A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. How far will the ball have traveled when it hits the ground for the fourth time? A 24 B 34.5 C 1.5 D 12

From the defined functions in problem, the functions that are mapped from z to z, and onto functions are f(n) = n - 1, [tex] f( n) = [\frac{n}{2}] [/tex]. So, option(a) and option(d) are right choice.

Onto functions work on the codomain. Here we want to check if it contains elements not associated with any element in the domain. Definition: A function f: A→B is onto if, for every element b∈B, there exists an element a∈A such that f(a)=b. An onto function is also called surjective. We have a number of functions that are mapped from Z to Z and we will identify which is onto function or not. Let's consider each one by one

a) f : Z→Z such that f( n) = n - 1

For all m∈Z( Co-domain) and consider (m - 1)∈Z( domain) s.t f( m) = m - 1 = m -1 i.,e., f(a) = b. So, it is an onto function.

b) f : Z→Z such that f( n) = n² + 1

For all m∈Z( Co-domain) and consider (m - 1)∈Z( domain) s.t f( m) = m² + 1 i.,e., two values of m exist and f(a) ≠ b.So, it is not onto function.

c) f : Z→Z such that f( n) = n³ ( cubic function), If f(n) = 2, where n( domain) and 2 (co-domain)

=> n³ = 2

=> n = 2⅓

So, it is not onto function.

d) f : Z→Z such that,[tex]f( n) = [\frac{n}{2}] [/tex]

For all m∈Z( Co-domain) and consider 2m∈Z( domain) s.t f( 2m) = [tex]f(2m) = [\frac{2m}{2}] [/tex]

= m

So, for every m there exits 2m such that, f(2m) = m. Hence, the onto functions are f( n) = n - 1 and [tex]f( n) = [\frac{n}{2}] [/tex].

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Answer:

Since line segment PQ is the result of reflecting line segment AB across the x-axis, we know that the y-coordinates of corresponding points on AB and PQ are the same but have opposite signs.

So if P has coordinates (2,-2) on PQ, then its corresponding point on AB must have coordinates (2, 2). Similarly, if Q has coordinates (8,-2) on PQ, then its corresponding point on AB must have coordinates (8, 2).

Therefore, the length of line segment AB is the distance between points (2, 2) and (8, 2) on the coordinate plane, which is:

AB = |8 - 2| = 6

So the answer is B) 6

The closest answer among the given options is B) 2,100.

To estimate the number of people in the town who would name chocolate as their favorite ice-cream flavor, we can use proportions. We know that 7 out of 50 people in the sample named chocolate as their favorite. To find the proportion of chocolate lovers in the sample, we can divide the number of chocolate lovers by the total number of people surveyed:

7 chocolate lovers / 50 people surveyed = 0.14

Now, we can apply this proportion to the total population of the town to estimate the number of chocolate lovers:

0.14 * 14,878 (total population) ≈ 2,082.92

Since we can't have a fraction of a person, we can round this number to the nearest whole number:

Approximately 2,083 people in the town would be expected to name chocolate as their favorite ice-cream flavor.

The closest answer among the given options is B) 2,100.

The length of the hip on a hip roof rises 1.5 feet vertically.

The hip roof has a slope of 6 inches per foot ( hip slope factor = 1.5) and a hip run of 14 feet

Length of hip = (square root of (hip run squared + (hip slope factor x roof span squared)))
Plugging in the given values, we get:
Length of hip = (square root of (14 squared + (1.5 x 14 squared)))
Length of hip = (square root of (196 + 294))
Length of hip = (square root of 490)
Length of hip = 22 feet (rounded to the nearest whole number)
Therefore, the correct answer is C. 22.
It's important to note that the hip slope factor is a value used to calculate the actual slope of the hip, which is typically steeper than the pitch of the roof. In this case, the hip slope factor of 1.5 means that for every foot of horizontal run, the hip rises 1.5 feet vertically.

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The angle -4 radians is equal to -229.0 degrees when rounded to the nearest 10th.

To convert from radians to degrees, we need to multiply the angle by 180/π. Therefore, to convert -4 radians to degrees, we have:

-4 radians x 180/π ≈ -229.2 degrees

Rounding this to the nearest 10th gives us:

-229.2 degrees ≈ -229.0 degrees

Therefore, the angle -4 radians is equal to -229.0 degrees when rounded to the nearest 10th.

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The total cost of metal that made up the cylinder tank is 4220.16 dollars.

The cylinder has a diameter of 8 ft and a height of 2 ft. The cylinder tank is made up of metals. The metal cost 28 dollars for each foot .

