A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. Find the rate of growth after 3 hours.
Answers
Step-by-step explanation:
Rate of growth equals 420/100 = 4.2 times per hour
So after t=three hours,
size of culture = 100*(4.2)^t = 100*4.2^3=7408.8 bacteria,
round to nearest unit 7409 bacteria after three hours (after initial size of 100).
Answer:
a) 100•4.2^t
b) P(3)= about 7409 bacteria
c) P’(3)= about 10,632 bacteria per hour
d) t= about 3.2 hours
Step-by-step explanation:
Related Questions
Melvin's bank account has a balance of $9685.06. The previous balance was $6955.01. Melvin made
deposit of $2815.85 and withdrew $100.00. How much did he earn in interest?
$18.40
$16.20
O$18.04
O $14.20
Answers
Melvin earned interest of $14.20.
The compensation a lender or financial institution receives for lending out money is called interest. The percentage of a stockholder's ownership in a company that is also referred to as interest.
The current balance is the previous balance increased by the deposit and interest and decreased by the withdrawal. Let x be the interest.
$6,955.01 + $2,815.85 + x − $100.00=$9,685.06
Combine like terms
$9,670.86 + x = $9,685.06
Subtract $ 9,670.86 from both sides of the equation
x = $14.20
Hence, Melvin earned interest of $14.20.
To know more about Interest check the below link:
https://brainly.com/question/25793394
#SPJ1
determine the values of k such that the given augmented matrix is that of a consistent linear system
Answers
a. The value of k from augmented matrix \(\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)\) is - 1.
b. The value of k from augmented matrix \(\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)\) is - 5.
The complete question is in the attachment. The augmented matrix is a consistent linear system if
Has at least one solution.The last column in the matrix is not a pivot column.a. The augmented matrix \(\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)\)
Making the second row become zero R₂ = R₂ + 3R₁
\(\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: (3 \times 3)&15 \:+\: (3 \times - 5)&3 \:+\: (3 \times k)\end{array}\right)\)
\(\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: 9&15 \:+\: (- 15)&3 \:+\: 3k\end{array}\right)\)
\(\left(\begin{array}{ccc}3&- 5&k\\0&0&3 \:+\: 3k\end{array}\right)\)
From the second row
0x + 0y = 3 + 3k
For the system to be consistent, then
3 + 3k = 0
3k = - 3
k = - 3/3
k = - 1
b. The augmented matrix \(\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)\)
Making the second row become zero R₂ = R₂ + R₁
\(\left(\begin{array}{ccc}k&1&- 6\\5 \:+\: k&- 1 \:+\: 1&6 \:+\: (- 6)\end{array}\right)\)
\(\left(\begin{array}{ccc}k&1&- 6\\k \:+\: 5&0&0\end{array}\right)\)
From the second row
(k + 5)x + 0y = 0
For the system to be consistent, then
k + 5 = 0
k = - 5
Learn more about consistent linear system here: https://brainly.com/question/4945755
#SPJ4
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that exactly 10 flights arrive on time.
Answers
Probability that exactly 10 flights arrive on time is 53.33%.
Given that,
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.
Recently, Southwest Air had the best rate with 80% of its flights arriving on time.
Total number flights in sample = 15
Probability that exactly 10 flights arrive on time is,
P = 10/15 × 80%
= 0.5333
= 53.33%
Hence the required probability is 53.33%.
Learn more about Probability here :
https://brainly.com/question/29083496
#SPJ1
Express 4 250 000 000 000 in standard form
Answers
hi <3
standard form is written in the form a x 10^n
where a is a number between 1 and 10
in this case, you would get 4.25 x 10^12
hope this helps :)
A police checkpoint is set up on New Years Eve to catch drunk drivers. It is known that 8% of drivers on New Years Eve have a blood-alcohol level that is above the legal limit. It is also known that 32% of drivers in the area never drink and drive, but are simply bad drivers. The remaining 60% of drivers never drink and drive and are good drivers. At this particular checkpoint, the police stop 85% of the drunk drivers, stop 38% of the bad drivers, and stop 2% of the good drivers. (a) There are four key events in this problem. Specify the four key events and define notation for each of them. (b) What is the probability that a randomly selected driver will be stopped at the checkpoint? (c) What is the probability that a driver who is stopped at the checkpoint is drunk?
Answers
Answer:
(a) Let the probability drivers are drunk = P(D) = 0.08
The probability that drivers in the area never drink and drive, but are simply bad drivers = P(B) = 0.32
The probability that drivers in the area never drink and drive, and are good drivers = P(G) = 0.60
Let S = event that the police stops the driver.
(b) The probability that a randomly selected driver will be stopped at the checkpoint is 0.2016.
(c) The probability that a driver who is stopped at the checkpoint is drunk is 0.337.
Step-by-step explanation:
We are given that 8% of drivers on New Years' Eve have a blood-alcohol level that is above the legal limit. It is also known that 32% of drivers in the area never drink and drive, but are simply bad drivers. The remaining 60% of drivers never drink and drive and are good drivers.
At this particular checkpoint, the police stop 85% of the drunk drivers, stop 38% of the bad drivers, and stop 2% of the good drivers.
(a) Let the probability drivers are drunk = P(D) = 0.08
The probability that drivers in the area never drink and drive, but are simply bad drivers = P(B) = 0.32
The probability that drivers in the area never drink and drive, and are good drivers = P(G) = 0.60
Let S = event that the police stops the driver
These are the four events stated in the question.
(b) So, the probability that the police stop the drunk drivers = P(S/D) = 0.85
The probability that the police stop the bad drivers = P(S/B) = 0.38
The probability that the police stop the good drivers = P(S/G) = 0.02
Now, the probability that a randomly selected driver will be stopped at the checkpoint is given by = P(S)
P(S) = P(D) \(\times\) P(S/D) + P(B) \(\times\) P(S/B) + P(G) \(\times\) P(S/G)
= (0.08 \(\times\) 0.85) + (0.32 \(\times\) 0.38) + (0.60 \(\times\) 0.02)
= 0.068 + 0.1216 + 0.012
= 0.2016
Hence, the probability that a randomly selected driver will be stopped at the checkpoint is 0.2016.
(c) Now, the probability that a driver who is stopped at the checkpoint is drunk is given by = P(D/S)
P(S/W) = \(\frac{P(D) \times P(S/D)}{P(D) \times P(S/D)+P(B) \times P(S/B)+P(G) \times P(S/G)}\)
= \(\frac{0.08\times 0.85}{0.08\times 0.85+0.32\times 0.38+0.60\times 0.02}\)
= \(\frac{0.068}{0.2016}\) = 0.337
Hence, the probability that a driver who is stopped at the checkpoint is drunk is 0.337.
Which one of the following equations defines the line that contains the point (1,2) and is parallel to the line 4x+3y=7?
Answers
Please help me figure out this math problem
Answers
Answer:
r3
Step-by-step explanation:
r
There are 18 students in the math club.
Of the 18 students, 1/6 have red hair. How many of the students have red hair?
Part b: of the 18 students, 4/6 have brown hair. How many of the students have brown hair?
Part c:
What is the relationship do you notice between the number of students with brown hair and the number of students with red hair?
Answers
a:1/6×18/1=18/6 when simplified is 3
b:4/6×18/1=72/6 when simplified is 12
c.The relationship between the number of students with brown hair and the number of students with red hair is that they are equivalent to one another.
i don’t know how to do it
Answers
The total resistance of three resistors in parallel s 2 Ohms. Option A
What is resistance?Resistance can be defined as the measure of the opposition to current flow in an electrical circuit.
Resistance is measured in Ohms, using the Greek symbol for omega (Ω).
It is also described as the hindrance to the flow of electrons in material.
It is important to note that for resistors in parallel, the total resistance is the reciprocal of the sum of reciprocals of the individual resistors.
This is represented as;
1/Rt = 1/R₁ + 1/R₂ + 1/R₃ ...
Where the variables , 'R' represented the resistors
Now, substitute the values, we have;
1/Rt = 1/4 + 1/8 + 1/8
Find the lowest common multiple
1/Rt = 2 + 1 + 1/8
1/Rt = 4/8
Take the reciprocal of the values
Rt = 8/4 = 2 Ohms
Learn about resistance at: https://brainly.com/question/14883923
#SPJ1
answer quick pls today
Answers
Answer:
60%
Step-by-step explanation:
Answer:
90%
Step-by-step explanation:
Triangle ABC has sides a>b>c. If one of the angles is 60 degrees, name the angle that can be equal to 90 degrees.
Answers
Answer:
angle b
Step-by-step explanation:
let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree
Select all the numbers that are not written in standard form.
A. 80 times 10 to the power of 7
B. 4.82 times 10 to the power of -5
C. 3.88 times 10 to the power of 3
D. 5 times 10 to the power of -2
E. 2.3 times 10 to the power of 3
F. 58.2 times 10 to the power of -4
G. 24 times to the power of 2
H. 500 times 10 to the power of -1
Answers
Answer:
the answer is because in standard form we do not accept this
In Exercises 9 to 14, find the limit of each function at the given point, or explain why it does not exist. 10. f(z) = Arg z at Zo--1 11. f(z) = (1-Im z)-1 at z,-8 and then at zo-8 +1 12.f(z) = (z _ 2) log(z-21 at zo = 2 13, f(z) =-, z#0 at zo = 0 14. f(z) = 2+21,
Previous question
Answers
The limit of each function at the given point i n the question 10 to 14, is explained below.
Limit Of A function:A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.
When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a
10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.
11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.
However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.
12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.
13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.
14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.
Learn more about limit of function, visit:
https://brainly.com/question/7446469
#SPJ1
100 Points! Geometry question. Photo attached. Only looking for an answer to B. Please show as much work as possible. Thank you!
Answers
Answer: Read the solution
Step-by-step explanation:
A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.
B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.
Identify the slope and y intercept of each graph. Drag the 3 points to the correct places on the graph drag and adjust the line so it goes through the points on the line
Y = 2x - 5
M =
B =
Answers
Answer:
slope: 2 , y-int: (0, -5)
Step-by-step explanation:
Set up the appropriate equation to solve for the missing angle.
Answers
65^2 = 4,225
46^2 = 2,116
To find the missing angle, we must subtract 2,116 from 4,225 and then identify the difference’s square root.
4,225 - 2,116 = 2,109
√2,109 ≈ 45
Hence, x ≈ 45.
Answer:
Using the Pythagorean Theorem, we know x^2 + 46^2 is equal to 65^2. With that in mind, it is important to note:
65^2 = 4,225
46^2 = 2,116
To find the missing angle, we must subtract 2,116 from 4,225 and then identify the difference’s square root.
4,225 - 2,116 = 2,109
√2,109 ≈ 45
Hence, x ≈ 45.
Step-by-step explanation:
Alan wants to play a game in which each player gets 3 cards. He has a total of 17 cards. How many people can play? How many cards will be remaining?
Answers
Answer:
5 people can play. 2 cards are left remaining.
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Answers
The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.
What is probability?Probability is defined as the total number of possible outcome of an event.
The repeated colour which are numbered from 1 to 8 are as follows:
Sections 1 and 8 are purple. The probability of getting a purple = 2/8 = 1/4Sections 2 and 3 are yellow. The probability of getting a yellow = 2/8 = 1/4 Sections 4, 5, and 6 are blue. The probability of getting a blue = 3/8Section 7 is orange. The probability of getting a orange = 1/8.Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.
Learn more about probability here;
https://brainly.com/question/24756209
#SPJ1
Answer: B: The probability of landing on yellow is less than the probability of landing on blue.
Step-by-step explanation:
The volume V, of a cylinder is V=pie times radius to the power of 2 h, where r is the radius of the cylinder and h is the height. Using rounding to the nearest whole number, which of the following is an estimate of the volume of a cylinder with a radius of 3.75 inches and height of 6.21 inches
Answers
Answer:
\(274\,\text{in}^3\)
Step-by-step explanation:
\(V=\pi r^2h=\pi(3.75)^2(6.21)\approx274\,\text{in}^3\)
given a pair of similar triangles find the missing length x and the missing angles a,b,c
Answers
Angles of similar triangles are always congruent a: 63, b: 88, c: 29 and x = 53.75
Find the missing length?Based on the information available, there are numerous equations for calculating the area of a triangle. As indicated in the calculator above, please use the Triangle formula for additional information and equations for calculating the area of a triangle as well as determining the sides of a triangle using whatever information is available.
find the ratio between the two triangles:
40 on the left corresponds to 50 on the right = 40/50 = 43/x
to find x:
40x = 43 × 50
40x = 215
x = 215/40
x = 53.75
"angles of similar triangles are always congruent."
a: 63
b: 88
c: 29
To learn more about Angle refers to;
https://brainly.com/question/29452561
#SPJ1
Full question:
Given a pair of similar triangles, find the missing length x and the missing angles A, B, and C.
Rhett is about to begin college and has received a 10-year $7,500
Federal Direct Unsubsidized Loan with an interest rate of 6.4%. He will
be required to begin making payments six months after graduation in
4.5 years. If Rhett decides to capitalize the interest accrued from the
time he receives the funds until he begins making payment, how much
total interest would he pay on this loan?
Answers
The total interest that he would pay on this loan is given as follows:
$2,160.
How to obtain the simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation shown as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.Considering this equation, the interest accrued is given as follows:
I(t) = Prt.
