Answer:
[tex]r=1.57[/tex], [tex]P(t)=71e^{3t\ln2}[/tex], [tex]P(8)=1191182336[/tex],[tex]P'(8)=2476994033[/tex] [tex]t=2.713\; hr[/tex]
Step-by-step explanation:
[tex](a)[/tex] Find the relative growth rate.
[tex]P=Ae^{rt}[/tex] where given [tex]A=71, P(t)=120\;\;and \;\; t=\frac{1}{3}[/tex]
Find the value of [tex]r[/tex]
[tex]\Rightarrow 120=71 e^{\frac{r}{3} }[/tex]
[tex]\Rightarrow \frac{120}{71} =e^{\frac{r}{3} }[/tex]
[tex]\Rightarrow 1.69=e^{\frac{r}{3} }[/tex]
[tex]\Rightarrow \ln1.69=\frac{r}{3}[/tex]
[tex]\Rightarrow 3\ln1.69=r \;\;\; or \;\;\; r=1.57[/tex]
[tex](b)[/tex] Find an expression for the number of cells after t hours.
[tex]P(t)=71e^{3t\ln2}[/tex]
[tex](c)[/tex] Find the number of cells after 8 hours.
[tex]P(8)=71e^{3\times 8\times \ln2}[/tex]
[tex]\Rightarrow P(8)=1191182336[/tex]
[tex](d)[/tex] Find the rate of growth after 8 hours.
[tex]P(t)=71e^{3\times t\times \ln2}[/tex]
Now differentiate w.r.t. [tex]t[/tex]
[tex]\Rightarrow P'(t)=71\times 3\ln2\times e^{3t\ln2}[/tex]
[tex]\Rightarrow P'(8)=3573547008\ln2[/tex]
[tex]=2476994033[/tex]
[tex](e)[/tex] When will the population reach 20,000 cells?
[tex]20,000=71e^{3t\ln2}[/tex]
[tex]\Rightarrow \ln\frac{20000}{71} =3t\ln2[/tex]
[tex]\Rightarrow \frac{ \ln\frac{20000}{71}}{3\ln2} =t[/tex]
S0, [tex]t=2.713 hr[/tex]
You’re taking an exam in math, and you spend 5 minutes for every 2 questions you answer on the test.(Plz answer! I’m failing and I need to get this correct!)
Given:
Time spend on every 2 questions = 5 minutes.
To find:
The missing values for the given table.
Solution:
Let x be the number of questions and y be the number of minutes.
We have,
Time spend on every 2 questions = 5 minutes
Time spend on 1 question = [tex]\dfrac{5}{2}=2.5[/tex] minutes
Time spend on x questions = [tex]2.5x[/tex] minutes
Now,
[tex]y=2.5x[/tex]
For x=0,
[tex]y=2.5(0)=0[/tex]
For x=1,
[tex]y=2.5(1)=2.5[/tex]
For x=2,
[tex]y=2.5(2)=5[/tex]
For x=3,
[tex]y=2.5(3)=7.5[/tex]
For x=4,
[tex]y=2.5(4)=10[/tex]
Therefore, the required table is
Questions : 0 1 2 3 4
Time (minutes) : 0 2.5 5 7.5 10
0.03is 10 times as much as
Answer:
0.03 is 10 times as much as 0.003
Step-by-step explanation:
its the answer
What is the multiplicative rate of the change of the function?
Since X increases by 1,
Divide the 2nd Y value by the first Y value:
4/6 = 2/3
The answer is 2/3
In triangle ABC, G is the centroid and BE = 9. Find BG and GE.
simplify 0.12×0.04÷ 0.0024 giving the answer in standard forrm
Answer:
2
Step-by-step explanation:
(0.12)(0.04)
0.0024
=2
Ignore the one I filled in
Please help tho!
Answer:
it's the last one
Step-by-step explanation:
The Picture has the question
Answer:
Pythagorean Theorem:
a² + b² = c²
x² + 5x² = 78²
6x² = 6084
6x²/6 = 6084/6
x²=1014
√x² = √1014
x = 31.84
Mark Brainliest Please
Answer:
x ≈ 15.3
Step-by-step explanation:
Based on the pythagoras theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
Since the legs are "5x" and "x" we know the following....
[tex](5x)^{2} + x^{2} = 78^{2} \\25x^{2} + x^{2} = 6084\\26x^{2} = 6084\\x^{2} = 234\\x = \sqrt{234} \\x = 15.3[/tex]
(This is round did to the nearest tenth)
Round 48.078 to the nearest tenth
Answer:
50
Step-by-step explanation:
48 rounds to 50
ANSWER: 50
Answer:
48.1
Step-by-step explanation:
5 and up, add 1
4 and down, don't change and the numbers after are gone.
17÷338
what is the remainder
Answer:
Step-by-step explanation:
= 19 R 15
= 19 15/17
338 divided by 17 equals
19 with a remainder of 15
Solution:
0 1 9
1 7 {3 3 8
− {0
3 3
− 1 7
1 6 8
− 1 5 3
1 5
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＼＼ ＿
＼( •_•) F
< ⌒ヽ A
/ へ＼ B
/ / ＼＼ U
ﾚ ノ ヽ_つ L
/ / O
/ /| U
( (ヽ S
| |、＼
| 丿 ＼ ⌒)
| | ) /
`ノ ) Lﾉ
what is the volume of this rectangular prism 7/5cm 5cm 7/2cm? plz help asap
Answer:
24.5 cm³Step-by-step explanation:
Volume of rectangular prism is:
V = lwhV = 7/5 × 5 × 7/2 = 49/2 =24.5 cm³Answer:
The volume of this rectangular prism with dimensions 7/5cm, 5cm and 7/2cm.
Volume=length× breadth× height
V=7/5cm×5cm×7/2cm= 49/2cm³= 24.5cm³
24.5cm³ is the right answer.3) Which expression is equivalent to: 6(7-2) *
O 67-62
O42-12
O 7-2
O 13 - 8
Answer:
42-12
Step-by-step explanation:
Here you go mate
Step 1
6(7-2) Equation
Step 2
6(7-2) simplify
6x5
answer
42-12=30 check
9/7 simplified is?
a) 21/14
b) 21/7
c) 22/7
d) 21/3
Answer:
None of those answers is true.
Step-by-step explanation:
Answer:
None
Step-by-step explanation:
Dogs or cats which one is better???
Answer:
dogs
Step-by-step explanation:
they are more freindly
Answer:
dogs
Step-by-step explanation:
i just had to take a test and one of the questions was to write an essay about dogs or cats being better so i searched it up and it said dogs
-[tex]-8\9 + 1/5+ -8/15
Answer:
[tex]-\frac{11}{9}[/tex] , OR [tex]-1\frac{2}{9}[/tex], OR -1.2
Step-by-step explanation:
[tex]-\frac{8}{9}+\frac{1}{5}+(-\frac{8}{15})[/tex] When there is a (+) in front of an expression in parentheses, the expression remains the same
[tex]-\frac{8}{9}+\frac{1}{5}-\frac{8}{15}[/tex] Calculate the sum or difference
[tex]-\frac{11}{9}[/tex]
lololljhfhjfgdfhfghghjf
yo
Help!!! Worth 50 points!
Answer:
Step-by-step explanation:
Hey I can't read what's in the picture it's blurry
Answer:
According to the words used by the poet, they made the reader visualize a little village with a group of hardworking men. I know this because of the little details the poet used, like ‘washing their red hands’, or ‘easing their stiff limbs’, meaning that they are tired for an exhausting day of work. To sum it up, the poet gave the effect of a hard working, nostalgic effect.
Step-by-step explanation:
Determine the x- and y- intercepts for the graph defined by the given equation.
y = x + 8
a. x-intercept is (0,8)
c. x-intercept is (-8, 0)
y-intercept is (-8, 0)
y-intercept is (0,8)
b. x-intercept is (0, -8)
d. x-intercept is (8,0)
y-intercept is (8,0)
y-intercept is (0, -8)
Answer:
Y-intercept is (0,8)
Step-by-step explanation:
The line of an equation is y=mx+b. M in this case is 1 and "b" is the y intercept. since in the place of b is positive 8 the y-intercept is 8
Given that points A, B, and C are the midpoints of their respective sides, which of the following is true about the figure?
Question 2 options:
A)
≅
B)
ΔBCZ ≅ ΔYAB
C)
≅
D)
ΔZYX ≅ ΔABC
Answer:
zx ≅ ab
Step-by-step explanation:
took the test
A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore.
x 0 1 2 3 4 or more
% 43% 35% 15% 6% 1%
(a) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.
(b) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)
(c) Compute μ, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)
μ = fish
(d) Compute σ, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)
σ = fish
Answer:
a. 0.57
b. 0.22
c. 0.87
d. 0.9450
Step-by-step explanation:
A.
