Answer:
[tex]P(t) = 10000e^{0.1733t}[/tex]
Step-by-step explanation:
The population of bacteria grows exponentially, which means that it can be represented by a function in the following format:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate.
A petri dish has 10, 000 bacteria in it.
This means that [tex]P(0) = 10000[/tex]. So
[tex]P(t) = 10000e^{rt}[/tex]
After 4 hours the bacteria’s population increased to 20,000.
This means that [tex]P(4) = 20000[/tex], and we use this to find the growth rate. So
[tex]P(t) = 10000e^{rt}[/tex]
[tex]20000 = 10000e^{4r}[/tex]
[tex]e^{4r} = \frac{20000}{10000}[/tex]
[tex]e^{4r} = 2[/tex]
[tex]\ln{e^{4r}} = \ln{2}[/tex]
[tex]4r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{4}[/tex]
[tex]r = 0.1733[/tex]
So, the formula is given by:
[tex]P(t) = 10000e^{0.1733t}[/tex]
Solve the inequality.
8 + 12x < -16
Answer:
x < - 2
Step-by-step explanation:
I hope this helps.
Answer:
x < -2
Step-by-step explanation:
1) 12x+8< -16 Rearrange the expression
2) 12x < -16+8 Separate the constants and variables
3) 12x< -24 Add the the number
4) 12x/12 < -24/12 Divide both sides by 12
5) x< -2 Answer
Hope that helps.
If our school store purchased 144 mittens last year, and this year we would like to purchase 30% more than last year. How many mittens do we need to order this year?
Answer: It would be 43 mittens
Step-by-step explanation:
3x + 4y + 4 > 0
how would i solve this?
The graph at the bottom shows the relationship of the amount of time (in seconds) to the distance (in feet) run by a jaguar.
What does the point (5,290) represent in the context of the situation?
Answer:
5,290 repersent the distence that the jaquar jumped . and ran.
Step-by-step explanation:
pleas mark brainist plz happy to help
PLZZ HELP !! Select the correct answer. What are the zeros of the function y= (x-4)(x^2 - 12x+36)
A. -6,4 and 6
B. 4 and 6
C. -6 and -4
D. 0, 4, and 6
The zeroes of any function are where the function touches or passes through the x-axis.
To find these zeroes, we can factor, and set each part equal to 0.
y = (x - 4)(x^2 - 12x + 36)
It looks like some of the factoring was already done for us! All we have to do is factor the quadratic. To do so, we need two numbers that multiply to equal (a * c) and add up to b. In this case those two numbers are -6 and -6.
y = (x - 4)(x - 6)(x - 6)
Finally, set each part equal to 0!
x - 4 = 0
x = 4
x - 6 = 0
x = 6
x - 6 = 0
x = 6
Therefore, the zeroes of the function are 4 and 6, option B.
Hope this helps!! :)
3 more than x is less than 6
Answer:
x = 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
its complicated to explain sorry, but trust me
PLEASE HELP 17 points
Answer: I say B its a bit hard but i think i got it not sure but Good Luck!
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
When dilating a shape, you need to take the side length and multiply it by the scale factor.
what is 2-2? i dont know
Answer:
2-2 = 0
Step-by-step explanation:
2 is a positive number
While the second 2 is a negative 2
(-2)
so a positive and a negative number can cancel eachother out
Therefore the answer is 0 since they are both 2 :)
Leo has 3 8/9 ounces of sunblock. He uses one-fifth of an ounce at the beach. How much does he have left?
Step-by-step explanation:
7/9pls mark as brainliest
Answer:
Step-by-step explanation:
It's 3 31/45
Ming works as a quality assurance analyst at a bottling factory. She wants to use a one-sample z interval to estimate what proportion of 500 ml bottles are underfilled. She wants the margin of error to be no more than 4% at 90% confidence. What is the smallest sample size required to obtain the desired margin of error?
