Which reason justifies the second statement in the proof below?
Given: parallelogram L E N S and parallelogram N G T H
Prove: Angle L is congruent to angle T.


A. In a parallelogram, consecutive angles are supplementary.
B. Alternate Interior Angles Theorem
C. In a parallelogram, opposite angles are congruent.
D. Corresponding Angles Postulate

SOMEONE PLEASE HELP!

Answer:

14.1

Step-by-step explanation:

To find the height of the rectangular prism, use the formula for the length of a diagonal of a right rectangular prism.

d=l2+w2+h2−−−−−−−−−−√

Substitute 8 for l, 19 for w, and 25 for d

Then solve for h

25=82+192+h2−−−−√

Simplify.

25=64+361+h2−−−−√

Square both sides.

625=425+h2

Subtract 425 from both sides.

200=h2

Take the positive square root of both sides.

200−−−√=h

Round to the nearest tenth.

14.1≈h

Therefore, the height of the rectangular prism is about 14.1ft

the probability that x is 4 is given by the formula  P(x) = [tex](1 - p)^(x-1) * p[/tex]

The formula for the probability of a geometric distribution is [tex]P(x) = (1 - p)^(x-1) * p[/tex]

Given the probability of success (p) is 0.3, the probability of x being 4 would be:[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]

P(x) = 0.0729 or 7.29%

The geometric distribution is a probability distribution for the number of failures before the first success in a series of independent trials.

In this problem, the probability of success (p) is 0.3 and the probability of failure (1-p) is 0.7.

Therefore, the probability that x is 4 is given by the formula  [tex]P(x) = (1 - p)^(x-1) * p[/tex]

Plugging in the values of p and x, we get:

[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]

This simplifies to

P(x) = 0.0729 or 7.29%

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The value of the expression for x=-3 is 78.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 6(2x²-5).

Here, x=-3

Substitute x=-3 in the expression 6(2x²-5), we get

6(2(-3)²-5)

= 6(18-5)

= 78

Therefore, the value of the expression is 78.

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Answer:

infinitely many

Step-by-step explanation:

this equation is true for each and every value.

so its solutions are infinite

The statement that is true about the proportional relationship is that; The time required to paint a house varies directly with the number of painters.

The parameters are;

p represents the number of painters.

h represent the number of hours required to paint the house

In this case, the  number of hours will be the output variable while the number of painters will be the input variable. Thus, we will have the relationship;

h = kp

where k is the constant of proportionality

When 2 painters are used, it takes 15 hours to paint and as such;

k = 15/2

k = 7.5 hours per painter

When 6 painters are used, it takes 5 hours to paint. Thus;

k = 5/6

k = 0.833 hours per painter

Thus, we can say that the time required to paint a house varies directly with the number of painters.

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The correct statement can identify by using a certain limit theorem.

The correct option is (c).

The sample size of J is 40.

The sample size of K is 100.

As per the central limit theorem, if the population with mean and standard deviation takes a large random sample from the population with replacement, then the distribution of the sample means will be approximately distributed.

Now from the definition of the central limit theorem, both J and K will the same means.

Write the expression for standard deviation.

[tex]s = \frac{\alpha }{\sqrt{n} }[/tex]

From the above expression, the standard deviation is inversely proportional to the sample size.

Thus, the correct statement is the expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

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The complete question is:

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

Which of the following must be true about J and K?

a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.

b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.

c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.

e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.

Vector identities can be derived using index notation. The following vector identities are to be proved: (iii) V - (V xa) = 0, (vii) V ab = (V a)b + a(V b).

Starting with the left-hand side:

V - (V x a) = V + (a x V) (by definition of cross product)

Using the vector triple product, a x (b x c) = (a . c) b - (a . b) c, we get:

V + (a x V) = V + (V . a) a - (V . a) a

= V (since the second term cancels out with the first term)

Thus, V - (V x a) = 0.

(vii) V ab = (V x (b x a))

Starting with the left-hand side:

V ab = V (ab)

Using the scalar triple product, a . (b x c) = (a x b) . c, we get:

V (ab) = (V x b) . (a x a)

= (V x (b x a)) (since a x a = 0)

Thus, V ab = (V x (b x a)).

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Data collected about a population is not characteristic of both surveys and experiments. The correct answer would be an option (C).

The purpose of a survey is to understand populations as a whole by utilizing pertinent questions to collect data from a sample of people.

Data collected about a population is not a characteristic of both survey and experiment because, in an experiment, the researcher typically manipulates one or more variables and measures the effect on another variable, while in a survey, the researcher usually only measures variables and does not manipulate them. As a result, in a survey, the data is typically collected about a sample of the population, rather than the entire population.

Hence, the correct answer would be option (C).

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Because it is typically too expensive and too time consuming, researchers often select a sample, a group of people that are representative of the larger population.

A sample is a smaller group of individuals selected from a larger population for the purpose of studying and making inferences about the population. Sampling is used when studying the entire population is not feasible due to limitations in time, resources, or practicality. The goal is to select a sample that accurately represents the population in terms of key characteristics such as age, gender, education level, etc. The sample must be representative of the population, meaning that it should accurately reflect the characteristics of the population. This is important because any biases or inaccuracies in the sample can lead to incorrect inferences about the population. A well-selected sample should also have a large enough size to provide meaningful results, yet not be so large that it becomes difficult to manage or too expensive to study.

In conclusion, sampling is a crucial step in research because it enables researchers to study a portion of the population, rather than the entire population, in order to make inferences about the larger group.

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Answer:

Step-by-step explanation:

To find the annual rate given the rate per compounding period, we need to convert the rate from the compounding period to the annual period. In this case, the rate is given as 0.425% per month.

One way to convert the rate is to multiply it by the number of compounding periods in a year:

r = 0.425%/month * 12 months/year

r = 5.1%/year

Therefore, the annual rate, r, is 5.1%.

Z-scores are used to standardize a raw score by converting it into the number of standard deviations it is above or below the mean.

The formula to convert a raw score into a z-score is:

z = (X - Mean) / Standard Deviation

Where X is the raw score, Mean is the mean of the population, and Standard Deviation is the standard deviation of the population.

For z = 2.00:

z = (X - Mean) / Standard Deviation

X = (z * Standard Deviation) + Mean

X = (2.00 * 38.2) + 202 = 238.4 + 202 = 440.4 (rounded to nearest whole number = 440)

For z = -2.00:

z = (X - Mean) / Standard Deviation

X = (z * Standard Deviation) + Mean

X = (-2.00 * 38.2) + 202 = -76.4 + 202 = 125.6 (rounded to nearest whole number = 126)

So for z = 2.00, the corresponding test score is 440, and for z = -2.00, the corresponding test score is 126.

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The two positive numbers are 1 and 1, depending on the given information.

Let first number be x. So, the second number is 1/x. Now, their sum is minimum, so representing the expression for given information -

Sum (x) = x + 1/x

Rewriting the expression -

Sum (x) = x + [tex] {x}^{-1} [/tex]

Finding the derivative

Sum' (x) = 1 + (-1) [tex] {x}^{-2} [/tex]

Sum' (x) = 1 + (-1)/[tex] {x}^{-1} [/tex]

Sum' (x) = (x² - 1)/x²

Now, to find the minimum -

x² - 1/x² = 0

Multiplying x² on Right Hand Side of the equation

x² - 1 = 0

Rewriting the equation

x = ± 1

As the numbers are positive, so x will be 1.

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The percentage values are as follows: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

1a. 150% of 50

=1.5*50

=75

1b. 150% of 90

=1.5*90

=135

2a. 100% of 60

=1*60

=60

2b. 50% of 100

=0.5*100

=50

3a. 350% of 70

=3.5*70

=245

3b.  150% of 70

=1.5*70

=105

4a. 350% of 50

=3.5*50

=175

4b.  350% of 90

=3.5*90

=315

5a.  450% of 100

=4.5*100

=450

5b. 200% of 30

=2*30

=60

6a. 250% of 50

=2.5*50

=125

6b. 350% of 40

=3.5*40

=140

7a. 350% of 80

=3.5*80

=280

7b. 150% of 100

=1.5*100

=150

8a. 400% of 80

=4*80

=320

8b. 300% of 50

=3*50

=150

The value of percent are: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.

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The function shown in the graph must be the function f(x)=2×4ˣ

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: f(x)=abˣ and when x is equal to 0 then f(0)=2

also if x increases by the functions gets multiplied by 4

Thus if f(0)=2 then f(1)= 8 , f(2)=32

or the function can be rewritten as f(x)=2×4ˣ

Thus f(0)=2×4⁰

              =2

f(1)=2×4¹

Hence, The function shown in the graph must be the function f(x)=2×4ˣ

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The number of white balls is equally likely to be any number between 1 and n−1.

Let W be the number of white balls in the bin after the nth iteration. W can be any number between 1 and n−1. We can calculate the probability of obtaining a specific number of white balls in the bin by considering the number of possible sequences of choices. There are 2^n possible sequences of choices as each choice is either a white ball or a black ball. The number of sequences in which W white balls are selected is (W choose 1)*(n−W choose 1), which is equal to W*(n−W). Therefore, the probability of W white balls in the bin after the nth iteration is P(W) = (W*(n−W))/(2^n).

Since P(W) is equal for all values of W between 1 and n−1, it follows that the number of white balls is equally likely to be any number between 1 and n−1.

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Answer:

y = (2/3)x + 10

Step-by-step explanation:

To find the equation of the line in slope-intercept form, y=mx+b, we need to know the slope and the y-intercept. The slope, or m, is rise over run. To find slope, we need to look at 2 points. For this question, I will be using the points (0,10) and (30,30). The rise, or change in y value, is 20, while the run, or change in x value, is 30. This means our rise over run in 20/30, or 2/3. Now that we have established the slope, or m, let's find the y-intercept, or b. To do this, you just need to look at where the line passes through the y-axis. In the image, you can see the line passes through the y-axis as x=10, making our y-intercept, or b, 10. Using this information, we can now find the equation of the line:

y = mx + b

m = slope, 2/3

b = y-intercept, 10

y = (2/3)x + 10

So, the equation of the line is y = (2/3)x + 10

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Answer: 12

Step-by-step explanation:

12/12 is greater than 11/12

12/12>11/12

The number line of x <-2 is added below

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

x < -2

For the inequality x < -2:

All real numbers that are less than -2 satisfy the inequality.

So, we can represent the solution set of the inequality using the interval (-∞, -2)

When represented on a number line, we have:

   -∞          -3        -2        -1        0        1        2        ∞

   --------------------------------------------------------------------------

   .           <-          o         .         .         .         .        .

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The transformed vertices of the ΔABC will be A'(- 2, 0), B'(2, 3)

and C'(0, - 1).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The given triangle has vertices A(0, 4), B(6, - 4) and C(- 2, 0).

We know a rotation of 90° counterclockwise transforms (x, y) to (- y, x)

and a dilation factor of (1/2) would make it (- y/2, x/2).

Therefore, The vertices of the triangle A'B'C' will be,

A'(- 4/2, 0/2), B'(-(-4)/2, 6/2) and C'(0/2, - 2/2).

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

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Answer:

approximately $4,609,968.67

Step-by-step explanation:

To calculate the future value of a lump sum after compounding over a certain number of years with a specific interest rate, you can use the formula:

FV = PV * (1 + r/n)^(nt)

Where:

FV is the future value

PV is the present value (6500)

r is the annual interest rate (3.96%)

n is the number of times compounded per year (semi-annually, so 2)

t is the number of years (414)

Plugging in the values, you get:

FV = 6500 * (1 + 0.0396 / 2)^(2 * 414)

The future value of $6,500 in 414 years at an interest rate of 3.96% compounded semi-annually is approximately $4,609,968.67.

86% of 22 is the correct answer

The degree of the polynomial that best describes the data is (c) cubic

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

See attachment

Find the first dfference D1 between the consecutive y-values

D1:   10     28.4     56.4    94

Calculate the second difference

D1:   18.4     28     37.6

Calculate the third difference

D3:   9.6     9.6

The third difference are equal

Hence, the degree is (c) cubic

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The equivalent expression is x + 3 + 4/(x - 1)

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x² + 2x + 1) / (x - 1)

Now,

x² + 2x + 1

= x² + (1 + 1)x + 1

= x² + x + x + 1

= x(x + 1) + 1(x + 1)

= (x + 1)(x + 1)

= (x + 1)²

Now,

(x² + 2x + 1) / (x - 1)

= (x + 1)² / (x - 1)

Now,

x + 3 + 4/(x - 1)

((x - 1)x + 3(x - 1) + 4) / (x - 1)

= (x² - x + 3x - 3 + 4) / (x - 1)

= (x² + 2x + 1) / (x - 1)

Thus,

x + 3 + 4/(x - 1) is the equivalent expression.