Therefore, the cost of the whole metal for the cylinder tank can be found as follows:

surface area of a cylinder = 2πr(r + h)

where

Therefore,

r = 8 / 2 = 4 ft

h = 2 ft

surface area of a cylinder = 2 × 3.14 × 4(4 + 2)

surface area of a cylinder = 25.12(6)

surface area of a cylinder = 150.72 ft²

Therefore,

1 ft² = 28 dollars

150.72 ft² = ?

cross multiply

cost of the whole metal of the cylinder = 150.76 × 28

cost of the whole metal of the cylinder = 4220.16 dollars

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Sam completed more of his science fair project than Paul.

To determine who completed more of their science fair project, we can compare the completion percentages of Paul and Sam.

Paul completed 65% of his science fair project, which can be expressed as 0.65 or 65/100.

Sam completed 17/24 of his science fair project, which can also be expressed as a decimal by dividing 17 by 24, which is approximately equal to 0.7083 or 70.83%.

Comparing the two completion percentages, we can see that Sam completed a higher percentage (70.83%) of his science fair project compared to Paul (65%). Therefore, Sam completed more of his science fair project than Paul.

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The money in the account will be $252.

For simple interest, use the formula:

I = Prt

where I stands for interest earned, P for principle (amount paid in the beginning), r for yearly interest rate (in decimal form), and t for the time in years.

P equals $200, r equals 0.052, and t equals 5. With these values entered into the formula, we obtain:

I = Prt = ($200)(0.052)(5) = $52

The account will thus have $52 in interest after 5 years. After five years, we add the interest to the principal to determine the account's total balance:

Total = $200 + $52 = $252

Therefore, after five years, the account will have $252.

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Therefore, we can say: limit sin(x) as x approaches pi/2 does not exist lim sin(x) as x approaches 0 = 0.

Although the function (sin x)/x is not defined at zero, it approaches 1 arbitrarily close as x approaches zero. In other words, when x gets closer to zero, the limit of (sin x)/x = 1.

We can put g(x) equal to -1/x and h(x) equal to 1/x because sin(x) is always between -1 and 1. As x approaches either positive or negative infinity, we know that the limit of both -1/x and 1/x is zero, and as a result, the limit of sin(x)/x is also zero.

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The intermediate step in completing the square in the equation -3x² + 54x = 51 is (x - 9)² = 64

Completing the square is a method of solving a qudratic equation by converting it into a perfect square binomial.

To find the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation?

-3x² + 54x = 51, we proceed as follows

-3x² + 54x = 51

Dividing through by -3, we have that

-3x²/-3 + 54x/-3 = 51/-3

x² - 18x = 51/-3

Next, we add half the square of the coefficient of x to both sides, that is (-18/2)² = (-9)²

x² - 18x + (-9)² = -17 + (-9)²

(x - 9)² = -17 + 81

(x - 9)² = 64

So, the intermediate step is (x - 9)² = 64

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The statement that best describes the data represented in the box plots is option B.

A box plot, also known as a box-and-whisker plot, is a graphical representation of a set of numerical data through their quartiles. It is useful for visualizing the distribution of data and identifying outliers.

The box in the plot represents the interquartile range (IQR), which is the range between the first and third quartiles (Q1 and Q3), and the line inside the box represents the median (Q2).

The 1st quartile is 135. The 3rd quartile is 195. To find the interquartile, you would subtract the 3rd quartile from the 1st quartile. 195-135=60. The interquartile range for the spring musical is 60

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In linear equation, The required days for which Bryan's workout would be the same in either pool is 2 days.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Here.

Let the number of days of B'ryan workout be x, the total yard he swims be y,

According to the question,

he swims at the rec center pool, will complete a 100-yard warm-up, and then swim laps in a lane that is 39 yards long.

y = 100 + 39x

Jason swims at the indoor pool at his gym, he will complete a 104-yard warmup, plus the main set that consists of 37 yards per lap.

y = 104 + 37x

Equating both the equation,

100 + 39x =  104 + 37x

39x - 37x =  104 - 100

2x = 4

x = 2  days

Thus, the requried days for which Bryan's workout would be the same in either pool is 2 days.

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each stack of bricks weighs 163.2 pounds. So the answer is D) 163.2 pounds. we need to form equation to solve this

what is equation  ?

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), that are separated by an equal sign (=). An equation tells us that the expressions on both sides have the same value or are equivalent.

In the given question,

If there are 20 stacks with an equal number of bricks on them, let's call the number of bricks on each stack "x". Then the total number of bricks is:

total number of bricks = 20 stacks × x bricks/stack = 20x bricks

We are also told that the total weight of all the bricks is 3,264 pounds. Let's call the weight of each brick "w". Then the total weight is:

total weight = number of bricks × weight per brick = (20x) bricks × w pounds/brick

We want to find the weight of each stack of bricks, which is equal to the weight of a certain number of bricks. Let's call this weight "s". Then we have:

s pounds/stack = x bricks/stack × w pounds/brick

We can solve for "s" by using the two equations above:

total weight = (20x) bricks × w pounds/brick = 3,264 pounds

s pounds/stack = x bricks/stack × w pounds/brick

Dividing the first equation by 20x, we get:

w pounds/brick = 3,264 pounds ÷ (20x) bricks/stack = 163.2 pounds/stack

Substituting this into the second equation, we get:

s pounds/stack = x bricks/stack × 163.2 pounds/stack

Dividing both sides by x, we get:

s pounds/stack ÷ x bricks/stack = 163.2 pounds/stack

Simplifying, we get:

s pounds/brick = 163.2 pounds/stack

Therefore, each stack of bricks weighs 163.2 pounds.

