A bacteria culture contains 2000 bacteria and doubles every half hour, find the size of the bacterial population after 5 hours
Answers
Since the bacteria culture doubles every half hour, the size of the bacterial population after 1 half hour is 2000 * 2 = 4000 bacteria.
The size of the bacterial population after 2 half hours is 4000 * 2 = 8000 bacteria.
This pattern continues, so the size of the bacterial population after 10 half hours (or 5 hours) is 8000 * 2^(10-2) = 8000 * 2^8 = 8000 * 256 = 2048000 bacteria.
Thus, the size of the bacterial population after 5 hours is 2048000 bacteria.
Related Questions
what is the soulution of the system? use any method
3y = –1/2x+2
y = –x + 9
(20, –4)
(3, 6)
(10, –1)
(–1, 8)
Answers
Answer:
c
Step-by-step explanation:
10,-1
your welcome
thats the right answer
Ashley is training to run a marathon. On Monday, she runs 21 miles in 3 hours. On Wednesday, she runs 10 1/2 miles in 1 1/2 hours. What is the constant of proportionality in miles per hour?
Answers
Answer:
10.5 mph
Step-by-step explanation:
To find the constant of proportionality in miles per hour, we need to divide the distance (in miles) by the time (in hours) for each of the two runs, and then take the average of the two rates.
For Monday's run:
Rate = Distance / Time = 21 miles / 3 hours = 7 miles per hourFor Wednesday's run:Rate = Distance / Time = 10 1/2 miles / 1 1/2 hours = (21/2) miles / (3/2) hours = 14 miles per hour
To find the average rate, we add the two rates and divide by 2:Average rate = (7 miles per hour + 14 miles per hour) / 2 = 10.5 miles per hour
Therefore, the constant of proportionality in miles per hour is 10.5. This means that Ashley runs at an average rate of 10.5 miles per hour during her training.
A table of values of a linear function is shown below. Find the output when the input is n. input: 1 2 3 4 n output: 3 1 -1 -3
Answers
We have the points of a linear function and need to find the equation that represent.
Because it is a linear function, we can find its equation with two points.
We get the points (1,3) and (2,1):
\(\begin{gathered} We\text{ call input as x and output as y:} \\ P_1=(x_1,y_1)=(1,3),P_2=(x_2,y_2)=(2,1) \\ y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1) \\ y-3=\frac{(1-3)}{(2-1)}(x-1) \\ y-3=-\frac{2}{1}(x-1)=-2(x-1) \\ y=-2x-2\cdot(-1)+3 \\ y=-2x+2+3 \\ y=-2x+5 \end{gathered}\)We can check that the points (3,-1) and (4,-3) also satisfy the equation that we found above:
\(\begin{gathered} \text{For point (3,-1):} \\ y=-2\cdot3+5=-6+5=-1 \\ \text{For point (4,-3):} \\ y=-2\cdot4+5=-8+5=-3 \end{gathered}\)The above shows that the points satisfy the equation.
So, for input=n the output is:
\(\text{output}=-2\cdot n+5\)Ssssssssssssssssssssssssssssssssssssssssssssssssss
Answers
Danielle wants to translate triangle XYZ so that vertex Y is moved from coordinates (-
4,2) to (0,-3). Which of the following mappings can be used to find the new
coordinates of X and Z?
A (x,y)-( * - 4, y + 5)
B (x,y)-(x+4, y - 5)
C(x,y)-(x - 4, y + 3)
D(x,y)-(x + 5, y - 4)
Answers
Answer:
We need to use the mapping \(U'(x,y) = (x+4,y-5)\) to find the new coordinates of X and Y.
Step-by-step explanation:
Vectorially speaking, we must look for the defintion of the translation operation such that vertex Y becomes vertex Y', which is represented by:
\(T(x,y) = Y'(x,y) - Y(x,y)\) (1)
Where \(T(x,y)\) is the translation vector.
If we know that \(Y(x,y) = (-4,2)\) and \(Y'(x,y) = (0,-3)\), then the translation vector is:
\(T(x,y) = (0,-3)-(-4,2)\)
\(T(x,y) = (4, -5)\)
If \(U(x,y) = (x,y)\), \(T(x,y) = (4, -5)\) and \(U'(x,y)\) is the translated vector, then we obtain the following definition:
\(U'(x,y) = U(x,y) +T(x,y)\) (2)
\(U'(x,y) = (x,y) + (4,-5)\)
\(U'(x,y) = (x+4,y-5)\)
The correct answer is B.
