Find the midpoint of the segment with the following endpoints.
(10, 2) and (5,-7)

This does not imply that there is a one-to-one correspondence between dorm rooms and students.

A one-to-one correspondence between sets A and B if pairing of each object in A with one and only one object in B, and also another statement is when we counting one- to - one or like counting, one, two, three and so on.

In the question says that : Each and Every student assigned per room then we would be able to guarantee that there is a one-to-one correspondence between dorm rooms and students.

However, the possibility that two students could be assigned per one room, there is no way to imply that there is a guaranteed one-to-one correspondence between dorm rooms and students. It is follows only one student assign one room it is able to guarantee a one-to-one correspondence between dorm rooms and students.

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Answer:

C

Step-by-step explanation:

Answer:

option c

hope helps you

have a nice day

Answer:

There are 4 possible scenarios where given relation could not be a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Step-by-step explanation:

From Function Theory, we remember that a relation is not a function when at least one element from domain (x-coordinate) is related to one or more elements from range (y-coordinate). Hence, there are four possibilities of making the relation not a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Dependent Variable = What is measured or observed; the "data" collected in the experiment.

Experimental Group = Those participants exposed to the independent variable.

Control Group = Those participants treated just like the experimental group EXCEPT they are not.

The dependent variable is the variable that is being measured or tested in an experiment.  

For example, in a study looking at how tutoring impacts test scores, the dependent variable would be the participants' test scores since that is what is being measured.

It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.

In an experiment, a researcher is interested in understanding the effect of an independent variable on a dependent variable. Control variables help you ensure that your results are solely caused by your experimental manipulation.

A control group in an experiment does not receive the treatment. Instead, it serves as a comparison group for the treatments. Researchers compare the results of a treatment group to the control group to determine the effect size, also known as the treatment effect.

Therefore,

Dependent Variable = What is measured or observed; the "data" collected in the experiment.

Experimental Group = Those participants exposed to the independent variable.

Control Group = Those participants treated just like the experimental group EXCEPT they are not.

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Answer:

2.65 sec , 118.85 feet

Step-by-step explanation:

Given a parabola in standard form

h(t) = at² + bt + c ( a ≠ 0 )

Then the maximum occurs when

t = - \(\frac{b}{2a}\)

h(t) = - 16t² + 84.8t + 6.49 ← is in standard form

with a = - 16, b = 84.8 , then

t = - \(\frac{84.8}{-32}\) = 2.65 seconds

The ball reaches its maximum height at 2.65 seconds

Substitute t = 2.65 into h(t) for maximum height

h(2.65) = - 16(2.65)² + 84.8(2.65) + 6.49

            = - 16(7.0255) + 224.72 + 6.49

            = - 112.36 + 231.21

            = 118.85

The maximum height is 118.85 feet

Answer:

When adding or subtracting a constant outside the radical sign, it only affects the overall value of the expression, but not the square root itself. The square root symbol only applies to the value inside it, so any constant added or subtracted outside will not change the result of the square root. For example:

√(9 + 4) = √9 + √4 = 3 + 2 = 5

√(9) + 4 = 3 + 4 = 7

As you can see, adding or subtracting a constant outside the radical sign only changes the final result of the expression, but not the value inside the square root.

Answer:

the effect is when graphing the constant determines how far up or down to move it, compared to the original parent function.

Step-by-step explanation:

The required equation will be y = 3ˣ · 150

Let's start by creating the beginning of the data sample, knowing the population of bees triples each year.

Year 0 = 150

Year 1 = 450

Year 2 = 1350

Year 3 = 4050

Year 4 = 12150

If we look at the numbers, we see they are all divided by 150:

Year 0 = 150 / 150 = 1

Year 1 = 450 / 150 = 3

Year 2 = 1350 / 150 = 9

Year 3 = 4050 / 150 = 27

Year 4 = 12150 / 150 = 81

We then see the result of the division by 150 is in fact the table of multiplication by 3.

So, by inverting the operation, we can see the number of bees (y) for any given year starting from now is 150 times 3 at the power of the year (x).

Hence the required equation will be y = 3ˣ · 150

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Option D (9) is not a probability and is not a possible answer choice for a probability question.

To find the probability of the intersection of events A and B (denoted as P(A ∩ B)), we need to know how many elements are in both A and B. Since there are 2 repeated elements between the events, this means that there are a total of 7 - 2 = 5 distinct elements between them.

Therefore, P(A ∩ B) = 5/7.

Note that none of the answer choices provided match this result exactly. Option A is the closest with a probability of 4/7, but this is the probability of A alone, not the intersection of A and B. Option B (2/7) is the probability of B alone and option C (5/7) is the probability of either A or B occurring, not the intersection.

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Answer:25% because it should do it twice well there is a 50 % chance it should

Step-by-step explanation:

Answer:

The last one   5x-3y=15   This is the same as  y= (5/3)x -5

Step-by-step explanation:

5x-3y=15

Move 5x to the right (becoming negative)

-3y = -5x +15

Divide everything by - 3

y= (5/3)x -5

y intersect= -5   ( line crosses y coordinate at -5)

Slope = 5/3      From -5  you start counting  (5 up,3 right,5 up,3 right....  OR    5 down,3 left,5 down,3 left........)

Answer:

x=83

Step-by-step explanation:

The total value of angles is 360

So you have 75+97+105= 277

So x = 360-277 = 83

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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The total value of the loan in simple interest is $59,625, which is the lowest amount and hence is the best option.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Compound interest is defined as the amount of interest which has been calculated on the principal amount and the amount accumulated over the previous period.

Principal amount, P = $50,000

Rate of interest, r = 5.25% = 0.0525

Time,t = 3 years 8 months = 3 + 0.6667 years = 3.6667 years

Part A :

For simple interest, total amount is,

A = P (1 + rt) = 50,000 ( 1 + (0.0525 × 3.6667 ))

                   = $59,625

Part B :

For compounded interest. total amount is,

A = P (1 + \(\frac{r}{n}\))^(nt), where n is the number of times compounding is done in an year.

Here, n = 4, since compounding is quarterly

A = 50,000 [ 1 + \(\frac{0.0525}{4}\)] ^(4 × 3.6667)

   = $60,537.9639 ≈ $60,537.96

Part C :

For continuously compounded interest, final amount is,

A = P \(e^r^t\)

   = 50,000 \(e^{0.0525*3.6667\)

   ≈ 60,613.83

Part D :

The option of simple interest is best for the small business owner since the total value of the loan is lowest for it.

Hence the value of the loan for simple interest is $59,625, value of the loan when compounded quarterly is $60,537.96 and the value of the loan when continuously compounded is 60,613.83. Simple interest is the best option since the value of the loan is lowest for it.

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Answer and Step-by-step explanation:

First, you create an expression that equals the perimeter of the shape.

5r + 2s + 3r + 2s + 5r + 2s + 3r + 2s

Simplify

16r + 8s

Now we look at the students' expressions.

I can see that Brain's expression is equivalent to perimeter of the shape. Do you know why?

It is because his answer is the un-distributive version of our answer.

He simply took out the common number that is in 16 and 8, which 8.

So, Brian is correct.

#teamtrees #PAW (Plant And Water)

Answer:

\(1156.8cm^3\)

Step-by-step explanation:

The volume of a cone is given as:

\(V =\frac{1}{3} \pi r^2h\)

where r = radius

h = height of cone

The height of the cone is 17.7 cm and its base radius is 7.9 cm (diameter is 15.8 cm).

Its volume is:

\(V = \frac{1}{3} * \pi = 7.9^2 * 17.7\\ \\V = 1156.8cm^3\)

Answer:

1157.3cm^3

Step-by-step explanation:

voume of a cone =V=πr^2h^3

Diameter = 15.8cm

Height = 17.7cm

Radius = diameter/2

= 15.8/2 = 7.9cm

Pi = 22/7

V = 22/7 ×7.9×7.9×17.7/3

= 22/7×62.41×5.9

V = 1157.25cm^3

Hence the volume of the cone is 1157.3cm^3

to the nearest 10th

A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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If the given quantities are 10 quarters 17 dimes 40 nickels 15 pennies then the total money would be 6.35 dollars.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Quarters are worth .25 of a dollar

10 x .25 = 2.5

Dimes are worth .10 of a dollar

17 x .10 = 1.7

Nickels are worth .05 of a dollar

40 x .05 = 2

Pennies are worth .01 of a dollar

15 x .01 =  0.15

Add this together

2.5 + 1.7 + 2 + 0.15

= 6.35

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Given:

The graph shows the prices of the current year for the number of bushels.

And the table shows the prices of the previous year.

Part A: We will find the rate of change of bushels of corn in the current year.

As the graph shows a line, so, the rate of change will be the slope of the line

We will find the slope using two points.

As shown the line passes through the points (0,0) and (3,24)

So, the slope will be as follows:

So, the rate of change = $8 per Bushel.

Part B: How many dollars more in the price of a bushel of corn in the current year than the previous year.

From the table: the price of the previous year = 21/3 = $7

And form the graph, the price of the current year = $8

So, the differnce = 8 - 7 = $1

So, the answer will be:

$1 more is the price of the current year than the price of the previous year.

to measure exactly 4 quarts well first fill the 3 quart pail 2 times and pour it into the 5 quart pail and remaining answer is below.

1 US liquid quart is the same as 2 pints, 4 cups, and 32 ounces in terms of volume. It's vital to remember that a dry quart equals 4.6546 cups when converting any dry component.

A liter contains 1.057 quarts, and a quart contains 0.946 liters. This is what? Because the measurements are so similar, you can treat liters and quarts the same for many conversions.

As we an infinite supply of water and a 5 quart and 3 quart pail, and we have to measure exactly 4 quarts

so, first we'll first fill the 3 quart pail and pour it into the pail of 5 quart.

now we'll again fill the 3 quart pail and pour it into the pail of 5 quart

this time the 5 quart pail will be filled before the 3 quart pail get completely empty.

at this time; 3 quart pail is containing the 1 quart in it. now pouring into the 3 quart pail and combining with the 3 quart, it will make 4 quarts after pouring into the 5 quart pail.

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Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

A cylinder which is option B is a geometric figure which has two circular bases lying in parallel planes.

One of the fundamental three-dimensional forms in geometry is the cylinder, which has two distant, parallel circular bases. At a certain distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

The cylinder has two key characteristics, namely surface area and volume, because it is a three-dimensional form. The combined curved surface area of the cylinder and the areas of the two circular bases make up its whole surface area. A cylinder's volume is the term used to describe the three-dimensional space it takes up.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases.

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Answer:

25.67 ; 25.71 ; 25.79

Step-by-step explanation:

Give the measurement :

25.67 cm, 25.79 cm, and 25.71 cm.

Arrangement of numbers on a line plot is arranged in ascending order ( lowest to highest)

Hence,

25.67 < 25.71 < 25.79

Therefore they will follow the arrangement :

25.67 ; 25.71 ; 25.79

Answer:

_

113 -✓5

Step-by-step explanation:

_

113-(-(-✓5))

_

=113-✓5 (decimal:110.763932)

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The AA (Angle-Angle) Postulate and the SSA (Side-Side-Angle) Theorem are used to prove that two triangles are similar.

:

The AA Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that if the corresponding angles in two triangles are equal, the triangles are similar.

The SSA Theorem, on the other hand, is not a valid theorem for proving triangle similarity. SSA stands for Side-Side-Angle, which means having two pairs of corresponding sides proportional and the non-included angle congruent. However, SSA alone does not guarantee triangle similarity because it can lead to ambiguous cases where two distinct triangles can be formed.

In summary, to prove that two triangles are similar, we use the AA Postulate, which requires that the corresponding angles are congruent. The SSA Theorem, while useful in certain cases, is not a valid standalone proof for triangle similarity.

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The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

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Answer:

convert 10 hours 30 minutes to hours= 10.5

683/10.5

=65.04km/h

We start by using the quotient rule to find the first derivative of f(x):

f'(x) = -(2(6+x))/((6+x)^2)^2 = -2/(6+x)^3

Next, we can use the formula for the geometric series with ratio r = -(x-(-6))/(-6) = (x+6)/6:

1/(6+x)^3 = (-1/6)(x+6)(-1/6)^n = (-1/6) * [(x+6)/6]^n

Therefore, we have:

f(x) = (-1/6) * [(x+6)/6]^n

Substituting in the value of n, we get the power series representation of f(x):

f(x) = (-1/6) * [(x+6)/6]^n = (-1/6) * [(x+6)/6]^0 + (-1/6) * [(x+6)/6]^1 + (-1/6) * [(x+6)/6]^2 + ...

Simplifying, we get:

f(x) = 1/36 - (x+6)/216 + (x+6)^2/1296 - (x+6)^3/7776 + ...

Therefore, the power series representation of f(x) centered at  is:

f(x) = ∑ (-1/6) * [(x+6)/6]^n, n = 0 to infinity

f(x) = 1/36 - (x+6)/216 + (x+6)^2/1296 - (x+6)^3/7776 + ...

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