So the answer is D) 163.2 pounds.

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it will cost Vince $5,175 to get new carpet installed, assuming the area to be covered is 500 square feet.

To calculate the cost for Vince to get new carpet installed, we need to add up the cost of the carpet, padding, labor, and hauling away the old carpet.

Let's assume that the area to be covered is 500 square feet. Then, the cost for each component can be calculated as follows:

Cost of carpet = $8/sq ft * 500 sq ft = $4,000

Cost of carpet padding = $0.30/sq ft * 500 sq ft = $150

Cost of labor = $0.75/sq ft * 500 sq ft = $375

Cost of hauling away old carpet = $1.30/sq ft * 500 sq ft = $650

Total cost = Cost of carpet + Cost of carpet padding + Cost of labor + Cost of hauling away old carpet

= $4,000 + $150 + $375 + $650

= $5,175.

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The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

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Answer:

153.47 Miles

Step-by-step explanation:

Starting with the total return fee you subtract the base fee from it

Then Divide the that total by .76

And there you go

Thanks for the Submission

The rate at which Sheila charges customers for each serving =  $2.5 per serving.

Here the table that shows the cost of a cake from Sheila based on the number of servings is:

SERVINGS          TOTAL COST

    100                       $280

    150                       $405

    200                       $530

    250                       $655

We need to find the rate at which Sheila charge customers for each serving.

Consider points (x₁, y₁) = (100, 280) and  (x₂, y₂) = (200, 530)

where x is the number of servings and y coordinate represents the cost of servings.

The rate at which Sheila charges customers for each serving would be,

r = (y₂ - y₁) / (x₂ - x₁)

r = (530 - 280) / (200 - 100)

r = 250 / 100

r = 2.5

Therefore, the required rate is $2.5 per serving.

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Answer:

We can start by using the Pythagorean identity to simplify the expression for cos J:

cos^2(J) + sin^2(J) = 1

Since we are given the value of sin J, we can substitute and solve for cos J:

cos^2(J) + (4/√82)^2 = 1

cos^2(J) + 16/82 = 1

cos^2(J) = 66/82

cos(J) = ±√(66/82)

We want to express cos J in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:

cos(J) = ±√[(2311)/(2*41)]

cos(J) = ±(√2/2) * (√33/√41)

Since J is in the first or second quadrant (based on the given value of sin J), we know that cos J is positive, so we can drop the negative sign:

cos(J) = (√2/2) * (√33/√41)

Therefore, the exact value of cos J in simplest radical form is (√2/2) * (√33/√41).

Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

Additional angles are two angles that add up to 180 degrees. The situation when they happen to be on the identical side of a straight line is a typical one.

For the top isosceles triangle:

Base angle = ?

Using the property of supplementary angles:

base angle + 113 = 180

base angle = 180 - 113

base angle = 67

Now, using the Triangle sum Theorem:

Vertex angle = ?

Vertex angle + 67 + 67 = 180

Vertex angle = 180 - 134

Vertex angle = 46

For the bottom isosceles triangle:

base angle  = Vertex angle of top triangle (vertically opposite angles)

base angle  = 46

Now,

For the values of x, use Triangle sum Theorem:

x + 46 + 46 = 180

x = 180 - 92

x = 88

Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

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Answer:

Step-by-step explanation:

1. Distribute the 10: 30p + 40

If you are solving for p, then subtract 40: 30p = -40

Then divide 30: p = -40/30, simplified to p = -4/3

Answer:

  30p -40

Step-by-step explanation:

You want to simplify the expression -10(-3p +4).

The distributive property tells you the product is ...

  -10(-3p +4)

  = (-10)(-3p) + (-10)(4)

  = 30p +(-40)

  = 30p -40

__

Additional comment

It is easy to get confused by minus signs. For any given numerical product the sign of the result will be negative if (and only if) the number of negative factors is odd.

Here, the first product is (-10)(-3p), which has an even number of minus signs. The result will be the same as with no minus signs:

  (-10)(-3p) = (10)(3p) = 30p

On the other hand, the product (-10)(4) has an odd number of minus signs. That result will be negative:

  (-10)(4) = -40

For this problem, you could start by distributing the minus sign, changing the sign of each term inside the parentheses:

  -10(-3p +4) = 10(3p -4)

Doing this can simplify the mental load of figuring the signs of the product terms.

