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The  total distance traveled by the "super ball" is 49 meters.

1. First bounce: The ball drops from 16 meters above the ground and rises to [tex]\(\frac{3}{4}\)[/tex] of that height.

Distance traveled in the first bounce:

[tex]\[16 + \frac{3}{4} \times 16\][/tex]

2. Second bounce: The ball drops from the new height and rises to [tex]\frac{3}{4}\)[/tex] of that height.

Distance traveled in the second bounce:

[tex]\[\left(\frac{3}{4} \times 16\right) + \frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\][/tex]

3. Third bounce: The ball drops from the new height and rises to [tex]\(\frac{3}{4}\[/tex] ) of that height.

Distance traveled in the third bounce:

[tex]\[\left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right) + \frac{3}{4} \times \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)\][/tex]

Now, the total distance traveled

[tex]\[ \text{Total distance traveled} = \left(16 + \frac{3}{4} \times 16\right) + \left(\frac{3}{4} \times 16 + \frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)[/tex]

                                         [tex]+ \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right) + \frac{3}{4} \times \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)\right) \][/tex]

[tex]\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{27}{4} + \frac{81}{16}\][/tex]

[tex]\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{27}{4} + \frac{81}{16}[/tex]

                                       [tex]= 16 + 12 + 9 + \frac{108}{16} + \frac{81}{16} \][/tex]

[tex]\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{108 + 81}{16}[/tex]

                                    [tex]= 16 + 12 + 9 + \frac{189}{16} \][/tex]

Add the whole numbers and fractions separately:

[tex]\[\text{Total distance traveled} = 37 + \frac{189}{16}\][/tex]

Now, convert the improper fraction to a mixed fraction:

[tex]\[ \frac{189}{16} = 11\frac{13}{16} \][/tex]

Finally, add the whole number and the mixed fraction:

[tex]\[ \text{Total distance traveled} = 37 + 11\frac{13}{16} \][/tex]

So, the total distance traveled by the "super ball" is :

[tex]\[ \text{Total distance traveled} = 37 + 12 = 49 \text{ meters} \][/tex]

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A jar has 1000 coins, of which 999 are fair and 1 is double-headed. pick a coin at random, and toss it 8 times. given that you see 8 heads,  the probability that the next toss of that coin is also a head  1.

Since the coin is double-headed, each toss will always result in a head. Therefore, the probability of getting a head on the next toss is 1, or 100%.   This is because the coin has been identified as having two heads, and thus it can never land on a tail.

The coin is still subject to the laws of probability, so it is not guaranteed that it will always land on a head, but it does make the probability of getting a head on the next toss one hundred percent.   It is important to note, however, that this probability is only true for the specific coin, and not for any other coin in the jar. The other 999 coins in the jar are all fair coins, meaning that the probability of getting a head on the next toss is still 50-50.

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The expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right))[/tex].

If there are N top applicants and M schools to choose from, then the expected number of schools that will be attended by at least one top applicant is [tex]\frac{M \choose N}{M^N}[/tex]. This is because each of the N top applicants can choose any of the M schools independently, and the probability of any one top applicant attending any given school is[tex](\frac{1}{M})[/tex]. Thus, the probability of at least one top applicant attending any given school is[tex](1 - \left( \frac{M-1}{M} \right)^N)[/tex]. Therefore, the expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right)).[/tex]

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The probability of getting an no head is 1/8 or 12.5%

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space / total outcome

The total outcome of tossing a coin thrice is 8

The sample space of getting no head i.e (TTT) is 1

Therefore the probability of getting no head = 1/8

in percentage; 1/8 × 100 = 100/8 = 12.5 %

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Answer:

Step-by-step explanation:

i know

The side WX is perpendicular to side XY,

similarly,  XY is perpendicular to side YZ, YZ is perpendicular to side WZ, and side WX is parallel to size YZ.

so WXYZ is a square.

A line's slope is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Given the slope of WX = [4 - 1] / [3 - (-1)] = 3/4

the slope of XY = [0 - 4] / [6 - 3]

slope of XY = -4/3

the slope of YZ = [-3 - 0] / [2 - 6]

the slope of YZ = 3/4

slope of WZ = [-3 - 1] / [2 - (-1)] = -4/3

for the perpendicular slope, m₁m₂ = -1

or m₁ = -1/m₂

where m₁ is perpendicular to m₂

so the slope of WX = -1/(the slope of XY)

so WX is perpendicular to side XY,

similarly,  XY is perpendicular to side YZ, YZ is perpendicular to side WZ, and side WX is parallel to size YZ.

so the coordinates form a square.

Hence WXYZ is a square.

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6. The costs are given as follows:

4 kites - $28.

7 kites  - $34.

10 kites - $40.

7. The linear function is defined as follows:

y = 20 + 2x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, the intercept b is given as follows:

b = 20.

When x increases by one, y increases by two, hence the slope m is given as follows:

m = 2.

Then the function is given as follows:

y = 2x + 20.

The costs are given as follows:

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The simplified form of the expression [tex]\frac{-8.97\times10^1}{-3.00\times10^3}[/tex] is 2.99×10⁻².

In scientific notations numbers are written in the form of a base that is

0  ≤ b < 10 and multiplied by 10ⁿ where n represents integers.

We write large standard numbers in scientific form in a compact manner.

The rational expression given is  [tex]\frac{-8.97\times10^1}{-3.00\times10^3}[/tex].

First, we'll solve for the base which is,

- 8.97/- 3.00.

= 2.99 and we know 10¹/10³ = 10¹⁻³ = 10⁻².

Therefore, The expression [tex]\frac{-8.97\times10^1}{-3.00\times10^3}[/tex] can be written as 2.99×10⁻².

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Answer: Your answer is 2x2√7 (Please Mark Branliest)

Step-by-step explanation:

Step 1: Rewrite 28x4 as (2x2)2⋅7

Step 1.1: Factor 4 out of 28 which should get you √4(7)x4

Step 1.2: Rewrite 4 as 22 which should get you √22⋅7x4

Step 1.3: Rewrite x4 as (x2)2 which should get you √22⋅7(x2)2

Step 1.4: Move the 7 which should get you √22(x2)2⋅7

Step 1.5: Rewrite 22(x2)2 as (2x2)2 which sould get you √(2x2)2⋅7

Step 2: Pull terms out from under the radical to get yourself 2x2√7

Literally nothing occurs. On the off chance that the two terminals are at an equivalent voltage, no ongoing streams, any more than if you contacted two impartial bits of metal together.

Cases 1 and 3 are basically something very similar. There's a voltage difference, so current normally streams. In any case, you don't have a circuit, so when electrons stream from the lower positive voltage (which is zero assuming it's released) to the higher positive terminal, the electrons develop and make a static charge that balances the voltages. This occurs in a small part of a second, so the current is negligible, and voltage promptly stops.

The standard metric unit on electric potential difference is the volt, truncated V and named to pay tribute to Alessandro Volta. One Volt is identical to one Joule per Coulomb. In the event that the electric potential difference between two areas is 1 volt, one Coulomb of charge will acquire 1 joule of potential energy when moved between those two areas. In the event that the electric potential difference between two areas is 3 volts, one coulomb of charge will acquire 3 joules of potential energy when moved between those two areas.

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The height of the tree is 38 feet.

Trigonometry is a topic the requires determination of length/ distance or measure of angle of the position of an object from a reference point. Thus the trigonometric functions are required.

In the given question, let distance from Woody's eyes to the top of the tree be represented by x. Then applying the appropriate trigonometric function, we have;

Tan θ = opposite/ adjacent

Tan 70 = x/ 12

x = 12 * Tan 70

  = 12(2.7475)

x = 32.97

x = 33 feet

Thus,

the height of the tree = woody's eyes from the ground + distance from Woody's eyes to the top of the tree

                                    = 5 + 33

                                    = 38 feet

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The inverse of the linear equation is:

y = x - 3

And its graph can be seen on the image at the end.

The dashed line is the parent linaer equation:

y = x

And it is its own inverse, so we ignore that one.

The other line is:

f(x) = x + 3

Now, remember that the inverse of f(x) will be a function g(x) such that:

f( g(x)) = x

         = g(x) + 3 = x

Solving that for g(x) we will get:

g(x) =x - 3

The graph of that lineis on the image at the end.

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Answer: (f∘g)(x)=15x

Step-by-step explanation:

The expression of (f∘g)(x) in the simplest form is (f∘g)(x)=15x and this can be determined by using the arithmetic operations.

Given :

f(x)=3x

g(x)=5x

The following steps can be used in order to determine the expression of (f∘g)(x):

Step 1 - Write the given function.

f(x)=3x

g(x)=5x

Step 2 - Now, replace 'x' with g(x) in order to determine the expression of (f∘g)(x).

(f∘g)(x)=3g(x)

(f∘g)(x)=3x5x

Step 3 - Simplify the above expression.

(f∘g)(x)=15x

The expression of (fog)(x) in the simplest form is (f∘g)(x)=15x

The  values of x is (4,-8) he two vectors will be orthogonal.

Let u=(x+4) i-4 j

x=x i+8 j

Now, U and v are orthogonal.

A number of vectors that are mutually perpendicular to each other, meaning they form an angle of 90° with a magnitude of one unit with each other, are called orthogonal unit vectors.

Therefore, u.v=0

⇒[tex]((x+4) i-4 j) \cdot(x i+8 j)=0 \\[/tex]

⇒[tex]x(x+4)-32=0 \\[/tex]

⇒[tex]x^2+4 x-32=0 \\[/tex]

⇒[tex]x^2+8 x-4 x-32=0 \\[/tex]

⇒[tex]x(x+8)-4(x+8)=0 \\[/tex]

⇒x=4, x=-8

Therefore, the value of x=4 and x=-8 the two vectors will be orthogonal.

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Using the distance formula, the most precise classification of LMNP is a parallelogram.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is given by the following formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²],

where d is the distance between the points (x₁, y₁) and (x₂, y₂).

we shall evaluate the distance between each points as follows:

distance between L and M = √[[-2 - (-5)]² + (14 - 8)²]

distance between L and M= √(3³ + 6²)

distance between L and M= √45

distance between M and N = √[[12 - (-2)]² + (7 - 14)²]

distance between M and N = √[14² + (-7)²]

distance between M and N = √245

distance between N and P = √[(9 - 12)² + (1 - 7)²]

distance between N and P = √[(-3)² + (-6)²]

distance between N and P = √45

distance between P and L = √[(-5 - 9)² + (8 - 1)²]

distance between P and L = √[(-14)² + 7²]

distance between P and L = √245.

Therefore, using the distance formula, the most precise classification of LMNP is a parallelogram.

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The image point is located at (16, 4).

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that, a point (8, 2) is dilated using a scale factor of 2.

A point (x, y) when dilated by a scale factor of k changes to (kx, ky).

Point (8, 2) will become,

(8 × 2, 2 × 2) = (16, 4).

Hence the dilated point is (16, 4).

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Answer:x = 7

Step-by-step explanation:

To solve the equation 9x = 7(x + 2), we can first expand the expression inside the parentheses:

9x = 7x + 14

Next, we can isolate x by subtracting 7x from both sides:

2x = 14

Finally, we can divide both sides by 2 to find the solution:

x = 7

Answer:

To solve the inequality - 3x ≤ 3, using the table provided, we can see that when x = -2, the value of 3x is -6, which is less than 3. So the solution of the inequality -3x ≤ 3 is x ≤ 1.

The probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.

The standard error of the mean is given by the formula: [tex]standard error=standard deviation / \sqrt{sample size}\\\\ = 8.2/\sqrt{45} \\\\ = 1.935[/tex]

Next, we can calculate the Z-scores for 80 and 83:

Z1 = (80 - 79.8) / 1.935 = 0.512

Z2 = (83 - 79.8) / 1.935 = 2.056

Finally, we can use a Z-score table or calculator to find the cumulative probability of a standard normal distribution between Z1 and Z2:

P(80 < Xbar < 83) = P(0.512 < Z < 2.056) = 0.0922

So the probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.

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The value of [tex]i^5[/tex] is i.

The correct option is (A).

Complex Numbers in Maths. Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.

Given:

[tex]i^5[/tex]

Now, we have to expand the complex number

[tex]i^5[/tex] = i x i x i x i x i

   = (i)² x (i)² x i

As, the value of i² = -1

[tex]i^5[/tex] = (i)² x (i)² x i

   = (-1) x (-1) x i

   = 1 x i

   = i

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A. Superman's average rate is = 104 m/s

B. The distance flew in 10 seconds =  1040 m.

C. After 18 seconds, Superman is 1164 meters away from Lois.

For B, To find the distance flown in 10 seconds, we can use the average rate calculated in part A and multiply it by the time elapsed:

104 m/s * 10 s = 1040 m

In this scenario, we have used the formula for average speed, which is given by:

To calculate the average speed, we found the difference between the two distances and divided it by the difference in time. To find the distance flown in 10 seconds, we simply multiplied the average speed by the time elapsed. The final answer to how close to Lois Superman is after 18 seconds is 1164 meters.

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Complete Question:

Superman needs to save Lois from the clutches of Lex Luthor. After flying for 14 seconds, he is 1372 meters from her. Then at 18 seconds he is 1164 meters from her.

A. What is Superman's average rate? _____ meters per second

B. How far does Superman fly every 10 seconds? _________meters

C. How close to Lois is Superman after 18 seconds? ________meters.

The height of the tree is 5.4 meters.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

The picture shows a man next to a tree.

The man has a height of 1.8 meters.

The man and the tree are drawn to the same scale.

The height of the tree = 1.8 x 3 = 5.4 meters

Therefore, the height is 5.4 meters.

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Answer:7.2

Step-by-step explanation: as the man is 1.8 you can see that if you add on top of him 4 more in total that would be the height of the tree so the calculation would be 1.8x4 which would be 7.2

The equation of the line in slope-intercept form is y = 1/4x + 4, with slope 1/4, and passes through the point (-4,3).

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

Given the slope, m = 1/4, and the point (-4,3), we can use the point-slope form of a line to find the y-intercept:

y - 3 = 1/4 × (x - (-4))

y - 3 = 1/4x + 1

We can simplify this equation:

y = 1/4x + 4

This is the equation of the line in slope-intercept form.

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Answer:

1050 feet

Step-by-step explanation:

We know

A cheetah runs 420 feet in 6 seconds

Find how many feet the cheetah runs in 1 second by taking

420 / 6 = 70 feet

How many feet could a cheetah run in 15 seconds?

70 x 15 = 1050 feet

So, the cheetah could run 1050 feet in 15 seconds.

Answer:

Divide 192 (students) by 3 ( buses).

192/ 3 = 64

Step-by-step explanation:

hsjdiwkdhd jdindid odj

Option B is correct, the missing length is 12.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

We know that the corresponding sides are in proportion .

Let x be the missing length

9/6=x/8

Apply cross multiplication

72=6x

Divide both sides by 6

x=72/6

x=12

Hence, Option B is correct, the missing length is 12.

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The variables for this problem are classified as follows:

a) The number of songs on a randomly chosen ipod is discrete.

b) The number of people in line at the bank at a randomly chosen time is discrete.

c) The time it takes to drive to the airport is continuous.

d) The amount of rain during the next thunderstorm is continuous.

Variables are classified as continuous or discrete depending if they can assume decimal values, as follows:

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A declared limit to the number of impressions that will be made from a particular plate (or matrix) is known as an "impression limit".

An "impression limit" is a predetermined maximum number of times that a printing plate (also known as a matrix) can be used to make an impression on the printing material before it becomes worn and less effective. The purpose of setting an impression limit is to ensure consistent, high-quality printing results.

A printing plate is typically made of metal, plastic, or rubber and is used to transfer an image or text onto paper or another printing surface. Each time the plate makes an impression on the printing material, a small amount of wear and tear occurs, causing the plate to degrade over time.

To prevent this degradation, an impression limit is set for each plate. This limit specifies the maximum number of times that the plate can be used before it needs to be replaced. The impression limit helps to ensure that each plate is used for a specific number of impressions only and then replaced, which helps to ensure consistent, high-quality printing results.

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The claim that a random sample is representative of the population of interest is only true under certain conditions.

The concept of population and sample is crucial in conducting a survey. In a survey, a sample is a smaller group of individuals selected from a larger group, also known as the population.

When a sample is selected randomly from a population, it is said to be representative of the population of interest.

However, just because a sample is selected randomly does not guarantee that it is representative of the population.

Therefore, the claim that the sample of 500 students selected from the statistics classes is representative of the population of interest (all the students enrolled in the university) is only partially true.

If the population of all students enrolled in the university is homogeneous with respect to their opinions on foreign language classes, and if the random sampling process was carried out correctly, then it is possible that the sample is representative of the population.

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