End of unit 4 assessment right triangle trigonometry

A random sample of 120 college seniors found that 30% of them had been offered jobs. the standard error of the sample proportion is 0.045.

When dealing with random samples and proportions, the standard error can be calculated using this formula:

SE_p =[tex]sqrt [ p × ( 1 - p ) / n ][/tex]

Where,

SE_p is the standard error of the sample proportion,

p is the sample proportion,n is the sample size.

Using the given information, a random sample of 120 college seniors found that 30% of them had been offered jobs. Hence, p=0.30 and n=120.

Substituting p=0.30 and n=120 in the above formula, we get:

SE_p = [tex]sqrt [0.30 × (1 - 0.30) / 120][/tex]

Simplifying,

SE_p = [tex]sqrt [0.21 / 120]SEp = 0.045[/tex]

Hence, the standard error of the sample proportion is 0.045.

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According to the question, it’s given that the sum of two numbers is 42.

On substituting the values -

[tex]\:\:\:\:\:\:\:\star \small \underline{ \boxed{ \sf{ x+\bigg(x-12\bigg) = 42}}}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf { x + x -12 = 42}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {2x -12 =42}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {2x = 42+12}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {2x = 54}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {x = \dfrac{54}{2}}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \pink{x = 27}}}}\\[/tex]

Henceforth,the larger number is 27 and the smaller number is (x-12)=(27-12)=15.

[tex]\:\:\:\:\:\:\longrightarrow\underline{\rm{\sf Larger \: Number =\pink{ \underline{27}}}}[/tex]

[tex]\:\:\:\:\:\:\longrightarrow\underline{\rm{\sf Smaller \: Number =\pink{ \underline{15}}}}[/tex]

The solution for the inequality is obtained as: x =>-2

In mathematics, "inequality" refers to a relationship between equations or values that is not equal to each other. Hence, inequality emerges from a lack of balance.

The given  inequality

-5x + 2 <= 12`

Subtract each side by - 2

-5x + 2 - 2 <= 12 - 2

-5x <= 10

Dive each side by -5 (it will reverse the sign)

-5x / -5 => 10/-5

x  => -2

Thus, the solution for the inequality is obtained as: x =>-2

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The answer of the given question based on the  linear regression  is , the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.

Distance is measurement of length between the two points or objects. It is a scalar quantity that only has a magnitude and no direction. In mathematics, distance can be measured in various units such as meters, kilometers, miles, or feet, depending on the context.

Distance can be calculated using the distance formula, which is based on the Pythagorean theorem in two or three dimensions.

Assuming the equation you meant to write is y = 34.38x - 91.75, where y is the predicted distance traveled in miles and x is the number of hours driven, we can use this equation to predict how far the person will travel after 10 hours of driving:

y = 34.38x - 91.75

y = 34.38(10) - 91.75

y = 343.8 - 91.75

y = 252.05

Therefore, the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.

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During 10 hours of driving, the projected distance according to linear regression is roughly 252.05 miles.

The term "distance" refers to the length between two points or objects. Having merely a magnitude and no direction, it is a scalar quantity. Depending on the situation, distance in mathematics can be expressed in a variety of ways, including meters, kilometers, miles, or feet.

The distance formula, which depends on the Pythagorean theorem in either two or three dimensions, can be used to compute distance.We may use this equation to forecast how far the individual would go after 10 hours of driving, assuming the equation you meant to write is

y = 34.38x - 91.75, where y is the expected distance travelled in miles and x is the number of hours driven:

y = 34.38x - 91.75

y = 34.38(10) - 91.75

y = 343.8 - 91.75

y = 252.05

The estimated distance that the driver will cover after 10 hours on the road is 252.05 miles.

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The complete question is,

The equation for linear regression is = 34.38x - 91.75. Calculate this person's estimated distance after 10 hours of driving using the equation: 4.38x-91-75.

A sketch of the graph of the function for a maximum of 4000 calculators is shown below.

The value of C(30) is equal to $12,710.

It cost $12,710 to produce 30 calculators.

C(0) is $11,750, which means that the fixed cost before any calculator is produced is $11,750.

The number of calculators that can be produced for $31,270 is 610 calculators.

The amount of profit that would be made if all the calculators are sold is $295,550.

In order to sketch the graph of the function on a coordinate plane, we would use an online graphing calculator to plot the given linear equation C(n) = 11,750 + 32n with a maximum of 4000 calculators.

In this scenario and exercise, the cost in dollars would be plotted on the y-axis of the graph while the number of calculators would be plotted on the x-axis of the graph.

For the value of C(30), we have:

C(n) = 11,750 + 32n

C(30) = 11,750 + 32(30)

C(30) = 11,750 + 960

C(30) = $12,710.

For the value of C(0), we have:

C(n) = 11,750 + 32n

C(0) = 11,750 + 32(0)

C(0) = 11,750 + 0

C(0) = $11,750.

This ultimately implies that, the fixed cost (y-intercept) is at (0, 11,750) and it means that the fixed cost before any calculator is produced is $11,750.

When cost is $31,270, the number of calculators can be determined as follows;

31,270 = 11,750 + 32n

32n = 31,270 - 11,750

32n = 19,520

n = 19,520/32

n = 610 calculators.

Lastly, we would determine the amount of profit as follows;

Profit = Selling price - Cost price

Profit = 2600(165) - [11,750 + 32(165) + 14,000 + 24500]

Profit = 429,000 - 133,450

Profit = $295,550.

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In Linear equation, 260.2 would they each earn if they divided their earnings equally.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                         Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

three friends earned $359 in August, $522 in July, and $420 in September

                = $359 + $522 $ 420  

                = 1301/5 = 260.2

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The atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by , where is in years and corresponds to 1950.

Substituting in gives , which means that the atmospheric carbon dioxide levels in parts per million (ppm) in the town is 386.50 in 2019.

This means that since 1950, the atmospheric carbon dioxide levels in parts per million (ppm) in the town have increased by 386.50.

This is a significant increase and reflects the growing levels of atmospheric carbon dioxide emissions globally due to human activity, leading to climate change.

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The scale factor that takes the segment of length l to the segment of length n is 2.25.

Length is a measurement of the distance between two points, usually expressed in units such as inches, feet, yards, meters, and kilometers. It is used to measure the size of objects, the distance between objects, and the length of a path or route. Length is one of the four fundamental units in the metric system, along with mass, time, and temperature.

This can be determined by a process of successive scaling. The initial segment of length l is first scaled by a factor of 1.5 to give a segment of length m. This segment is then scaled by a factor of 1.5 to give a segment of length n. Multiplying the two scaling factors together, 1.5 x 1.5, gives 2.25, which is the scale factor from the initial segment of length l to the final segment of length n.

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The scale factor that takes the segment of length l to the segment of length n is 2.25.

Length is a measurement of the distance between two points, usually expressed in units such as inches, feet, yards, meters, and kilometers. It is used to measure the size of objects, the distance between objects, and the length of a path or route. Length is one of the four fundamental units in the metric system, along with mass, time, and temperature.

This can be determined by a process of successive scaling. The initial segment of length l is first scaled by a factor of 1.5 to give a segment of length m. This segment is then scaled by a factor of 1.5 to give a segment of length n. Multiplying the two scaling factors together, 1.5 x 1.5, gives 2.25, which is the scale factor from the initial segment of length l to the final segment of length n.

To calculate the scale factor that takes the segment of length l to the segment of length n, the following formula can be used:
n = (1.5)²×l
Therefore, the scale factor is (1.5)² = 2.25. This means that the segment of length l needs to be scaled by a factor of 2.25 in order to produce the segment of length n.

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The average rate of change of f(x) from x = -3 to x = 6 is 7.

What is meant by average?

The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.

To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.

For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:

[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]

The value of the function at [tex]x = 6[/tex] is:

[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]

The difference in the function values is:

[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]

The difference in the input values is:

6 - (-3) = 9

Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:

average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]

So, the average rate of change of f(x) from x = -3 to x = 6 is 7.

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The given equation of the circle is:

[tex] \rm \: x^2 + y^2 = 20[/tex]

We can write this equation in standard form by completing the square:

[tex] \rm x^2 + y^2 = 20[/tex]

[tex] \rm x^2 + y^2 - 20 = 0[/tex]

[tex] \rm (x^2 - 2x + 1) + (y^2 - 20) = 1[/tex]

[tex] \rm (x - 1)^2 + y^2 = 21[/tex]

Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.

Answer:

no solution

Step-by-step explanation:

2x - 6 = 2x + 6 ( add 6 to both sides )

2x = 2x + 12 ( subtract 2x from both sides )

0 = 12 ← false statement

this false statement indicates the equation has no solution

The given statement " let a be an n \times n matrix. a is diagonalizable if it has n eigenvalues, counting multiplicities." is False. Because Matrix has only one linearly independent eigenvector.

Having n eigenvalues, counting multiplicities, only guarantees that A is diagonalizable over the field of complex numbers, but not necessarily over other fields such as the real numbers.  The correct statement is Let A be an n × n matrix. A is diagonalizable if and only if it has n linearly independent eigenvectors.

For example, the matrix:

A = [0 1; -1 0] hhggjjjhjhjhj

has eigenvalues i and -i, but it is not diagonalizable over the field of real numbers, since it has only one eigenvector which is also linearly independent. However, it is diagonalizable over the field of complex numbers. So, the given statement is false.