According to the given information, the perimeter of the given right-angle triangle is 30ft.

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the length of the missing side of the right triangle, BC:

[tex]BC^2 = AB^2 - AC^2\\BC^2 = 13^2 - 12^2\\BC^2 = 169 - 144\\BC^2 = 25[/tex]

BC = 5

Now that we know all three sides of the triangle, we can find the perimeter by adding them together:

Perimeter = AB + AC + BC

Perimeter = 13 + 12 + 5

Perimeter = 30

Therefore, according to the given information, the perimeter of the given right-angle triangle is 30ft.

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Answer:

its in the picture

Step-by-step explanation:

Graph the absolute value using the vertex and a few selected points.

x          y

−1        -4

 0       -3

 1        -2

 2       -3

 3       -4

basically, the answer is the graph that looks like this...

hope this helps ;)

Step-by-step explanation:

Let's assume the basic fee for water is $X per unit and the tariff for consumption is 5% increase per unit. VAT (Value Added Tax) is calculated at a rate of Y% on the total cost, including the basic fee and the tariff.

Given that the consumption is 15 units, the total cost for the consumption of 15 units of water without VAT can be calculated as:

Total cost without VAT = Basic fee + (Tariff rate * Number of units)

Tariff rate = 5% increase per unit, so it would be 1 + 5% = 1.05

Total cost without VAT = X + (1.05 * 15) = X + 15.75

Now, let's assume the VAT rate is Z%. The total cost including VAT can be calculated as:

Total cost including VAT = Total cost without VAT + (VAT rate * Total cost without VAT)

Total cost including VAT = (X + 15.75) + (Z% * (X + 15.75))

To calculate the amount by which the total cost, including VAT, for the consumption of 15 units of water will increase, we need to subtract the initial cost from the increased cost:

Increased cost = Total cost including VAT - Total cost without VAT

Increased cost = [(X + 15.75) + (Z% * (X + 15.75))] - (X + 15.75)

Simplifying, we get:

Increased cost = Z% * (X + 15.75)

So, the amount by which the total cost, including VAT, for the consumption of 15 units of water will increase depends on the value of Z% (the VAT rate) and X (the initial basic fee for water). Once we have these values, we can calculate the increased cost accordingly.

Answer: the point that were left are 429

Step-by-step explanation:

i got this by multiplying 660 and 35% or .35 and got 429 and the amount left is 65% and to get that you would subtract 100% and 35% which gets you 65%.

I promise its right please rate and like and if you want give  brainliest

According to the given information, we know that:

Force (F) is constant

Mass (m) of the first object is 4 kg, and its acceleration (a) is 13 m/s².

Using Newton's second law of motion, we know that:

F = m*a

Solving for the force (F) acting on the first object:

F = m*a = 4 kg * 13 m/s² = 52 N

Now, if the same force acts upon an object with a mass of 26 kg, we can use the same equation to find its acceleration (a):

F = m*a

a = F/m

a = 52 N / 26 kg = 2 m/s²

Therefore, the acceleration of the second object is 2 m/s².

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Answer: Im gonna guess and say its c

Step-by-step explanation:

Answer:

Properties of Hyperbolic Functions

This function's domain is (−∞,∞) and the range is (−1,1) .

Step-by-step explanation:

Hope this helps! =D

Answer:

I think 7.0 is the answer but I would not say that it is correct

Step-by-step explanation:

Answer:

195.5 sq. ft.

Step-by-step explanation:

If you ever wondered how to find the area of your kitchen floor using a scale drawing, you're in luck! I'm going to show you how to do it in a few easy steps. First, you need to know the scale factor, which is the ratio of the scale drawing to the actual floor. In this case, the scale factor is 1 in = 2 ft, which means that one inch on the paper is equal to two feet on the ground. Pretty neat, huh?

Next, you need to multiply the scale drawing dimensions by the scale factor to get the actual floor dimensions. For example, if the scale drawing is 5 3/4 inches long and 8 1/2 inches wide, you multiply those numbers by 2 to get 11 1/2 feet long and 17 feet wide. That's how big your kitchen floor really is!

Finally, you need to multiply the actual floor dimensions to get the area of the floor. This is where it gets tricky, because you have to deal with fractions and decimals. But don't worry, I'll walk you through it. You can use the distributive property to multiply two numbers with fractions. For example, (11 1/2) x (17) = (11 x 17) + (1/2 x 17) = 187 + 8.5 = 195.5. That's the answer! Your kitchen floor has an area of 195.5 square feet. Congratulations, you just learned how to use a scale drawing to find the area of your kitchen floor!

I hope you enjoyed this lesson and found it funny. If not, maybe you should try a different scale factor or a different kitchen. Just kidding!