Answer: The population after 3 hours is 13.9 mill.
Step-by-step explanation:
When we have an exponential with:
A = initial population.
r = constant relative growth rate:
t = time.
The function that models this is:
P(t) = A*e^(k*t)
In this case we know that:
A = 3.9 mill.
r = 0.4225 1.
Then the function that models the population of this yeast cell is:
P(t) = (3.9 mill)*e^(0.4225*t)
where t represents the time in hours.
Then if we want to know the population after 3 hours, we should replace t by 3.
P(3) = (3.9 mill)*e^(0.4225*3) = 13.85 mill.
And we want to round our answer to one decimal place, then we must look at the second decimal place, we can see that is a 5, so we should round up.
The population after 3 hours is 13.9 mill.
The exponential function is often used to model the growth or decay of a population
The population size of the yeast cell after 3 hours is 7.9 million
The given parameters are:
[tex]\mathbf{a = 3.9m}[/tex] --- initial number of cells
[tex]\mathbf{r = 0.4225/hr}[/tex] --- rate
The nth term of an exponential function is:
[tex]\mathbf{f(n) = a(1 + r)^{n-1}}[/tex]
After 3 hours; n = 3
So, we have:
[tex]\mathbf{f(3) = a(1 + r)^{3-1}}[/tex]
Substitute values for a and r
[tex]\mathbf{f(3) = 3.9(1 + 0.4225)^{3-1}}[/tex]
[tex]\mathbf{f(3) = 3.9(1 + 0.4225)^{2}}[/tex]
[tex]\mathbf{f(3) = 3.9 \times (1.4225)^{2}}[/tex]
[tex]\mathbf{f(3) = 7.9}[/tex]
Hence, the population size of the yeast cell after 3 hours is 7.9 million
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A relative-frequency distribution is to a variable as a __________ distribution is to a random variable.
Answer:
Probability distributionStep-by-step explanation:
The answer is probability distribution
What is probability distribution?
Probability distribution is a function used to express all the range of random variables and the chances or possibilities of their occurrence.
Basically the function assigns probabilities to some sets of values.
Also There are three major types of probabilities:
Theoretical Probability.
Experimental Probability.
Axiomatic Probability.
A relative-frequency distribution is to a variable as a Probability distribution is to a random variable.
Probability is a type of mathematics which deals with numerical descriptions of how likely an event would occur, or how likely it is that a the occurrence would be true.
The probability of an event is usually between 0 and 1, where 0 represent impossibility and 1 represents the chance of it occurring.
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Given f(x)2x and g(x) = x^2+3 , find f(g(x)).
Answer:
2x^2 + 6.
Step-by-step explanation:
Replace the x in f(x) by g(x):
f(g(x)) = 2(x^2 + 3)
= 2x^2 + 6.
What is the answer to 2+2-3+5=
Answer:
6
Step-by-step explanation:
add,subtract
You spend $4.50 on 5 pounds of apples. What is the unit rate in dollars per pound?
Answer:
$0.90 per pound.
Step-by-step explanation:
4.50:5
5/5=1
4.50/5=0.90
Is the answer True or false
Answer:
true
Step-by-step explanation:
true
What is the volume of a block 6 cm on all sides?
Answer:
3
Step-by-step explanation:
its right
Answer:
The volume is 226 cm
Step-by-step explanation:
To calculate volume, you must do "length X width X height"
Melissa is buying a sweater. The original cost of the sweater is $18.00. The sweater is 15% off, and the sales tax is 8%. How much will the sweater cost?
Answer:
$14.07
Step-by-step explanation:
100-15=85
You change this into a multiplier 0.85.
18x0.85=15.30
100-8=0.92
0.92x15.30=14.07
Hope this helps you
Simplify 5 - 2 · 3 + 4.
A. 13
B. 3
C. -5
D. 21
Answer:
B
Step-by-step explanation:
5 - 2 * 3 + 4
Multiply first
5 - 6 + 4
subtract and add from left to right
5 - 6 + 4 = -1 + 4
-1 + 4 = 3
write a verbal sentence to represent 3n-35=79
Answer: three n minus thirty-five equals seventy-nine
Step-by-step explanation:
the histogram to the right displays the height of 122 trees and Mr. Maciag's subdivision. He is very excited about autumn and the leaves changing colors. Height ranged between 108 cm and 345 cm. Let the function "f" map a tree height to the frequency of the column that tree belongs to. What is the value of f(250)? Explain the steps you followed to find the value.
Answer: 50
Step-by-step explanation:
f(250) = ?
