Lines x and y are parallel.

Which angles are congruent to ∠1? Click and drag the angle labels to the box.

WORTH 100 POINTS!! IF WRONG, WILL LOSE POINTS!

According to the central limit theorem, difference of sample mean of two normal populations will also fill normal distribution if the sample size is at least 30 .

What does a statistical sample distribution mean?

An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population. It describes a variety of potential possibilities for a statistic, such the mean or mode of some variable in a population.

What are the different forms of sample distribution?

This idea, which is a sort of probability distribution, is frequently used to gather precise data from a huge population that has been divided into a number of samples that have been chosen at random.

                             This idea is further broken down into three categories: sampling Distribution of the mean, percentage, and T-Sampling.

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The complete question is -

Ata large university, the division of computing services surveyed random sample of 45 biologv majors and 55 business majors from populations of over 1,000 biology and O00 business majors. The sampled students were asked how many hours they spend per week using any university computer lab. Let represent the average hours per week spent in any university computer lab by the 45 biology majors, and let 1, represent the average hours per week spent in any university computer lab by the 55 business majors. Which of the following Is the best explanation for why the sampling distribution of can be modeled with a normal distrlbution? A) The two sample standard deviations are assumed to be equal_

The required line representing the equation part of the constraint is go through (0, 4) and (7,0).

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The line representing the equation 7x1 + 4x2 = 28 is a boundary line that separates the feasible solutions from the infeasible solutions in a linear programming problem.

The line passes through two points, which can be determined by substituting the x1 and x2 values into the equation. By substituting the values (4,0) and (7,0) into the equation, we can see that both points satisfy the constraint.

This means that any point on the line also satisfies the constraint, and any point above or to the right of the line would be infeasible as they would not meet the requirement of the constraint.

Understanding the position and shape of the constraint lines is important in solving linear programming problems and finding the optimal solution.

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The amount of tip will be $6.36. And the total amount of the restaurant bill with the tip will be $48.76.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

One way to compute a 15% tip for a bill is to multiply it by 0.15. A restaurant bill was $42.40.

Then the amount of tip is given as,

Tip amount = $42.40 x 0.15

Tip amount = $6.36

The total amount is given as,

Total amount = $42.40 + $6.36

Total amount = $48.76

The amount of tip will be $6.36. And the total amount of the restaurant bill with the tip will be $48.76.

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The height of the cone is 0.083 inches

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

Volume = 1024π cubic inches

Radius = 16 feet

Convert the radius to inches

So, we have the following representation

Radius = 192 inches

The volume of a cone is

Volume = 1/3πr^2h

Substitute the known values in the above equation, so, we have the following representation

1/3πr^2h =  1024π

So, we have

r^2h =  3072

This gives

h = 3072/(192^2)

Evaluate

h = 0.083

Hence, the heightt is 0.083 inches

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The cardinal number of the set , n ( D ) = 1 .

The natural numbers that are used to determine the cardinality of sets are extended into cardinal numbers . The shortened term "cardinals" is frequently used to describe cardinals. The number of objects contained within a finite set , known as the cardinality , is equal to a natural number .

The cardinal number here would therefore be the number of unique values which is only 1 and that 1 is eight .

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Answer: 200                                            

Becase 80% of 1000 is 800 and 1000- 800 =200

The cost when the two options are the same is equal to $60.

Based on the information provided above, Rhianna's Tees charges a $20 setup fee and then to buy the shirts for $8 each. The total cost, y, can be represented by this equation:

y = 8x + 20    ....equation 1.

where:

x represents the number of shirts.

For the second option, the total cost of the shirt can be represented by this equation:

y = 6x + 30        ....equation 2.

By equating equation 1 and equation 2, we have the following:

8x + 20 = 6x + 30

8x - 6x = 30 - 20

2x = 10

x = 5

Now, we can determine the cost as follows;

y = 8x + 20

y = 8(5) + 20

y = 40 + 20

y = $60.

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An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is always the same. In this case, the common difference is 3, so every term is 3 more than the previous term.

The [tex]$n^{th}$[/tex] term in the arithmetic sequence can be found using

[tex]$a_n = a_1 + (n - 1)d$[/tex]

where $a_1$ is the first term (2 in this case), $d$ is the common difference (3 in this case), and $n$ is the term number.

To find the page number that $11{,}111$ appears on, we need to find the term number that corresponds to this value:

[tex]$11{,}111 = 2 + (n - 1) \cdot 3$[/tex]

Solving for $n$, we have:

$11{,}109 = 3n - 1$

$3n = 11{,}110$

$n = 37{,}037$

Since each page contains 100 numbers, the number 11,111 appears on page $\left\lceil \frac{37{,}037}{100} \right\rceil = 371$.

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According to this information, investments with 4.2, 1.3 and 2.8 interest have a profit of more than $100. On the other hand, investments with interest of 0.75 and 5.2 have a profit of less than $100.

To calculate the profit of these investments we must carry out the following procedure:

1. We must divide the interest in 100

2. We must multiply the interest by the total value of the investment ($1500).

3. We must multiply the result by the number of years of the investment.

4. We must classify the result as less than or greater than $100.

According to the above, investments with 4.2, 1.3 and 2.8 interest have a profit of more than $100. On the other hand, investments with interest of 0.75 and 5.2 have a profit of less than $100.

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The simplified expression for this problem is given as follows:

9 - 13j/7.

The expression for this problem is defined as follows:

16 + (-4) - 5j/7 - 6j/7 + 7.

The plus sign means that the sign is maintained, hence:

16 + (-4) - 5j/7 - 6j/7 + 7 = 12 - 5j/7 - 6j/7 + 7.

Then we combine the like terms, as follows:

Hence the simplified expression is given as follows:

9 - 13j/7.

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The formula to solve for the height of a given triangle is =h=2A/b

Given the area of a triangle formula = A=1/2×b×h

where , A=area of the triangle.

b=base of the triangle.

h=height of the triangle.

To find the height of the triangle using this formula=

A=1/2×b×h

2A=b×h

h=2A/b

thus,h=2A/b is the formula to solve for the height of a given triangle.

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Answer: 4

Step-by-step explanation:

(-88) - (-44) = -36

remove the (-) = 36

36 ÷ 9 = 4

The value of the exponential function is g ( x ) = ( 1/4 )ˣ  and the graph is plotted

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the equation will be

Substituting the values in the equation , we get

g ( x ) = ( 1/4 )ˣ

when x = 0

g ( 0 ) = ( 1/4 )⁰

g ( 0 ) = 1

Now , when x = 1

Substitute the value of x = 1 in the equation , we get

g ( 1 ) = ( 1/4 )¹

g ( 1 ) = ( 1/4 )

Now , when x = 2

Substitute the value of x = 2 in the equation , we get

g ( 2 ) = ( 1/4 )²

g ( 2 ) = ( 1/16 )

Now , when x = 3

Substitute the value of x = 3 in the equation , we get

g ( 3 ) = ( 1/4 )³

g ( 3 ) = ( 1/64 )

Now , when x = 4

Substitute the value of x = 1 in the equation , we get

g ( 4 ) = ( 1/4 )⁴

g ( 4 ) = ( 1/256 )

Hence , the equation is g ( x ) = ( 1/4 )ˣ and the graph is plotted

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Answer:

AA postulate

Step-by-step explanation:

We can prove as:
We have vertically opposite angles, which are equal
Also, we have been given two corresponding equal angles, thus we can prove using AA similarity postulate.

The value of the trigonometric function is -

sin(θ) = 21 / 29,

cos(θ) = 20/29,

csc(θ) = 29/21,

sec(θ) = 29/20,

cot(θ) = 20/21.

In a nutshell, trigonometric functions, also referred to as circular functions, are the functions of a triangle's angle. This suggests that these trig functions provide the relationship between a triangle's angles and sides. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given that,

tan (θ) = - 21 / 20

We can infer from the value that the triangle's two legs are 21 and 20, respectively.

Using the Pythagorean theorem, we can:

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex](21)^{2} + (20)^{2} = c^{2}[/tex]

441 + 400 =[tex]c^{2}[/tex]

c = 29

The value of :

sin(θ) = 21 / 29

cos(θ) = 20/29

csc(θ) = 29/21

sec(θ) = 29/20

cot(θ) = 20/21

Hence, the value of the trigonometric function is

sin(θ) = 21 / 29,

cos(θ) = 20/29,

csc(θ) = 29/21,

sec(θ) = 29/20,

cot(θ) = 20/21.

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Given the following subset phrases are neither is a subset of the other. A set whose elements are all members of another set is simply referred to as a subset.

Because U.S. citizenship can also be acquired through other means, the group of people born in the country is a subset of the group of people who are citizens of the country. The group of Java learners all belong to the group of learners of a programming language, so Because Java is simply one of the many distinct kinds of programming languages, the group of students studying Java is a subset of the group of students studying a programming language. Since fish are just one of the many different marine species that dwell in the ocean, fish are a subset of the animals that live in the ocean.

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The total area of the quilt as perceived is 101 square inches

The six-sided figure is not given, however we can deduce the following parameters from the question:

The shape is made of a triangle and a trapezoid

The side lengths derived from the question are:

The triangle on top:

base: 6 inches and height: 7 inches

The trapezoid at the bottom:

Parallel sides: 16 inches and 9 inches with a height of 6.4 inches

So, we have the total area of the figure to be

Area of figure = 1/2 * 6 * 7 + 1/2 * (16 + 9) * 6.4

Area of figure = 101

Based on the deduced parameters, the total area is 101 square inches

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The number of associates assigned to the case and the number of partners assigned to the case is 6 and 4.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given that,

The daily rate charged to the client for each associate is $600 and the daily rate for each partner is $1100.

