrt{164} \\CD=12.81\)

Answer:

your answer is 38 with a remainder of 1

Step-by-step explanation:

Nominator

191

Denominator

5

38.2= 38 Remainder 1

The result of 191/5 is a terminating decimal with 1 digit to the right of the decimal point.

191 divided by 5 in decimal = 38.2

191 divided by 5 in fraction = 191/5

191 divided by 5 in percentage = 3820%

On dividing 191 by 5, the remainder is 1.

The divisor is the integer that divides a given number. The resultant number is sometimes referred to as the quotient. The residual is the number that the divisor leaves after partially dividing the original integer.

Dividend = Divisor x Quotient + Remainder

On dividing 191 by 5

Step 1: Divide 191 into 5 parts: 191/5 = 38(integer part only)

Step 2: Divide the quotient you just calculated by the divisor (5).

38 × 5 = 190

Step 3: Subtract the result from the initial dividend from step 2 (191) (191):

191 - 190 = 1

Step 4: The remainder is the outcome of step 3:

1 is the result of dividing 191 by 5.

Therefore, the remainder after dividing 191 by 5 is 1.

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The equation of to represent the two unknowns y and x is undefined hence it can be said not to be existing.

Equation of a straight line is the equation of the form

y = mx + c

y and x are the unknown variables

m is the slope

c is the intercept in the y axis

The equation given in the problem is a special type which is a vertical line

A vertical line has no intercept on the y axis hence c =0/ This reduces the equation of a straight line to

y = mx + c

at c = 0 we have:

y = mx + 0

y = mx

The slope of the vertical line is undefined. From first principles we have that slope is

m = change in y / change in x

for a line to be vertical the change in x is at the lowest absolute value and the smallest absolute number is zero. note negative number is not inclusive.

Therefore the slope at change in x = 0 represents a vertical line which is

m = change in y / change in x

m = change in y / 0

m = undefined

so y = undefined

check using calculator any number divided by zero gives error which is defined mathematically to be undefined,

We can conclude that the relationship between y and x from the graph is undefined.

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Answer:

40

Step-by-step explanation:

one cubic cm would be 2x2x2=8 half cm³

you have 1x2x2.5 cm cube = 5 cm³

5 x 8 = 40

another way to look at it:

2 1/2 = 5 half-cubes long

2 = 4 half cubes wide

1 = 2 half cubes tall

5 x 4 x 2 = 40

Answer: 0.2737

Step-by-step explanation:

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The probability of finding a five-leaf clover is closer to one in a million.

\( \frac{1}{1000000} \)

The probability of finding a four-leaf clover is closer to one in ten thousand.

\( \frac{1}{10000} \)

If you get a five-leaf clover, then it will bring you good luck and financial gain.

Hope it helps you!!

Answer:

one in a million

Step-by-step explanation:

The odds of finding a five-leaf clover are closer to one in a million. A six-leaf, plus an entire plant of five and four-leaf clovers is even more amazingly rare.

)hope this helped(

Therefore , the solution of the given problem of  equation comes out to be for 0 brothers, 78°, for 1 brother, 132°, for two brothers, 66°,for 3 brothers, 42° and for 4 brothers, 42°.

A linear recovery model is founded on the formula: y=mx+b. B is the slope, and m is the y-intercept. The phrase "Bivariate logistic formulas have two components" is frequently used, despite the fact that y and y are two separate elements. When it comes to using linear functions, there are no easy solutions. and. Y=mx+b is the expression, where m stands for slopes and b for the y-intercept.

Here,

(Frequency  Total Frequency) x 360 equals angle (0).

the aggregate of all frequencies is the total frequency.

We can see from the provided chart that:

13 individuals lack relatives.

22 individuals each have one sibling.

11 individuals have two siblings, and 7 people have three.

7 individuals have 4 brothers.

13 + 22 + 11 + 7 + 7 = 60 is the overall frequency.

Using the aforementioned method, we can now determine the angle for each category:

For 0 siblings: Angle = (13 ÷ 60) x 360 = 78°

For 1 sibling: Angle = (22 ÷ 60) x 360 = 132°

For 2 siblings: Angle = (11 ÷ 60) x 360 = 66°

For 3 siblings: Angle = (7 ÷ 60) x 360 = 42°

For 4 siblings: Angle = (7 ÷ 60) x 360 = 42°

The total of all angles ought to

All the angles should total up to 360 degrees, which we can verify by:

78° + 132° + 66° + 42° + 42° = 360°

Therefore, the angles needed to represent the number of siblings among 60 individuals on a pie chart are:

for 0 brothers, 78°

for 1 brother, 132°

For two brothers, 66°

for 3 brothers, 42°

for 4 brothers, 42°

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the solution is option A. 20,496 sq in.

why it is and what is rectangular prism?

To calculate the amount of fabric needed to make the tent, you need to find the total surface area of the tent.

The formula for the surface area of a rectangular prism (which is the shape of the tent) is:

Surface Area = 2ab + 2bc + 2ad

Where a, b, c, and d are the dimensions of the rectangular prism.

Substituting the given values, we get:

Surface Area = 2(80)(81) + 2(81)(48) + 2(80)(76)

Surface Area = 20,496 square inches

Therefore, the answer is option A. 20,496 sq in.

A rectangular prism is a three-dimensional shape that has six rectangular faces, with opposite faces being congruent and parallel. It is also known as a rectangular parallelepiped.

Rectangular prisms can be described by their length, width, and height, which are typically denoted as a, b, and c, respectively. The volume of a rectangular prism is given by the formula V = abc, and the surface area can be found using the formula SA = 2ab + 2ac + 2bc.

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If you conduct a hypothesis test at a 95% level, it means that you are using a significance level of 0.05. This significance level represents the probability of rejecting the null hypothesis when it is actually true.

In hypothesis testing, the null hypothesis is the assumption that there is no significant difference or relationship between the variables being tested. The alternative hypothesis, on the other hand, suggests that there is a significant difference or relationship.

Now, when you conduct a hypothesis test at a 95% level, you set a threshold for rejecting the null hypothesis. This threshold is determined by the significance level of 0.05. If the p-value (the probability of obtaining the observed data or more extreme values assuming the null hypothesis is true) is less than 0.05, you would reject the null hypothesis in favor of the alternative hypothesis.

However, there is still a chance of making a Type I error, which is rejecting the null hypothesis even though it is actually true. The probability of making a Type I error is equal to the significance level you set, which is 0.05 in this case.

So, if you conduct a hypothesis test every so often at a 95% level, you can expect to reject the null hypothesis about 5% of the time, even though you should not. This means that approximately 5% of your tests will result in a Type I error.

To summarize:
- Conducting a hypothesis test at a 95% level means using a significance level of 0.05.
- The null hypothesis assumes no significant difference or relationship between variables.
- The alternative hypothesis suggests a significant difference or relationship.
- If the p-value is less than 0.05, the null hypothesis is rejected.
- However, there is a chance of making a Type I error, which is rejecting the null hypothesis even though it is true.
- The probability of making a Type I error is equal to the significance level, which is 0.05 in this case.
- Therefore, you can expect to reject the null hypothesis about 5% of the time, even though you should not.

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Answer:

A

Step-by-step explanation:

Answer:

52 tickets cost $10 and 18 tickets cost $12

Step-by-step explanation:

10x+12y=804. (1)

x+y=70. (2)

From (2)

x=70-y

Substitute x=70-y into (1)

10x+12y=804

10(70-y)+12y=804

700-10y+12y=804

700+2y=804

2y=804-700

2y=104

y=104/2

y=52

Recall

x+y=70

x+52=70

x=70-52

x=18

52 tickets cost $10 and 18 tickets cost $12

By solving a system of equations we will see that the correct option is A.