In the context of this problem, the values of these parameters are given as follows:
P = 7500, r = 0.064, t = 4.5.
Hence the interest accrued on the payment is obtained as follows;
I(4.5) = 7500 x 0.064 x 4.5 = $2,160.
More can be learned about simple interest at https://brainly.com/question/25793394
#SPJ1
A hallow sphere sits snugly inside a foam cube so that the sphere touches all sides. Find the volume of the foam. Round answer to nearest tenth.
Answers
Answer:
5832
Step-by-step explanation:
Find the average rate of change between the following points. A. x= -6 to x=4B. x= -2 to x=2
Answers
We have a funtion f(x) in the picture and watn to know the average rate of change in some interval of x, so:
\(\begin{gathered} \text{The rate of change of a function is its derivative:} \\ \frac{df}{dx} \\ \text{The average of th rate betwe}en_{}\text{ x1 and x2 is:} \\ \text{average of rate=}\frac{1}{(x_2-x_1)}\int ^{x_2}_{x_1}\frac{df}{dx}dx \\ \text{average of rate=}\frac{1}{(x_2-x_1)}(f(x_2)-f(x_2)) \\ \text{average of rate=}\frac{(y_2-y_1)}{(x_2-x_1)} \end{gathered}\)In case a), (x1, y1) = (-6, 1) and (x2, y2) = (4, 3), so:
\(\text{average of rate=}\frac{3-1}{4-(-6)}=\frac{2}{10}=0.2\)In case b), (x1, y1) = (-2, -3) and (x2, y2) = (2, -1), so:
\(\text{average of rate=}\frac{(-1-(-3))}{(2-(-2))}=\frac{2}{4}=\frac{1}{2}=0.5\)Of the 450 parking spaces in a parking
lot 8% of the spaces are reserved for
handicapped parking. Of those parking
spaces NOT reserved for handicapped
parking, 18 are suitable for compact cars
only. How many spaces that are NOT
reserved for handicapped parking are
suitable for noncompact cars?
A. 432
B. 424
C. 414
D. 396
E. 369
Answers
Answer:
D. 396
Step-by-step explanation:
8/100 × 450 = 414
414 - 18 = 396
Answer:
answer could be e. 369
Step-by-step explanation:
762×819 _7299
will give brainliest
Answers
The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).
How to simplify the addition between two rational equations
In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:
(n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given(n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse[3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator(3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / ResultTo learn more on rational equations: https://brainly.com/question/20850120
#SPJ1
The sale price of a laptop bag is $35.00. This is 80% of the original price.
What was the original price of the laptop bag?
Answers
Answer:
$43.75
Step-by-step explanation:
(35/8)x10=43.75
It is expected that 30% of the criminals in our prisons are violent offenders, 65% are nonviolent, and 5% are actually innocent. A sample of 300 inmates showed that 90 were violent offenders, 200 were nonviolent, and 10 were innocent. At the .05 significance level, can we conclude that the observed frequencies are different than the expected frequencies?
Answers
PLEASE HELP!!!! I REALLY NEED THIS!!!
Answers
because x=5
What is the surface area of the right cylinder below?
Answers
Answer:
Ok to find the surface area of this cylinder first we need the circumference to find this we do C=πd
C=3.14*18
C=56.52
now we have to multiple this by the height of two
113.04
now we have to find the area of the bottom to do this we do A=πR^2
A=3.14*81
A=254.34
multiple this by two for the two sides we get
508.68
now we add this to 113.04 we get
621.72
since I used 3.14 instead of more digits of pie we can round this up so the answer is C.
Your Welcome
BIFFY OUT!!!
Pairs of shorts had a mark_up of 17%which includes profit and GST at a price of k29. 25.Find the cost price.
Answers
The cost price of the shorts is K22.50.
To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.
Let's assume the cost price of the shorts is represented by C.
The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.
117% of the cost price C can be calculated as (117/100) * C.
GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.
Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.
Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:
Selling price before GST = Selling price - (Selling price × R)
In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:
K29.25 = Selling price - (Selling price × 0.17)
Simplifying the equation
K29.25 = Selling price × (1 - 0.17)
K29.25 = Selling price × 0.83
Selling price = K29.25 / 0.83
Now we can substitute the selling price in terms of the cost price:
K29.25 / 0.83 = (117/100) × C
Simplifying the equation:
C = (K29.25 / 0.83) × (100/117)
Calculating the cost price C:
C = K22.50
Therefore, the cost price of the shorts is K22.50.
for such more question on cost price
https://brainly.com/question/25799822
#SPJ11