Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 2), (2, 4), (3, 8), (4, 16)

Part A: Is this data modeling a linear function or an exponential function . (2 points)

Part B: Write a function to represent the data. Show your work. (4 points)

Part C : Determine the average rate of change between day 2 and day 4. Show your work (4 points )

He may keep 82 movies on each shelf, using up to 492 movies and leaving 3 movies to retain.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. Arithmetic operators carry out operations on numbers. Variables are assigned values using assignment operators. Logical operators compare two values and return either "true" or "false" depending on whether the comparison is true (or false).

Here,

Movies that movie store has=495 movies

Number of shelves=6

If the owner wanted to make sure each shelf had the same number of movies,

=495/6

=82.5

He can keep 82 movies in each shelf that will use up to 492 movies and 3 movies will be left to keep.

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Two similar triangles have,

The ratio of two sides of one triangle  = Ratio of two sides of the other triangle

The distance between Alanton and Bishop is 14 miles.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

Alanton:

16 miles from Oakley.

8 miles from Crawford.

28 miles from Fayeville

We can have two similar triangles as shown below.

Two similar triangles have,

The ratio of two sides of one triangle  = Ratio of two sides of the other triangle

AB / AC = DE/ DF

8 / 16 = x / 28

1/2 = x/28

x = 28/2

x = 14

Thus,

The distance between Alanton and Bishop is 14 miles.

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The graph of line 3x-y= -1 will be as follows.

What is a line?

A line is an endlessly long, straight object that, despite being drawn with a minimum width, is considered to have no particular width in mathematics.

Main Body:

slope = m = 3     point = (0,1)

The formula for one point form for a line is -

y-y₁ = m(x-x₁)

y- 1 = 3(x-0)

3x-y =-1

Now the graph for the line will be plotted by using the point given and the slope--

on Graph mark the point (0,1)

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Answer:

Note: A percentage is always a number over 100.      (34% = [tex]\frac{34}{100}[/tex])

Cost of meal = 100%

Cost of tip = 34%

Total = 134%

134% = [tex]\frac{134}{100}[/tex]

To find the total and the tip, you must multiply it by [tex]\frac{134}{100}[/tex]

Answer:

Bill times the 0.34 percent equals the price of the tip. After you find what the tip is, you add the base price (the bill price) to the tip and you get the total number paid. However, another way you can solve (in one step) this is by adding 1.00 to the percent you are multiplying by which in this case we add 0.34 by 1.00 and this gives us 1.34. Suppose we set the bill to 4 dollars and use the normal way (2-step equation) by doing 3(0.34) which is 1.02 and 1.02 + 3 = 4.02 as our final answer / final bill. However, when we do our one-step equation, we can write this as 3x(1.34) and this is equal to 4.02.

1st Step

Bill(0.34) = tip

tip + bill = total

2nd Step (one-step equation)

Note: we are going to set the bill in this equation as $4

4(1.34) = total; Total = 4.02 ← We added 1.00 to the tip percentage in decimal form.

There is a change of 1/2 for Adam to get strictly more heads than Ben.

The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)

If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.

Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.

Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.

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Answer:

x=2/11 + (1/11) (√15) or 2/11 - (1/11) (√15)

Step-by-step explanation:

Plug it into the quadratic formula

The values of x are 9/11 and -5/11.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To use the quadratic formula to solve 11x² - 4x = 1.

We first need to rewrite the equation in the form ax² + bx + c = 0.

So,

11x² - 4x - 1 = 0

Now,

We can use the quadratic formula, which states that the solutions for the equation ax² + bx + c = 0.

x = (-b ± √(b² - 4ac)) / 2a

Now,

In our case,

a = 11, b = -4, and c = -1.

Substituting these values into the formula, we get:

x = (-(-4) ± √((-4)² - 4(11)(-1))) / 2(11)

x = (4 ± √(196)) / 22

x = (4 ± 14) / 22

So,

The solutions for the equation 11x² - 4x = 1

x = (4 + 14) / 22 = 9/11

x = (4 - 14) / 22 = -5/11

Therefore,

The values of x are 9/11 and -5/11.

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Check the picture below.

so the rocket will hit the ground when y = 0, so hmmm, there's no simple factoring that'd give us integers, so we'll plug the quadratic into the quadratic formula

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+240}x\stackrel{\stackrel{c}{\downarrow }}{+115} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (240) \pm \sqrt { (240)^2 -4(-16)(115)}}{2(-16)} \implies x = \cfrac{ -240 \pm \sqrt { 57600 +7360}}{ -32 }[/tex]

[tex]x= \cfrac{ -240 \pm \sqrt { 64960 }}{ -32 }\implies x=\cfrac{ -240 \pm 8\sqrt { 1015 }}{ -32 }\implies x=\cfrac{ 240 \mp 8\sqrt { 1015 }}{ 32 } \\\\\\ x=\cfrac{ 30 \mp \sqrt { 1015 }}{ 4 }\implies x\approx \begin{cases} -0.46\\\\ 15.46 ~~ \textit{\large \checkmark} \end{cases}[/tex]

now, let's notice, "x" cannot be negative, so the negative value is tossed.

Answer:

  875 cm³

Step-by-step explanation:

You want the volume of the 15 cm high frustum of a 30 cm high pyramid with a 10 cm square base.

The volume of a pyramid is given by the formula ...

  V = 1/3Bh

Where B is the area of the base:

  B = s²

For the given pyramid, the volume is ...

  V = 1/3(10 cm)²(30 cm) = 1000 cm³

The volume of the frustum is the volume of the whole pyramid, less the volume of the part that is cut off. The part that is cut off has dimensions that are 1/2 of those of the whole pyramid, so its volume is ...

  V = (1/2)³ × (1000 cm³) = 125 cm³

Then the volume of the remaining frustum is ...

  1000 cm³ -125 cm³ = 875 cm³

The volume of the frustum is 875 cm³.

__

Additional comment

The volume can also be calculated from the areas of the two bases of the frustum and its height.

  V = (1/3)(B₁ +B₂ +√(B₁B₂))h

The top base is 5 cm square, so this evaluates to ...

  V = (1/3)(100 cm² +25 cm² +√(100·25) cm²)(15 cm) = 1/3(175 cm²)(15 cm)

  V = 875 cm³

Answer:

Step-by-step explanation:

they will sprint 75 yard in total

Answer:

1870

Step-by-step explanation:

10 x 2 = 20

25 x 2 = 50

50 x 2 = 100

20 + 50 + 100 = 170

170 x 11 = 1870

I cried over this problem so you dont have to :)

For all proportional relationships, the true statements are:

A, D, and E.

A proportional relationship between two variables x and y is written as:

y = k*x

Now let's analyze each of the given statements:

A) The origin is the point (0, 0).

If you evaluate the general equation in x = 0 you get:

y = k*0 = 0

So yes, this equation passes through the point (0, 0).

B) This is false, as we saw above.

C) The formula for the constant of proportionality is:

y = k*x

y/x = k

So we can see that k = rise/run

the statement is false.

D) Yes, this is true, a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept, particularly if the y-intercept is zero, then we have a proportional relation.

E) Yes, slope, unit rate, constant of proportionality, are all equivalent terms for a proportional relation.

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The angle ∠C is 130° by the alternative angles.

Given that,

In the figure we have a diagram.

We have to find the angle c.

The angles created on the opposing side of the transversal with regard to both straight lines when two straight lines are cut by it are referred to as alternative angles. Therefore, the angles that are on the opposing sides of the transversal and have distinct vertices are those.

We know that,

By alternative angles

∠M=∠C

So,

130°=∠C

Therefore, The angle ∠C is 130° by the alternative angles.

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On solving the system of equations by substitution method , the solution is x = 0 , y = 1 and x = 4 , y = 9    .

In the question ,

it is given that

the system of equation is

y = x² - 2x + 1

y = 2x + 1

by using substitution method ,

Substituting y = 2x + 1 in y = x² - 2x + 1

we get

2x [tex]+[/tex] 1 [tex]=[/tex] x² - 2x [tex]+[/tex] 1

x² - 2x [tex]+[/tex] 1 - 2x - 1 [tex]=[/tex] 0

x² - 4x = 0

x(x-4) = 0

So , x=0      or    x = 4

for x=0 , y = 2x+1 = 1

for x = 4, y = 2(4) + 1 = 9

Therefore, the solution for the system of equations is x=0 , y=1 and x=4 , y=9    .

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Based on the information illustrated, the analysis implies the following:

a. nonstatistical.

b. statistical.

c. nonstatistical

d. statistical

A statistical question is one that can be answered by collecting varying amounts of data. A statistical question is one that does not have a single answer. Instead, you should expect a range of responses.

Identifying a statistical question necessitates knowledge of statistics. Statistics is a mathematical study that involves the collection, analysis, and interpretation of changing data. A statistical question will ask a question with a variable answer; data must be collected and analyzed, and the answer will provide an explanation of the information.

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statistical or nonstatistical  What's the difference? is that statistical is of or pertaining to statistics while nonstatistical is not statistical.

Statistical sampling is more objective and uses probability to determine the appropriate sample size. While it is does not eliminate sampling risk, statistical sampling allows the auditor to measure sampling risk and take steps to control it. Nonstatistical sampling relies more on the auditor's judgment.

Thus, the correct answer is nonstatistical statistical nonstatistical statistical

Answer: 70%

Step-by-step explanation:

Percentage is always out of 100. And 10x10 =100 so you do the same to 7 multiply it by ten then your answer is 70 which is 70%.

The maximum area is 640,000.

Given fencing yards = 3200

let the length be x and the width be y

The parameter of the rectangle is given as;

2(L + B),that is

2(x + y) = 3200

x + y = 1600

y = 1600-x

let the area of the rectangle be A, then

A = x y

A = x(1600-x)

A = 1600x - x^2

finding the maximum derivative of A with respect of x

da/dx = 1600 - 2x

set da/dx to zero,

1600 - 2x = 0

1600 = 2x

x = 1600/2

x =800

substitute the value of x = 800 in to y

y = 1600 - 800

y = 800

The maximum area is 800 x 800

Therefore Maximum area = 640,000.

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The two trains will pass each other after 7 hours.

Both trains need to cover a distance of 525 miles before they cross each other.

We know, d = s × t

where d ⇒ total distance travelled

s ⇒ speed of the train

t ⇒ time taken for both trains to meet

For train A,

s = 30 miles per hour

Distance covered by train A in t hours = 30 × t

For train B,

s = 45 miles per hour

Distance covered by train B in t hours = 45 × t

As the total distance is 525 miles,

30t + 45t = 525

75t = 525

t = 7 hours

Hence, the trains will pass each other after 7 hours.

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The number of minutes after Cayaln puts the trays in the oven will he first remove the scones, muffins, and cookie at the same time is 300 minutes

Find the least common multiple of 25, 12 and 10 minutes

The least common multiple of of 25, 12 and 10 minutes is 300 minutes.

Therefore, the number of minutes Cayal removes the scones, muffins, and cookie at the same time is 300 minutes

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Answer:

x=17

It just is. I don't know how to explain it.

The greater factor of 432, if 12 is the greatest common factor between the two factors is 36

The Greatest Common Factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The factors of 432 are 36,12, 24 ,18,4,108

But the two factors of 432 that has a multiple of 12 is 12 and 36

12× 36 = 432

The factors of 12 = 1,2,3,4,6,12

The factors of 36 = 1,2,3,4,6,9,12,18,36

the common factors are ; 1,2,3,4,6 and 12

therefore the greatest common factor = 12

since the GCF between 12 and 36 is 12, the second number will be 36

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The size of angle x is 54 degrees.

Let O be the complete angle,

<O = 360

Angle between diagonals = 360/5 = 72 degrees.

All diagonals of regular pentagon are equal and their opposite angles are equal .

