Answer:
Both cultures will have the same population after 11 hours.
Step-by-step explanation:
Exponential equation for population growth:
The exponential equation for population growth is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
A culture of 100 bacteria grows at a continuous rate of 20%.
This means that [tex]P(0) = 100, r = 0.2[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P_{1}(t) = 100(1+0.2)^t[/tex]
[tex]P_{1}(t) = 100(1.2)^t[/tex]
The other culture starts to hours later, and we want to take that time as a parameter. So
[tex]P_{1}(2) = 100(1.2)^2 = 144[/tex]
Which means that when culture 2 growth starts, the population size of culture 1 is described by the following equation:
[tex]P_{1}(t) = 144(1.2)^t[/tex]
Two hours later 60 of the same type of bacteria are placed in a culture that allows a 30% growth rate.
This means that [tex]P(0) = 60, r = 0.3[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P_{2}(t) = 60(1+0.3)^t[/tex]
[tex]P_{2}(t) = 60(1.3)^t[/tex]
After how many hours do both cultures have the same population?
This is t for which:
[tex]P_{1}(t) = P_{2}(t)[/tex]
So
[tex]144(1.2)^t = 60(1.3)^t[/tex]
[tex]\frac{(1.3)^t}{(1.2)^t} = \frac{144}{60}[/tex]
[tex](\frac{1.3}{1.2})^t = \frac{144}{60}[/tex]
[tex]\log{(\frac{1.3}{1.2})^t} = \log{\frac{144}{60}}[/tex]
[tex]t\log{\frac{1.3}{1.2}} = \log{\frac{144}{60}}[/tex]
[tex]t = \frac{\log{\frac{144}{60}}}{\log{\frac{1.3}{1.2}}}[/tex]
[tex]t = 11[/tex]
Both cultures will have the same population after 11 hours.
PLSSSS HELP MEEE WITH THISSSS
Answer:
x=-6 y=-26
Step-by-step explanation:
in the first is -4 every time, in the second is -20 every time
PLEASE HELP The diameter D of a sphere is 19 m. Calculate the sphere's surface area A.
Use the value 3.14 for at, and round your answer to the nearest tenth.
Answer:
A = 1,133.5 m³
Step-by-step explanation:
Surface area of a sphere, A = 4πr²
π = 3.14
Radius, r = diameter / 2
= 19 m / 2
= 9.5 m
Surface area of a sphere, A = 4πr²
A = 4 * 3.14 * (9.5)²
= 4 * 3.14 * 90.25
= 1,133.54
A = 1,133.54 m³
To the nearest tenth
A = 1,133.5 m³
If the dimensions of the following cylinder are quadrupled, what will be the surface area of the new similar cylinder?
13,816 in. 2
85,106.56 in. 2
6,908 in. 2
27,632 in. 2. I WILL GIVE BRAINLIEST!
Answer:
27,632
Step-by-step explanation:
In the comments that is the answer to the next question but the answer for this question is 27632 in.^2
35 POINTS PLEASE HELP ME. Tell whether each triangle with the given side lengths is a right triangle.
11, 60, 61
Answer:
Step-by-step explanation:
no not right angle
i need help with this
Answer:
1. measure of angle E is 90 degrees
2. Measure of angle F + measure of angle G is 90 degrees
Step-by-step explanation:
Angle E is 90 degrees because it is marked as a right angle (the square)
A triangle has 180 degrees so if E is 90 degrees then the other 2 also have to equal 90 degrees
If a jeweler buys a piece for $250 from a wholesaler and the markup is 30% what is the markup
Answer:
Markup will be 30% of 250$ =75$
Answer:
75 dollars
Step-by-step explanation:
I hope this answer helped you. I'm not gonna give a step by step explanation though
Write a ratio and a percent for the shaded area.
6/100 - 60%
6/10 - 60%
12/20 - 60%
36/100 - 36%
Acellus
Find the area of the following
parallelogram:
1.5 cm
2.5 cm
2.25 cm
A= [?] cm?
Enter the exact answer as a decimal.
Enter
Answer:
Question:Find the area of the following
parallelogram:
1.5 cm
2.25 cm
Solution:[tex] \huge\fbox\purple{Area = Product of the given 2 sides}\ [/tex]
(1.5×2.25)cm²= 3.375 cm²Hope it helps
-------☆ﾟ.･｡ﾟᵴɒƙυᴚᴀ_ƨȶäᴎ❀
Step-by-step explanation:
[tex]3.375 \: {cm}^{2} [/tex]
I hope it helps
have a great day
#Captainpower
HELP ME PLZ!!! This is too hard
Answer:
The solution of this trigonometric identity is [tex]\theta = 56.310^{\circ} \pm 180\cdot i ^{\circ}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
Step-by-step explanation:
Let [tex]7\cdot \tan \theta - 8 = 5\cdot \tan \theta -5[/tex], we proceed to simplify the expression and solve afterwards either by algebraic or by trigonometric means:
[tex]7\cdot \tan \theta -8 = 5\cdot \tan \theta -5[/tex]
[tex]2\cdot \tan \theta = 3[/tex]
[tex]\tan \theta = \frac{3}{2}[/tex]
[tex]\theta = \tan^{-1} \frac{3}{2}[/tex]
The tangent is a trigonometric function with a period of 180°. Hence, we find that the family of angles associated with such value is:
[tex]\theta = 56.310^{\circ} \pm 180\cdot i ^{\circ}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
Find the value of each trigonometric ratio to the nearest ten-thousandth
what 2 factors can be multiplied to give 120 and added or subtracted to give 7
Write the decimal as a percent
Answer:
3/5
Step-by-step explanation:
Answer:
66%
Step-by-step explanation:
0.6 repeating is 66%.
