A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of each bounce will be one half of the height of the previous bounce.

a. Find an exponential equation that gives the height h the ball will attain during the nth bounce.
h =

b. If the ball is dropped from 13 feet above the ground onto hard a surface, how high will it bounce on the 5th
bounce?

On the 5th bounce, the ball will reach a height of ____feet.

Answer:

[tex]6\sqrt{2}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]\sqrt{(4-(-2))^2+(8-2)^2} \\ \\ =\sqrt{6^2+6^2} \\ \\ =6\sqrt{2}[/tex]

Answer:

6(sqrt(2))

Step-by-step explanation:

Use the "distance formula" (sqrt((x2-x1)^2 - (y2-y1)^2)), plugging in (4,8) for x1 and y1, and (-2,2) for x2 and y 2

The equation that represents a line which is parallel to the y - axis would be B. x = −8.

When a line is parallel to the y - axis, this means that the line does not cross the y - axis in any way and is both vertical and straight because the y - axis is vertical and straight.

Any line that is parallel to the y - axis will need to be expressed in terms of terms of x because the y axis is expressed in terms of x as x = 0. From the options, the only equation expressed in terms of x is x  = -8. This line is therefore parallel to the y - axis.

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Ethical research methods include D. doing your best to select an unbiased sample.

In research, ethical considerations are a set of principles that guide your research designs and practices. Active consent, informed consent, anonymity, confidentiality, potential for harm, and results communication are among these principles.

The standards of conduct for scientific researchers are governed by research ethics. To protect the dignity, rights, and welfare of research participants, it is critical to follow ethical principles. Many ethical norms in research, for example, guidelines for authorship, copyright and patenting policies, data sharing policies, and peer review confidentiality rules are intended to protect intellectual property interests while encouraging collaboration.

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The graph of the cosine function y = 3cos(4θ) - 1 is given by the image presented at the end of the answer.

The cosine function is defined by the rule presented as follows:

g(x) = acos(bx+c)+d.

The coefficients have the roles listed as follows:

In this problem, the definition of the function is:

y = 3cos(4θ) - 1

Considering the amplitude of 3 and the vertical shift of -1 the function will oscillate between:

-4 and 2.

(Without the vertical shift it would be between -3 and 3).

The period of the function will be as follows:

2π/b = 4

b = 2π/4

b = π/2.

Considering these features, the graph is given at the end of the answer.

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Answer:

False

Step-by-step explanation:

If is a real number and m and n are positive integers

Answer:

answer in the picture step by step

The probability that at least one of the shirts you draw will be pink 46/51.

What is probability?

The likelihood of an event happening is determined by probability. There are many instances in real life where we may need to make predictions about how something will turn out combination . The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence. By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. The likelihood of an event occurring might range from 0 to 1.

Here the number of pink shirts=8

Number of green shirts=6

Number of red shirts=4

Here if you draw 2 shirts random then,

P(neither the shirt is blue) = [tex]\frac{6}{18} *\frac{5}{17}[/tex] = [tex]\frac{5}{51}[/tex]

Now the at least one of the shirt is pink then,

=> P( at least one shirt is pink)= 1-[tex]\frac{5}{51}[/tex] = [tex]\frac{51-5}{51}[/tex] = [tex]\frac{46}{51}[/tex]

Hence the probability that at least one of the shirts you draw will be pink 46/51.

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Answer: 30[tex]\pi \\[/tex] or 94.247

Step-by-step explanation:

Circumference=2[tex]\pi[/tex]r

2·[tex]\pi[/tex]·15=30[tex]\pi[/tex]=94.247

Answer:

94.2in.

Step-by-step explanation:

The formula for circumference is 2radius x π

π≈3.14

So we can say:

30in.x3.14=circumference

30x3.14=94.2

94.2in=circumference

(i.e. I don't know what you mean by using T.)

It's because this requires two different processes or pieces, the absolute value function is an example of a piecewise function. A piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain.

Step-by-step explanation:

E=29

G = 180-29-107= 44

F = 180-29-29 = 122

H = 180-29-29 = 122

S = 180-107 = 73

M = 107

C = 73

D = 107

T = 73

B = 107

N = 73

K = 44

A = 360-44-44-107 = 165

O = 180-44 = 136

P = 44

J= 136

=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

Given,

In the question:

Figure A is a polygon that has been graphed on a coordinate grid.

To select the option:

Which of the following transformations will result in a similar image to figure A?

Now, According to the question;

The correct options are:

=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

{If the two figures are similar, then their angles are not changed. The ratio of length are the same.}

Hence, => Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

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Where g(x) is the translation 1 unit left of f ( x ) = 9x – 8 then g(x) is

Translation refers to a type of transformation that involve a straight line movement.

Movements as seen in translation includes

The up and down movements are on the vertical direction controlled by the y coordinate.

The left and right movements are on the horizontal direction controlled by the x coordinate.

When translating a graph, adding units moves the graph to the left and removing units moves the graph to the right.

hence we say

f(x) = 9x – 8

g(x) = f(x + 1)

= 9(x+1) – 8

= 9x + 9 - 8

= 9x + 1

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For some n or x value, neither equation can equal 107. f(x) = 2x + 7 or

t(n) = 2n + 7.

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1. the equation that exemplifies the additive identity property is: C. 33 + 0 = 33.

2. The equation that exemplifies the multiplicative identity property is: A. 9.5 × 1 = 9.5.

The additive identity property states that the sum of adding zero to any number will give you the same number itself.

For example, 4 + 0 = 0.

The multiplicative identity property states that a number multiplied by 1 will always give you a product that is the same number itself.

For example, 4 × 1 = 4.

1. The equation, 33 + 0 = 33, shows the additive identity property, because the sum is the same number itself after 0 is added to it.

2. The equation, 9.5 × 1 = 9.5, also shows the multiplicative identity property.

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Slope equals the change in the vertical (Y value) divided by the change in the horizontal (X value), the slope of a horizontal line is zero and equation of line is Y =12. So option C is correct.

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This value c is known as the y-axis intercept.

Here,

Since the Y-axis is vertical, a line perpendicular to it would be horizontal..  The slope of a horizontal line is zero, because slope is the change in the vertical (Y value) divided by the change in the horizontal (X value), and the vertical coordinate does not change from the -3 of the point given.

If we start with the slope-intercept form of an equation of a line

Y = mX + b,

we can write Y = 0X + (12)

Y =12

Slope is the vertical change (Y value) divided by the horizontal change (X value); the slope of a horizontal line is zero, and the equation of the line is Y =12.

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Answer: The answer is -2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

-4 + (-1) - (-3)      Distribute the + and - since they are outside the parenthesis

-4 - 1 + 3            Subtract 1 to -4

-5 +3                 Add 3 to -5

-2

The number of people travelled by train from the station on tuesday is 357.

Let us assume the number of people who travelled by train from the station on tuesday be x. Using the concept of ratio and proportion to solve and calculate x.

Forming the ratio-

20 : 17 = 420 : x

Solving the ratio and proportion for the value of x

x = (420 × 17) ÷ 20

Performing multiplication in numerator

x = 7140 ÷ 20

Performing division on Right Hand Side of the equation

x = 357

Therefore, based on the information, 357 people used to travel.

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Applying the definition of exterior angle, the measure of angle B is: c. 33°

When a side of a triangle is extended through an interior angle, the angle formed is called the exterior angle of a triangle.

The angle to the exterior angle of the triangle, when added to the exterior angle will have a sum of 180 degrees, which means their supplementary angles.

Therefore:

4x - 15 + 14x - 21 = 180

4x + 14x - 15 - 21 = 180

18x - 36 = 180

18x = 180 + 36

18x = 216

18x/18 = 216/18

x = 12

m∠B = 4x - 15 = 4(12) - 15 = 33°

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Answer:

its B. 33

Step-by-step explanation:

Answer: 1 11/20

hope this helps :)

Answer:

Step-by-step explanation:

Some of the other answers are good examples of solving a system of three equations in three unknowns, which is what this problem is asking. Though the simplest way to solve this problem is actually to notice that, if we sum the three equations, we get:

  X + Y = 10

  X + Z = 20

+  Y + Z = 24

----------------

2X + 2Y + 2Z = 54

Factoring out the 2, we have 2(X + Y + Z) = 54, and dividing both sides by 2 reveals that X + Y + Z = 27.

This won't always work when you're solving three equations in three unknowns, but it's a trick that shows up frequently enough on assignments, standardized tests, etc. that it's worth mentioning.

The number of green marbles removed from the bag is 3.

We will use the Formula of Probability:

In mathematics, the probability is defined as the ratio between the number of favorable outcomes and the total number of outcomes.

p(A) = n(A) / n(S)

p(A) is the probability of event A.

n(A) is the number of outcomes with respect to A.

n(S) is the total number of possible outcomes.

Given in the Question:

A bag contains 14 blue, 6 red, 12 green, and 8 purple marbles.

So the total number of marbles in the bag = 40

It is given that 25 marble are removed from the bag randomly

thus, the remaining marbles in the bag = 40 - 25 = 15

It is given that the probability of drawing a green marble from the bag after removing 25 marbles is 3/5.

So, for finding the number of green marbles in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of green marbles and p(A) = 3/5 and  n(s) = 15 (after removing)

Thus, the number of green marbles in the bag after removing = 3/5 × 15

So, the number of green marbles left in the bag = 9

then, the green marbles removed from the bag = 12 - 9 = 3.

