Use the information to answer the question.
Two triangles are shown.
R
75⁰
20
X
60°
16
XX75°
Y
60°
not drawn to scale
How can AA criterion be used to show that A POR and A XYZ are similar? Move options to the blanks to complete the steps.
Z
1. Translate A PQR to take point Q to point
2. Rotate the image of A PQR so that the image of side QP aligns with side
3. Dilate the image of A POR to take point P to point
4. Show that the image of side PR aligns with side
N
N
XZ
and the image of side QR aligns with side
YX
YZ

The probability that the number of these selected teens that have heard of a fax machine is exactly six is 0.225 and the probability that the number is more than 8  is 0.064.

The first probability can be calculated using binomial distribution formula, where the number of success (teens who have heard of a fax machine) is 6 and the number of trials is 12. The probability of success is 0.49. The calculation is:

[tex](12 choose 6) * (0.49)^6 * (0.51)^(12-6) = 0.225[/tex]

The second probability can be found by summing the probabilities of having more than 8 teens out of 12 who have heard of a fax machine. This can be calculated using binomial distribution formula for 9, 10, 11, and 12 success. The calculation is:

[tex](12 choose 9) * (0.49)^9 * (0.51)^(12-9) + (12 choose 10) * (0.49)^10 * (0.51)^(12-10) + (12 choose 11) * (0.49)^11 * (0.51)^(12-11) + (12 choose 12) * (0.49)^12 * (0.51)^(12-12)\\ = 0.064[/tex]

So the answer is (0.225, 0.064).

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The volume of the solid generated by revolving the plane region about the x-axis is 125/6 units3.

The volume of the solid generated by revolving the plane region about the x-axis can be found by using the Shell Method. This method involves integrating the area of the cross-section of the solid with respect to the x-axis. The area of the cross-section can be found by calculating the area of the region bounded by the curve y=x and the origin, which is a triangle. The area of the triangle is 1/2 * base * height, or 1/2 * x * x. The definite integral that represents the volume of the solid is then given by:

[tex]V = ∫0 x (1/2 x2) dx[/tex]

Evaluating this integral yields[tex]V = (1/6 * x3)|0x[/tex]. Plugging in x=0 and x=5 yields [tex]V = (1/6 * 53)|0x = 125/6[/tex] units3. Therefore, the volume of the solid generated by revolving the plane region about the x-axis is 125/6 units3.

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A) The average velocity for the time period [1, 1.01] is equals to the -22.23 ft/s.

ii) The average velocity for the time period [1, 1.005] is equals to -22.115 ft/s.

iii) The average velocity for the time period [1, 1.001] is equals to -22.023 ft/s.

B) The estimate value of the instanteneous velocity when t = 1s is equals to -22 ft/s.

The average velocity over an interval [a,b] for a defined position function f(t) can be displayed by the difference quotient {f(b)-f(a)}/{b-a}. When these two points come very close to each other and at any point both of them appear almost the same point then the average velocity becomes instantaneous velocity at that time, which is also the derivative of the function at that point. We have, baby alien throw a ball into the air with a velocity of 24 ft/s on planet. The height in feet or

the displacement relation is defined as ,

y (t) = 24t - 23t².

where, y--> displacement/height

t --> time

Initial time , to = 1 sec

Therefore, the velocity will be

dy/dt = v(t) = 24 - 46t

A) The average velocity on an interval [a,b] is

Vₐᵥ = { y( b) - y(a) }/(b - a)

Now, see the intervals ,

Vₐᵥ = {y( 1.01) - y(1)}/(1.01 - 1)

= {24(1.01) - 23(1.01)² - 24×1 + 23× 1 }/0.01

= {24.24 - 24 - 23.4623 + 23}/0.01

= - 22.23 ft/s

Vₐᵥ = {y( 1.005) - y(1)}/(1.005 - 1)

= {24(1.005) - 23(1.005)² - 24×1 + 23× 1 }/0.005

= -22.115 ft/s

Vₐᵥ = {y( 1.001) - y(1)}/(1.001 - 1)

= {24(1.001) - 23(1.001)² - 24×1 + 23× 1 }/0.001 = { 24.024 - 24 + 23 - 23(1.001)²}/0.001 = - 22.023 ft/s

B) The instanteneous velocity is defined as V (t) = dy/dt = 24 - 46t

At t = 1 s then V(t) = 24 - 46(1) = 24 - 46

=> V = - 22 ft/s

Hence, instanteneous velocity is - 22 ft/s.

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Complete question:

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 24 ft/s. Its height in feet after t seconds is given by y = 24t - 23t².

A. Find the average velocity for the time period beginning when t=1 and lasting

.01 s:

.005 s:

.001 s:

NOTE: For the above answers, you may have to enter 2 or 3 significant digits if you are using a calculator.

B. Estimate the instanteneous velocity when t=1.

The intersection of the lines is (2, 4) which is the solution of the equations.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

y = 2x

y = -(1/2)x + 5

From equations 1 and 2, then we have

2x = -(1/2)x + 5

(5/2)x = 5

x = 2

Then the value of the variable 'y' is given as,

y = 2 (2)

y = 4

The intersection of the lines is (2, 4) which is the solution of the equations.

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Answer:

[tex]-\frac{28}{3}[/tex]

Step-by-step explanation:

[tex]\frac{-3-(-1/5)}{(1/10)-(-1/5)}=-\frac{28}{3}[/tex]

Answer:

17

Step-by-step explanation:

if the sequence is 3n+5

we do 3x4(since we are working out the 4th term) +5

3x4=12  12+5=17

Lindsay is more likely to think she sang more poorly than Nicole. It can be inferred that Lindsay is more likely to have negative self-evaluation despite the similar scores.

People with social anxiety disorder often have negative self-evaluations and experience intense self-consciousness in social situations, even if they have performed well. This can lead to feelings of shame, embarrassment, and low self-esteem.

So, even though Lindsay and Nicole received the same score, Lindsay's social anxiety disorder may cause her to believe that she performed poorly, despite receiving a high score. On the other hand, Nicole, not having social anxiety disorder, may be more likely to have a positive self-evaluation and feel confident about her performance, despite receiving the same score.

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Complete Question:

Both Lindsay and Nicole just completed a solo in a musical competition. The judges awarded them both 9 out of 10. Lindsay has a social anxiety disorder and Nicole does not. Based on this information,

____. what can be said?  

From the figure the measure of angle GEF is 122

Information from the problem says that

angle GEF is thirteen less than 5 times angle DEG and angle DEF is 149 degrees

angle GEF = 5 * angle DEG - 13

From the figure

angle GEF + angle DEG = angle DEF (adjacent angles)

substitute for angle GEF

5 * angle DEG - 13 + angle DEG = angle DEF

6 * angle DEG - 13 = 149

6 * angle DEG = 149 + 13

6 * angle DEG = 162

angle DEG = 27

angle GEF = 5 * angle DEG - 13

angle GEF = 5 * 27 - 13

angle GEF = 135 - 13

angle GEF = 122

hence angle GEF = 122

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Answer:

∠ T and ∠ Y

Step-by-step explanation:

the corresponding angles are the letters that have the same position in the names of the 2 triangles , that is

∠ R and ∠ W ( first letters in each of the 2 triangles )

∠ S and ∠ X ( second letters in each of the 2 triangles )

∠ T and ∠ Y ( third letters in each of the 2 triangles )

then the only letters ( angles ) from the list ,corresponding are

∠ T and ∠ Y

Answer:

Angle T and angle Y are corresponding angles.

a-1. The null hypothesis for the treatments is: μDay = μAfternoon = μNight

a-2. The alternate hypothesis for the treatments is: Not all means equal.

b. The decision rule for treatments is to use an analysis of variance (ANOVA) with a significance level of 0.05. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a difference in the mean production rate by shift.

c-1. The null hypothesis for the blocks is: μS = μL = μC = μT = μM

c-2. The alternate hypothesis for the blocks is: Not all means are equal. The decision rule for blocks is the same as for treatments, use an ANOVA with a significance level of 0.05. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a difference in the mean production rate by employee.

d & e. The ANOVA table is shown below:

Source SS df MS F p-value

Treatments 144.0 2 72.0 13.09 0.0047

Blocks 48.0 4 12.0 2.18 0.18

Error 60.0 8 7.5

Total 252.0 14

f-1. Based on the ANOVA results, we can reject the null hypothesis for the treatments (p-value = 0.0047 < 0.05) but not for the blocks (p-value = 0.18 > 0.05).

f-2. The results indicate that there is a difference in the mean production rate by shift, but there is not enough evidence to conclude that there is a difference in the mean production rate by employee. This suggests that the difference in production rate is due to the shift worked, rather than the specific employee.

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Water output rate of Chang family was 30 L per hour and the water output rate of Robinson family was 35 L per hour.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the water output rate of Chang family and y be the water output rate of Robinson family.

x + y = 65

25x + 15y = 1275

Multiplying the first equation throughout with 15,

15x + 15y = 975

Subtracting 15x + 15y = 975 from 25x + 15y = 1275,

10x = 300

x = 30

y = 65 - 30 = 35

Hence the water output rate of Chang family and the Robinson family is 30 L per hour and 35 L per hour respectively.

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The probability of drawing a jack or a queen or a heart from a standard 52-card deck is 1/4.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

There are a total of 52 cards in a standard playing deck, and there are 4 jacks, 4 queens, and 13 hearts.

The probability of drawing a jack or a queen or a heart is equal to the sum of the probabilities of drawing each individual card type.

So, the desired probability is:

P(jack or queen or heart) = P(jack) + P(queen) + P(heart)

= 4/52 + 4/52 + 13/52

= 21/52

= 1/4

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The displacement of the particle at t = 1 second is -3 .meters

The displacement of a particle in a straight line can be calculated using the following formula:  Displacement (d) = 2sin(πt) + 3cos(πt). This formula takes into consideration the sine and cosine of the angle, pi (π), multiplied by the time (t). The sine of the angle represents the vertical displacement, while the cosine represents the horizontal displacement.

For example, let's say we want to calculate the displacement of a particle at t = 1 second. First, we'll plug in the values into the formula:

d = 2sin(πt) + 3cos(πt)

d = 2sin(π*1) + 3cos(π*1)

d = 2sin(π) + 3cos(π)

d = 0 + (-3)

d = -3

Therefore, the displacement of the particle at t = 1 second is -3 meters.

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Answer: 15%

Step-by-step explanation:

60 cans ---------- 100%

1 can --------------- 100/60 %

9 cans -------------- (100 * 9) / 60

900/60 %

90/6 %

15%

Answer:

Step-by-step explanation:0.15

Answer:

Step-by-step explanation:

True, The demand for popcorn is determined by the number of producers that are willing and able to produce popcorn.The demand for popcorn is determined by the number of producers that are willing and able to produce popcorn.The demand for popcorn is determined by the number of producers that are willing and able to produce popcorn.

From the figure if PQRST~DEFGH then ∠P is 109 degrees and ∠F is 99 degrees.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given that PQRST is a polygon which is similar to the DEFGH

Similar polygons are two polygons with the same shape, but not the same size.

Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.

∠C≅∠T

∠P≅∠D

So ∠P is 109 degrees.

∠F is 99 degrees.

Hence, from the figure if PQRST~DEFGH then ∠P is 109 degrees and ∠F is 99 degrees.

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Answer:

x=14

Step-by-step explanation:

Half circle total degree is 180°

180°=(2x-4)+101°+47°

so, 2x-4=180-101-47

     2x-4=32

     2x=32-4

      2x=28

       x=14

Answer:

[tex]103 \: square \: inches[/tex]

Total weight of the science project is, 158.3 pounds

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Aimee weighed the four parts of her science project at 42.6 pounds, 37.25 pounds, 29.45 pounds, and 49 pounds.

Hence, Total weight of the science project is,

⇒ 42.6 + 37.25 + 29.45 + 49 pounds

⇒ 158.3 pounds

Thus, Total weight of the science project = 158.3 pounds.

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The graphed piecewise function is the one in option C.

y = x² + 2    if x < 1

y = -x + 2  if x ≥ 1

Here we can see the graph of a piecewise function.

The first part seems to be a quadratic function, with an y-intercept of 2, and ends with an open circle at x = 1, then we have something of the form:

quadratic equation for x < 1

And then we have a linear equation that has a closed circle at x = 1, so we have:

linear equation for x ≥ 1

Then the correct option is C.

y = x² + 2    if x < 1

y = -x + 2  if x ≥ 1

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Answer: [tex]\sqrt{2} *3i[/tex]

Step-by-step explanation:

1. separate using the radical rule

sqrt{-a}=sqrt{-1}\sqrt{a}

[tex]\sqrt{-18} = \sqrt{-1} *\sqrt{18}[/tex]

2. imaginary numbers

[tex]\sqrt{-1} = i[/tex]

3. solve the rest regularly

[tex]\sqrt{18} = \sqrt{2} *3[/tex]

4. combine

[tex]\sqrt{2} *3*i =\sqrt{2}*3i[/tex]

The graphs of the transformations in each case are as follows;

a) f(x) =4+4  = 8

b) f(x) = 4-3 = 1

c) f(x) = 4

d) f(x) = 4

e)  f(x) = 4

f)  f(x) = 4

The shifts, reflections, rotations and dilation operations are facilitated by transformation operations. On this note, it therefore follows that the graph of the given function as given is a straight horizontal line which is parallel to the x-axis and consequently, the transformations are as given above.

here, we get,

a) f(x) =4+4  = 8

b) f(x) = 4-3 = 1

c) f(x) = 4

d) f(x) = 4

e)  f(x) = 4

f)  f(x) = 4

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Based on the best-fitting line, the approximate weight of a catfish 33 inches long is 30pounds.

