Answer:
x² = 2
x = sqrt. of 6
x = (+-)2.449
Step-by-step explanation:
brainliest plz
A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If the height of the bounce follows geometric progression, find the general term that represent the situation in term of k. [2 marks] Hence, if the ball dropped from a height of 235ft, determine i. the highest height achieved by the ball after six bounces ii. the total distance travelled by the ball when it strikes the ground for 12th time [2 marks] [3 marks b) The number of cell double after each process of cell division every 2 hours. If there are 120 bacteria initially, how many bacteria will be there after one and half day? [4 marks]
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.
Read more about exponential functions at:
https://brainly.com/question/11487261
help with 14 please!!! please also explain!!
Answer:
f = ab/(a + b)Step-by-step explanation:
#14Given:
1/f = 1/a + 1/bSolving for f:
1/f = b/ab + a/ab1/f = (a + b)/ab cross - multiplyf(a + b) = ab divide by (a + b)f = ab/(a + b)Find the volume of the composite solid.
Answer:
volume________
7 ft 8 ft 7.5 ft 7 ftI’m a little lost on this
A landowner recently sold a large plot of land. The sale decreased his total acreage by 12%. Let v be the original acreage.
a. Write two equivalent expressions that represent the new acreage.
Answer:
.88v or [tex]\frac{22}{50}[/tex]v
Step-by-step explanation:
Answer:
Step-by-step explanation:
Link is needed
A bag of M&M’s has 7 red, 2 green, 3 blue, and 8 yellow M&M’s. What is the probability of randomly picking: (Round to 4 decimal places)
Answer:
Y = 40%
R or G = 25%
O = 0%
Step-by-step explanation:
Total M&M's = 7+2+3+8 = 20
PY = 8/20 = .4 or 40%
P(R or G) = (2+3)/20 = 5/20 = .25 = 25%
PO = 0/20 = 0%
Same value as 40% of 84
Answer:
33.6
you are welcome :)
Step-by-step explanation:
X-6y=6 find an ordered pair
Answer:
(6,0) or (0,-1)
Step-by-step explanation:
X-6y=6
X=6+6y
X/6=1+y
X/6-1=y
y=X/6-1
We'll use substitution to solve the ordered pair. Let's say Y = 0. We'll insert it back into our equation.
0=X/6-1
1=X/6
6=X
(6,0)
We can also start with X being = 0.
y=0/6 -1
y=-1
(0,-1)
I've attached what that would look like as a graph.
Write the equation in function form:
8x + 4y = 20
x^2-6x+13 step by step to vertex form
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
What is 449,650 rounded to the nearest ten thousand?
400,000
440,000
449,000
450,000
Answer:
450,000
Step-by-step explanation:
The ten thousand digit is 4 and if we compare it to 9, it is bigger then 5 therefore it is rounded up and you get the answer of 450,000
Evaluate the expression 6^2-(8–4^2+7
Answer
11
you can confirm from by yourself or tell
please mark this answer as brainlist
please ans very easy question
Answer:
what is the question please tell me on comment
I’m doing my math homework and I don’t understand it all. I did most of it in class but I don’t get it still so here’s the question
Question:
-4/3(3q -10)
Answer:
-4q+ 40/3
Step-by-step explanation:
Find the sum of A.5 B.3 C.4 D.1
Answer:
D. Maybe? brainliest suggested
Step-by-step explanation:
Aashi buys
2 packets of bread rolls costing £1.40 for each packet
1 bottle of ketchup costing £1.80
3 packets of sausages
Aashi pays with a £10 note.
She gets 45p change.
Work out the price in pounds (£) of one pack of sausages.
(you will get brainliest) !! :D
Price of one unit Sausage = 1.65
Sum ( Price x Quantity) = Total Expenditure
Price of Bread x Quantity of Bread + Price of Ketchup x Quantity of Ketchup + Price of Sausage x Quantity of Sausage
Total Expenditure Value = 10 - 0.45 = 9.55
Let price of sausage = P
Therefore, 2 (1.40) + 1 (1.80) + 3 P = 9.55
2.80 + 1.80 + 3 Ps = 9.55
4.6 + 3 P = 9.55
3P = 9.55 - 4.60 = 4.95
P = 4.95 / 3 = 1.65
To learn more, refer https://brainly.com/question/16910784?referrer=searchResults
Please help I’m timed thank you!!!
Answer:
BAP=12
ABP=32.5
BCP=45.5
If the sales tax rate is 8.9%, how much tax will be paid on a $457 tv?
State your answer in terms of dollars, rounded to the nearest cent (hundredth).
Do not include a $ sign with your response.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
should be 40
1.6[3(5(2))-5]
1.6[30-5]
1.6[25]
40
An academy requires there to be 3 teachers for every 72 students and 5 tutors for every 60 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 132 students?
Simplify.
- 2x - } – 5x + i + x
-
х
-
17/3
-
3
+
10
х
Enter your answer in the box.
Do not use decimals in your answer.
Answer:
I'dont think it's 77 or not right
Given info:-
Evaluate:
[(1⅕ - 2/5).(-3/5)³]÷(-9)
⇛[6/5 - 2/5).(3³/5³)]÷(-9)
Take the LCM 5 & 5 is 5.
⇛[(6-2 /5). (3*3*3/5*5*5)]÷(-9)
⇛[(4/5).(27/125)]÷(-9)
⇛[4/5 × 27/125)]÷(-9)
⇛[(4*27)/(5*125)]÷(-9)
⇛[20/625] ÷ (-9)
⇛[20/625] ÷ 1/9
⇛20/625 × 9/1
⇛(20*9)/(625*1)
⇛180/625
Now, reduce the fraction by extracting and cancaling out with 5.
⇛36/125 or 0.228 Ans.
Hope this helps!
evaluate f(m-5) and simplify if f(x)=5x-9
Answer:
f(m-5) = 5m-34
Step-by-step explanation:
f(x)=5x-9
Replace x with m-5
f(m-5) = 5(m-5) -9
Distribute
= 5m-25 -9
= 5m-34
Answer:
answer is 5m - 34
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!
help #2 #4 #6 #8 #10 #12
__% of 4 is 7
Please answer its due today
Answer:
175%
hope that helps. :)
Can someone help me please
Answer:
The financial aid covers $ 1,875
Student needs to pay out-of-pocket $635
Step-by-step explanation:
(2,500) * (3/4) = 7500/4 = 1,875
2,500 - 1,875 = 635
PLZ HELP. SEE PICTURE FOR DETAILS ON THE PROBLEM
Answer:
[tex] \frac{1}{3} x + \frac{1}{2} [/tex]
This is the answer after simplifying
if y varies inversely as x, when y=20 and x=2 find the equation for y. then, find y when x=4
Answer:
the equation for y=20=1/2
Step-by-step explanation:
y=1/4
y=0.25
Please help me with number 8
Answer:
jjejejkwkwkqkkqkqkqkkqkqkq
Question 7 of 10
Which statement best describes an example of a short-term investment
strategy?
A. Mariam buys an IRA that she can't withdraw from without penalty
until she's 59.5.
B. Mariam invests $4,000 in a mutual fund to create a new income
stream.
O C. Mariam buys a certificate of deposit to set aside money for a
down payment on a car.
D. Mariam buys 100 shares of stock in a proven company known for
solid, dependable performance over time.
SUBMIT
Answer:
C
Step-by-step explanation:
Its not A because she can't withdraw it for however many years.
Its not B because creating a new income stream is a long term investment.
Its not D because it says she buys stock of a long-term performing company