Answer:
B is the answer
Step-by-step explanation:
16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Answers
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
Which of the following represents a rotation of JKW, which has vertices J (-7, 15), K (21, -62), and W (-14 , -32), about the origin 180"?
Answers
Answer:
The fourth option:
J(7, - 15)
K ( -21, 62)
W(14, 32)
Explanation:
The counterclockwise rotation by 180 degrees about the origin corresponds to the following transformation of coordinates.
\((x,y)\to(-x,-y)\)This means that if we have the point J (-7, 15), then under 180 counterclockwise rotation about the origin, it transforms to
\(\begin{gathered} J(-7,15)\to J(--7,1-5) \\ \to J(7,-15) \end{gathered}\)Similarly, the point K(21, -62) transforms to
\(K\mleft(21,-62\mright)\to K(-21,62)\)and
\(W(-14,-32)\to W(14,32)\)Hence, to summerise, a 180-degree counterclockwise rotation about the origin brings about the following changes
\(\begin{gathered} J\mleft(7,-15\mright) \\ K(-21,62) \\ W\mleft(14,32\mright) \end{gathered}\)3 problems for 1 final answer. fairly easy 8th grade math.
Answers
When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)
How do i determine the value of A/5 + √(B - C)?
First, we shall determine the value of A. Details below:
A = Product of roots in x² - 11x + 30Value of A =?Quadratic equation is expressed as:
x² - (sum of root)x + product of root
Comparing the above with x² - 11x + 30, we have
x² - 11x + 30 = x² - (sumof root)x + product of root
Product of roots = 30
Thus,
A = 30
Next, we shall determine the value of B. details below:
f(x) = x² + 5Value of B = f(2) =?f(x) = x² + 5
f(2) = 2² + 5
f(2) = 9
Thus,
B = 9
Next, we shall determine the value of C. Details below:
(x² - 2x - 24) / (x + 4)Value of C = Remainder =?Let
x + 4 = 0
Thus,
x = -4
Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:
Remainder = x² - 2x - 24
Remainder = (-4)² - 2(-4) - 24
Remainder = 0
Thus,
C = 0
Finally, we shall determine value of A/5 + √(B - C). Details below:
A = 30B = 9C = 0Value of A/5 + √(B - C) =?A/5 + √(B - C) = 30/5 + √(9 - 0)
A/5 + √(B - C) = 6 + √(9
A/5 + √(B - C) = 6 + 3
A/5 + √(B - C) = 9
Thus, the value of A/5 + √(B - C) is 9 (option B)
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 19
Blue 20
Green 14
Yellow 8
Purple 10
Based on these results, express the probability that the next spin will land on blue or green or purple as a fraction in simplest form.
Answers
The probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.
Given that, a spinner is divided into five coloured sections that are not of equal size: red, blue, green, yellow, and purple.
What is probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
The spinner results are as follows:
Colour Frequency
Red 19
Blue 20
Green 14
Yellow 8
Purple 10
Total number of outcomes = 19+20+14+8+10=71
The probability of getting blue =20/71
The probability of getting green =14/71
The probability of getting purple =10/71
So, the probability of getting blue or green or purple = 20/71 + 14/71 + 10/71
=44/71
Therefore, the probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.
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PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
I think it is 1 in 12 ft.
Step-by-step explanation:
A group of tourists are on a 3-day long trip. They hike 1/8 of the trail on the first day. On the second day, they hike 4/7 of the remaining distance. On the third day, they hike 1/3 of the remaining distance, plus the final 8 km. How many kilometers long is the trail?
Answers
Answer: 32 km (I believe)
Explanation: So, on the first day the tourists walked x/8 km.
Then the remaining distance after the first day is (x- x/8) = 7x/8 km.
On the second day, the tourists walked 4/7 of the REMAINING path, so now we multiply 4/7 by 7x/8 to get x/2 km.
So, the remaining path to travel after 2nd day is (7x/8-x/2) = 3x/8
Remember, on the third day they walked 1/3 of the remaining trail and the last 8 km.
So now, we do (3x/8 - 3x/8 x 1/3) = 8
Now, x/4 =8 ; to find x, we do 8 x 4 to get 32
So, our answer is 32
I hoped this helped!
A prism is completely filled with 96 cubes that have edge length of 1 cm. What is the volume of the prism? Enter your answer in the box. . 412 cm
Answers
Answer:
96
y-step explanation:
volume of 1cm cubes = 1 x 1 x 1 = 1 cm^3
so it will take 96 cubes to fill the prism
Which of the following best describes the graph below?
54 -3 -2 -1
PINT
123 to
3
A. It is not a function.
B. It is a many-to-one function.
C. It is a function, but it is not one-to-one.
D. It is a one-to-one function.
Answers
Find the volume & surface area of a cylinder with radius 4 cm and height 9 cm
Answers
Answer:
V= 452.39cm³ (to 2 d.p. )
S.A. = 326.73cm² (to 2 d.p. )
Step-by-step explanation:
Vcylinder = π r² h = π (4)² (9) = 144 π = 452.3893421cm³ = 452.39cm³ (to 2 d.p. )
S.A. cylinder = 2π r h + 2π r² = 2π (4)(9) + 2π (4)² = 104π = 326.725636cm² = 326.73cm² (to 2 d.p. )
Which of the following is a true statement about a tangent and a radius?
A. A tangent and a radius of a hexagon are always equal lengths.
B. A tangent and a radius of a circle meet to form a 90 angle.
C. A tangent and a radius in a cylinder form two legs of a right triangle with the cylinders altitude serving as the hypotenuse.
D. A tangent and a radius intersect at the foci of an ellipse.
Answers
A tangent and a radius of a circle meet to form a 90 angle is a true statement about a tangent and a radius.
The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary use, it also refers to the length of such line segments.
A tangent is a line that very slightly touches the circumference of a circle. The angle between a radius and a tangent is always exactly 90 degrees if the radius and circumference are drawn at the same location.
Hence the correct option is B
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let C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
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which fraction would make this statement true, using multiplicative inverse4/9x__=1
Answers
The expression is,
\(\frac{4}{9}\times a=1\)Simplify the expression for a.
\(\begin{gathered} \frac{4}{9}\times a=1 \\ a=1\times\frac{9}{4} \\ =\frac{9}{4} \end{gathered}\)So missing is filled by fraction 9/4.
Answer: 9/4
Round your answer to one decimal digit. The volume of a cylinder is 1800cm squared. if the height of the cylinder is 40cm then the diameter of cylinder is
Answers
\(_____________________________________\)
\(\sf\huge\underline\red{SOLUTION:}\)
Use formula:
\(\sf{V = \pi(\frac{d}{2})^2h}\)
Solving for diameter:
\(\sf d = 2 \times \sqrt{ \frac{V}{\pi h} } \\ \sf = 2 \times \sqrt{ \frac{40}{\pi \times 1800} } \approx0.16821 \\ = \sf \large\boxed{\sf{\green{d = 0.17}}}\)
\(\sf\huge\underline\red{FINAL \: ANSWER}\)
\(\large\boxed{\sf{\green{d=0.17}}}\)
\(_____________________________________\)
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢ
A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
Answers
Step-by-step explanation:
To eliminate x in the system of equations:
1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:
Equation 1: 36x -54y = 90
Equation 2: -36x - 8y = -28
2. Add the two equations together to eliminate x:
(36x - 54y) + (-36x - 8y) = 90 - 28
Simplifying, we get:
-62y = 62
3. Solve for y:
y = -1
4. Substitute y = -1 into one of the original equations, say Equation 1:
4x - 6(-1) = 10
Simplifying, we get:
4x + 6 = 10
5. Solve for x:
4x = 4
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.
you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answers
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
The sun of two numbers is 33. The larger number is 3 more than two times the smaller number. What are the numbers?
Answers
Given:
Sum of two numbers = 33
The larger number is 3 more than two times the smaller number.
Find the number
Sol:
Let a smaller number be "x"
So larger number is:
\(\begin{gathered} \text{ Smaller number = }x \\ \\ \text{ larger number = }2x+3 \end{gathered}\)Sum of the two numbers is 33.
Then,
\(\begin{gathered} \text{ Smaller number }+\text{ Larger number = }33 \\ \\ x+2x+3=33 \end{gathered}\)Solve for "x"
\(\begin{gathered} x+2x+3=33 \\ \\ 3x+3=33 \\ \\ 3x=33-3 \\ \\ 3x=30 \\ \\ x=\frac{30}{3} \\ \\ x=10 \end{gathered}\)So, the smaller number is 10
\(\begin{gathered} \text{ larger number =}2x+3 \\ \\ =2(10)+3 \\ \\ =20+3 \\ \\ =23 \end{gathered}\)The larger number is 23.
\(\begin{gathered} \text{ Smaller number = }10 \\ \\ \text{ Larger number =}23 \end{gathered}\)The circumference of a circle is 113.04 kilometers. What is the circle's diameter?
Answers
Answer:
A circle has a circumference of 113.04What is the diameter of the circle?so do 113.04 and divide it by 3.14 and youget 36 units.
Write a polynomial that represents the area of the shaded region
Answers
The polynomial that represents the area of the shaded region is given as follows:
x² - 3x + 36.
How to obtain the area of a rectangle?The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:
A = lw.
For the entire region, the area is given as follows:
A = (x + 1)(x + 1)
A = x² + 2x + 1.
The area of the white region is given as follows:
Aw = 5(x - 7)
Aw = 5x - 35.
Then the area of the shaded region is given as follows:
As = A - Aw
A = x² + 2x + 1 - (5x - 35)
A = x² + 2x + 1 - 5x + 35
A = x² - 3x + 36.
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Find the number of different ways that an instructor can choose 3 students from a class of 27 students for a field trip.
Hint: The order of selection of the students for the trip does not matter.
Answers
Answer:
9
Step-by-step explanation:
help me with this please
Answers
Answer:
the numbers that right of the origin on the x axis are positive numbers
Answer:
positive
Step-by-step explanation:
positive runs on the right of x -axis
negative runs on the left of the x-axis
prime and odd will never be running on either side of x-axis
hope it helps!!!!!!
Find the largest number which divides 248 and 1032 leaving the remainder 8 in each case.
Answers
Answer:
...... .................
A ball is thrown downward from the top of a 150-foot building with an initial velocity of 23 feet per second. The height of the ball h after t seconds is given by the equation h= - 16t? - 23t+150. How long after the ball is thrown will it strike the ground?
Answers
Answer:
362 the answer
Step-by-step explanation:
follow nmn i hope its help
Point M is the midpoint of AB . AM=2x+9, and AB=8x−50.
What is the length of AM?
Answers
Using the midpoint theorem, the length of AM is 43
Calculating Length of a lineFrom the question, we are to determine the length of AM
From the given information,
Point M is the midpoint of AB
Thus,
From the midpoint theorem
We can write that
AM + MB = AB
AM = MB
AM + AM = AB
2AM = AB
Also, from the given information,
AM = 2x + 9
and
AB = 8x - 50
Therefore,
From 2AM = AB
2(2x + 9) = 8x - 50
Solve for x
2(2x + 9) = 8x - 50
4x + 18 = 8x - 50
18 + 50 = 8x - 4x
68 = 4x
x = 68/4
x = 17
But,
AM = 2x + 9
Substituting the value of x
Thus,
AM = 2(17) + 9
AM = 34 + 9
AM = 43
This means the length of AM is 43
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A charity is raising money by selling two thousand raffle tickets for $2 each. There is one grand prize worth $500, three secondary prizes worth $200 each, and eight third level prizes worth $20 each. What is the expected value of a $2 ticket? Answer is negative $1.358 but how do you calculate that?
Answers
The expected value of a $2 ticket is $0.63
How to determine the expected value of a $2 ticketTo calculate the expected value of a $2 ticket, we need to multiply the probability of winning by the value of the prize, then sum those products:
The Probability of winning the grand prize = 1/2000
Product: (1/2000) x $500 = $0.25
The Probability of winning a secondary prize: 3/2000
Product: (3/2000) x $200 = $0.30
The Probability of winning a third level prize: 8/2000
Product: (8/2000) x $20 = $0.08
The sum of the products:
$0.25 + $0.30 + $0.08 = $0.63
So the expected value of a $2 ticket is $0.63, meaning that on average, a person can expect to win $0.63 for every $2 they spend on a ticket.
The charity is expected to make a profit, which is why the answer is negative.
That is -$2 + $0.63 = -$1.37
So the expected profit for the charity per ticket sold is -$1.37, which is approximately the same as the given answer of negative $1.358(rounding off)
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Show all 4 steps of the following:
x - 3/5= 1/6
Answers
Answer: x=23/30
Step-by-step explanation: Hope this help :D