Research is a term that is often used when talking about science. This is because scientists use step-by-step research to prove what is right and what is wrong. In research, researchers try and learn something by doing experiments.

Research is a process that is carried out by turning problems into questions. Research is a step carried out with the intention of research to answer that question. Research is a project that starts with a problem that comes from an observation.

The full question is:

Sebastian decided to research the relationship between the length in inches and the weight of certain species of catfish. He measured the length and weight of a number of specimens he caught, then threw them back into the water. After plotting all of his data, he drew the line that fit best. Based on the best-fitting line, what is the approximate weight of a catfish 33 inches long?

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The solution to the two functions f(x) = 3ˣ and g(x) = -x + 4 is, 1

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The number of visitors increases exponentially as the temperature increases, and this situation can be  expressed by the function

f(x) = 3ˣ

The number of people who leave the park early depending on the change in temperature, and it  can be  expressed  by the function,

g(x) = −x + 4

the solution of both the graphs = ?

the intersection of the two curves of graphs of the functions is the solution,

Basically, it represent that,

both function have same value for particular value of x,

So,

when both functions have same value that will be our solution,

f(x) = 3ˣ

g(x) = −x + 4

it is shown in the graph, both functions are intersecting each other at x = 1

f(1) = 3

g(1) = −1 + 4 = 3

Hence, the solution for the equations is 1

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Based on the survey results, the statement that is the most accurate is B. Students who play a sport do not tend to play a musical instrument.

A table where each cell shows the frequency (or proportion) obtained for that row and column combination for the two variables.

The rows represent the categories for one category variable, the columns represent the categories of a second category variable.

Hence, from the given two-way table, it is seen that the response of the students are recorded and the statement that is the most accurate is B. Students who play a sport do not tend to play a musical instrument.

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The table below shows the survey results of 100 students who were asked 2 questions: “Do you play a sport?” and “Do you play a musical instrument?” Based on the survey results, which statement is the most accurate?

Students who play a sport also tend to play a musical instrument.

Students who play a sport do not tend to play a musical instrument.

Students who do not play a sport tend to play a musical instrument.

Students who do not play a sport also tend not to play a musical instrument.

Alternate interior angles are never supplementary would be two parallel lines being intersected by a transversal, such that one pair of alternate interior angles measures 180 degrees (i.e., they are supplementary). This would show that the statement is false and that alternate interior angles can indeed be supplementary.

When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines.

A transversal intersection of two parallel lines produces same-side interior angles, whose sum is 180 degrees. As the sum of the same side interior angles is 180 degrees therefore the angles are supplementary.

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[tex] \frac{1}{4} \sqrt{3} \: a {}^{2} [/tex]

Step-by-step explanation:

for equilateral triangle

The line that goes between the coordinates (-6, 5) & (-3, -3) has the equation y = -8/3 x + 13, as stated in the question.

A line is an infinitely long, completely straight, one-dimensional form that has no thickness and may be drawn in both directions. In order to stress that a line has no "flutters" anywhere along its length, it is occasionally referred to as a straight line or, more formally, a straight line (Casey 1893).

y - y1 = m (x - x1)

By using formula :

m = (y2 – y1) / (x2 - x1)

In other (x1, Y1)& are the two pairs on the line (x2, y2).

m = ( -3 - 5) / (-3 - (-6)) = (-8) / (-3 + 6) = -8 / 3

Due to this reason, the line has a slope of -8/3.

Afterwards when, we may input either points (-6, 5) and slope (8/3), respectively, into the generate the result of both the line to obtain:

y - 5 = -8/3 (x - (-6))

Expanding the right-hand side, we get:

y - 5 = -8/3 x + 8

Finally, rearranging the terms, we get:

y = -8/3 x + 8 + 5

y = -8/3 x + 13

Consequently, the line's equation becomes y = -8/3 x + 13 and it passes through to the coordinates (-6, 5) & (-3, -3).

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The complete question is: Complete the equation of the line through (-6,5)(−6,5)left parenthesis, minus, 6, comma, 5, right parenthesis and (-3,-3)(−3,−3)left parenthesis, minus, 3, comma, minus, 3, right parenthesis.

Answer:

Logarithmic

Step-by-step explanation:

the answer is 47 I know because Im in 8th grade