An ice cube is freezing in such a way that the side length s, in inches, is s of t equals one half times t plus 2 comma where t is in hours. The surface area of the ice cube is the function A(s) = 6s2.

Part A: Write an equation that gives the volume at t hours after freezing begins. (2 points)

Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points)

Part C: After how many hours will the surface area equal 216 square inches? Show all necessary calculations, and check for extraneous solutions. (4 points)

Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.

A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.

Given :

PR is a line.

Q is the midpoint of PR. So PQ = PR.

QR = x + 9

PR = 3x + 9

According to the question, verification is

PQ = PR

X + 9 = 3x + 9

3x – x = 9 - 9

2x = 0

x = 0

Therefore, as PQ = PR

x + 9 = 3x + 9

0 + 9 = 0(3) + 9

     9 = 9

  PR = 3(0) + 9

  PR = 0 +  9

  PR = 9

Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.

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Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.

A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.

Given :

PR is a line.

Q is the midpoint of PR. So PQ = PR.

QR = x + 9

PR = 3x + 9

According to the question, verification is

PQ = PR

X + 9 = 3x + 9

3x – x = 9 - 9

2x = 0

x = 0

Therefore, as PQ = PR

x + 9 = 3x + 9

0 + 9 = 0(3) + 9

    9 = 9

 PR = 3(0) + 9

 PR = 0 +  9

 PR = 9

Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.

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The Answer is

D) x=3 and x=-4

Answer: it D

x=3 and x=-4

Answer:

C 64

Step-by-step explanation:

1. 2(2)(4)(8(2)-3(4))

2.2(8)(16-12)

3. 16(4)

4. 64

The diagonal distance across the plaza is 70.7 meters

Given,

In the question:

Elise walks diagonally from one corner of a square plaza to another.

Each side of the plaza is 50meters.

To find the diagonal distance across the plaza.

Now, According to the question:

We have been given that Elise walks diagonally from one corner of a square plaza to another. Each side of the plaza is 50 meters.

Since we know that diagonal of a square is product of side length of square and [tex]\sqrt{2}[/tex]. So we will find diagonal of our given square plaza by multiplying 50 by [tex]\sqrt{2}[/tex] .

Diagonal distance across the plaza = 50 x  [tex]\sqrt{2}[/tex] .

We know that the value of  [tex]\sqrt{2}[/tex]  = 1.41421

Diagonal distance across the plaza = 50 x 1.41421

Diagonal distance across the plaza = 70.7105 ≈ 70.7

Hence, The diagonal distance across the plaza is 70.7 meters.

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Answer: 6.5

Step-by-step explanation:

To perform this kind of exercise, it is necessary to replace the value indicated in each variable each time you find the variable in the equation.

Answer:

6.5

Step-by-step explanation:

Substitute the known variables into the equation

7(0.5) + 5 - 8(0.25)

Multiply: 3.5+5-2

Solve: 6.5

Answer:

x=5

Step-by-step explanation:

step one: distribute to get rid of parentheses. this means multiplying -3 by the numbers inside of the parentheses next to it.

-3(-6)= 18 and -3(-4x)=12x

this makes the equation now 8x+38=18+12x

step two: move x to one side of the equation. we can do this by using inverse operations, so we're going to subtract 8x from both sides.

8x-8x=0, 12x-8x= 4x.

this makes the equation now 38=18+4x

step three: isolate x. this means getting rid of the 18. to do this, we are going to use inverse operations again. this means subtracting 18 from both sides.

18-18=0, 38-18=20.

this makes the equation now 20=4x

step four: divide to get x by itself. we don't want to know what 4x is, we just want to know what plain x is. so we're going to use inverse operations for the last time and divide both sides by 4 because 4x is the same thing as saying "four times x"

20/4= 5, 4x/4=x

this makes the equation now 5=x

that's your answer, x=5. hope this helped!

[tex]f(x)=-\cfrac{1}{2}x^2 + 5x\hspace{13em}g(x)=x^2+2 \\\\[-0.35em] ~\dotfill\\\\ g(-2)=(-2)^2+2\implies g(-2)=4+2\implies g(-2)=6 \\\\[-0.35em] ~\dotfill\\\\ f(~~g(-2)~~)\implies f(6)\implies f(6)=-\cfrac{1}{2}(6)^2+5(6) \\\\\\ f(6)=-\cfrac{36}{2}+30\implies f(6)=-18+30\implies \stackrel{f(~~g(-2)~~)}{f(6)}=12[/tex]

The cost of the circular floor is $3299.77.

The space a circle takes up in a two-dimensional plane is known as the area of the circle.

For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much cloth is required to completely cover a circular table, for example.

Area of circle = [tex]\pi r^{2}[/tex]

Given in question,

[tex]\pi[/tex] = 3.14

Diameter = 33

Radius = Diameter/2

           = 33/2

           = 16.5

Area = 3.14*16.5*16.5

        = 854.865 square

Cost per square = $3.86

Cost for 854.865 square = 3.86*854.865

                                         = 3299.78

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The constant of variation when the amount of money that Mary earns varies directly with the number of hours is 8.

According to the question,

We have the following information:

The amount of money that Mary earns varies directly with the number of hours worked. And Mary earns $320 for working 40 hours.

Now, following expression can be used to express this relationship where y is the amount of money and x is the number of hours.

y = kx

320 = 40k

Dividing by 40:

k = 320/40

k = 8

Hence, the constant of variation when the amount of money that Mary earns varies directly with the number of hours is 8.

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Answer:

2.44$ per muffin

Step-by-step explanation:

15/6.15

The value of the expression in the form of the scientific notation is 7.539 x 10⁵.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may be called scientific form.

When a number is written using only the digits of the number, that is considered standard notation. Since words are not used in conventional number notation, this is the way that numbers are typically written.

The expression is (7.62 × 10⁵) – (8.1 × 10³). The expression will be solved as,

E = (7.62 × 10⁵) – (8.1 × 10³)

E = (7.62 × 10⁵) – (0.081 × 10⁵)

E = 7.539 x 10⁵

Therefore, the value of the expression in the form of the scientific notation is 7.539 x 10⁵.

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Correct P-value = 0.6386 approximately equal to 0.64.

What is Permutation Distribution?

The permutation test is a statistical technique that is becoming more popular for creating sample distributions (or sometimes called a randomization test). Similar to bootstrapping, a permutation test resamples the observed data to create the sampling distribution, or "permutation distribution," rather than assuming it.

Group 1 data(in state sudents):  2 3 3 6 2 1 1 5 3 2.5

Group 2 data(out of state sudents):1 2 2 1 2 1 4 3 9 1 12 5 2

Summary Statistics For Permutation Distribution:

Permutations Unique Values Mean St. Dev. Min Q1 Median Q3 Max

10,000 71 -0.0153 1.15 -2.91 -0.877 0.00769 0.804 3.37

Permutation Test:

Number of Permutations Test Statistic Observed Value Number of Permutations with (x1 - x2) As or More Extreme Than Observed Value Permutation     P-value

10,000 x1 - x2 -0.612 6,386 0.6386

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The graph of the proportional relationship that models Angie's earnings is given as follows:

Graph B.

A proportional relationship is defined as follows:

y = kx.

Meaning that it is a special case of a linear function, with intercept of zero, meaning that it always passes through the origin.

Angie charges a flat rate for each ride, hence her total earnings are modeled by a proportional relationship.

From the graphs given by the image at the end of the answer, the only one that passes through the origin is graph B, hence graph B could represent her earnings.

The graphs are given by the image shown at the end of the answer.

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Answer:

A

Step-by-step explanation:

an open circle on a value means that x cannot equal that value

a closed circle on a value means that x can equal that value

from the number line

closed circle at - 3 means x can equal 3

open circle at 2 means that x cannot be equal to 2

all values between - 3 and 2 are solutions for x, then

x ≥ - 3 and x < 2 or - 3 ≤ x < 2

the value for x = 2

the explanation is above

i hope i helped

Drawing an altitude and computing the side lengths of the resulting half triangle for an equilateral and isosceles triangle, would give the trigonometric functions for multiples of 30 and 45 respectively.

In a 30°-60°-90° right triangle, the longer leg is [tex]\sqrt{3}[/tex] times longer than the shorter leg, and the hypotenuse is twice as long. In a 45°-45°-90° right triangle, sides opposite to the equal angles (45°) are equal and the hypotenuse is [tex]\sqrt{2}[/tex] times the other sides.

To find the trigonometric functions of multiples of 30°, first consider a equilateral triangle of, say, side-length 2. Draw an altitude for the triangle. Each of the half triangle are 30°-60°-90° right triangle. Clearly the base will be divided into 2 equal parts of length 1 each. Now using Pythagorean Theorem on one of the 30°-60°-90° right triangle, trigonometric functions for multiples of 30° could be obtained.

Draw x and y axis. Now take a length of , say , 2 in the x-axis and using a compass pointed at origin and mark the point on y axis with a length 2. Now join these points on x and y axis. A 45°-45°-90° isosceles right triangle with side-length 2 is obtained. Now using Pythagorean Theorem, trigonometric functions for multiples of 45° could be obtained.

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Therefore the solution of this problem is a)critic value t = 2.8982 b)margin of error=  2.985146

In statistics, the standard deviation measures how widely distributed or how much a set of values might vary. In contrast to a high standard deviation, which indicates that values are widely dispersed, a low standard deviation indicates that values are typically close to the set's mean.

Here ,

where s is the sample's standard deviation

Finding the number of degrees of freedom is the first step in solving this problem. The sample size has been reduced by 1.

So

df = 18 - 1 = 17

99% confidence interval

We must now determine the value of T, which can be done by consulting the t table, which has 17 degrees of freedom (on the y-axis) and a confidence level of).

[tex]1 - \frac{1-0.99}{2} =0.995[/tex]

So we have T = 2.8982.

The margin of error is:

M = T*s = 2.8982*1.03 = 2.985146

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The equation that represents this situation is y=  4x

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

Point = (8, 36)

This point can be represented as

(x, y) = (8, 36)

From the above parameter, we can calculate the constant of variation

The constant of variation is calculated as

Constant of variation = y/x

Substitute the known values in the above equation

So, we have the following equation

Constant of variation = 36/8

Evaluate the quotient

Constant of variation = 4

Recall that:

Constant of variation = y/x

So, we have

y/x = 4

This gives

y = 4x

Hence, the equation is y = 4x

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The solution to the given system of equation has exactly one solution at (0,2).

The addition property of equality is used in the elimination technique to solve systems of linear equations.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given pair of equations is

18x - 2y = -4  ....(i)

4x - y = -2    .....(ii)

To solve the equation apply elimination method.

Multiply equation (ii) by 2 and subtract it from (i):

18x - 2y = -4

8x - 2y = -4

(-)  (+)     (+)

_________

10x = 0

x = 0

Putting x = 0 equation (ii)

0 - y = -2

y = 2

So there is exactly one solution (0,2).

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The solution to the given system of equation has exactly one solution at (0,2).

Which property is used in elimination method?
The addition property of equality is used in the elimination technique to solve systems of linear equations.

What is elimination formula?

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Given pair of equations is
18x - 2y = -4  ....(i)
4x - y = -2    .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-)  (+)     (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
So there is exactly one solution (0,2).

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The answer to this Question based on Linear pair is 180 degree

What is Linear Pair?

A linear pair is a pair of adjacent angles that are supplementary, meaning they add up to equal 180 degrees. Linear pairs can be found in many shapes and geometric shapes, such as squares, rectangles, and parallelograms. Linear pairs can also be found in the angles of intersecting lines. When two lines intersect, four angles are formed, and two of them will always form a linear pair. Linear pairs can also be found in circles, as the angles formed by two chords that intersect with each other will always form a linear pair.

Suppose any triangle we are given 6 angles in which 3 are interior and 3 are exterior

suppose we take any pair of interior and exterior and we can see that it will always form a linear pair and its sum will be equal to 180 degree

Here in this question sum of angle 1 and 2

sum of angle 5 and 6

sum of angle 3 and 4

all will be same and will be equal to 180 degree by Linear Pair

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Answer:

a,b,c

Step-by-step explanation:

a) m∠3 + m∠4 = 180°

b) m∠2 + m∠4 + m∠6 = 180°

c) m∠2 + m∠4 = m∠5

these are the correct answers  for edge 2023 geometry assignment; Triangle Angle Theorems

hope this helps!

Answer:

2 5/6 OR 3

Step-by-step explanation:

1. Divide Both sides by four.

2. -15/-4 can be simplified to 15/4 by removing the negative sign from both the numerator and the denominator.

3. Add 1/2 to both sides

4. Least common multiple of 4 and 2 is 4. Convert 15/4 and 1/2 to fractions with the denominator 4.

5. Since 15/4 and 2/4 have the same denominator, add them by adding their numerators.

6. Add 15 and 2 to get 17.

7. Multiply each side by 2/3, the reciprocal of 3/2 (cancel out 3/2 and leave only X)

8. multiply 17/4 by 2/3 by multiplying numerator times numerator and denominator times denominator.

9. By doing the multiplications 17x2/4x3 you should get 34/12

10. Reduce the fraction 34/12 to lowest terms by extracting and cancelling out 2.

11. You should get 17/6.

Final Step: if you are asked for a mixed number, the answer is 2 5/6 OR if asked for a decimal, put 2.833333333 or 3 IF asked to round.

Answer:

3+3+3+3+3+3+3+3+3=27

Step-by-step explanation:

just add it together.

Answer:

(not a possible parabola)

Step-by-step explanation:

see the plot...

$7325.98  is the amount you have in the account in 5 years

Compound interest is the interest determined on the principal and the interest accumulated over the previous period.

Given that: You deposit $6000 in an account earning 4% interest compounded monthly.

Amount (A) = P(1+r)^t

Where P is the principal, r is the interest rate and t is the time

P = $6000, r =  4% / year = 4/12 = 1/3 % / month = 1/300 , t = 5 years = 5×12 = 60 months

A = P(1+r)^t

A = 6000(1 + 1/300)⁶⁰

A = $7325.98

Thus, you will have $7325.98  in the account in 5 years

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The decimal fraction as a decimal number.14,25

What is decimal?

The base-10 number system, arguably the most widely used number system, is referred to as decimal. The 10 single-digit digits of the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number following nine is 10. 19 is followed by 20, and so on.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

14 25/100= 14*100+25/100=

1400+25/ 100

= 1425/100

= 14.25

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Answer:

2

Step-by-step explanation:

y would be the first number in the equation on the left side of the equal sign. This looks lik the y=mx+b formula, so m, being slope, would be 7, -3 would be x, and b would be 4.

Answer: it’s already in its simplest form

Step-by-step explanation:

Answer: The fraction [tex]\frac{1}{12}[/tex] is already at its simplest form.

Step-by-step explanation: Sorry if this isn't correct, hope this helps!

 168 divided by 12  is 14.

 14 <-- quotient

 ---

168

  12

  --

   48

   48

   --

      <-- remainder

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