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Explanation:

Focus on triangle TUS. The inner angles here are:

Note how the angle measure for S is the supplement of 2x, which is adjacent to the angle S we have.

Add up those three angles and set the sum equal to 180

T+U+S = 180

y+x+180-2x = 180

y-x = 180-180

y-x = 0

y = x

We'll use this later.

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The diagram shows that angle VTU = y+y = 2y.

Focus your attention on triangle TUV.

Since TU = UV, this means the base angles T and V (which are opposite the congruent sides) are congruent angles. We found that angle T was 2y earlier. This means angle V is also 2y.

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Now shift your focus to triangle TSV.

This triangle has the inner angles

Recall earlier that we found y = x at the conclusion of the first section. Using that and the fact that the angles of triangle TSV add to 180, we get...

T+S+V = 180

2x+y+2y = 180

2x+3y = 180

2x+3x = 180 .... replace y with x, since y = x

5x = 180

x = 180/5

x = 36

This is the value of y as well.

The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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After a dilation with a scale factor of 2.5 and center of dilation (0, 0), the coordinates of the vertices of triangle A'B'C' are A' (-5, -2.5), B' (2.5, 5), and C' (5, -10).

Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as triangles.

For the given coordinates, the dilation with a scale factor of 2.5 and center of dilation (0, 0) should be calculated as follows:

Point A (-2, -1) → Point A' (-2 × 2.5, -1 × 2.5) = Point A' (-5, -2.5).

Point B (1, 2) → Point B' (1 × 2.5, 2 × 2.5) = Point B' (2.5, 5).

Point C (2, -4) → Point C' (2 × 2.5, -4 × 2.5) = Point C' (5, -10).

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Events a and b are not mutually exclusive.

Based on the information provided, it is not possible to determine the relationship between events a (the ticket has a value of 8) and b (the ticket is white) without further information. The relationship between two events can be classified as mutually exclusive, dependent, or independent based on their probabilities and how they are related.

Mutually exclusive events: Events that cannot occur at the same time. If events a and b are mutually exclusive, it means that a ticket cannot have a value of 8 and be white at the same time. In this case, a and b are not mutually exclusive because it is possible for a ticket to have a value of 8 and be white.

Dependent events: Events that are influenced by each other. To determine if events a and b are dependent, we need to know if the occurrence of one event affects the probability of the other event. Without further information, we cannot determine whether a and b are dependent or not.

Independent events: Events that are not influenced by each other. If events a and b are independent, it means that the probability of one event occurring does not affect the probability of the other event occurring. Without further information, we cannot determine whether a and b are independent or not.

In conclusion, based on the given information, we can only say that events a and b are not mutually exclusive. We cannot determine whether they are dependent or independent without additional information.

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Answer:

the answer is 13/103

Step-by-step explanation:

In a memory test where test subjects are asked to memorize a large number, historical records show that 80% of test subjects pass the test. A random sample of 625 people is chosen to take the test.

(a) The mean of p^​, the proportion of people who pass the test in the sample, can be calculated using the formula for the mean of a binomial distribution:

Mean (p^​) = p = 0.80

(b) The standard deviation of p^​ can be calculated using the formula for the standard deviation of a binomial distribution:

Standard Deviation (p^​) = sqrt((p(1-p))/n) = sqrt((0.80(1-0.80))/625) ≈ 0.0126

(c) To approximate the probability that more than 84% of the people in the sample pass the test, we can use the normal approximation to the binomial distribution. We first calculate the z-score corresponding to a proportion of 84%:

z = (x - p) / sqrt((p(1-p))/n) = (0.84 - 0.80) / 0.0126 ≈ 3.1746

Using a standard normal distribution table or a calculator, we find the probability that z is greater than 3.1746, which is approximately 0.0008.

Therefore, the approximate probability that more than 84% of the people in the sample pass the test is 0.0008 (rounded to four decimal places).

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Explanation:

Given the functions

f(x) = x-5

G(x) = x^2

We are to find the composite function G(f(x))

Answer:

Which equation?

Step-by-step explanation:

Answer: 9.12 meters

Step-by-step explanation:

1) First calculate how much centimeters in 120 pencils so multiply 7.6 * 120 pencils = 912 cm.

2) Then look up how much meters in 912 cm and you get your answer 9.12 meters.

Answer:

5:9

Step-by-step explanation:

100:180 can be simplified by dividing by 20, which results in the ratio 5:9

Answer:

1 : 1.8

Step-by-step explanation:

ratio of pigs : sheep = 100 : 180 ( divide both parts of the ratio by 100 )

= 1 : 1.8

Answer:110.5inches2

Step-by-step explanation:

to find the area of a triangle use the formula 1/2(base times height) where in this case  base is 17 and height is 13. applying this formula= 1/2(17x13)=1/2(221)=110.5inches2

Answer:

here

Step-by-step explanation:

8/1 or 8

Answer:

1) NO

2)YES

3)YES

4)NO

5)NO

Answer:

x =5

Step-by-step explanation:

Tangents from same external point have equal length.

KJ = LJ

4x - 1 = 2x + 9

Add 1 to both sides

4x = 2x + 9 + 1

4x  = 2x + 10

Subtract '2x' from both side

4x - 2x = 10

2x= 10

Divide both sides by 2

x = 10/2

x = 5

Answer:

C (-3)^2 = 9 not -9

Step-by-step explanation:

-3*-3 = 9  not -9

The square root of a negative number is imaginary not real

Answer:

C

Step-by-step explanation:

and you can also tell because the square roots of negative numbers will always be a non-real number so it will definitely not be -3

Answer:

176

Step-by-step explanation:

Apply PEMDAS

Solve the parenthesis first

11 ( 7 + 9 )

11 ( 16 )

Now open the parenthesis and you will have your answer

11 times 16

176

Answer:

a) 2(n + 5)

b) 2n + 5

Step-by-step explanation:

Writing an     algebraic expression:

  a) Sum of n and 5 ⇒   n + 5

     Twice sum of n and 5 ⇒   2*(n +5)  = 2*n + 2*5

                                                                = 2n + 10

b) Twice n ⇒ 2*n = n

Sum of twice n and 5 ⇒   2n + 5

Answer:

$ 0.50 in Dimes

Step-by-step explanation:

5 Quarters: $1.25

5 Dimes: $0.50

5 Nickels: $0.25

Total: $2.00

5 Dimes

Hope this helped! :D

The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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The system of equations has no solutions because they lines are parallel

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

y = 1/4x + 1

y = 1/4x - 3​

See attachment for the graph

From the graph, we can see that the lines are parallel lines (they do not intersect)

This means that the system of equations has no solution

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Answer: A (3, -4)

Step-by-step explanation:

A minimum is at the lowest point on the parabola. The minimum and maximum can be seen by looking at the vertex.

If you go right 3 spaces on the x-axis horizontally, then down 4 spaces vertically on the y-axis you get (3, -4).

4 is negative because you are going down below the x-axis.

Answer:

-6

Step-by-step explanation:

Natural numbers are any whole number that is 0+. So, we 100% know that -6 is an integer, as natural numbers are only positive.

Answer:

20.5 feet

Step-by-step explanation:

The slope of the line segment joining the pair (a,0) and (0,b) is -b/a. It means that the steepness of the line joining these points is -b/a.

The slope of a line is defined as the ratio of change in y coordinates (vertical component) and change in x coordinates (horizontal component)

We have two points, let's say P and Q

Where P has coordinates (a,0)

And Q has coordinates (0,b)

To find the slope of a line whose two points are given is given by the formula:

Slope, m =  \(\frac{Y_{2} - Y_{1}}{X_{2}-X_{1} }\)

Substituting values of points P and Q in the above equation we get,

Slope, m = \(\frac{b-0}{0-a}\)

m = -b/a

So, the slope of the line segment joining the pair (a,0) and (0,b) is -b/a.

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Answer: =7y^2+20y−3

Step-by-step explanation:

20 questions make up the entire survey. With regard to those facts, Noah has responded to 16 out of the total of 80 questions.

Suppose there are x total questions.

Now, 80% of x=16

\(\frac{80}{100}\) × \(x = 16\) (The word 'of' means multiplication)

0.8x=16

x = \(\frac{16}{0.8}\)

x=20

So, a survey has a total of 20 questions.

To determine the percentage, divide the value by the total value and divide the outcome by 100. The percentage is determined by employing the equation (value/total value)100%.

The value of either a number out of 100 is what is known as that of the percentage of that number. To use the equation (part/whole) 100, it is determined. 26 boys and 24 girls, for instance, make up a class. In those other words, 52 boys out of 100 make up 52% of the class, or 26/(26+24) 100 = 26/50 100.

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Answer:

0.68754935415

Diameter = Circumference

Pi

0.68754935415 = 2.16

Pi

The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31

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

√(2 + 2x) - 6 = 2

So, we have

√(2 + 2x) = 8

Take the square of both sides

so, we have the following representation

2 + 2x = 64

Evalyate the like terms

2x = 62

Divide by 2

This means that

x = 31

Hence, the solution is x = 31

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Complete question

What is √(2 + 2x) - 6 = 2