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Answer:

The slope of the line passing through the points (1, -1) and (4, 8) is 3.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the following formula:

[tex]slope = (y2 - y1) / (x2 - x1)[/tex]

Here, the given points are (1, -1) and (4, 8). So,

[tex]slope = (8 - (-1)) / (4 - 1) = 9 / 3 = 3[/tex]

Therefore, the slope of the line passing through the points (1, -1) and (4, 8) is 3.

Given how many coins are provided in the bag determines the chances for example of its a single nickel and a single quarter it'd be q50/n50 though if there's two nickels and one quarter there would be a n75/q25 chance.

Substitute r = 2 and s = 3 into the expression:

5r + 7s - 3(r + s) + 4 = 5(2) + 7(3) - 3(2 + 3) + 4

= 10 + 21 - 15 + 4

= 20

Therefore, the value of the expression when r = 2 and s = 3 is 20.

Given:-

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Solution:-

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put the given values in the equation

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hope it helps ⸙

In response to the stated question, we may state that As a result, the trigonometry value of x is 11/4.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

Because AB is the midpoint of triangle CDE, it is parallel to CD and equal to half of CD.

As a result, we have:

AB = 1/2 CD

We also know that AD has a length of 3x - 1 and DB has a length of x + 4.

Given that AB is the mid-segment, we may write:

1/2 (AD + DB) = AB

In place of the values we have:

3x - 1 + x + 4 = 2AB

4x + 3 = 2AB

We also know that AB = 7, therefore we may use this number instead:

4x + 3 = 2(7) (7)

4x + 3 = 14

4x = 11

x = 11/4

As a result, the value of x is 11/4.

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Applying the triangle proportionality theorem, the value of x is calculated as: D. 15.

The Triangle Proportionality Theorem (also known as the Side-Splitter Theorem) states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally

Based on the triangle proportionality theorem, we have:

x - 6 / 3 = x / 5

Cross multiply:

5(x - 6) = 3x

5x - 30 = 3x

Combine like terms to find the value of x:

5x - 3x = 30

2x = 30

x = 30/2

x = 15

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The probability that the waves are turbulent given that the water is cold is approximately 0.4353.

Suppose the water has a 0.51 chance of being cold and the waves have a 0.57 chance of being turbulent. In the same way, suppose that given the waves are turbulent, the water has a 0.39 chance of being cold. What is the chance that the waves are turbulent given that the water is cold?

To answer the question, we must use Bayes' theorem :P (A|B) = P (B|A) × P (A) / P (B)

Where A and B are arbitrary events. P (A) and P (B) are the probabilities of events A and B happening separately.

P (B|A) is the probability of event B happening, given that event A has happened. P (A|B) is the probability of event A happening, given that event B has happened.

We must find P (waves are turbulent | water is cold), which is P (B|A). We know that:

P (water is cold) = 0.51

P(waves are turbulent) = 0.57

P(water is cold | waves are turbulent) = 0.39

Using Bayes' theorem, we can calculate P (waves are turbulent | water is cold) as:

P (waves are turbulent | water is cold) = P (water is cold | waves are turbulent) × P (waves are turbulent) / P (water is cold)

P(waves are turbulent | water is cold) = 0.39 × 0.57 / 0.51

P (waves are turbulent | water is cold) = 0.4353 (rounded to the nearest millionth)

Therefore, the probability that the waves are turbulent given that the water is cold is approximately 0.4353.

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Answer: The probability is approximately 15.74%.

Step-by-step explanation: The probability that a worker selected at random makes between $450 and $550 can be found by standardizing the distribution of weekly wages using the formula:

z = (x - μ) / σ

where x is the weekly wage, μ is the mean weekly wage, and σ is the standard deviation of weekly wages.

Then we can use a standard normal distribution table or calculator to find the probability that a worker selected at random makes between $450 and $550.

Using this formula, we get:

z1 = (450 - 400) / 50 = 1

z2 = (550 - 400) / 50 = 3

The probability that a worker selected at random makes between $450 and $550 is equal to the probability that a standard normal random variable Z is between 1 and 3. This can be found using a standard normal distribution table or calculator.

Using a standard normal distribution table, we find that P(1 < Z < 3) = 0.1574.

Therefore, the probability that a worker selected at random makes between $450 and $550 is approximately 15.74%.

Hope this helps, and have a great day!

The probability of a sample of 10 parts containing more than 3 defective ones is approximately 0.026.

We can use the binomial distribution to calculate the probability of getting more than 3 defective parts in a sample of 10 parts. Let X be the number of defective parts in the sample. Then X follows a binomial distribution with parameters n=10 and p=0.1, where n is the sample size and p is the probability of a part being defective.

We can calculate the probability of getting more than 3 defective parts is:

P(X > 3) = 1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

Next, we can find that:

P(X > 3) = 0.026

Therefore, the probability of a sample of 10 parts containing more than 3 defective ones is approximately 0.026.