P(X>=1)
= 0.35 + 0.15 + 0.06 + 0.01
= 0.57
This is the probability of catching one or more fishes.
b.
P(X>=2)
0.15 + 0.06 + 0.01
= 0.22
This is the probability of catching 2 or more fishes.
C.
Compute μ
μ = E(X)
= (0x0.43) + (1x0.35) + (2x0.15) + (3x0.06) + (4x0.01)
= 0+0.35+0.3+0.18+0.04
= 0.87
D.
The standard deviation
Sd = √V(X)
V(X) = E(X²) - (E(X))²
E(X²) = (0²x0.43)+(1²x0.35)+(2²*0.15)+(3²*0.06)+(4²*0.01)
E(X²) = 0.35+0.6+0.54+0.16
= 1.65
V(X) = 1.65 - (0.87)²
= 1.65 - 0.7569
= 0.8931
Sd = √0.8931
= 0.9450
Round 4213 to 3.sf, 2,sf and 1.sf
Answer:
3sf-0.421, 2sf- 42, 1sf-0004
Answer:
4210 4200 4000
Step-by-step explanation:
your welcome :)
The equation y=39/4x describes the number of miles y that an airplane travels in x minutes. What is the constant speed of the airplane in miles per minute? How many miles does the airplane travel in hours?
Answer:
The plane goes 9.75 Miles/Minute
The plane goes 585 Miles/Hour
find the value of p in the figure
Answer:
Im pretty sure the answer is maybe 90 degrees
Craig earns extra money as a lifeguard he earns $37 for 4 hours and $64.75 for 7 hours. write and equation for the following proportional relationship
Answer: m = 9.25h
Step-by-step explanation:
The money he earns per hour is $9.25
m = total money h = hours he worked
m = 9.25h
In ASTU, mZS = (6x – 15)°, mZT = (2x − 2)°, and
mZU = (4x – 7)º. What is the value of x?
Answer:
x = 17
Step-by-step explanation:
all three expressions should be added together and set equal to 180 degrees
6x - 15 + 2x - 2 + 4x - 7 = 180
now combine like terms
12x - 24 = 180
add 24
12x = 204
x = 204/12
x = 17
Who can help me out with this question
Answer:
i think it is d) neither
Step-by-step explanation:
......
Solve this problem
...........
Answer:
40.5
Step-by-step explanation:
[tex]\frac{2^3*3^4*4}{2*32} \\\\Firstly\ we\ have\ to \ expand\ the\ terms\ as\ factors:\\\\=\frac{(2*2*2)*(3*3*3*3)*(2*2)}{(2)*(2*2*2*2*2)`}\\\\We\ cancel \ terms\ that \ are\ common\ to \ both \ numerator\ and\ denominator\ to\ get:\\\\=\frac{3*3*3*3}{2}\\\\ =\frac{81}{2} \\\\We\ simplify\ the\ terms\ to \ its\ lowest\ form:\\\\=40.5[/tex]
Therefore the answer to the problem = 40.5
What is the final price of a $50 pair of headphones with sales tax of 5%.
Answer:
$52.50
Step-by-step explanation:
$50+5%= $52.50
Hope this helps
Find the value of g (x) = 7/8 x - 1/2 where x is 7
Answer:
5.625
Step-by-step explanation:
What is the constant of proportionality for the following situation?
A student reads 65 pages per hour.
Answer:
for every 1 hour he reads 65 pages
Step-by-step explanation:
make a graph
65,1
and you got up from there
rise over run
ok
kazito sold an item for sh 4950 and made a 12 ¹/2profit.what was the cost price of the item?
Answer:
[tex]Cost\ Price = 4331.25[/tex]
Step-by-step explanation:
Given
Selling Price = Sh. 4950
Profit = 12.5%
Required
Determine the cost price
Profit is calculated as:
[tex]Profit = \frac{Selling\ Price - Cost\ Price}{Selling\ Price} * 100\%[/tex]
Substitute values for Selling Price and Profit
[tex]12.5\% = \frac{4950 - Cost\ Price}{4950} * 100\%[/tex]
Cross Multiply:
[tex]4950 * 12.5\% = (4950 - Cost\ Price) 100\%[/tex]
[tex]\frac{4950 * 12.5\%}{100\%} = (4950 - Cost\ Price)[/tex]
[tex]618.75 = (4950 - Cost\ Price)[/tex]
Collect Like Terms
[tex]Cost\ Price = 4950 - 618.75[/tex]
[tex]Cost\ Price = 4331.25[/tex]
Hence, the cost price of the item is: Sh. 4331.25