this one as well please

The movement of the ping pong ball follows a exponential progression.

1. Ping pong ball

The given parameters are:

[tex]\mathbf{a = 235}[/tex] --- the initial height

[tex]\mathbf{r = 75\%}[/tex] --- the common ratio

(a) The expression after bouncing k times

To do this, we make use of

[tex]\mathbf{T_n = a \times r^n}[/tex]

So, we have:

[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]

In this case; k = n.

So, the equation becomes

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

Hence, the expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

(b) The height after bouncing 6 times

This means that k = 6.

So, we have:

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]

[tex]\mathbf{T_6 = 41.82}[/tex]

Hence, the height after the 6th bounce is 41.82 ft

(c) The total distance after the 12th bounce

First, we calculate the total height after the 12th bounce using:

[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]

[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]

[tex]\mathbf{S_k = 909.92}[/tex]

So, the total distance is:

[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]

[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]

[tex]\mathbf{Distance = 1584.84}[/tex]

Hence, the total distance after the 12th bounce is 1584.84ft.

(2) Cell division

The given parameters are:

[tex]\mathbf{r = 2/2hr}[/tex] --- rate

[tex]\mathbf{a = 120}[/tex] --- initial number of cells

[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half

So, the number of bacteria is:

[tex]\mathbf{T_t = ar^t}[/tex]

This gives

[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]

[tex]\mathbf{T_t = 31457280}[/tex]

Hence, there will be 31457280 bacteria after a day and a half.

Read more about exponential functions at:

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Answer:

82.2

Step-by-step explanation:

The difference is subtracting:

678 - 595.8 = 82.2

Answer:

82.2

Step-by-step explanation:

Check the image below.

Answer:

So, I believe n/2 may be even and 3n+1 is odd. They succumb to 3n if that helps.

Step-by-step explanation:

I'm not certain on what to do but I hope this helps some what.

Explanation:

A solution is where the lines intersect. Graph A shows exactly one solution, and it is at (-2,2)

Graph B doesn't have any solutions since the lines are parallel, and parallel lines never intersect. We consider this system to be inconsistent.

Graph C has infinitely many solutions. The two lines perfectly overlap, meaning there are infinitely many intersection points. All solutions here are of the form (x,y) = (x,2x-1)

Answer:

3/8"

Step-by-step explanation:

Reduce the fraction.  The numerator and denominator are both divizable by 2 which leaves 3/8

Answer:

[tex]\begin{cases}n+d = 27\\0.05n+0.10d = 2.75\\\end{cases}[/tex]

====================================================

Explanation:

n = number of nickels

d = number of dimes

The n and d are placeholders for positive whole numbers.

Since we have 27 coins, we know that n+d = 27. The two subcounts must add to the grand total of 27. That explains how the first equation is set up.

The second equation is set up by looking at the dollar amount each group of coin brings in.

0.05n = amount of money in dollars the nickels bring in

0.10d =  amount of money in dollars the dimes bring in

0.05n+0.10d = total amount of money in dollars = 2.75

The single curly brace to the left of the equations tells the reader we're dealing with a system of equations. The equations are tied together.

Answer:

2a) because they are continuous lines that don't intercept

Step-by-step explanation:

Answer:

2a) They all have the slope of 2x.

2b) R) y = 2x-3

2c) R is the lowest line because the b value (-3) has the least value out of the 3 choices.

Answer:

-28

Step-by-step explanation:

You have to do the parenthesis 1st, then the [tex]\frac{8}{3}[/tex], and multiply the result :D

Answer:

43

Step-by-step explanation:

274 would be absurd and 83 would be close to a right angle which that angle is no where near. It looks like half a right angle meaning 45 and 43 is the closest to that so I think its 43

Answer:

8

Step-by-step explanation:

Answer:

x= 98

First, you have to find what the third angle is so;

180-53-45=82

The third angle in 82.  

A straight line is 180º. So you need to subtract 180-82 to get 98.

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(n) = 2n + 3

h(n) = n − 1

(g * h)(n) = g(h(n))

= g(n − 1)

= 2(n − 1) + 3

= 2n − 2 + 3

= 2n + 1

Answer:

$135

Step-by-step explanation:

120+(12*1.25)

120+15

135

Her score in computer to get a proportionally weighted average of 46% will be 134.

The total score for both subjects = 200 + 300 = 500

Since the proportionally weighted average is 46%, then her score will be:

= 46% × 500

= 0.46 × 500

= 230

Since she had 32% for her statistics test, which was out of a total of 300. Her score will be:

= 32% × 300

= 0.32 × 300

= 96

Therefore, her score in computer will be:

= 230 - 96

= 134

Read related link on:

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Answer:

Olivia typed speed per minutes is 54 words

Step-by-step explanation:

Given:

Olivia typed 36 word in 2/3

Solution:

By Unitary method, calculate the speed of typing by Olivia as-

2/3 Minutes → 36 Words

1 Minutes → 36 ÷(2/3) Words

1 Minutes → 36x3÷2 Words

1 Minutes → 54 Words

Therefore Olivia typed speed is 54 word.