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Let Y have a distribution function given by 0, Fly) = y <0 y 20.

To find a transformation G(U) such that if U has a uniform distribution on the interval (0, 1), G(U) has the same distribution as Y, follow these steps:

1. Identify the distribution function of Y:

F(y) = 0 for y < 0, and F(y) = 1 - e^(-y) for y ≥ 0.
2. Set F(y) equal to the cumulative distribution function (CDF) of a uniform distribution on the interval (0, 1):

F(y) = U.
3. Solve for y in terms of U to obtain the transformation G(U).

So, for y ≥ 0,
1 - e^(-y) = U

Now, solve for y:
e^(-y) = 1 - U
-y = ln(1 - U)
y = -ln(1 - U)

Therefore, the transformation G(U) is given by G(U) =. ln(1 - U)

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Answer: A = bh

Step-by-step explanation

Area of a parallelogram is base multiplied by the height .

Therefore, the table showing the original points and their corresponding dilated points is:

Original Point     Dilated Point

(0,1)                  (0,1/2)

(4, -3)                (2, -3/2)

(-6,1)                 (-3,1/2)

I believe you might have meant "dilated point", which is a term commonly used in geometry. A dilated point is a point that has been enlarged or reduced in size with respect to a fixed center of dilation.

To dilate a point, you need to multiply its coordinates by a scale factor, which is a constant value greater than zero. If the scale factor is greater than one, the point will be enlarged, and if it is less than one, the point will be reduced in size. The fixed center of dilation is the point about which the dilated point is enlarged or reduced.

given by the question.

To apply the dilation rule of (1/2x, 1/2y) to a given point (x,y), we need to multiply the x-coordinate and y-coordinate of the original point by 1/2.

Using this rule, we can find the dilated points for the given set of points as follows:

For the point (0,1), we have:

1/2x = 1/2 * 0 = 0

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (0, 1/2).

For the point (4, -3), we have:

1/2x = 1/2 * 4 = 2

1/2y = 1/2 * (-3) = -3/2

So, the dilated point is (2, -3/2).

For the point (-6,1), we have:

1/2x = 1/2 * (-6) = -3

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (-3,1).

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2= 2

4=10

i cant see 6 or 8

The number of feet of fabric will the individual need to make 11 blankets is 79.2 feet

To find out how many feet of fabric the individual will need to make 11 blankets, we can use the unitary method.

We know that the individual used 7.2 feet of fabric to make one blanket. So, to find out how much fabric is needed to make 11 blankets, we can set up a proportion

7.2 feet of fabric is needed for 1 blanket

x feet of fabric is needed for 11 blankets

We can solve for x by cross-multiplying and then dividing

7.2 × 11 = x

x = 79.2 feet

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3 meats x 4 vegetables x 7 desserts = 84 choices.

There are 84 different choices for a complete meal from the given options. To calculate this, use the formula: number of choices

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To estimate the number of new subscribers in Charlottesville and Albemarle County, we'll use the given joint probability density function (pdf) f(x,y).

Here's a step-by-step explanation:
1. Identify the random variables: In this case, X represents the number of new subscribers (in thousands) in Charlottesville, and Y represents the number of new subscribers (in thousands) in Albemarle County outside of Charlottesville.
2. Understand the joint probability density function (pdf): The function f(x,y) describes the probability of having a specific number of new subscribers in both areas. The joint pdf is used to find the probability of a particular combination of X and Y values.
3. Determine the desired outcome: In this case, you want to estimate the number of new subscribers in both Charlottesville (X) and Albemarle County (Y) next year.
4. Calculate the probabilities: To find the probability of a specific combination of X and Y values, you'll need to evaluate the joint pdf f(x,y) at those values.
5. Analyze the results: Based on the probabilities you've calculated using the joint pdf, you can make informed estimates about the number of new subscribers in both areas next year.
By following these steps and using the joint probability density function f(x,y), you can estimate the number of new subscribers for F XYZ finity Cable in Charlottesville and Albemarle County next year.

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The closest option is (A) (3,3), which is the correct solution to the system of equations.

To find the solution to the system of equations, we need to substitute the value of y in the first equation with the value given in the second equation:

-6x + y = -21 ...(1)

2x - 1/3 y = 7 ...(2)

Substituting y=7 in the first equation, we get:

-6x + 7 = -21

Simplifying the above equation:

-6x = -28

Dividing both sides by -6, we get:

x = 28/6 = 14/3

Substituting x=14/3 and y=7 in the second equation, we get:

2(14/3) - 1/3(7) = 7

Simplifying the above equation, we get:

28/3 - 7/3 = 7

21/3 = 7

Therefore, the solution to the system of equations is (14/3, 7).

Hence, the answer is not in the given options, but the closest option is (A) (3,3), which is not the correct solution to the system of equations.

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