a) 271
b) 423
c) 651
d) 888
Answer:
Sample size is [tex]n=423[/tex]
Step-by-step explanation:
Given that,
Margin of error [tex]=4[/tex]%
Confidence level [tex]=90[/tex]%
Suppose, sample proportion[tex]=0.5[/tex]
i.e. [tex]\hat{P}=0.5[/tex]
We know that,
Margin of error [tex]=2^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]
∴ [tex]1.64\sqrt{\frac{0.5(0.5)}{n} } \leq 4\%[/tex]
[tex]\Rightarrow 1.64\sqrt{\frac{0.25}{n} } \leq 0.04[/tex]
[tex]\Rightarrow \frac{0.5}{\sqrt{n} } \leq \frac{0.04}{1.64}[/tex]
[tex]\Rightarrow \frac{0.5}{\sqrt{n} } \leq 0.0243[/tex]
[tex]\Rightarrow \sqrt{n}\geq \frac{0.5}{0.0243}[/tex]
[tex]\Rightarrow \sqrt{n}\geq 20.57[/tex]
squaring on both side,
∴ [tex]n=423.1249[/tex]
Hence, the sample size is,
[tex]n=423[/tex]
Hence, the correct option is [tex](b).[/tex]
Answer:
423
Step-by-step explanation:
I need help bad!!! Please help!
Answer:
Both Question (bottom right corner)
Step-by-step explanation:
Question 2 is obviously a variable because the amount of goals you can score in a game varies, one game it could be 10 then next it could be 5, But for question 1 the amount of work hours she puts in, (assuming she choses when to work and when not to) is also a variable because the amount she works varies from day to day.
Both these examples how data that varies from day to day.
Hope this helps!
ANSWER FAST PLS HAVE 5 MIN FOR THIS
Employees of a painting service paint the interior walls of homes and office buidings.
The following table shows the number of cons of point the employees use, and the
number of square feet they cover.
Cans of paint
3
Area painted (square feet) 375
1125 1500
Which equation describes the relationship between the number of cons of paint
used, and the number of square feet that are covered?
1
2
750
A
y = 375x + 375
B
y=+*
375
y = 50x + 325
D
y = 375x
Answer:
Y=375x
Step-by-step explanation:
thats the answer
PLEASE ANSWER ASAP FOR BRAINLEST WITH WORK!!!!!!!!!!!!!!!
Answer:
The answer is 43 because 600/14 = 42.8571429 rounded to the nearest whole number is 43.
Step-by-step explanation:
the equation of a circle whose center is (-5, 3) and whose radius is 6?
Answer:
Center:(-5,3)
The center of a circle is a point from which all points on a circle are the same distance.
Radius:6
The radius of a circle is the length of a line segment from its center to its perimeter.
The radius is typically denoted as "r" or "R".
Diameter:12
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.
Circumference or (or Permieter) = 2*π*R = 2*3.14*6 = 37.6991118430775
The circumference of a circle is the distance around it.
Area:113.097335529233
Area of a Circle is the amount of space occupied by the circle.The area of a circle is p times the radius squared, which is written: A = π*R2.
The formula for the velocity of an object is v=d/t, where v is the velocity of an object, dis the distance traveled, and t is the time elapsed, while the distance is traveled. If you had only this formula to work with, what should your first step be in determining how long it takes for light to reach Earth from the Sun? What additional information do you need to calculate this?
Answer:
To know the distance between the sun and the earth you need isolate d of the equation:
[tex]v = \frac{d}{t} \\ d = vt[/tex]
and the additional information needed is the velocity of light and the time elapsed to be in the earth
Ivy and Andrey were asked to find an explicit formula for the sequence -100,-50,0,50,...−100,−50,0,50,...minus, 100, comma, minus, 50, comma, 0, comma, 50, comma, point, point, point, where the first term should be f(1)f(1)f, left parenthesis, 1, right parenthesis.
Ivy said the formula is f(n)=-100+50(n-1)f(n)=−100+50(n−1)f, left parenthesis, n, right parenthesis, equals, minus, 100, plus, 50, left parenthesis, n, minus, 1, right parenthesis.
Andrey said the formula is f(n)=-150+50nf(n)=−150+50nf, left parenthesis, n, right parenthesis, equals, minus, 150, plus, 50, n.
Which one of them is right?
Answer:
both
Step-by-step explanation:
Help plis
17. Find the sum of (10x + 3) and (- 4x - 2).
Answer:
6x + 1
Step-by-step explanation:
1. (10x + 3) + (-4x -2) --> sum means to add.
2. Combine like terms --> 10x - 4x = 6x; 3 - 2 = 1.
3. 6x + 1
Which equation is equivalent to 1/5x - 3 = 2/3
A : x-15=10
B : 3x-15=10
C : 3x-45=10
D : 5x-45=3
answer quick will give 20 points
Answer:
1
Step-by-step explanation:
the answer is the correct soulotion to what x and y repersent. (sorry for bad grammar, english isnt my first language)
Answer:
The correct answer to your question I believe is 1
Step-by-step explanation:
So yes the first person is correct :) Hope I helped though. Have a great day! Bye! You got this!
