A ball is dropped from a height of 5 ft and bounces to 60% of its previous height on each subsequent bounce. Which statement is true regarding the vertical distance the ball has traveled when it hits the ground for the fourth time?

A) 10.88 ft vertical distance traveled total
B) 16.76 ft vertical distance traveled total
C) 18.06 ft vertical distance traveled total
D) 21.76 ft vertical distance traveled total

1. Triangular, 2. Upwards, 3. (- ∞, 3),(3, ∞), 4. (-1, 0) and (-3, 0), and (0, 1),

5.  (-3, -1), 6. symmetry is along the x-axis.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A modulus function | x + 2 | - 1.

The shape of the graph is triangular.

The graph opens in the upwards direction positive y-axis.

The graph is decreasing at the interval (- ∞, 3) and it is increasing at an interval (3, ∞).

The x-intercepts of the graph is (-1, 0) and (-3, 0), and The y-intercepts of the graph is (0, 1).

The special point of the graph is (-3, -1) where the graph is increasing from decreasing.

Yes, the line of symmetry is along the x-axis.

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Answer:

60%

Step-by-step explanation:

Since the entire percentage is 100 than  40 plus 60 is a hundred

Final answer:

The height of an airplane during its descent to an airport runway is influenced by factors like approach angle, stall speed, and descent rate.

Explanation:

The height of an airplane as it descends to an airport runway is determined by various factors such as approach angle, stall speed, and glide slope.

During descent, the pilot manages corrections for side-winds, updrafts, and downdrafts to aim for a specific touchdown point on the runway.

Typically, the descent rate of an aircraft during landing is about 500 feet per minute, translating to approximately 8 mph.

Answer:

Likely is the answer

Step-by-step explanation:

If you know the probability line you will know how to get the answer

Answer:

[tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Let

x------->the probability of its complement

we know that

The Complement Rule states that the sum of the probabilities of an event and its complement must equal [tex]1[/tex]

so

in this problem

[tex]\frac{2}{7}+x=1[/tex]

solve for x

Adds [tex]-\frac{2}{7}[/tex] both sides

[tex]x=1-\frac{2}{7}[/tex]

[tex]x=\frac{5}{7}[/tex]

The probability of its complement is 5/7

The complement of a probability event is the event that contains all of the universal elements of the event but is not found in the provided event.

From the given information:

The complement of an event is mathematically calculated as:

P(C') = 1 - (x)

P(C') = 1 - 2/7

P(C') = 5/7

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Answer:

4800 acres.

Step-by-step explanation:

We have been given an equation [tex]a=640s[/tex], which gives the relationship between s square miles and acres.

To find the number of acres Pam owns we will substitute [tex]s=7.5[/tex] in our given equation.

[tex]a=640\times 7.5[/tex]

[tex]a=4800[/tex]

Therefore, Pam owns 4800 acres.

Answer:

-10u^3

5u^3

15u^3

-5u^3

Step-by-step explanation:

Given tiles

-15u^3+5u^3

10u^3+(-5u^3)

10u^3+5u^3

5u^3+(-10u^3)

Monomial : that type of polynomial in which only one term .

coefficient of like terms means  same viable with same power  -15 and 5 .

Therefore, coefficient of these two terms added and no change in power of u^3

Answer:

The difference of fifty-four and seven times a number is written as 54 - 7x.

Step-by-step explanation:

Given: expression “the difference of fifty-four and seven times a number”

We have to write the given algebraic expression represents “the difference of fifty-four and seven times a number”

Consider the given algebraic expression represents “the difference of fifty-four and seven times a number”

Let the number be x

Then, seven times a number is 7x

And the difference of fifty-four and seven times a number is written as 54 - 7x.

Thus, The difference of fifty-four and seven times a number is written as 54 - 7x.

Answer:

a

Step-by-step explanation:

Answer:

The total affect of the decrease in the interest rate = $29400

Step-by-step explanation:

The initial amount of money which has been deposited into the account = $30000

The rate at which the initial money was deposited = 7%

But it is given that the federal reserve decreases the reserve rate from 7% to 5%

Now, we need to find the affect of this decrease on the deposited money

The rate of change in the interest rate = 7 - 5 = 2%

So, The affect of this decrease = 2% of 30000

                                                    = $600

So, The money becomes = 30000 - 600

Therefore, The total affect of the decrease in the interest rate = $29400

Answer:

A. a = 16.23 and b = 17.99

Step-by-step explanation:

The addition of the three angles of the triangle is equal to 180°. So,

C + 64° + 85° = 180°

C =  180° - 64° - 85°

C = 31°

The law of sine states:

sin(A)/a = sin(B)/b = sin(C)/c

where c is the side opposite to angle C

Taking angles A and C, and sides a and c, we get

sin(A)/a = sin(C)/c

sin(64°)/a = sin(31°)/9.3

sin(64°)*9.3/sin(31°) = a

a = 16.23

Taking angles B and C, and sides b and c, we get

sin(B)/b = sin(C)/c

sin(85°)/b = sin(31°)/9.3

sin(85°)*9.3/sin(31°) = b

b = 17.99

Answer:

the next five terms are:

[tex]\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }[/tex]

Step-by-step explanation:

A geometric serie is a succession of terms on which every terms is the result of the last term multiply to a common ratio. for example, a geometric serie with inicial terms equal to 2 and the common ratio is 3, the four first numbers of the serie is given by

2, 6, 18, 54

Where every term is calculate as:

first term = 2

second term = first term x common ratio = 2 * 3 = 6

third term = second term x common ratio = 6 * 3 = 18

fourth term = third term x common ratio= 8 * 3 = 54

Then, with this exercise we have the same situation, the first term is [tex]\frac{a}{b^{2} }[/tex] and the common ratio is [tex]\frac{b}{a^{2} }[/tex], so we get:

first term = [tex]\frac{a}{b^{2} }[/tex]

second term = first term * common ratio = [tex]\frac{a}{b^{2} } *\frac{b}{a^{2} } = \frac{1}{ab}[/tex]

third term = second term * common ratio = [tex]\frac{1}{ab} *\frac{b}{a^{2} } =\frac{1}{a^{3} }[/tex]

fourth term = third term * common ratio = [tex]\frac{1}{a^{3} } *\frac{b}{a^{2} } = \frac{b}{a^{5} }[/tex]

fifth term = fourth term * common ratio= [tex]\frac{b}{a^{5} } *\frac{b}{a^{2} } = \frac{b^{2} }{a^{7} }[/tex]

sixth term = fifth term * common ratio= [tex]\frac{b^{2} }{a^{7} } *\frac{b}{a^{2} } = \frac{b^{3} }{a^{9} }[/tex]

so, the next five terms are:

[tex]\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }[/tex]

N can have 6 different positive integer values.

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

The expression is :

18/N +2

An integer is a whole number that includes all positive numbers, negative numbers and zero.

An integer cannot be a fraction.

The value of N has to be determined for the expression such that, the value of the expression is a positive integer.

For the expression to be positive integer, the 18/N should be an integer value, so the number N should completely divide 18.

The factors of 18 is 1,2,3,6,9,18.

If N is any value among these, it will divide 18 to give a integer and the value of the expression will be a positive integer value.

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warehouse location (24,-32)

airport location (-24,32)

 distance = sqrt((x2-x1)^2 +(y2-y1)^2)=

Sqrt(24--24)62 +(32--32)^2) =

sqrt(48^2 +64^2) =80

then distance from airport to the factory = -24 to 24 = 48

80+48 = 128 miles total

The slope of the line that contains the given points T(6, 3) and V(8, 8) will be 2.5.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

T(6, 3) and V(8, 8)

The slope is given as,

m = (8 - 3) / (8 - 6)

m = 5 / 2

m = 2.5

The slope of the line will be 2.5.

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Marie's total earnings for the two weeks were $525. She paid $262.5 to taxes and $131.25 to college tuition, leaving her with a balance of $131.25.

To find out the amount left, we need to first calculate Marie's total earnings for the two weeks by adding what she earned each week. $280 for the first week plus $245 for the second week gives her a total earnings of $525.

Marie gave half of her earnings to taxes, which is 0.5 * $525 = $262.5. After that, she spent one-fourth of her earnings on college tuition, which equals 0.25 * $525 = $131.25. Summing up both amounts, we find that she spent $262.5 + $131.25 = $393.75 on taxes and tuition.

To find out the amount Marie has left, we subtract the total expenses from her total earnings. Thus, $525 - $393.75 = $131.25 is the total amount she has left after paying her taxes and tuition.

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After calculating her total earnings, subtracting the amounts for taxes and tuition, Marie had $131.25 left. Her total earnings were $525. 1/2 went to taxes, and 1/4 went to tuition.

First, find her total earnings for the two weeks:

Total Earnings = $280 + $245 = $525

Next, calculate how much went to taxes. Since 1/2 of her total earnings went to taxes:

Taxes = 1/2 x $525 = $262.50

Then, calculate how much went to college tuition. Since 1/4 of her total earnings went to tuition:

College Tuition = 1/4 x $525 = $131.25

Finally, subtract the amounts for taxes and tuition from her total earnings to find out how much money she had left:

Money Left = $525 - $262.50 - $131.25 = $131.25

Marie had $131.25 left after paying taxes and college tuition.

Answer:

March.

Step-by-step explanation:

We have been given that in March Tom had -£165 in his bank account. In April he had -£156.

We know that the a biggest negative number has least value as biggest negative numbers lie on the extreme left on the number line.

Since -£165 is more negative than -£156, so -£165 is the least amount.

Therefore, Tom had least amount of money in his account in March.