First, let's define the variables:

First, we know that 70 tickets were sold, so:

x + y = 70

And we know that they reached $804, then we have:

x*$10 + y*$12 = $804

Then our system is:

x + y = 70

x*$10 + y*$12 = $804

To solve this, we first need to isolate one of the variables in one of the equations, I will isolate x on the first equation:

x = 70 - y

Now we can replace that in the other equation to get:

(70 - y)*$10 + y*$12 = $804

$700 - y*$10 + y*$12 = $804

$700 + y*$2 = $804

y*$2 = $804 - $700 = $104

y = $104/$2 = 52

So, 52 $12 tickets were sold, then the other 18 tickets were $12, so the correct option is A.

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The probability that an irs auditor will catch only 2 income tax returns with illegitimate deduc-tions = 0.24

Let us assume that X be the number of returns containing illegitimate deductions in the sample.

Here, X has a hypergeometric distribution.

We need to find the probability that an IRS auditor will catch only 2 income tax returns with illegitimate deduc-tions.

Here, N = 15, r = 9, n = 5

So, P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

We know that the combination formula:

⁹C₂ = 9! / (2! × 7!)

     = 36

⁶C₃ = 6! / (3! × 3!)

     = 20

¹⁵C₅ = 15! / (5! 10!)

      = 3003

P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

              = (36 × 20) / (3003)

              = 0.24

Therefore, the required probability is: 0.24

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Answer: d=13

Step-by-step explanation:

d+13=26

d=13

If this wasn't what you asked for please rephrase the question. Thank you!

Answer:

volume = 25.1 m³

Step-by-step explanation:

volume = 1/3πr²h = 1/3(3.14)(2²)(6) = 25.1 m³

The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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if it crosses the y-axis as -12, that means that's its y-intercept, and we know its slope.

\(\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~~ \implies ~~y=\stackrel{\stackrel{m}{\downarrow }}{5}x\underset{\underset{b}{\uparrow }}{-12}\)

The Pearson correlation coefficient can be used as both a descriptive statistic and an inferential statistic.

As a descriptive statistic, the Pearson correlation coefficient describes the strength and direction of the linear relationship between two variables. It provides a numerical measure between -1 and 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

As an inferential statistic, the Pearson correlation coefficient can be used to test hypotheses and make inferences about the population correlation based on a sample. Hypothesis testing allows you to determine whether the observed correlation in the sample is statistically significant or occurred by chance. By examining the p-value associated with the correlation coefficient, you can make inferences about the strength of the relationship in the population.

Therefore, the correct answer is that the Pearson correlation coefficient can be used as both a descriptive and an inferential statistic.

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Answer:

CHEATING ON CLASSWORK

Step-by-step explanation:

IS FORBIDDEN

Answer: The number is -12

Step-by-step explanation:

The situation can be represent by the equation  

 \(\frac{n}{-2} = -4 + 10\)     Now solve for n   by combining like terms on the right side

\(\frac{n}{-2}\) = 6     multiply both sides by -2  

n = -12

The distance between the foci of the ellipse is approximately 16.97 units.

To find the distance between the foci of an ellipse, you can use the formula:

c = √(a^2 - b^2)

where "a" is the length of the semi-major axis and "b" is the length of the semi-minor axis. The distance between the foci is denoted by "c".

Given that the major axis has a length of 36 and the minor axis has a length of 12, we can calculate the semi-major axis (a) and the semi-minor axis (b) as follows:

a = 36/2 = 18

b = 12/2 = 6

Now we can calculate the distance between the foci (c):

c = √(18^2 - 6^2)

c = √(324 - 36)

c = √288

c ≈ 16.97

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Answer:

15.58

Step-by-step explanation:

82 x 0.19 = 15.58

Your final cost will be 97.58 (82 + 15.58)

Answer: The correct answer is D

Step-by-step explanation: I took the unit test

Answer:

C

Step-by-step explanation: