A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 2/5 the height on each successive bounce. (a) Write a function representing the rebound height for each bounce. (b) Graph the function. (c) After how many bounces would a new softball rebound less than 1 inch?

f(x) = 25(0.4)x; 6 bounces.
f(x) = 0.4(25)x; 6 bounces.
f(x) = 25(0.4)x; 4 bounces.
f(x) = 0.4(25)x; 4 bounces.

We find that Grayson charges more than Ian when the number of hours of service h is less than 2.

To determine for how many hours Grayson charges more than Ian, we can set up an equation where the cost of Grayson's tax preparation service is greater than Ian's service. Grayson charges $35 per hour plus a $35 administration fee, while Ian charges $45 per hour plus a $15 administration fee. The number of hours for which the service is required is represented by h.

Grayson's total charge for h hours would be:

Grayson's Cost = $35h + $35

Ian's total charge for h hours would be:

Ian's Cost = $45h + $15

To find the number of hours where Grayson's cost is more than Ian's cost, we set Grayson's Cost > Ian's Cost:

$35h + $35 > $45h + $15

Simplifying, we get:

$35h - $45h > $15 - $35

-$10h > -$20

Dividing both sides by -10 (and remembering to reverse the inequality when dividing by a negative):

h < 2

Thus, Grayson charges more than Ian for fewer than 2 hours of tax preparation.

Option : a is the correct answer.

            a.  rectangle.

From the figure that is provided to us we see that the cross-section is in the shape of a quadrilateral such that it has two pair of parallel sides.

b)

          circle

A circle does not have any edge or sides.

Hence, option: b is incorrect.

c)

           Trapezoid

A trapezoid is a quadrilateral with one pair of parallel sides and one pair of unparallel sides.

Hence, option: c is incorrect.

d)

             Pentagon

A pentagon is a polygon with 5 sides.

Hence, option: d is incorrect.

      Hence, the best possible answer is:

              Rectangle

The greatest Common factor of 12 and 36 is 12.

A number that divide another number is called factor.

Factors of 12 is 2, 3, 4, 6, 12

Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.

Therefore, the greatest common factor of 12 and 36 is 12.

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Final answer:

To transform x²+14x into a perfect square trinomial, add 49 to it, which is the square of half the coefficient of x.

Explanation:

The number that should be added to the expression x²+14x to change it into a perfect square trinomial is obtained by taking half of the coefficient of x, which is 14, and then squaring that value. Therefore, (14 / 2)² = 7² = 49. So, the number to be added to make x²+14x a perfect square trinomial is 49.

Answer:

The elevator will take you up at 300 feet in 36 seconds.

Step-by-step explanation:

Let the time taken to go up 300 feet be = t seconds

Given is that the elevator takes you up at 500 feet in 60 seconds.

So, we can derive a relation as:

[tex]\frac{500}{60}= \frac{300}{t}[/tex]

=> [tex]500t=300\times60[/tex]

=> [tex]500t=18000[/tex]

t = 36 seconds

So, the elevator will take you up at 300 feet in 36 seconds.

The required form can be given as,
5 thousand into standard form can be given as = 5000,
456 in word form would be written as four hundred fifty-six,
68 in point form 0.68

Given that,
To write 5 thousand, 456 and 68 hundredths in standard form, word form, and point form.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
5 thousand = 5000
456 in word form = four hundred fifty-six
Point form of 68 hundredths, = 0.68

Thus, the solution is given above in the solution part,

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Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?

Let, The amount invested in Account A=x

Then, the amount invested in Account B=2000-x

The formula of Simple Interest =[tex] \frac{Principle*Rate*Time}{100} [/tex]

Interest earned in Account A in 1 year=[tex] \frac{x*3*1}{100} [/tex]

Interest earned by Account A=[tex] \frac{3x}{100} [/tex]

Interest earned in Account B in 1 year=[tex] \frac{(2000-x)*5*1}{100} [/tex]

Interest earned by Account B=[tex] \frac{5(2000-x)}{100} [/tex]

Total Interest Earned= Interest earned by Account A+ Interest earned by Account B

Total Interest Earned=[tex] \frac{3x}{100} [/tex]+[tex] \frac{5(2000-x)}{100} [/tex]

75=[tex] \frac{3x}{100} [/tex]+[tex] \frac{10000-5x)}{100} [/tex]

75=[tex] \frac{3x+10000-5x)}{100} [/tex]

Multiply by 100 on both sides

75*100=[tex] \frac{100(10000-2x))}{100} [/tex]

7500=10000-2x

Let us subtract 7500 from both sides

7500-7500=10000-7500-2x

0=2500-2x

Adding 2x on both sides, we get

0+2x=2500-2x+2x

2x=2500

To solve for x, divide by 2 on both sides

2x/2=2500/2

x=1250

So, The Amount invested in Account A= $1250

The Amount invested in Account B= $2000-1250=$750

Final answer:

When a number in scientific notation is multiplied by 100, its exponent of 10 increases by 2 since 100 is equivalent to 10 squared (10²). For example, 3.14 x 10⁴ multiplied by 100 becomes 3.14 x 10⁶.

Explanation:

When you multiply a number in scientific notation by 100, the exponent of 10 increases by 2.

This is because 100 can be written as 10² or 10 squared.

So, if we have a number like 3.14 × 10⁴ and we multiply by 100, we are essentially multiplying by 10².

We keep the coefficient the same (3.14) and add the exponents of 10:

The resulting scientific notation is 3.14 × 10⁶, which means the exponent of 10 increased by 2 as we multiplied by 100.

Answer:

[tex](2;3)[/tex]

Step-by-step explanation:

We can find the solution directly on the graph. The solution of a system of equations is the intersections between the two lines. Remember that each equation in this case represent a line, where the common points are always shown as an intersection.

To prove this result, we can apply other methods. Using the substitution method, we have to isolate one variable from one equation and then replace it in the other equation, like this:

[tex]\left \{ {{y=-x+52'} \atop {y=2x-1}} \right.[/tex]

The variable y is already isolated, now we just replace the first equation in the second:

[tex]-x+5=2x-1\\5+1-2x+x\\6=3x\\x=\frac{6}{3}=2[/tex]

Then, we replace the x-value in one equation, no matter which one:

[tex]y=2x-1\\y=2(2)-1\\y=4-1=3[/tex]

[tex](2;3)[/tex]

In iscosceles right triangle the value of the unknown sides is equal to [tex]3\sqrt{2}[/tex] and it can be deteremine by using pythagorean theorem.

Given :

Let the length of unknown sides be 'a'. Than to deteremine the value of a, pythagorean theorem can be used.

[tex]\rm (Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2[/tex]

[tex]6^2 = a^2+a^2[/tex]

[tex]2a^2 = 36[/tex]

[tex]a^2 =\dfrac{36}{2}[/tex]

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

Therefore, by applying pythagorean theorem the value of a which is [tex]3\sqrt{2}[/tex] can be determine.

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Answer:

g(x) = (x - 8)² - 64 will be the answer.

Step-by-step explanation:

The given function in the standard form is g(x) = -16x + x²

We have to write this function in the vertex form.

Since vertex form of a quadratic function is in the form of

f(x) = (x - h)² + k

Therefore, g(x) = x² - 16x may be written as

g(x) = x² - 16x + 64 - 64

      = x² - 2(8x) + 64 - 64

      = (x - 8)² - 64

Therefore, g(x) = (x - 8)² - 64 will be the answer.

The probability that mattias picks an outfit at random that includes red shoes is 0.5

Calculating the probability that mattias picks an outfit at random that includes red shoes?

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

The tree diagram

On the tree diagram, we have

Total Outfits = 12

Outfits with red = 6

So, we have the probability to be

P = Outfits with red /Total Outfits

This gives

P = 6/12

Evaluate

P = 0.5

Hence, the probability is 0.5

Question

Mattias gets dressed in the dark one morning and chooses his clothes at random. He chooses a shirt (green, red or yellow), a pair of pants (black or blue), and a pair of shoes (checkered or red).

What is the probability that mattias picks an outfit at random that includes red shoes?

1. The Temple in Jerusalem was destroyed in the year of 70 AD.

The first Temple was built by King Solomon for seven years in the 10th century BC. The first Temple was destroyed by the Babylonians in 586 BC. The construction of the new Temple began 535 BC and it is completed in 516 BC. The rebuilding of the Temple was approved by Darius I. It was, however, destroyed by the Romans in 70 AD. Despite the fact that the Temple was destroyed, all the outer walls still stand, and for a long time, it was believed that only the west wall stood.

The provincial governors in Rome were given orders to openly persecute the Christians by Emperor Trajan.

This can be concluded from the letter sent to him by Pliny, governor of Bithynia (province of Asia Minor). He had doubts about the investigation and the way of punishing those who were accused as Christians because he never been present at any trials of Christians. This implies that there have already been trials for Christians and that he did not know the details about Trajan’s decree of prosecuting Christians.

The Roman emperor who passed a decree to require everyone to participate in the cult of emperor worship was Decius.

Emperor Decius (249-251) announced the edict that orders everyone to do sacrifice to the Roman gods and to him personally. According to the edict, the sacrifice had to be carried out in the presence of a Roman magistrate who issued a certificate that this had been done. There is no evidence that it was directed against the Christians, but it was fatal for them because was contrary to their beliefs.

1 Peter 3:17: "For it is better, if  God should will it so, that you suffer for doing what is right rather than for doing what is wrong."

The quote is from the First Epistle of Peter, which is part of the New Testament. It is written by Peter the Apostle in Rome (where he was a bishop) as the letter which is sent to believers in Asia Minor who were persecuted and tortured.

The most damaging charge brought against the Christians in Rome was that they were constant law-breakers who did not discharge their duties to the state.

The Roman authorities consider Christians as opponents of the state that promoted treasonous activities and they were apprehended for disobedience. Suspected Christians have often refused to deviate from Christianity in order to comply themselves with acts of a state cult, which was understood as a public cancellation of loyalty to the state.

c(2) = 50 +5(2) = 60

p(2) = 80-2(2) = 76

60 * 76 = 4560 when the price is 60

The rocks are at the same height approximately 1.31 seconds after Noelle drops her rock and Cesar throws his, and at this time, they are both at a height of approximately 8.57 meters.

To determine the moment when Noelle's and Cesar's rocks are at the same height, we need to set the two functions equal to each other and solve for x. Noelle's rock has the height function f(x) = -4.9x² + 17 and Cesar's rock has the height function g(x) = -4.9x² + 13x.

We solve for x when f(x) = g(x):
-4.9x² + 17 = -4.9x² + 13x
This simplifies to:
17 = 13x
Solving for x gives us:
x = 17/13
x ≈ 1.31 seconds

At approximately 1.31 seconds after Noelle drops her rock and Cesar throws his, both rocks are at the same height. To find this height, we substitute x back into either f(x) or g(x). Using Noelle's function, we get:
f(1.31) = -4.9(1.31)² + 17 ≈ 8.57 meters

Therefore, both rocks are at a height of approximately 8.57 meters 1.31 seconds after their respective releases.

Answer:

8.6

Step-by-step explanation:

I took the test

None of the options are entirely correct. The domain of the function is  [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.The domain is  representing all real numbers. The function doesn't directly indicate completion time or maximum height.

Let's analyze the given function  [tex]\( h(t) = -3t^2 + 15t + 18 \)[/tex] to determine the domain and its meaning:

1. **Domain of the function**:

  The domain of a quadratic function is all real numbers unless there are restrictions. In this case, there are no restrictions mentioned in the problem, so the domain is all real numbers. However, in the context of the roller coaster ride, the time ( t ) cannot be negative because it doesn't make sense for time to be negative in this scenario. Therefore, the practical domain is [tex]\( t \geq 0 \).[/tex]

2. **Time to reach maximum height**:

  The time to reach the maximum height of the roller coaster can be found using the vertex formula:  [tex]\( t = -\frac{b}{2a} \)[/tex] , where  [tex]\( a = -3 \) and \( b = 15 \)[/tex] (coefficients from the quadratic function). Substituting these values into the formula:

[tex]\[ t = -\frac{15}{2(-3)} = -\frac{15}{-6} = \frac{15}{6} = \frac{5}{2} \][/tex]

  Since time cannot be negative in this context, the time to reach the maximum height is [tex]\( t = \frac{5}{2} = 2.5 \)[/tex] seconds.

Now, let's analyze the given options:

- **Option 1: The domain of the function is [0, 6], and it represents the car's time to reach maximum height.**

 - The domain given is correct  [tex](\( t \geq 0 \)),[/tex]  but it incorrectly states that it represents the time to reach maximum height. The correct time to reach maximum height is [tex]\( t = 2.5 \)[/tex] seconds, not 6 seconds.

[tex]\( t \geq 0 \),[/tex]

- **Option 2: The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.**

 - This option gives an incorrect domain. The domain is  [tex]\( t \geq 0 \), not \( t \geq -1 \).[/tex]

- **Option 3: The domain of the function is [0, 6], and it represents the car's time to complete the hill.**

 - This option correctly identifies the domain as  [tex]\( t \geq 0 \).[/tex] However, it incorrectly states that it represents the time to complete the hill. The function does not directly represent the time to complete the hill; it represents the height of the car at any given time.

- **Option 4: The domain of the function is [-1, 6], and it represents the car's time to complete the hill.**

 - This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \),[/tex] not  [tex]\( t \geq -1 \).[/tex]

Therefore, none of the options are entirely correct. The domain of the function is  [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.

Answer:

the speed of a vehicle and the time it takes the vehicle to travel 60 miles is a positive correlation

The square root of 252 in simplest radical form is 6√7.

To find the square root of 252 in simplest radical form, we can break it down into its prime factors. The prime factorization of 252 is 2 * 2 * 3 * 3 * 7. To simplify the square root, we group the factors into pairs and put one factor from each pair outside the square root and leave the other inside. In this case, we have (2 * 3) * (2 * 3) * 7. Simplifying this further, we get 6 * 6 * 7, which equals 252.

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