With angle center O it forms a triangle:

sum of angles = 180

x + x + 72 = 180

2x + 72 = 180

2x = 180 - 72

2x = 108

divide by 2 on both sides

2x/2 = 108/2

x = 108/2

x = 54 degrees.

Therefore the size of angle x is 54 degrees.

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The ratio of 15 and square of m is 15/m².

A ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities. This ultimately implies that, a ratio can be expressed as a quotient.

In Mathematics, quotient can be defined as a mathematical expression that is simply used to represent the division of a numerical value by another numerical value or variable.

In this scenario, the numerical value 15 would be the numerator while the variable m would be the denominator, and it should be expressed as follows:

Ratio = 15/m²

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24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.

Here,

Since there are 5 peoples,

let us fix the first person and remaining will be set according to that.

this can be arranged in,

(5-1)!=4!

=24 ways

When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.

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Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

Given,

In the question:

Why are the tops of mountains round and the soil often rough, rocky, and thin in many places in the Northeast?

Now, According to the question:

The correct answer is:

Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

Other question is

4 + 2

By addition:

4 + 2 = 6

Hence, Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

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Answer:

Step-by-step explanation:

50 would be the reliability of that measure  by standard error.

What is the standard deviation?

A measure that has no random error and no true score (i.e., is only random error) has zero reliability. A measure that has random error.

50 would be the reliability of that measure .

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The values of a and b are 8 and - 9.

Given that:

f(x) = x + a/x + b ........ (1)

f(1) = 0, f(2) = - 3

Putting the value of x = 1 in equation (1). We get,

f(1) = 1 + a/1 + b

f(1) = 1 + a + b ....... (2)

Putting the value of x = 2 in equation (1). We get,

f(2) = 2 + a/2 + b

f(2) = (4 + a + 2b)/2 ........ (3)

Putting the value of f(1) = 0 in equation (2). We get,

a + b = - 1 ......... (4)

Putting the value of f(2) = -3 in equation (3). We get,

=> -3 = (4 + a + 2b)/2

=> -6 = (4 + a + 2b)

=> a + 2b = - 10 ......... (5)

To find the value of a and b we have to solve equations (4) and (5) by elimination method.

So, for that subtract equation (4) from (5).

We got the value of b = - 9.

Then put the value of b in equation (4).

We got the value of a = 8.

Checking the value of a and b satisfies the value of the function's output and input.  

Hence,  the values of a and b are 8 and - 9 respectively.

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The number of the given statement will be inequality -2 < x <  4.

We have been given the statement "the sum of five times a number and three is between -7 and 23".

Let the number would be x

As per the given statement, we can represent this algebraic form with inequality as:

⇒ -7 < 5x + 3 < 23

Subtract 3 on both sides of the above inequality

⇒ -7 - 3 < 5x  < 23 - 3

⇒ -10 < 5x <  20

Divided by 5 into both sides of the above inequality

⇒ -2 < x <  4

Thus, the number of the given statement will be inequality -2 < x <  4.

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The question seems to be incomplete the correct question would be

Find the number if the sum of five times a number and three is between -7 and 23.

The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.

Find the greatest common factor of 32 and 48

The greatest common factor of 32 and 48 is 16

So, the greatest number of bags Caesar can make is 16 bags

Number of pasta in each bag = 32/16

= 5 boxes of pasta per bag

Number of sauce in each bag = 48/16

= 8 jars of sauce per bag

If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.

He could use 8 bags but this is not the greatest number he could use.

Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.

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The probability of getting at least one question right is 96.875%.

The question states that at least one guess should be right. This ultimately means that all guesses cannot be wrong, which is the only possibility being excluded here.

Probability for wrong guess =12=0.5

Probability for all wrong guesses =0.5*0.5*0.5*0.5*0.5=0.03125 or 3.125%

There is only 3.125% chance of all wrong guesses. Rest of the possibilities are our favorable conditions, i.e. at least one correct guess.

Therefore,

Probability of at least one correct guess=1-0.03125=0.96875 or 96.875%

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