From decimal to percent:
To get a percent from a decimal number, move the decimal over twice to the right. In this case, 0.66 would become 66% because the decimal moved to the right twice.
From decimal to fraction to percent:
I already know that 2 divided by 3 is 0.6 repeating. 2 divided by 3 could also be written as [tex]\frac{2}{3}[/tex]. So the first step is complete, from the decimal 0.6 repeating to the fraction [tex]\frac{2}{3}[/tex]. Now from [tex]\frac{2}{3}[/tex] to a percent. If you get a 2 out of 3 ([tex]\frac{2}{3}[/tex]) you would get a 66%.
Hope this helps! Please vote me as Brainliest. Let me know if you need more of an explanation. Hope it's not too late. Good luck with whatever you are doing! Have an amazing day!
What is the relationship between the number of sides of the base of a prism and the number of lateral faces? The number of sides of the base of a prism is less than the number of lateral faces. The number of sides of the base of a prism and the number of lateral faces is equal. The number of sides of the base of a prism is greater than the number of lateral faces. There is no consistent relationship between the number of sides of the base of a prism and the number of lateral faces.
Answer:
Every prism has as many faces, and edges, as its base has sides. Thus, a prism with an octagonal (eight sided) base has eight lateral faces, and eight lateral edges. Each lateral face meets two other lateral faces, as well as the two bases. As a consequence, each lateral face is a four sided polygon.
The number of sides of the base of a prism and the number of lateral faces is equal.
What is a prism?A prism is a three-dimensional object with two congruent and parallel faces, called the bases and it encloses the space between the bases. Every cross-section parallel to the base of a prism is congruent to its base.
How do we solve the given question?In the question, we are asked to tell the relationship between the number of sides of the base of a prism and the number of lateral faces.
We let the number of sides of the base of the prism be s, and let the number of lateral faces of the prism be f.
We know that a prism has two parallel and congruent bases and every corresponding side of the base are connected by a pane. These planes are the lateral faces of the prisms. As each corresponding pair of sides is connected by one lateral face, the number of the lateral face is equal to the number of sides of the base.
∴ The number of sides of the base = The number of lateral faces of the prism
or, s = f.
∴ We can say that the number of sides of the base of a prism and the number of lateral faces are equal.
Learn more about prisms at
https://brainly.com/question/1297098
#SPJ2
Choose the correct equation
Answer:
A: 160+12m=400
Step-by-step explanation:
i am very smart just trust me on this one
Answer:
a
Step-by-step explanation:
You have 4 blue shirts, 6 white shirts,
2 green shirts, and 6 red shirts.
What is the probability of selecting a BLUE
shirt from your dresser?
Please help me!! I’ll give you brainliest if you give me a good answer :(
Answer:
4.5%
Step-by-step explanation:
Give an example of a number that has many factors and an example of a number that has few factors.....
Answer:
42: 1, 2, 3, 6, 7, 14, 21, 42
43: 1, 43
Step-by-step explanation:
Michelle invests $1000 at a bank offering 3% compounded quarterly.
Answer:
A = 1000(1 + .03 /4)4t
Explanation:
The money invested is the principal that is $ 1000.
The quarterly interest = 3/4 = 0.75 %
Assuming the number of years the money invested was x, then the interest period (n) will be 4 x (quarters)
Using the formula, A = P (1 + r/100)∧n
Therefore, the growth of the investment will be given by
1000( 1.0075)∧n, where n is the interest period.
machine K and J were both serviced this week.
-Machine K is serviced every 6 weeks
-machine J is serviced every 8 weeks
what is the fewest numbers of weeks that will pass before both machines are serviced again in the same week?
Answer:
the 3rd raikages will
Step-by-step explanation:
Can you help me please I’ll mark you brainliest
Answer:
4
Step-by-step explanation:
Since its a 45-45-90 triangle then the 2 legs are going to be the same.
Answer:
90°
Step-by-step explanation:
Always remember that the sum of all angles is 180°.
So there are two 45° angles, so just add them up and you get 90
So if you subtract 90 from 180, you get 90, and that's your answer
Suppose a jar contains 13 red marbles and 11 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Of the last 20 contestants on a game show, 8 won a prize what is the experimental probability that the next contestant will win a prize?
Answer:
2/5
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
Experimental probability is based on the result of an experiment that has been carried out multiples times
probability that the next contestant will win a prize = number of contestants that won in the last games / total number of contestants in the last games
8/20
To transform to the simplest form. divide both the numerator and the denominator by 4
2/5
HELP PLS!!!!!
A company produces individually wrapped spherical cookies. The minimum amount of wrapping material needed to
cover a cookie, assuming no edges overlap, is 314 square inches. What is the diameter of one cookie?
5 in
10 in
20 in
25 in
Answer:
10 in
Step-by-step explanation:
r^2= 314/3.14
r^2=100
r=10 in
hope i helped!
Triangle IJK, with vertices I(-9,-8), J(-5,-6), and K(-7,-3), is drawn on the coordinate grid below.
Answer:
[tex]Area= 8[/tex]
Step-by-step explanation:
Given
[tex]I = (-9,-8)[/tex]
[tex]J = (-5,-6)[/tex]
[tex]K = (-7,-3)[/tex]
The complete part of the question is to calculate the area of IJK
The area is calculated using:
[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3 |[/tex]
Where:
[tex]I = (-9,-8)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]J = (-5,-6)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]K = (-7,-3)[/tex] --- [tex](x_3,y_3)[/tex]
So, we have:
[tex]Area = \frac{1}{2}|(-9*-6) - (-5*-8) + (-5*-3) - (-7*-6) + (-7*-8) - (-9*-3) |[/tex]
Solve the brackets
[tex]Area = \frac{1}{2}|54 - 40 + 15- 42 + 56 - 27 |[/tex]
[tex]Area = \frac{1}{2}|16|[/tex]
The absolute value of 16 is 16
So:
[tex]Area = \frac{1}{2} * 16[/tex]
[tex]Area= 8[/tex]
Guests at a campground can stay in a teepee
shaped like the rectangular pyramid shown. If
the height of the teepee is 18 feet, find the total
volume of the teepee.
10 feet
15 feet
Answer:900ft
Step-by-step explanation: v=l×w×h/3 =15×10×18/3=900
The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph: A graph titled Motion of a Car is shown with Time in hours labeled on x-axis and Distance from Starting Point in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, and the scale on the y-axis shows the numbers 0, 16, 32, 48, 64, 80, 96. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 1, 16. The second straight line joins 1,16 and 4,16, and the third straight line joins ordered pair 4,16 with the ordered pair 5,48.
Which of the following best describes the motion of the car that is shown?
A) It travels for 1 hour, then stops for 3 hours, and finally travels again for 2 hours.
B) It travels for 1 hour, then stops for 3 hours, and finally travels again for 5 hours.
C) It travels for 1 hour, then stops for 4 hours, and finally travels again for 5 hours.
D) It travels for 1 hour, then stops for 3 hours, and finally travels again for 1 hour.
Answer:4
Step-by-step explanation:because 4
Answer:
its D i just did the test
Step-by-step explanation:
If Laura were able to find a 0 iron, about how far could she hit it?
Answer:
I got 219 but I'm not sure that's the answer.
Step-by-step explanation:
27 502 tickets were sold for a ball game at the stadium.34 206 were printed .how many ticket were sold?
Answer:
6704
Step-by-step explanation:
34206-27502=x
A company sells fruit smoothies in two sizes: 6 ounces and 20 ounces. You know that a 6-ounce bottle contains 96 milligrams of sodium. If the amount of sodium is directly proportional to the fluid ounces of smoothie, how many milligrams of sodium does a 20-ounce bottle contain?
And can yall put an explanation please
Answer:
320 milligrams of sodium
Step-by-step explanation:
Create a proportion where x is the milligrams of sodium a 20 ounce bottle has:
[tex]\frac{96}{6}[/tex] = [tex]\frac{x}{20}[/tex]
Cross multiply and solve for x
1920 = 6x
320 = x
So, a 20 ounce bottle will have 320 milligrams of sodium
PLEASE HELP ME
Which situation can be represented by this equation?
6 + 0.50x = 26
Anne earns money walking dogs. She charges $6 per walk plus $0.50 per dog. What is x, the amount of money Anne charges to take one dog on 26 walks?
Anne pays $6 to enter a carnival and $0.50 for every ride she goes on at the carnival. What is x, the number of rides Anne can go on if she has $26 to spend at the carnival?
Anne earns $6.50 per hour for babysitting. What is x, the number of hours Anne babysits if she earns $26?
Anne earns $6.50 per hour for babysitting. What is x, the number of hours Anne babysits if she earns $26?
Answer:
Anne pays $6 to enter a carnival and $0.50 for every ride she goes on at the carnival. What is x, the number of rides Anne can go on if she has $26 to spend at the carnival?
Step-by-step explanation:
Answer:
it the second situation mate
Step-by-step explanation:
hope i helped you amd it is correct..
How many fewer minutes did Iman cycle in week 1 than in week 4?