What is the coefficient of the x^2-term of the product
Answer:
it's x
Step-by-step explanation:
x is what is being raised by 2
Answer:
1
Step-by-step explanation:
The coefficient of x^2 is 1 because there is no real number in front of it
Hope this helped! Please mark me brainliest!
1. How would you describe the strugure of the Yavapai-Apache Nation's government? 2. What is one check or balance mentioned in this section of the constitution?
I will give brainliest
The students at Job's high school
were surveyed to determine their
favorite foods. The results are shown
in the table below. Suppose students
were randomly selected and asked
what their favorite food is. Find the
probability of each event. Write as a
fraction in simplest form.
Favorite Food Responses
Pizza 19
Steak 8
Chow-mein 5
Seafood 4
Spaghetti 3
Cereal 1
16. P(steak)
17. P(Spaghetti)
18. P(cereal or seafood)
19. P(not chow-mein)
19. P(pizza)
20. P(cereal or steak)
21. P(not steak) 22. P(not cereal or seafood)
23. P(chicken) 24. P(chow mein or spaghetti)
There are 4 boys eating oranges. Each boy eats 1 / 2 of an orange. How many oranges did the boys eat?
Answer:
2 oranges
Step-by-step explanation:
Two halves make a whole orange, and since there's four of them, they are eating 2 oranges.
Answer:they would have eaten 2 because 1/2+1/2 is a whole and since there are 4 boys eating 1/2 of an orange they would have eaten 2 oranges
The second angle of a triangle is three times as large as the first angle. The third angle is 40° greater than the first angle. How large are the angles?
Find the measure of each angle. a. Angle A = ? b. Angle B = ? c. Angle C = ?
Answer:
angle A=140
angle B=105
angle C=60
angle A=140
angle B=105
angle C=60
Step-by-step explanation:
PENN
HELP MEEEEE this is so harddd. the picture is above.
Answer:
A)
Step-by-step explanation:
V=1/3([tex]\pi[/tex]r²)h
3* V=1/3(πr²h)*3 to get rid of the 1/3 on that side
3V/(πr²)=(πr²)h/(πr²) to get rid of the πr² on the other side(they cancel out)
3V/(πr²)=h is the final answer so that matches A
helppppppppppppppppp
Dawn has two bank accounts she has been using to save money for a car. The difference between account A and account B is $100. If she uses StartFraction 3 Over 8 EndFraction of account A and StartFraction 7 Over 8 EndFraction of account B, Dawn will have a down payment of $2000. Choose the statements that are true when solving for the amount Dawn has in each account. Check all that apply.
One of the equations that represents this scenario is A – B = 100.
One of the equations that represents this scenario is StartFraction 3 Over 8 EndFractionA + StartFraction 7 Over 8 EndFractionB = 2000.
To eliminate the A variable, multiply the first equation by 3 and the second by 8.
To eliminate the B variable, multiply the first equation by 7 and the second by 8.
To eliminate the B variable, multiply the first equation by 7 and the second by –8.
Answer:
1) One of the equations that represents this scenario is A – B = 100.
2)One of the equations that represents this scenario is StartFraction 3 Over 8 EndFractionA + StartFraction 7 Over 8 EndFractionB = 2000.
4) To eliminate the B variable, multiply the first equation by 7 and the second by 8.
Step-by-step explanation:
Answer:
a b and d
Step-by-step explanation:
Helpppppp Fast!!!!!!!!!!!!
Answer:
1 1/3 feet by 3 feet
Step-by-step explanation:
Using first principal find the gradient of the curve whose equation is y=x^5. show working pleas
Answer:
The gradient of [tex]y = x^{5}[/tex] is [tex]\frac{dy}{dx} = 5\cdot x^{4}[/tex].
Step-by-step explanation:
Geometrically speaking, the gradient of a curve is the slope of the tangent line at a given point of the curve. From perspective of Differential Calculus, the gradient is the first derivative of the curve. Let [tex]y = x^{5}[/tex], then the gradient of the curve is:
[tex]\frac{dy}{dx} = 5\cdot x^{4}[/tex] (1)
The gradient of [tex]y = x^{5}[/tex] is [tex]\frac{dy}{dx} = 5\cdot x^{4}[/tex].