Which of the following is a solution set for the following graph?

The distance that exists between star A and B is given as 29.87 light years

We can solve this by creating a triangle where Point a Is star a, point b is star b and the point c is earth

the angle is given as 60 degrees

AC = 22 light years

BC = 34 light years

ab² = ac² + bc² - 2 *ac * bc* cos60

we would have to put in the values

ab² = 22² + 34² - 2 * 34 * 22 * cos 60

ab² = 484 + 1156 - 748

ab² = 892

square both sides

ab = 29.87 light years

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The questionnaire given to patients about their quality of life before and after the surgery included in the research design does add risks to the overall study design. Hence, the given statement is false.

Even though the questionnaire itself may not cause any additional physical risks, it can still have an impact on the overall study design. The questionnaire can add additional burden to the participants, who may already be dealing with physical and emotional stress from the surgery. Also, the questionnaire results may not be accurate if participants are not fully honest or unable to understand the questions being asked. Therefore, the inclusion of such a questionnaire in the research design should be carefully considered after evaluating its potential impact on the overall study.

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None of the options are correct. A variable can only hold one piece of data at a time.

A variable is a named storage location in a computer's memory that is used to store a single value. The value can be of any data type, such as a number, a string, or a boolean. A variable can only hold one piece of data at a time, meaning that it cannot store multiple pieces of data simultaneously. This is why it is important to use multiple variables if you need to store multiple pieces of data. Each variable should be given a unique name so that it can be easily referenced and identified when needed.

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If heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and standard deviation of 0.55 cm , If 20 of the plants are randomly selected , then the probability that the mean plant height is less than 9.5 cm is 0.9388  .

We can use the Z-score formula to find the probability that a randomly selected plant has a height less than 9.5 cm:

Z  = (x - mean)/(standard deviation/sqrt(sample size))  ;

Where x is the value we want to find the probability for, in this case x = 9.5

So , Z = (9.5 - 9.31)/(0.55/√20) = (0.19)/(0.123) = 1.54

Now we can use the standard normal table to find the probability that a Z-score is less than 1.54  .

From the z table ; we get , the p value is 0.9388  .

Therefore , The probability that a randomly selected plant from this species has a height less than 9.5 cm is about 0.9388  .

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Answer:$742; $38,584

Step-by-step explanation: 14% of $5,300 is $742 (0.14 x 5300). There are 52 weeks in a year so $742 x 52 weeks = $38,584.

No, Andy do not have enough loan, he need $200 more dollars to purchase Michael Jackson white glove.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Adams awesome pawnshop will lend up to 42% of the value of a borrowers collateral.

Andy want wants to use his $10000 signed Michael Jordan Rookie card. his $3000 signed Joe Montana cleats and his $2000 signed Tiger Woods golf ball as collateral for a loan.

Now, 42% of (10000+3000+2000)

= 42/100 ×15000

= 0.42×15000

= $6300

Cost of Michael Jackson white glove costs $6500

No, Andy do not have enough loan, he need $200 more dollars to purchase Michael Jackson white glove.

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The height of the triangle with area of 60 square inches and the base of 12 inches is 10 in.

An equation is an expression that shows the relationship between numbers and variables.

The area of a triangle is the amount of space it occupies. The area is the product of the base and height divided by 2. It expressed as:

Area = (1/2) * base * height

Given that the area is 60 square inches and the length of the base must be 12 inches. Let h represent the height

Therefore:

Area = (1/2) * base * height

60 = (1/2) * 12 * h

6h = 60

h = 10 in

The height of the triangle is 10 in.

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Applying the corresponding angles theorem, the values of x and y are:

x = 13

y = 24

The Corresponding Angles Theorem states that if two lines are cut by a transversal and the pairs of corresponding angles are congruent, then the two lines are parallel.

From the diagram given, we have:

63 + (5x - 8) + (7x - 31) = 180 [corresponding angles theorem]

63 + 5x - 8 + 7x - 31 = 180

12x + 24 = 180

12x = 180 - 24

12x = 156

x = 13

5x - 8 + 4y + 27 = 180

Plug in the value of x:

5(13) - 8 + 4y + 27 = 180

65 - 8 + 4y + 27 = 180

84 + 4y = 180

4y = 180 - 84

4y = 96

4y/4 = 96/4

y = 24

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For the given graphs, 3) graph represents a function.

Despite the fact that the offered collection of points does in fact depict a relation (since xs and ys are connected), the set they provided me with has two points with the same x-value: (2, 3) and (2, 3). This relation cannot be a function because x = 2 offers me two possible destinations, or two possible y-values.

The only thing I have to do to determine whether the relation they have given me is a set of points is to look at the points' x-values; if any x appears more than once, the relation is not a function.

As, there exist an image for all the elements of the given graph and there exist unique pre-image for the range.

Domain = [-6, 6]

Range = [-3, 3]

For the second graph, the image for every co-domain is 4. So, it is not a function.

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The interval of times that represents the middle 99. 7% of his finishing

times in the 400 meter race = (57, 63)

We know that the empirical rule or 68-95-99.7 rule states that for a normal distribution, 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Here, mean (μ) = 60 seconds, standard deviation (σ) = 1 second

To  determine the interval of times that represents the middle 99. 7% of his finishing times in the 400 meter race.

the 99.7% are within three standard deviations would be,

μ ± 3σ

= (60 - 3(1), 60 + 3(1))

= (57, 63)

The required interval is:  (57, 63)

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Answer:

Step-by-step explanation:

The slope of the given line in the graph is "undefined".

Slope, usually referred to as rise over run, is the "steepness" of the line.

By dividing the difference in y values between two points by the difference in x values, we may determine slope.

Thus, as the line is passing through the y axis and parallel to the x axis, the slope of the given line is undefined.

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Answer:4.5

Step-by-step explanation:

The linear model for the price of a home P=2,000t+97,000

if 1980 -> t=0 then, 1986 -> t=6 (six years later).

The two points are (t, price) -> (0,97000) and (6,109000)

we want an equation in the form y=mx+b,

the y-intercept(b) is the y=p value when x =tis 0: so b=

m is the slope: m={{y2-y1}/{x2-x1}}={{t2 - t1}/{P2 - P1}}

given two points

(t, P) = (0, 97k) and (6, 109k)

slope = (97 - 109)/(0 - 6)=2

P - 97 = 2(t - 0) < point-slope form

P = 2t + 97 < in thousands

P = 2,000t + 97,000

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Based on the information, it can be inferred that Nata has to work 7 days a week.

To calculate how many days Nata works we must perform the following mathematical operation.

We must find how many days in total Ana and Mary work together, that is, we must add the days that they work.

Based on the above, we can say that Ana and Mary work 7 days a week, so Ana could work Monday, Tuesday and Wednesday and Mary could work Thursday, Friday, Saturday and Sunday.

So, Nata will have to accompany both of them every day, so she will have to work 7 days.

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Answer:

see below

Step-by-step explanation:

11: write 3 equiv ratio of 1:3, so it' could be 3:9, 2:6, 4:12

12.  20:15 = 4:3, 12:9, 8:6

A system of equations that could be used to find the number of adults and the number of children in the theatre is:

x + y = 362

y = x + 140

In order to write a system of linear equations to describe this situation, we would assign variables to the number of adults and number of cats respectively, and then translate the word problem into algebraic equation as follows:

Since the total number of adults and children at this theatre is 362, a linear equation which represents this situation is given by;

x + y = 362

Additionally, there are 140 more adults than children;

y = x + 140

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Answer:

-1.5 or 1 1/2

Step-by-step explanation:

from the graph you see on Y-axis when Y =2, x=0. so you got a point: (0,2)

then on the right lower quadrant, when x = 2, y = -1, another point (2,-1)

slope = (y2 -y1)/(x2-x1) = [2-(-1)] / (0-2) =-1.5

the way the slope's direction is, you know the slope must be negative.

Answer: about 0.79

Step-by-step explanation:

First divide 8 by 9 --> (8/9) = about 0.8889

then square that value --> (0.8889)^2 = about 0.79.

PEMDAS is your friend!

Answer:

angle 1 = 118 deg

angle 2 = 62 deg

Step-by-step explanation:

To find angle one you must know that angles 1 and 118 deg are alternate angles. Therefore since these lines are parallel, angles 1 and 118 are equal.

To find angle 2 to you must know that angle 1 + angle 2 = 180.

angles on a straight line always equal 180 deg

therefore:

180

118 -

62 deg

hope this helps :)

Answer:

m<1 = 118°

m<2 = 62°

Step-by-step explanation:

The horizontal lines are parallel.

Angles 1 and 118° are alternate interior angles of parallel lines cut by a transversal, so they are congruent.

m<1 = m<2 = 118°

Angles 1 and 2 are a linear pair, so they are supplementary. That means that their measures add to 180°.

m<1 + m<2 = 180°

118° + m<2 = 180°

m<2 = 62°

Answer: ASA

Step-by-step explanation: Hello! You can use ASA to prove that the triangles ABC and ABD are congruent.  This is because you are given two angles of each triangle.  You know that your answer should be ASA or AAA, which are the only two triangle congruence postulates that involve two or more congruent angles.  Lastly, you can use the reflexive property.  An example of reflexive property is 3 = 3, which means anything is congruent to itself.  You know that both triangles share line segment AB, meaning that they have one side and two angles that are congruent.  Since you know that the two angles and the included side are congruent, ASA proves that both triangles ABC and ABD are congruent.  I hope this helps you!

There are 5 short answer questions on the test.

Algebra is a common thread that runs through practically all of mathematics. It involves the study of variables and the rules for manipulating them in formulas.

let us assume,

x = the number of multiple choice questions worth 3 points each

y = the number of short answer questions worth 8 points each

since the test has total of 25 questions we have

x + y = 25

the algebra test is worth 100 points

3×x + 8×y = 100

by solving the system of equations

x + y = 25

3×x + 8×y = 100

we find

x = 20

y = 5

there are 5 short answer questions on the test.

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Answer: 20/3 / 1/6 is a division problem that can be simplified as follows:

20/3 divided by 1/6 = (20/3) * (6/1) = (206) / (31) = 120/3 = 40

The value of the division is 40. However, without knowing the context, it is impossible to know what the meaning of this value is. In particular, without knowing the units of 20/3 and 1/6, it is not possible to interpret the division as miles per gallon or any other unit.

It is important to note that 20/3 and 1/6 should be represented as mixed numbers (6 2/3 and 1/6) or as decimal numbers (6.66 and 0.16666) in order to be able to proceed with the division.

Step-by-step explanation:

The probability of getting orange 21% more in that large bag is 0.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

In this situation, the company claims that in the large bag of M&M's 20% of them were orange. Since the oranges are 20%, the probability of getting orange 21% more in that large bag is not possible. This will be zero.

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Note that after 15 minutes, Liam is 25 blocks away from his house. This prompt is a distance - time graph problem.

A distance-time graph depicts how far an object has moved in a given amount of time. It is a basic line graph that depicts distance versus time findings. The Y-axis represents distance. The X-axis represents time.

It should be noted that a distance-time graph depicts how the distance and speed of an item vary over time. The movement of three items over time is depicted in this graph. The slope, or steepness, of each line shows the speed of the item. In general, the quicker the item, the steeper the slope.

Note that by the 13th minute, Liam had already covered 25 blocks but remained stationary at that location for 3 minutes.

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Considering the attached image. This transformation can be described by (x' , y') = (x' -y')

Transformation refers to movements objects make especially as described on a coordinate plane

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. the four ways include

Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Examining the preimage and the image of the attached picture show that the translation involved is reflection

And the transformation rule for reflection over y axis is

(x, y) → (x, -y)

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The value of PR when the Pythagorean formula is used would be = 33.

A kite is a type of quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

The value of PR can be determined with the use of the Pythagorean formula = c² = a² +b²

where c = 65

a = 56

b = PR = X

b = c² - a²

b² = 65² - 56 ²

b² = 4225 - 3136

b² = 1089

b= √ 1089

b = 33.

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Complete question:

Quadrilateral QRST is a kite. What is PR?

As per the compound interest, the lost annual income from savings on those refunds is $21,555,000

In math the term called compound interest is defined as a type of interest that not only accrues on the principal but also on the accrued interest and the interest rates on loans are quoted in terms of annual percentage rate, which does not account for the compounding of interest, and therefore understates the true cost of borrowing.

Here we know that the 479,000 people each receive an average refund of $4,500, based on an interest rate of 1 percent.

Then the lost annual income from savings on those refunds is calculated as,

As we all know that the lost annual income is the amount of interest these people could have earned on their income, in which  the extra tax had not been deducted.

Then With $4,500 each person,

Then the total amount of the deducted income is calculated as,

=> 479,000 x 4,500 = 2,155,500,000.

Here we have the  1% interest rate, then the net return on these fund if they were saved

=> 2,155,500,000 x 1% = 21,555,000.

Therefore the total lost annual income is 21,555,000

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Answer:

672 in.³

Step-by-step explanation:

V = LWH

V = 8 in. × 12 in. × 7 in.

V = 672 in.³

Answer: D 672

Step-by-step explanation: The formula for volume is L x W x H = V so if you plug all those numbers in and multiply u get 672