The law firm assigned a total of 10 lawyers to the case and was able to charge the client $8000 per day for these lawyers' services.

Here we assume number of associate be x and no of partners be y.

Based on the above information, the calculation is as follows:

x +  y = 10

x = 10 - y

Now put the value of x in the below equation

600x + 1100y = 8,000

600 (10 - y) + 1100y = 8000

6000 - 600y  + 1100y = 8000

2000 = 500y

y = 4

So x = 10 - 4

= 6

Hence, The number of associates assigned to the case and the number of partners assigned to the case is 6 and 4.

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The probability that candidate B is going to win the election is 2.

The probability of candidate A winning the election is 0.5, the probability of candidate B winning the election is 2, the probability of candidate C winning the election is 1/3 and the probability of candidate D winning the election is 2/3.

Therefore, the candidate most likely to win the election is candidate B, and the probability that they are going to win is 2. This can be calculated using the formula for probability, which states that the probability of an event occurring is the number of favourable outcomes divided by the total number of outcomes. In this case, the number of favourable outcomes is 1 and the total number of outcomes is 3, so the probability of candidate B winning is 1/3.

Therefore, the probability that candidate B is going to win the election is 2.

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Answer:

250

Step-by-step explanation:

190 students = 76%

190/76=2.5

2.5 x 100 =250

The solution is the length of the drain line is 20 ft.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

You pace off the length as being 24 strides long.

we know, 1 strides = 2.5 feet

i,e, we have, 60 ft.

now,

You know from prior experience that each of your strides is of a yard.

again, 1 yard = 3 ft.

so,  the length of the drain line = 60/3

                                                    = 20 ft.

Hence, The solution is the length of the drain line is 20 ft.

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Answer: $22.50

Step-by-step explanation

In this case, x is what the original number was in case you didn’t know.

x - (x * 20/100) = 18

x -0.2x=18

0.8x=18

18/0.8=x

X = 22.5

To create a scale illustration of her bedroom, Elena must draw a 10cm by 6cm rectangle.

To create a scale illustration of her bedroom she must take into account the scale she will be using. In this case it would be 1:50, that is, each original unit must be divided into 50 parts. Therefore, we must divide the lengths into 50 as shown below. Additionally we must take the values in cm.

According to the above, a scale model would be 10cm by 6cm.

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Answer: No

Step-by-step explanation:

No, because it does not add the same value every time

Answer:

No

Step-by-step explanation:

The left side does add up the same each time (+1) but the right side does not as it adds +2 +2 +4 +8 +16

Answer:  Richard is 22 and Teo is 9

Step-by-step explanation:

The system of equations graphically on the set of axes is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

y = (1/6)x + 7

y = -2x - 6

The graph of each equation is given below.

The point of intersection is (-6, 6).

i.e,

(1/6)x + 7 = -2x - 6

(1/6)x + 2x = -6 - 7

13x/6 = -13

x/6 = -1

x = -6

So,

y = -2x - 6

y = -2 x -6 - 6

y = 12 - 6

y = 6

Thus,

The system of equations graphically is given above.

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Answer:4

Step-by-step explanation: answer 4

The area of triangle cde with altitude ef is 8 square units. This is calculated by finding the height from point "e" to "f", and the base from point "c" to "d", and then using the formula: Area = (base * height) / 2. The answer is 8 square units.

The area of a triangle can be calculated using the formula:

Area = (Base x Height) / 2

To find the height, we need to find the distance between the point where the altitude intersects the base (in this case, point "f" on the y-coordinate of point "e"), and the other two points of the triangle (in this case, "c" and "d").

The equation for a line in the form y = mx + b can be used to find the y-coordinate of point "f". Using the coordinates of points "c" and "e", the slope can be found by:

m = (3 - (-2)) / (2 - 3) = -1

The y-intercept can be found using the coordinates of point "c" and the slope:

b = -2 - (3 * -1) = 1

So the equation of the line that passes through points "c" and "e" is:

y = -x + 1

We can now use this equation to find the y-coordinate of point "f":

y = -x + 1

y = -0 + 1

y = 1

The height of the triangle is now the distance between points "e" and "f":

height = |3 - 1| = 2

The base of the triangle can be found by taking the distance between points "c" and "d":

base = |(-1) - (3)| = 4

So the area of the triangle is:

Area = (base * height) / 2

Area = (4 * 2) / 2

Area = 8

The area of the triangle is 8 square units.

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