Look at the triangles. What information is needed to prove that △ABC∼△DEF?
Options are listed at the bottom

If 100 sixth grade students prefer hip hop music, the number of sixth graders at the school is 250.

Percentage is a measure of frequency that is used to express a number as as a fraction of 100. In order to change a value to percentage, multiply the number by 100. The sign that represents percentage is %.

In order to determine the number of sixth graders, divide the number of sixth graders that prefer hip hop music by the percentage.

Number of sixth graders = number that prefer hip hop / percentage

100 / 40%

100 / 0.4 = 250

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The value of x is 22.5528.

Let ABC be the triangle , <A = 70, <B = 30 ,<C = 80.

Sum of angles in a triangle is 180.

70 + 30 + <C = 180

<C = 180 - 100

<C = 80.

Let sides be a = x , b = 12 and c = ?

According to sines law,

a/sin A = b/sin B = c/sin C

substitute a ,b,A,B values

a/sin A = b/sin B

x/sin 70 = 12/sin 30

x = 0.9397*12/1/2

= 11.2764*2/1

x = 22.5528.

Therefore the value of x is 22.5528.

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The solution of x when solving x/2 + 1 = √3 is :

x is 2√3 - 2 .

Here in the question given equation ,

x/2 + 1 = √3

To find solution,

we have to subtract 1 from LHS and RHS of equation,

⇒ x/2 + 1 - 1 = √3 - 1

⇒ x/2 = √3 - 1

Next multiply both sides  by 2

2( x/2) = 2(√3 -1)

By simplifying both sides we get,

x = 2√3 - 2

So the value of x = 2√3 -2.

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The probability of an event is 0.29,0.06. An event's probability is always between 0 and 1.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.

-0.5 cant be a probability because it is less than 0

0.29 can be a probability because it is more than zero.

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The numbers that could be a probability of an event are  0.29 and 0.06

An event's probability is always between 0 and 1. (inclusive).

This implies:

There can be just one.

It must be zero or less.

Evaluation of Option (a) - 0.5

This cannot represent probability (b) 0.29 because it is less than 1,

This can be used to represent probability (c) 0.06 since it lies between 0 and 1.

This can be used to indicate probability (d) 1.18 since it is less than 1.

Given that this is larger than 1, it cannot be a probability (e) 0

A probability is not zero.

This ranges from 0 to 1, so it can be used to express probability.

Therefore, 0.29 and 0.06 can be used to indicate probabilities.

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Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.

In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the   system of experimentation.

Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.

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The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1

Arithmetic sequence can be represented with the formula as follows:

aₙ = a + (n - 1)d

where

Therefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..

a = 4

d = 7 - 4 = 3

Therefore,

aₙ = 4 + (n - 1)3

aₙ = 4 + 3n - 3

aₙ = 3n + 4 - 3

aₙ = 3n + 1

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Naoki shifted the base of ladder by 14 feet as the updated distance is 39 feet and old distance was 25 feet.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc). Finding the elements of vectors, modeling the mechanics of waves (both electromagnetic and physical), summarizing the strength of fields, and using dot and cross products are all physics applications of trigonometry. You can use trigonometry quite a bit in projectile motion.

Here,

The length of ladder= 65 foot

It rest at a wall at height of 60 foot.

So distance of foot of ladder from wall,

=√(65²-60²)

=√625

=25 foot

Now, as the ladder is shifted, it rest on the wall at height of 52 foot.

=√(65²-52²)

=√1521

=39 foot

Shift in the base of ladder,

=39-25

=14 foot

As the updated distance is 39 feet and the previous distance was 25 feet, Naoki moved the base of the ladder up by 14 feet.

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0.1717 is Probability that none has ever been married from selected 5 young women in age category at random.

In the question we have,

the number of females age 20 to 24 has never been married = 70.3%

the number of young women in this age category (20 to 24) at random = 5

We shall find out the probability that none has been maaried from selected group of 5 females.

Probability of female age 20 to 24 has never been married = 0.703

So, the probability that none has been married from selected group of 5 females ( p)= 0.703×0.703×0.703×0.73×0.73

= 0.1717

Therefore, The probability that none has ever been married is 0.1717.

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81 of 270 pages in a book is a part of the situation.

A division is a process of splitting a specific amount into equal parts.

Given,

81 of 270 pages in a book.

Eighty one of two hundred seventy pages in a book.

In the given situation, A book has 270 pages in that we have taken 81 pages which are part of the book.

We have taken pat of the book,

In the given situation, book is whole and 81 is the part.

Hence  81 of 270 pages in a book is a part of the situation.

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The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.

So, the ratio of gallons of blue paint to gallons of yellow paint is

= 5 to 9  or 5:9

Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint

= 1- 5/9

=4/9

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Answer:

Step-by-step explanation:

interior angles of polygons:

180(n-2)

1. =180(11-2)

=180(9)

=1620

2. 180(17-2)

=180(15)

=2700

When the directrix is at x = 5 and  point in the vertex is at h = 2. Then P would be -3

In the equation of parabola, P is defined as the distance between the directrix and the vertex

The vertex is defined by the points V ( h, k )

h is for the x coordinate

k is for the y coordinate

when the directrix is given in the x, we solve for P using h

P = h - point given for directrix

P = 2 - 5

P = -3

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The solution to the equation given as √|x|² = x is x ≥ 0

From the question, the representation of the equation is given as

√|x|² = x

To start with;

We evaluate the square root expression in the equation

So, we have the following representation

|x| = x

The above implies that the absolute value of a number equals the number

As a general rule of absolute values, the absolute value of a number is positive

This can be represented as

x ≥ 0

Hence, the solution to the equation is x ≥ 0

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There is a 0.33 percent chance that a woman is the owner of each of the firms identified. Therefore, there is a 0.036 percent chance that women own ALL three of the called businesses.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The probability that each of the firms called is owned by a woman is 0.33. Therefore, the probability that ALL three of the firms called are owned by women is:

percentage=0.33*0.33*0.33

percentage=0.035937

=0.036

There is a 0.33 percent chance that each of the businesses is run by a woman. As a result, there is a 0.036 percent chance that women own ALL three of the businesses mentioned.

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Answer:

Step-by-step explanation:

The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!

Answer:

1/23

Step-by-step explanation:

The slope of the linear equation is 0, and the solution of the second equation is x = 10.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

So if the line passes through (-12, 6) and (4, 6), the slope is:

slope = (6 - 6)/(4 + 12) = 0

The slope is 0.

2) How to solve the equation for x?

Here we have the equation:

2/8 = 3/(x + 2)

If we move the denominators we get:

2*(x + 2) = 3*8

2x + 4 = 24

2x = 24 - 4

2x = 20

x = 20/2 = 10

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2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given that, Ariana purchased two drill set from a sale, each of them costs $25 less than its original price,

If f is the original price, then she must have purchased it at (f-25) and for two sets it's 2(f-25)

She paid $86 for her purchase, so,

2(f-25) =  $86

Hence, 2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.

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Answer:

A

Step-by-step explanation:

∠ A = ∠ P

∠ C = ∠ R

AC = PR

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

The included side is the side between the vertices of the 2 angles.

Then the triangles are congruent by the ASA postulate

The surface area of the triangular prism is  936 cm².

In geometry, a triangular prism is a three-sided prism.

Therefore, the surface area of the triangular prism can be calculated as follows:

surface area of triangular prism = bh + L(x + y + z)

where

Therefore,

surface area of triangular prism = 24 × 18 + 7(18 + 30 + 24)

surface area of triangular prism = 432 + 7(72)

surface area of triangular prism = 432 + 504

surface area of triangular prism = 936 cm²

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Slope:

The slope is found with m = (y2 - y1) / (x2 - x1).

You can use any two points, so I'd pick ones with positive x and y values.

Using (1,5) and (3,3):

    m = (3 - 5) / (3 - 1) = (-2)/(2) = -1

The slope is -1.

To find the y-intercept, we can go to the point (-1,7) and use the slope of -1.  A slope of -1 means that if x goes up by 1, then then y goes down by 1.  So if we go from x=-1 to x=0, then the y-value of 7 will go down by 1.

y-intercept (0,6)

The equation in slope-intercept form is y = -x + 6, since we already found the slope and y-intercept.

The formula for nth term in the given arithmetic sequence is 10 - 3n

For an nth term in an arithmetic sequence

U(n) = a + (n - 1)d

Where n is the number of terms

a is the first term

d is the common difference

From the sequence above

a = 7

d = 4 - 7 = - 3

The formula for an nth term is

U(n) = 7 + (n - 1)-3

= 7 - 3n + 3

Hence, the formula for nth term is 10-3n

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Dean halverson recently read that full-time college students study 20 hours each week. 0.000519 is the p -value.

Given :

Population mean, μ = 20

Sample mean, xbar = 22.4

Sample standard deviation, s = 3.7

Sample size, n = 31

The hypothesis :

H0 : μ = 20

H0 : μ > 20

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (22.4 - 20) ÷ (3.7/√(31))

T = 2.4*5.6 ÷ 3.7

Test statistic = 3.632

Using the Pvalue calculator :

df = n - 1 = 31 - 1 = 30

Pvalue(3.632, 30) = .000519.

The p-value is .000519.

The result is significant at p < .05

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Answer:

Step-by-step explanation:

a) 1/2 of 18 = ?

→ 1/2 of 18

→ (1/2) × 18

→ 18/2 = 9

So, answer is 9.

b) 2/3 of 27 = ?

→ 2/3 of 27

→ (2/3) × 27

→ 54/3 = 18

So, answer is 18.

Answer:f(10) or the power generated by the wind turbine at the wind speed of 10 m/s is 190.26 kW

Answer:

it is important because this will be helpful for your incomes, tax, bills etc. This also will plan for other things that you might pay like savings.

Step-by-step explanation: