The movement of the ping pong ball follows a exponential progression.
The expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]The height after the 6th bounce is 41.82 ftThe total distance after the 12th bounce is 1584.84ft.There will be 31457280 bacteria after a day and a half.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.
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I will thank you
Answer: 89674 buckets were produced in 4 months
Answer:
Step-by-step explanation:
First you have to do 5263 / 7 = 751.9 (rounded 751.857143)
Then do 751.9x121.6= 91 431
You get 121.6 because that is how many days are in 4 months.
Hope this helps !!!!
Have a good day/night!!<333
In BOMAMS 'M' stands for
⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ B = Bracket
⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ O = Open
⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ D = Division
⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ M = Multiplication
⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ A = Addition
⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ S = Subtraction
Answer:
B= Bracket
O= Open
D=Divide
M=Multiplication
A=Addition
S=Subtraction
Question
Jackson's backpack weighed 15 kg. Convert the weight to pounds. Round to the nearest pound.
Answer:
[tex]15 \times 2.205 = 33.0693 \: lb[/tex]
Unit conversion is a way of converting some common units into another without changing their real value. The Weight of Jackson's backpack is 33.075 pounds.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
Since 1 kg is equal to 2.205 pounds. Therefore, the Weight of Jackson's backpack is,
15 kg = 2.205 × 15 kg = 33.075 pounds
Hence, the Weight of Jackson's backpack is 33.075 pounds.
Learn more about Units conversion:
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Describe a way to make the arithmetic problem 45% x 680 mentally
Answer:
306.
Step-by-step explanation:
Firstly, we are aware 100% of 680 is obviously 680,
Next, we know half of a 100% is 50% therefore half of 680 is 340.
Then, we know 45% is 5% less than 50%
To find 5% of a number mentally, divide it by 10 as 100÷5=20
680÷20=34
Lastly 50% subtracted by 5%: 340-34=306.
Now we know, 45% of 680 is 306.
Hope this helps.
Hope this helps.Please mark BRAINLIEST.
100 OOO 000
- 62431556
Answer:
37568444
hope this helps
What is the answer to this question?
Rewrite 1/2 as 4/8
Now add 5 3/8 + 2 4/8
Answer: 7 7/8
Help thank you so very much
Answer:
x-0 12
Step-by-step explanation:
i hope cant help p please follow me in brainly and hearts and give me a star
Neil change the oil in his vehicle the car requires 6 quarts of oil if Neil wants to change his or every month for a year how many quarts of oil will Neil need?
Answer:
72 quarts
Step-by-step explanation:
1 year = 12 months, and Neil changes the oil each month, and each month he uses 6 quarts of oil. So, the number of quarts he will need for a year is
6 + 6 + ... + 6, twelve times, which equals 12(6) = 72 quarts.
How much greater is the surface area of the rectangular prism than the surface area of the cube?
A. 36 cm2
B. 33 cm2
C. 18 cm2
D. 45 cm2
Answer: 18 cm2
Step-by-step explanation: the surface area of the cube is 54 cm2 and the rectangular prism is 72 cm2 so 72 - 54 = 18
What is the range of the given function ?
Answer:
6740
Step-by-step explanation:
Answer:
There is no function provided
FYI
Domian is all x-values
range is all y-values
For ex..
(-3,6)
-3 is domain
6 is range
Step-by-step explanation:
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 100 m long and 60 m wide.
Find the area of the training field. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.
Step-by-step explanation:
given,
length = 100 m
breadth = 60 m
we know,
area = l × b
now,
100 × 60 = 6000 m
therefore, area of rectangular field is 6,000 m.
and for both the semicircle if we add both the semicircle we will get a complete circle.
as the width of the rectangle is the diameter of circle so the radius of the circle is 60/2 = 30m
we know,
Area = πr²
now,
→ 3.14 × 30²
→ 3.14 × 900
→ 2826 m
so,
area of rectangle + area of circle = area of the training field.
→ 6000 + 2826 = 8826.
therefore, area of training field is 8,826 m.
hope this answer helps you dear...take care and may u have a great day ahead!
Answer:
8826 m²
Step-by-step explanation:
The field is composed of a rectangle and a circle .( the 2 semicircles form a complete circle when placed together )
area = area of rectangle + area of circle
= lb + πr² ( r = 60 ÷ 2 = 30 )
= (100 × 60) + (3.14 × 30²)
= 6000 + (3.14 × 900)
= 6000 + 2826
= 8826 m²
Please Help
Geometry
Solve for in terms of A and w. A=w
Answer:
Step-by-step explanation:
Given A = w:
w in terms of A is w = A, and
A in terms of w is A = w
please help need this done by tomorrow thank you [PHOTO]
Answer:
31
Step-by-step explanation:
sum of the bordering angles is 180° so
(5x-16) + (x+10) = 180
5x - 16 + x + 10 = 180
6x - 6 = 180
6x = 186
x = 186 ÷ 6
x = 31
Answer:
The answer is x=31.
5x-16+x+10=180
6x-6=180
6x=186
x=31
Then, 5(31)-16=
155-16= 139
Also, x+10=
31+10=41
Solution check:
139+41=180, so x=31 is correct.
I NEED ANSWERS TO THESE QUESTIONS
1.How are the areas of a circle and a parallelogram related?
2. Find the area of a circle with a radius of 6.9 m to the nearest tenth. Leave your answer in terms of π.
3. The average crop circle is between 100 and 300 ft in diameter. Find the area of a crop circle that is 300 ft in diameter. Use 3.14 for π.
4. A baker makes a giant cookie for special occasions that is 16 in. in diameter. How many 4-in. diameter cookies would it take to equal the area of one giant cookie?
5. Compare and Contrast What is the difference between the circumference and area of a circle
6. Reasoning A round pizza has an area of 254.34 in.2. Explain how to estimate the length and width of the square box needed to package the pizza
I only have the answer for 1, but !
1. The area of a parallelogram is base times height. Since the area of that rectangle is twice the area of the circle, then the area of the circle is half the base times the height. It will be half of 2πr· r. The area of the circle will be πr2
Sowy about all my questions b-b-but please help with another one?
Answer:
A
Step-by-step explanation:
count both sides divide by missing pieices
Three consecutive integers have a sum of 45. Find the integers.
Answer:
14,15,16
Step-by-step explanation:
Call n the first integer so you get:
n+(n+1)+(n+2)=45
3n+3=45
3n=42
n=14
The integers are:
14,15,16
Answer:
14,15,16
Step-by-step explanation:
Let the integers be x, (x+1),(x+2)
So,
x+(x+1)+(x+2)=45
x+x+1+x+2=45
3x+3=45
3x=45-3
x= 42/3
x=14
Now put the value.
x= 14(x+1)= 14+1= 15(x+2)=14+2= 16Now, Add these integers
you'll get
14+15+16=45
ACME insurance company estimates that the probability of the owners’ of a house worth between $120,000 to $170,000 making a claim for $5000 is 0.08, and that the probability of the house and contents being totally destroyed is 0.0041. Should that tragedy happen, the company will have to pay $150,000. The company charges $1300 for the insurance policy.
What is the expected value of this policy to the insurance company?
Round your answer to two decimal places.
The expected value of this policy to the insurance company is $285.00.
Using this formula
Policy expected value=Insurance policy charges-[(Probability × Claim)+(Probability × Claim)]
Let plug in the formula
Policy expected value=$1,300-{(.0041)($150,000)+(.08)($5,000)]
Policy expected value=$1,300-($615+$$400)
Policy expected value=$1,300-$1,015
Policy expected value=$285.00
Inconclusion the expected value of this policy to the insurance company is $285.00
Learn more here:
https://brainly.com/question/19819099
evaluate: 16^1/2 x 2^-3
Answer:
64
Step-by-step explanation:
16^1
---------------------- = 64
2 x 2 - ^3
Apply exponent rule
16^1 = 16
= 16
------------------
2x2 - ^3
16 = 2x 8
2 x 8
-----------
2 x 2 - ^3
Cancel the common factor <2>
8
---------
2-^3
Factor the number 8 = 2^3
2^3
----------
2-^3
Apply exponent rule.
= 2^3 - (-3) = 6
3- (-3) = 6
= 2^6
2^6 = 64
64 is the answer
Answer:
0.5
Step-by-step explanation:
[tex] {16}^{ \frac{1}{2} } \times 2 {}^{ - 3} [/tex]
[tex] \sqrt{16} \times \frac{1}{{2}^{3} } [/tex]
[tex]4 \times \frac{1}{2 \times 2 \times 2} [/tex]
[tex] \frac{1}{ 2} [/tex]
You deposit $200 in a savings
account that pays a simple
interest rate of 3.25% per year.
How much interest will you earn
after 5 years?
Answer:
$16.25
Step-by-step explanation:
First, you have to find 3.25*5 which is 16.25.
16.25 is the percent rate of your total interest over the course of 5 years.
In other words, you have to do 200*0.1625 which is 32.5.
So, your answer is $16.25.
Good luck!
what is the answer for this equation 3x-2=2x+9
Answer:
x = 11
Step-by-step explanation:
3x-2x=9+2 1st and 2nd principle
X=11
5x + 2 = 3x + 4(2x - 1)
show steps
Answer:
x=1
Step-by-step explanation:
5x+2=3x+4(2x-1)
5x+2=3x+8x-4
5x+2=11x-4
5x-11x=-4-2
-6x=-6
6x=6
x=1
Consider the functions p(x) = 5x3 + 6x2 + 4x and qx) = 5640.
-
1. Use graphing technology to find a value of that makes p(x) = q() true.
Need help please someone!
Answer: 270 inches squared
What is the product of 14.5×100
Answer:
1450
Step-by-step explanation:
Any number times 10 goes up one value.
ones become tens, and tens become hundreds etc..
87x10=870
And a number times 100 goes up two values.
23.5x100= 2350
hope this helped ;)
Step-by-step explanation:
you don't have a calculator ? with that you would have gotten the answer immediately.
so you had to write the question in here, need to wait for an answer, ...
but actually, this is very easy to solve even without a calculator, as this is how our decimal numbers work : based on powers of 10.
multiplying by 100 moves the decimal point 2 positions to the right (and fill up with zeros where necessary) :
14.5 × 100 = 1450
a multiplication by 10 moves the decimal point 1 position to the right.
a multiplication with 1000 3 positions to the right. and so on.
a division by 100 moves the decimal point 2 positions to the left (and fill up with zeros where necessary). and so on.
PLEASE HELP ITS MATH THANK YOUUUU
Answer:
44 millimeters
Step-by-step explanation:
The ratio is set up as millimeters : meters
On the map, 4 millimeters : 9 meters
The actual length ratio is represented as x millimeters : 99 meters
Since we know its proportional, we can set up the equation:
4/9 = x/99
Solve:
4/9 = x/99
4 * 99 = 9x
396 = 9x
x = 44 millimeters
Another Way
Since we already know it is proportional, 99 = 9 x 11
So we can multiply 4 x 11 to get 44 millimeters.
-Chetan K
Plz help me fast urgent thank you :) 20 points
Answer:
C
Step-by-step explanation:
2 times 7 is 14 highest dollar per hour rate
Answer:
Point C
Step-by-step explanation:
In order to determine the price point that will provide the most revenue, you could multiply the price per taco by its corresponding quantity demanded:
A) $3.00 × 2 tacos demanded = $6
B) $2.50 × 4 tacos demanded = $10
C) $2.00 × 7 tacos demanded = $14
D) $1.50 × 8 tacos demanded = $12
E) $1.00 × 12 tacos demanded = $12
Of all the given values, it turns out that at Point C, where price per taco is $2, and the quantity demanded for that price is 7, provides the most return for Rocco's.
Therefore, the price point that providees the most return is $2.
MC)
The equation represents Function A, and the graph represents Function B:
Function A
f(x) = 6x-1
Function B
4
3
2
1
- 2
-3
-4
-5
-6
Which equation best compares the slopes of the two functions?
Previous Question
Take 2points on graph
(0,1)(1,4)[tex]\\ \sf\longmapsto slope=m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{4-1}{1-0}[/tex]
[tex]\\ \sf\longmapsto m=3[/tex]
What is 24659 rounded to the nearest Highest Place
Answer:
20000
Step-by-step explanation:
You take the first non zero number on the left then add zeros for the remaining digits.
HELP POINTS FOR Each answEr quantity 4 times x plus 3 end quantity divided by 5 equals quantity 8 times x minus 1 end quantity divided by 9.
[tex]\displaystyle \frac{4x+3}{5} ^{/9}=\frac{8x-1}{9} ^{/5} \\\\\\ 36x+27=40x-5 \\\\ 40x-36x=27+5\\\\ 4x=32 \\\\ \boxed{x=8 }[/tex]
Step-by-step explanation:
Given fractional expression:
(4x+3)/5 = (8x-1)/9
By doing cross multiplication, we get
⇛4x(9) + 3(9) = 8x(5) - 1(5)
⇛36x + 27 = 40x - 5
Now, combine the like terms in one side.
⇛27x - 40x = -5 + 36
⇛-13x = 31
⇛x = 31/-13 Ans.