Is asking, "What is the frequency (number of trees) that have a height of 250"
Look at the graph to see that when x = 250 (height), y = 50 (trees).
Therefore, f(250) = 50
6 of 7
Which is the equation of a line parallel to the line with equation y = 3x - 4?
A
y = (1/3)X + 4
B
y = (1/3)x - 4
С
A) y = -3x + 2
A) y = 3x + 2
SUBMIT ANSWER
Socrative
there are 1012 souvenir paperweights that need to be packed in boxes each box will hold 11 paperweights how many boxes will be needed
if a sample of 35 golfers is taken from a population of 72 golfers the sample mean, x, is the mean of how many golfers scores
Answer: 35
Step-by-step explanation:
The sample mean, denoted by (pronounced "x bar"), represents the average value of a given variable in a sample. In this case, we are trying to find the sample mean of golfers' scores.
To calculate the sample mean, we need to sum up all the individual scores in the sample and divide by the number of golfers in the sample. Given that we have a sample of 35 golfers from a population of 72 golfers, we can conclude that the sample mean, , represents the mean of the scores of these 35 golfers.
Mathematically, the formula for calculating the sample mean is: = (x1 + x2 + x3 + ... + xn) / n where x1, x2, x3, ..., xn represent the individual scores, and n represents the sample size. Therefore, the sample mean, , is the average of the scores of the 35 golfers in the sample. To find the exact value, you would need to know the actual scores of each golfer.
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Carmelita used the multiplication table below to write ratios that are equivalent to StartFraction 3 Over 7 EndFraction. A multiplication table. In the row labeled 3, the numbers 3, 6, 9, 12, 15, 18, 21, 23, and 27 are highlighted. In the row labeled 7, the numbers 7, 14, 21, 28, 35, 42, 49, 56, and 63 are highlighted. One number is missing from the equivalent ratio, as shown. StartFraction 21 Over Blank EndFraction What is the missing number? 7 9 24 49
Answer:
The answer is 49.! :)
Step-by-step explanation:
If you look at the table, it shows 3;7. If you look at the 21 in the 2 row, and look under it in the other orange row its 49. So the answer would be 49! :)
Answer:
49
Step-by-step explanation:
Need help ASAP step by step plz 14 points :)
Answer:
39
Step-by-step explanation:
it’s just simple multiplication and addition
Felipe mixes 8 oz a raven 8 oz of sunflower seeds 12 oz of almonds and 12 oz of dried fruit for a recipe how many pounds of mix does Felipe make with his recipe
Francesca plans to compete in a biathlon that involves running and cycling. During one training session, she covered a total distance of 46 miles in four hours. If she ran at a rate of 5 mph and cycled at a rate of 15 mph, how long did she spend cycling?
Answer:
.
Step-by-step explanation:
Use the distance formula
d = vt
where:
d = distance (miles)
v = speed (mph)
t = time (hours)
Let x = run time
Let y = bike time
Total time: x + y = 4
Using these variables we can write an equation representing the formula.
dTotal = drun + dbike
49 = 9x + 22y
Next, we get the equation in terms of only x or y. We'll get it in terms of x.
49 = 9x +22(4 - x)
49 = 9x + 88 - 22x
-39 = -13x
3 = x
Plug in this value of x into the variables to find the distance for each part.
run distance = 9x
bike distance = 22(4 - x)
Juan is saving money for a new car. He has already saved $200 and plans to save $25 per week. This situation can be represented by the function f(x) = 200 + 25x, where x is the number of weeks. How much money has Juan saved after 8 weeks?
Answer:
400
Step-by-step explanation:
200 + 25(8)
200 + 200 = 400
Answer:
400
Step-by-step explanation:
25x8+200=200+200=400
The lengths of a professor's classes has a continuous uniform distribution between 49.2 min and 55.5 min. One class is randomly selected. If P(x > c) = 0.488 , find c
Answer:
52.4 min
Step-by-step explanation:
100% of the times are between 49.2 min and 55.5 min.
48.8% of the times are between x and 55.5 min.
Write a proportion:
(55.5 − 49.2) / 1 = (55.5 − x) / 0.488
0.488 (55.5 − 49.2) = 55.5 − x
3.0744 = 55.5 − x
x = 52.4256
Rounded to the tenths place, the time is 52.4 min.
16.3 as a mixed decimal
A TV is 20% off the original price amount is $180. What is the original amount?
Answer: $200
Step-by-step explanation: $200=100% so then $200-20%=$180=80%
Answer:
9005
Step-by-step explanation:
180$ divided by 20% is 900$
Determine the equation that best represents the line shown on the graph.
Answer:
B
Step-by-step explanation:
Its right
Tom ate at a restaurant. His bill was $12.00. He left a 15% tip. Determine whether each statement about Tom's payment is true or false.
Answer:
True, True, False, True
Step-by-step explanation:
$12.00 ⋅ 0.15 = $1.80
Tom paid $1.80 as tax. That takes care of the second question.
$12.00 + $1.80 = $13.80
So Tom paid more than $12.00 for his meal. That takes care of the first question.
We already know that Tom paid $1.80 as tax. So we know the third question is not right.
And we already know that $12.00 + $1.80 = $13.80. So the fourth question is correct.
Answer:
thanks
Step-by-step explanation:
I’m taking my dog to get groomed in the morning
Amber invest $1,000 for 10 years compounded daily. Jin invests $1,000 for 10 years compounded continuously. If both investments are made at 8% interest rates, determine each of the following. Amber has a total of $ after 10 years. Jin has a total of $ after 10 years. So earns $ more interest.
Compound interest is the interest that is compounded daily, weekly, monthly, annually e.t.c on a loan, investment, or an amount of money kept in a financial institution.
Amber has a total of $2,225.35 after 10 years. Jin has a total of $ 2,225.54 after 10 years. So earns Jin $0.19 more interest.
For Amber:The formula to find the amount compounded daily after 10 years is:
A = P(1 + r/n)nt
Where
P = Principal ( Initial amount) = $1000
R = Interest rate = 8%
n = Number of times interest is compounded = Daily = 365 days
t = Time in years = 10 years
First, convert R as a percent to r as a decimal
r = R/100
r = 8/100
r = 0.08 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 1,000.00(1 + 0.08/365)^(365x10)
A = 1,000.00(1 + 0.000219178)^(3650)
A = $2,225.35
The interest for Amber is:
P (principal) = $1,000.00
A( Amount) = $2,225.35
I (interest) = P - A
= $$2,225.35 - $1,000.00
= $1,225.35
For JinThe formula to find the amount compounded continuously after 10 years is:
A = Pe^rt
Where
P = Principal ( Initial amount) = $1000
R = Interest rate = 8%
n = Number of times interest is compounded = Continuously
t = Time in years = 10 years
First, convert R as a percent to r as a decimal
r = R/100
r = 8/100
r = 0.08 rate per year,
Then solve the equation for A
A = Pe^rt
A = 1,000.00(2.71828)^(0.08)(10)
A = $2,225.54
The interest for Jin is:
P (principal) = $1,000.00
A( Amount) = $2,225.54
I (interest) = P - A
= $$2,225.54 - $1,000.00
= $1,225.54
Comparing the interest for both Amber and Jin, we find the difference to know who earns more.
Jin's interest - Amber's interest
= $1,225.54 - $1,225.35
= $0.19
Jin earns more interest.
Therefore, Amber has a total of $2,225.35 after 10 years. Jin has a total of $ 2,225.54 after 10 years. So earns Jin $0.19 more interest.
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PLEASE PLEASE PLEASE HELP ME Which of these lines has a slope of -3?
The equation of the line showing the slope of -3 is represented by the fourth graph in the image. The correct option is D.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
The line is passing through the points ( 0,0) and (1,-3). The slope of the line is calculated by using the formula below:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -3 -0 ) / ( 1 - 0 )
Slope = -3
Therefore, the equation of the line showing the slope of -3 is represented by the fourth graph in the image. The correct option is D.
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Which of the following coordinates would be the reflection of the point (7, -2) over the x-axis.
a)( -7,-2) b) (7,2 ) c) (-7,2) d) ( 2,7)
Answer:
The correct answer is B) (7,2).
Step-by-step explanation:
I hope this helps!
Which type of parent function is graphed on the coordinate plane?
Answer:
f(x)=∛x
Step-by-step explanation:
please I need help. you will get points
Answer:
t(32) = 94
Step-by-step explanation:
a. I think s is the independent variable
b I think t or t(s) is the dependent variable since the total amount of money depends on how many treats are sold.
t(32) = 30 + 2(32)
t(32) = 30 + 64
t(32) = 94
I'm a little unsure on the dependent and independent variable but I know the function is correct.
Hope this helps :)
Solve and Simplify -3-7/8
Answer:-1.25
Step-by-step explanation: First you add -3 and -7 it is -10/8 then you devide -10/8 and it is -1.25