Therefore, only 3 green marbles are removed from the bag.

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By simplifying each expression:

−6(3i) (−2i) = -36

2(3 − i)(−2 + 4i) = -4+28i

2i(4 − 5i) = 10+8i

Simplifying each expression step by step:

1. −6(3i)(−2i) =  -6 (-6i²)

= 36 (-1)

= -36

2. 2(3 − i)(−2 + 4i)

= 2 x (-6+12i+2i-4i²)

= -12 +24i +4i - 8i²

= -12 - 8i² +28i

=-12 - 8 (-1) + 28i

= -4+28i

3. 2i(4 − 5i)

= 8i - 10i²

= 8i -10(-1)

= 10+8i

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The length of the chord used in this situation is approximately 40.54 ft.

To find the length of the chord used in the situation, we can use the formula for the chord length in a circular arc:

Chord length = 2√(r² - (r - h)²)

where r is the radius of the arc and h is the measure of the middle ordinate.

Given that the radius of the arc is 70 ft and the measure of the middle ordinate is 6 ft, we can substitute these values into the formula:

Chord length = 2√(70² - (70 - 6)²)

Chord length = 2√(4900 - 4489)

Chord length = 2√(411)

Chord length ≈ 2 * 20.27

Chord length ≈ 40.54 ft

Therefore, the length of the chord used in this situation is approximately 40.54 ft.

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y = 4/3 ( x + 3 )² + 7 is equation of the parabola .

In math, what is a parabola?

The h and k of the above vertex form are the coordinates of the vertex. So our function has the following form

  y = a ( x- h )²  + k

  y = a ( x - ( - 3 ))² + 7

  8 = a ( -4 - ( -3 ) + 7

  8 = a (  6 )

   a = 8/6

    a =  4/3

the a value we can write the final vertex form

  y =  a ( x - ( - 3 ))² + 7

y = 4/3 ( x + 3 )² + 7

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Answer:

  (c)  Neither

Step-by-step explanation:

You want to know the kind of sequence that as terms 2, 7, 14, 23, 34, ....

The first differences of terms of this sequence are ...

  7 -2 = 5

  14 -7 = 7

  23 -14 = 9

  34 -23 = 11

These difference are not constant, so the sequence is not arithmetic.

These differences do not have a common ratio, so the sequence is not geometric.

However, these differences do have a common difference:

  7 -5 = 2

  9 -7 = 2

  11 -9 = 2

The fact that second differences are constant means this is a polynomial sequence of second degree. It is a quadratic sequence, neither arithmetic nor geometric.

__

Additional comment

The sequence is described by the quadratic equation ...

  a(n) = n² +2n -1

Answer:

100 meters every minute

Step-by-step explanation:

d=100(1)

d=100

Hopes this helps please mark brainliest

The simple interest using I = prt if Oliver borrowed $1,500 to purchase a riding lawn mowerat the rate of f 12% for 6 monthsis

The concept that will be used is the concpt of simple interest and thei can be calculates using the simple interst formular which is

I = [(prt)/100]

where p = principal =  $1,500

     I = intereste rate

     t=time

Then this can be expressed as

I= (prt)/100

I =  ($1,500* 6/12 * 12 )/100

=  $90

In conclusion the simple interest is now  $90 which is the second option that is given.

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The value of p that is statistically significant at a 5% level of significance refers to a p-value of 0.05 or less.

The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the degree of significance, which is decided by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. The null hypothesis is anticipated to be shown as untrue or rejected if the result is statistically significant.

The symbol indicates the degree of significance (alpha). Therefore, the following definition applies to the level of significance:

Level of Significance = p (type I error) =

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The percentage of women that answered that they don't even like soccer is 85%

From the information, in the a survey of 500 women, 75 answered that they like soccer. Those that don't like soccer will be the difference between the values. This will be:

= 500 - 75

= 425

Therefore, the percentage of women that answered that they don't even like soccer will be:

= Those that don't like soccer / Total number × 100

= 425/500 × 100

= 85%

The percentage is 85%.

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Complete question

In a survey of 500 women, 75 answered that they like soccer. What percentage of women answered that they don't even like soccer?

Answer: 120

explanation: We already have our first value 36 and the second value 30. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 136 = 30% × Y

STEP 236 =

30

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 30 we will arrive at:

STEP 3Y = 36 ×

100

30

STEP 4Y = 36 × 100 ÷ 30

STEP 5Y = 120

Finally, we have found the value of Y which is 120 and that is our answer.

You can easily calculate 36 is 30 percent of what number by using any regular calculator, simply enter 36 × 100 ÷ 30 and you will get your answer which is 120