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Options C and D are subsets of R³, which are {(-5x,4x,3x)| x arbitary} and {(x,y,z)| x+y+x=0}

A) Correct. We have to check whether the potential subspace containing the zero vector is a great place to start on these sorts of problems. No zero vector so this is not a subspace.

B) This is a subspace. The set of solutions of a homogeneous linear system is always a subspace it is known as a "null space" of some corresponding linear transformation.

Let, [tex]M=\left[\begin{array}{ccc}2&9&0\\8&0&-5\\\end{array}\right][/tex]  then the set in B) is just Null(M). Again, Nullspaces are always subspaces.

Alternatively, you could solve the corresponding system Mx=0 and find the elements of that set  [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex]  for any choice of z∈R. So this

can be a set in the span of   [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex]

C) Correct. we can see a subspace because the elements are just multiples of (−5,3,4) and again spans are subspaces.

D) Correct. This can be a  subspace for the same reasons as part B.

E) Correct. Not a subspace. An easier counter-example: (1,1,1) is in there. But (−1)(1,1,1)=(−1,−1,−1) is not.

F) Not a subspace. (0,0,0)  is not in there.

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The angle measures for this problem are given as follows:

ADC is an isosceles triangle, with an angle of 44º, hence the base angles have the measure given as follows:

2x + 44 = 180. (sum of the internal angles of a triangle).

2x = 136

x = 136/2

x = 68º.

Hence the measure of angles ACB and BCD is of 34º, as the bisection divides the angle into two angles of equal length.

Considering the two base angles of 34º, the measure of angle ABC is given as follows:

m < ABC + 2 x 34 = 180

m < ABC = 112º.

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Answer:

If y=6 when x=3 find y when x =-33.

Step-by-step explanation:

Answer:

-2/-3

Step-by-step explanation: Because -2/-3=2/3.

The present value of the cash flows is $30,030.78.

In order to determine the value today of the series of payments, the present value has to be determined. Present value is the sum of the discounted cash flows.

Present value = 5,100 / (1.079)^6 + 5,100 / (1.079)^7 + 5,100 / (1.079)^8 + 5,100 / (1.079)^9 + 5,100 / (1.079)^10 + 5,100 / (1.079)^11 + 5,100 / (1.079)^12 + 5,100 / (1.079)^13 + 5,100 / (1.079)^14 + 5,100 / (1.079)^15 + 5,100 / (1.079)^16+ 5,100 / (1.079)^17 + 5,100 / (1.079)^18 + + 5,100 / (1.079)^19 + + 5,100 / (1.079)^20 = $30,030.78

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The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

RECT is a square (not drawn to scale).

RA = 13² - 3x - 3  

AC = x(x + 2)

The diagonals of the square will be RC and ET. And "A" is the intersection point. Then the equation is given as,

RA = AC

13² - 3x - 3 = x(x + 2)

169 - 3x - 3 = x² + 2x

x² + 5x - 166 = 0

x = [- 5 ± √(5² - 4 × 1 × (-166))] / (2 × 1)

x = 10.62, -15.62

Then the length of AC is given as,

AC = 10.62 (10.62 + 2)

AC = 134.13 units

The diagonals of the square are congruent. Then we have

ET = RC

ET = 2 AC

ET = 2 x 134.13

ET = 268.3 units

Then the length RT is given as,

RT = ET / √2

RT = 198.7 units

The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.

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The items that are most likely to be measured in ounces are a Paper bag, a can of pop, and a table.

The weight of objects is typically measured in units of mass, such as grams or kilograms, or in units of weight, such as ounces or pounds. In general, smaller and lighter objects are measured in ounces, while heavier objects are measured in pounds or kilograms.

In this case, the paper bag, can of pop, and table are likely to be measured in ounces. These objects are relatively light and can be easily lifted and weighed on a scale, which would make it convenient to use ounces as a unit of measurement. On the other hand, a frying pan is likely to be a heavier object and would typically be measured in pounds or kilograms.

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