Step-by-step explanation:

ratio

to

sind = d/e

sinf = f/e

Answer:

180

Step-by-step explanation:

2:3 = 300

2x +3x = 300

5x = 300

x = 300/5

x= 60

2X60= 120 (girls)

3X60= 180 (boys)

if u want to to check whether the ans is correct then try adding your outcomes 120+180 that is = 300 . so the correct ans is 180.

Answer:

[tex] \rm y = x + 16 [/tex]

Step-by-step explanation:

A function is given to us and we need to write the inverse of the function in slope intercept form . The given function is ,

[tex]\rm\implies f(x) = x - 16 [/tex]

Let ,

[tex]\rm\implies y = f(x)[/tex]

So that ,

[tex]\rm\implies y = x - 16 [/tex]

Interchange x and y ,

[tex]\rm\implies x = y - 16 [/tex]

Solve for y ,

[tex]\rm\implies y = x + 16[/tex]

Now replace ,

[tex]\rm\implies y = f^{-1}(x) [/tex]

We have ,

[tex]\rm\implies f^{-1}(x) = x+16 [/tex]

And in slope intercept form ,

[tex]\rm\implies \boxed{\pink{\frak {y = x +16}}}[/tex]

The number of order of each aircraft is an illustration of simultaneous equations.

You should order 7 Airbus A330-300s, 5 Boeing 767-300ERs and 9 Boeing Dreamliner 787-9s

To do this, we make use of the following representations:

From the question, we have the following equations

[tex]\mathbf{330A + 270B + 240C = 5850}[/tex] ----the number of passengers

[tex]\mathbf{B + C = 2A}[/tex] --- the relationship between the number of planes

[tex]\mathbf{250A + 200B + 240C =4950 }[/tex] --- the budget

Make A the subject in [tex]\mathbf{B + C = 2A}[/tex]

[tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex]

Substitute [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex] in [tex]\mathbf{330A + 270B + 240C = 5850}[/tex]

[tex]\mathbf{330 \times \frac{1}{2}(B + C) + 270B + 240C = 5850}[/tex]

[tex]\mathbf{165B + 165C + 270B + 240C = 5850}[/tex]

[tex]\mathbf{435B + 405C = 5850}[/tex]

Divide through by 15

[tex]\mathbf{29B + 27C = 390}[/tex]

Make C the subject

[tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]

Substitute [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex] in [tex]\mathbf{250A + 200B + 240C =4950 }[/tex]

[tex]\mathbf{250 \times \frac{1}{2}(B + C) + 200B + 240C =4950 }[/tex]

[tex]\mathbf{125B + 125C + 200B + 240C =4950 }[/tex]

[tex]\mathbf{325B + 365C =4950 }[/tex]

Divide through by 5

[tex]\mathbf{65B + 73C =990}[/tex]

Substitute [tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]

[tex]\mathbf{65B + 73\times\frac{390 - 29B}{27} =990}[/tex]

Multiply through by 27

[tex]\mathbf{65B \times 27+ 73\times(390 - 29B) =990 \times 27}[/tex]

[tex]\mathbf{1755B+ 28470 - 2117B =26730}[/tex]

Collect like terms

[tex]\mathbf{1755B- 2117B =26730 - 28470}[/tex]

[tex]\mathbf{-362B =-1740}[/tex]

Solve for B

[tex]\mathbf{B =\frac{1740}{362}}[/tex]

[tex]\mathbf{B =5}[/tex] --- approximated

Substitute [tex]\mathbf{B =5}[/tex] in [tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]

[tex]\mathbf{C = \frac{390 - 29 \times 5}{27}}}[/tex]

[tex]\mathbf{C = \frac{245}{27}}}[/tex]

[tex]\mathbf{C = 9}[/tex] --- approximated

Recall that: [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex]

So, we have:

[tex]\mathbf{A = \frac{1}{2} \times (5 + 9)}[/tex]

[tex]\mathbf{A = \frac{1}{2} \times 14}[/tex]

[tex]\mathbf{A = 7}[/tex]

Hence, you should order 7 Airbus A330-300s, 5 Boeing 767-300ERs and 9 Boeing Dreamliner 787-9s

Read more about simultaneous equations at:

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Answer:

134

Step-by-step explanation:

So assuming x is the score on the computer science exam, it would take 300*0.32+x=500*0.46=230 to get x=134

Answer:

side HG would be proud of the side EF and parallelogram EFGH

Answer:

A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

A is equal to the amount of students that were absent.

Answer:

To divide two fractions, flip the second fraction and change the operation from division to multiplication. Therefore, there are 20 fifths in four wholes

(A)

Answer:

square root of 25 is 5

Step-by-step explanation:

when you take the numbers that multiply together to make 25 which in this case is 5 5*5=25

Answer:

i dont get it

Step-by-step explanation:

Answer:

omg so many Q's

Step-by-step explanation: