Which relationships describe angles 1 and 2?

Select each correct answer.


adjacent angles


complementary angles


vertical angles


supplementary angles

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.

given

The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.

To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.

As a result, we have:

sin 30° = (6/2x)

Adding two times to both sides:

2x * sin 30° = 6

Using sin 30°, which has a value of 0.5:

x = (6/(2 * 0.5)) = 6/1 = 6

Consequently, the side YZ is 6 units long.

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

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Answer:

Step-by-step explanation:

[tex]A=\frac{1}{2} h(a+b)[/tex]

[tex]24=\frac{1}{2} h(5+6)[/tex]

[tex]24=\frac{11} 2 h[/tex]                  

[tex]11h=48[/tex]                                (multiplied both sides by 2)

[tex]h=\frac{48}{11}=4\frac{4}{11}=4.36 units[/tex]      (divided both sides by 11)

There are 5 possible ways for the ride to begin.

The ferris wheel has 5 cars with 4 seats in each car, making a total of 20 seats. If there are 20 people ready for the ride, then each car can have 4 people. Therefore, there are 5 possible ways for the ride to begin.

If two certain people want to sit in different cars, then there are 4^2 (4x4) combinations of cars for these two people. This gives us 16 possible ways for the ride to begin.

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As per the standard deviation, the cutoff salary for teachers in the top 10% of earners in this country is approximately $43,120.

Now, we need to determine the cutoff salary for teachers in the top 10% of earners in this country. To do this, we need to find the salary that corresponds to the 90th percentile of the distribution.

The 90th percentile represents the point below which 90% of the data falls. In other words, if we arrange all the salaries in ascending order, the 90th percentile is the value that is greater than 90% of the salaries.

We can use a standard normal distribution table or a calculator to find the z-score that corresponds to the 90th percentile. The z-score represents the number of standard deviations away from the mean that corresponds to a particular percentile.

Using the standard normal distribution table, we can find that the z-score for the 90th percentile is approximately 1.28. This means that the cutoff salary for teachers in the top 10% of earners is:

Cutoff salary = Mean + (Z-score x Standard deviation)

Cutoff salary = $38,000 + (1.28 x $4,000)

Cutoff salary = $43,120

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Answer:

First, you distribute 2(2x-1/2)

2(2x) and 2(-1/2)

Now, you have 3x-2=4x-1

Then, you move 2 to the right side by adding so you can cancel it out.

Then, you move 4x to the left side by doing the same thing with 2

Now, divide both sides by -1

The answer is C, z= -1.

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

3x-2=4x-1

3x=4x+1

-x=1

-x/-1 = 1/-1

= x=-1

As per the combination method, there are 495 groups of 4 people that can answer the 4 different phone lines when there are 12 people in the office.

To start, we need to determine how many ways we can choose 4 people from a group of 12. We use the formula for combinations, which is:

ⁿCₓ = n! / x!(n-x)!

Where n is the total number of people (in this case, 12) and x is the number of people we want to choose (in this case, 4). The exclamation point symbol (!) denotes the factorial operation, which means we multiply the number by every positive integer less than it down to 1.

So, for this problem, we have:

¹²C₄ = 12! / 4!(12-4)!

= (12 x 11 x 10 x 9) / (4 x 3 x 2 x 1)

= 495

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There is 78.54 mI of miIk in the gIass.

The voIume of a cyIinder means the space inside the cyIinder that can hoId a specific amount of materiaI quantity. In simpIer words, the capacity of a cyIinder to hoId a thing is its voIume. Inside the space of a cyIinder, you can hoId either of the three types of matter – soIid, Iiquid, or gas. This capacity can onIy be witnessed in a three-dimensionaI cyIinder, i.e., you cannot hoId any Iiquid, soIid, or gas in a two-dimensionaI cyIinder.

The equation for the voIume of a cyIinder is V = Ah,

where A is the area of the base and h is the height.

Thus, the voIume can aIso be expressed as V = πr2h.

Find capacity of the gIass :

VoIume of the gIass = πr²h

Given radius = 5 ; Height = 2

VoIume of the gIass = π(5)²(2)

VoIume of the gIass = 157.08cm³

Find the voIume of the miIk :

If the gIass is haIf fuII,

VoIume of the miIk = 177.08 ÷ 2

VoIume of the miIk = 78.54 cm³

Convert cm³ to mI :

1 mI = 1000 cm³

78.54cm³ = 78.54 mI

There is 78.54 mI of miIk in the gIass.

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The coordinates of the vertices for the image if the preimage is translated 4 units down are A′(-4, -1), B′(0, 1), C′(-2, -4).

What is meant by preimage?

In geometry, a preimage is the original figure or shape before any transformation is applied. It is the initial configuration of the object that is being transformed. For example, if we have a square and we rotate it by 90 degrees, the original square is the preimage and the resulting figure after the rotation is the image.

To translate the preimage 4 units down, we need to subtract 4 from the y-coordinates of all vertices. Therefore, the coordinates of the image vertices are:

A′(-4, 3-4) = (-4, -1)

B′(0, 5-4) = (0, 1)

C′(-2, 0-4) = (-2, -4)

Therefore, the vertices of the image triangle are A′(-4, -1), B′(0, 1), and C′(-2, -4).

So, the correct option is: A′(-4, -1), B′(0, 1), C′(-2, -4).

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The process of trying out the resulting equation on a second sample to see if it still fits well is called “cross-validation”.

Cross-validation is a technique used to evaluate the performance of a statistical model on a new independent dataset, which was not used in training the model. This process helps to assess the generalization capability of the model and helps to determine whether the model is overfitting or underfitting the data. By testing the model on a new independent dataset, we can get a better idea of how well the model is likely to perform on new data in the future. Cross-validation can also help in selecting the best model from a set of competing models.

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Answer:

Step-by-step explanation:

You want three additional equivalent expressions to 6(3x +8) +32 +12x, one of which is the expression in simplest form.

Any expression you write along the path to simplifying the given expression will be an equivalent. Here's one way to get three different expressions:

  6(3x +8) +32 +12x . . . . . . given

  18x +48 +32 +12x . . . . . . eliminate parentheses

  30x +48 +32 . . . . . . . . . . combine x terms

  30x +80 . . . . . . . . . . . . . . combine constants (2 terms)

We can write another equivalent by factoring out a common factor:

  10(3x +8)

Answer: 37.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The vertices of the image triangle N′M′O′: N′(-1, 2), M′(-4, 1), O′(-3, 3).

What are vertices?

Vertices (singular: vertex) are the points where two or more straight lines or edges meet in a geometric shape such as a polygon, polyhedron, or graph. In two-dimensional shapes like polygons, a vertex is a corner where two sides intersect.

We can do this by finding the difference between the x-coordinate of the preimage vertex and -3, doubling this difference, and then subtracting this result from the x-coordinate of the preimage vertex. This will give us the x-coordinate of the image vertex.

For example, to find the x-coordinate of the image of vertex N, we have:

x-coordinate of N = -5

Difference between x-coordinate of N and -3 = -5 - (-3) = -2

Double the difference = -2 x 2 = -4

Subtract this result from the x-coordinate of N = -5 - (-4) = -1

Therefore, the x-coordinate of the image of vertex N is -1.

Using the same method, we can find the x-coordinates of the image vertices:

x-coordinate of N′ = -1

x-coordinate of M′ = -4

x-coordinate of O′ = -3

To find the y-coordinates of the image vertices, we don't need to do any calculations since the reflection is over a vertical line and does not affect the y-coordinates. Therefore, the y-coordinates of the image vertices are the same as the y-coordinates of the preimage vertices:

y-coordinate of N′ = 2

y-coordinate of M′ = 1

y-coordinate of O′ = 3

Putting it all together, we get the vertices of the image triangle N′M′O′:

N′(-1, 2), M′(-4, 1), O′(-3, 3)

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The person can get 3 fives, 2 sixes, and 1 two in 336 ways.

To find the number of ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die, we can use the formula for combinations with repetition:

[tex]C(n + k - 1, k) = C(6 + 3 - 1, 3) * C(3 + 2 - 1, 2) * C(1 + 1 - 1, 1)[/tex]

where n is the number of possible outcomes (in this case, 6), k is the number of choices to make (in this case, 3 for fives, 2 for sixes, and 1 for twos), and C(n + k - 1, k) represents the number of combinations with repetition.

Using this formula, we can calculate:

[tex]C(8, 3) * C(4, 2) * C(1, 1) = 56 * 6 * 1 = 336[/tex]

Therefore, there are 336 ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die.

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Answer:

8x^(3)+10x^(2)-13x-15

Step-by-step explanation:

To determine if a system of linear equations has infinitely many solutions, you need to solve the system and check the resulting equations.

Here are the general steps:

If you obtain a valid solution for each variable, then the system has a unique solution.

If you have two or more variables and only obtain a solution for some of them, then the system has infinitely many solutions.

It's also important to note that if you have a system with fewer equations than variables, it may also have infinitely many solutions.

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Answer:

[tex]11xy - 9x + 2y[/tex]

Step-by-step explanation:

[tex]6xy - 9x + 5xy + 2y[/tex]

Add the xy terms together:

[tex]11xy - 9x + 2y[/tex]

Answer:

The volume of a tetrahedron can be found using the formula:

V = (1/3) * A * h

where A is the area of one of the faces of the tetrahedron, h is the height of the tetrahedron, and V is the volume of the tetrahedron.

In this case, we are given that the area of one of the faces is 21 m² and the height of the tetrahedron is 6 m. Substituting these values into the formula, we get:

V = (1/3) * 21 m² * 6 m

V = 42 m³

Therefore, the volume of the tetrahedron is 42 cubic meters.

Answer:

To solve for m, we need to isolate the variable by performing the same operation to both sides of the equation.

Dividing both sides of the equation by 6 will give us:

6m/6 = 33/6

Simplifying:

m = 5.5

Therefore, the solution to the equation 6m = 33 is m = 5.5.

To solve for p, we need to isolate the variable by performing the same operation to both sides of the equation.

Subtracting 7.04 from both sides of the equation will give us:

p + 7.04 - 7.04 = 11.8 - 7.04

Simplifying:

p = 4.76

Therefore, the solution to the equation p + 7.04 = 11.8 is p = 4.76.

To solve for n, we need to isolate the variable by performing the same operation to both sides of the equation.

First, we need to simplify both sides of the equation by finding a common denominator for the fractions:

n + (3/5) = 8/10 can be written as:

n + (3/5) = (4/5)

Next, we can subtract (3/5) from both sides of the equation:

n + (3/5) - (3/5) = (4/5) - (3/5)

Simplifying:

n = 1/5

Therefore, the solution to the equation n + (3/5) = (8/10) is n = 1/5.

These are your answers for questions 1-3.

Answer:

To add these fractions, we need to find a common denominator. The least common multiple of 3, 5, and 6 is 30, so we can convert each fraction to an equivalent fraction with a denominator of 30:

7/3 = 70/30

21/5 = 126/30

7/6 = 35/30

Now we can add the fractions:

7/3 + 21/5 + 7/6 = 70/30 + 126/30 + 35/30

Combining the numerators, we get:

= (70 + 126 + 35) / 30

= 231 / 30

Simplifying this fraction by dividing the numerator and denominator by their greatest common factor, which is 3, we get:

= 77 / 10

Therefore, the sum of the fractions 7/3, 21/5, and 7/6 is equal to 77/10.

Yes, we  would use the normal approximation to predict these results.

When it comes to hypothesis testing and confidence intervals, the normal distribution plays a crucial role.

When sample sizes are large enough, the normal distribution can be used as a reasonable approximation for the binomial distribution.

This is because the binomial distribution approaches the normal distribution as sample size increases.

To calculate the normal approximation, you will need to determine the mean and standard deviation of the binomial distribution.

The mean is np and the standard deviation is the square root of np(1-p),

where n is the sample size and p is the probability of success.

The probability of success in this case is 45%, or 0.45.

Therefore, the mean is 10 * 0.45 = 4.5 and the standard deviation is the square root of 10 * 0.45 * (1 - 0.45) = 1.37.

Now that you have the mean and standard deviation, you can use the normal distribution to make predictions about the sample.

If you want to find the probability that exactly 5 students will go to prom, for example, you would use the formula for the normal distribution with a mean of 4.5 and a standard deviation of 1.37.

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The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.

We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:

x = (9 mi/h) * (0.25 h) = 2.25 mi

y = (8 mi/h) * (0.25 h) = 2 mi

The distance between the two people is given by:

[tex]d = sqrt(x^2 + y^2)[/tex]

Taking the derivative with respect to time t, we get:

[tex]d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))[/tex]

Substituting the values we found earlier, we get:

[tex]d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h[/tex]

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The quotient of 3.013 × [tex]10^{8}[/tex] and 6.55 × [tex]10^{5}[/tex] expressed in scientific notation is equal to 0.46 × [tex]10^{3}[/tex].

In Mathematics, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Generally speaking, any numerical data (number) can be written in scientific notation as shown below:

a × [tex]b^n[/tex]

Where

Next, we would rewrite the given numerical data (number) in scientific notation by dividing by 6.55 × [tex]10^{5}[/tex] as follows:

Scientific notation = 3.013 × [tex]10^{8}[/tex]/(6.55 × [tex]10^{5}[/tex])

Scientific notation = 0.46 × [tex]10^{8-5}[/tex]

Scientific notation = 0.46 × [tex]10^{3}[/tex].

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Ms. Leon will have a total of $840 in her savings account by the end of 4 years.

To calculate the total amount that Ms. Leon will have in her account at the end of 4 years with simple interest, we can use the following formula:

A = P(1 + rt)

where:

A = the total amount in the account at the end of the time period

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

t = the time period (in years)

Putting in the given values, we get:

A = 750(1 + 0.03 × 4)

A = 750(1.12)

A = $840

Therefore, at the end of 4 years, Ms. Leon will have a total of $840 in her savings account.

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Answer:

Let's use "x" to represent the total number of students in the class.

According to the problem, the number of boys is 7/10 of the total number of students, and the number of girls is 3/10 of the total number of students. We can set up the following equation based on this information:

Number of Boys = 7/10 x

Number of Girls = 3/10 x

The problem also tells us that there are 16 more boys than girls in the class. We can set up another equation based on this information:

Number of Boys = Number of Girls + 16

Now we can use these two equations to solve for the total number of students:

7/10 x = 3/10 x + 16

Subtracting 3/10 x from both sides, we get:

4/10 x = 16

Multiplying both sides by 10/4, we get:

x = 40

Therefore, there are 40 students in the class. To find the number of boys and girls, we can use the equations we set up earlier:

Number of Boys = 7/10 x = 7/10 * 40 = 28

Number of Girls = 3/10 x = 3/10 * 40 = 12

So there are 28 boys and 12 girls in the class.

Probability that exactly four workers carpool to work is 0.214990847, or approximately 21.5%.

We must apply the binomial distribution formula to resolve this issue. The number of successes in a certain number of independent trials that all have the same chance of success are described by the binomial distribution, which is a type of probability distribution. In this scenario, the number of successes is the number of workers who carpool, and the probability of success is 0.1.

The binomial distribution's formula is:

[tex]P(X=k) = to (n pick k) * p*k*1-p (n-k)[/tex]

Where n is the total number of trials (in this case, 8), p is the success probability (0.1), and (n choose k) is the binomial coefficient, which is equal to [tex]n! / (k! * (n-k)![/tex] and P(X=k) is the probability of obtaining exactly k successes.

This formula can be used to determine the likelihood that four employees will carpool to work:

[tex]P(X=4) = (8 pick 4) * 0.14 * 0.94 * 0.214 = 0.214990847.[/tex]

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This gives us a present value for the company with debt of $35,564 and a present value for the competitor without debt of $36,944. The difference in present values is $1,380, rounded to the nearest dollar. Therefore, the company with debt gives the contract a higher present value of $1,380.

The company with debt will have the higher present value for this contract. This is because, despite having a higher yield, the competitor without debt is only earning 2.3% on their excess money, while the company with debt is earning 8%.

To calculate the difference in present values, we need to first calculate the present value of each company's contract. To do this, we will use the present value formula, which is:

[tex]PV = C / (1 + r)n[/tex]

Where C is the contract amount, r is the rate of return, and n is the number of years. For the company with debt, we can substitute $40,000 for C, 8% for r, and 1.75 for n. For the competitor without debt, we can substitute $40,000 for C, 2.3% for r, and 1.75 for n.

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