PLS HELP. A scientist studying bacteria begins with 20 cells. The bacteria population doubles every hour. Complete the table below to determine after how many hours there will be more than 500 bacteria cells. Time (hours) Number of bacteria cells 0 20 1 40 2 80 3 4 5 6 Write an exponential function to model this situation. Predict the bacteria population after 11 hours.
Answers
Answer: 3, 160 || 4, 320 || 5, 640 || 6, 1280
Step-by-step explanation:
The exponential function to model this situation is [tex]P(t) = 20\times 2^t[/tex]
What is an exponential function?An exponential function is a mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Given that, a scientist studying bacteria begins with 20 cells.
The bacteria population doubles every hour.
Let P(t) determines the population of the bacteria in 't' hours.
Hence, by the given information our function P(t) is modeled as:
[tex]P(t) = 20\times 2^t[/tex]
To find the population of the bacteria after 11 hours, put t = 11,
[tex]P(11) = 20\times 2^{11[/tex]
= 40,960
Hence the population of the bacteria after 11 hours will be 40,960.
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Related Questions
The mean and standard deviation of a normal distribution are 150 and 12 respectively. What percentage of values lie between:
a) 138 and 162
b) 126 and 174
c) 126 and 162
d) 162 and 174
Answers
Answer:
Step-by-step explanation:
Use a calculator with built-in statistical functions. The function applying here is normcdf(, the "cumulative density function."
(a) The percentage of values lying between 138 and 162 is
norm(138,162, 150, 12), which comes out to 0.683, or 68.3%.
(b) Find norm(126, 174, 150,12): 0.945, or 94.5%
(c) Find norm(126,162, 150,12); 0.819, or 81.9%
(d) Find norm(162, 174,150,12): 0.136, or 13.6%
10. The boys and girls in Mrs. Hall's class are collecting cans for the food drive. The
ratio of cans saved by the boys versus the girls is 2:5. The girls have saved 15 more cans
than the boys.
Answers
Answer:
hope it helps you
this is my answers
PLEASE HELP ILL GIVE BRAINLIEST!!!!!:(((((((
Answers
Answer:
1-A, 2-D, 3-E, 4-B, and 5-C
Answer:
Step-by-step explanation:
1: A
2: D
3: E
4: B
5: C
When you have that eqation all you have to do is take the numbers on the left in the parentheses and then you have to put those numbers into x and then you do the equation and see if the equation equals the numbers in parentheses on the right side
Can i be made brainliest
If f(x) =5x, what is f(6)
Answers
Answer:
30.. You plug in 6 for x... so therefore 5 times 6
11.18034 rounded to the nearest tenth
Answers
Answer:
11.2
Step-by-step explanation:
Find the number in the tenth place 1 and look one place to the right for the rounding digit 8 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
Hope this helps!
I don’t understand this. Please help
Answers
I'll do problem 5 to get you started.
The answer is choice B and choice DThe reason why choice B is one answer is because we have something in the form y = k/x to indicate an inverse variation. Replace x with H and y with T, and you'll get the same basic equation.
With inverse variation equations, as one variable goes down, the other variable goes up. Think of a see-saw as one way to visualize what's going on.
Or you can think of the T as T/1. So the equation T = L/H is the same as T/1 = L/H. If H were to decrease, then T would increase, and vice versa. T and H are on opposite sides of their respective fractions which may help see this opposite moving nature of each variable.
The reason why choice D is also an answer is because we can multiply both sides of T = L/H by H to get HT = L or TH = L. The equations T = L/H and TH = L are equivalent equations.
Answer:
5. 2nd and 4th boxes
Step-by-step explanation:
These look like proportionality questions. Typically we hear about two main types of proportionalities:
Directly proportional, which means that two variables change in the same way (Ex. one goes up, the other goes up).Inversely proportional, which means that two variables change in opposite ways (Ex. one goes up, the other goes down).Directly proportional variables are, intuitively, on opposite sides of an equation and both in the numerator on their side. Inversely proportional variables are on opposite sides but with one in the numerator and one in the denominator.
I can't see what the top one is asking for nor the bottom of 6., but let me try and use 5. as an example. If H increases as T decreases, then the two are inversely proportional. So the form would either have to be H=1/T or T=1/H. Other variables can be thrown into the mix and not change the outcome, so the 2nd and 4th boxes are your answers for 5.
Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page
Answers
Answer:
Step-by-step explanation:
13 pages : 1/2 hour Multiply both sides by 2
26 pages : 1 hour ------>> 26 pages/hr
Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages
Split up the fraction: (1/26) hr / page
Cynthia wants to buy a rug for a room that is 18ft wide and 26ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 240 square feet of carpeting. What dimensions should the rug have?
Answers
The room is 18 ft by 26 ft which is 468 ft^2
She can afford a 240 ft^2 rug
12 * 20 = 240
She can afford a rug that is 12 ft wide by 20 ft long
The dimensions that the rug she wants to buy should have is: 12 ft by 240 ft
How to find the area of the rectangle?The formula for the area of a rectangle is expressed as:
Area = length * Width
Now, we are told that:
Dimensions of room = 18 ft by 26 ft
If she leaves a strip of 3ft across the room, then, we can say that area that needs carpeting = 12 ft by 20 ft
Let us check with the 240 square feet of carpeting
12 * 20 = 240 ft
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I need help I've been suffering on this questiona all day
Answers
Answer:
-6.8
Step-by-step explanation:
When your going up you add a number.
2 is not a solution for
True
False
Answers
Answer:
False
Step-by-step explanation:
2 is a solution because to circle is closed. All answers including 2 and above are solutions.
Answer:
False
Step-by-step explanation:
circle is closed so all awnsers 2 and above is correct
A scale drawing of a car has a scale of 1 inch to 3 feet if the length of the car is 5 inches on the drawing, what is the actual length of the car?
Answers
Answer:
3 fet
Step-by-step explanation:
10!•4!/6!•5!
Evaluate
O 1,008
O 4/3
2/3
Answers
Answer:
1008
Step-by-step explanation:
10!•4!
---------
6!•5!
Rewriting as
10 * 9*8*7*6! * 4!
---------
6!•5*4!
Canceling like terms
10 * 9*8*7
---------
5
1008
Answer:
1,008
Step-by-step explanation:
The answer is not 4/3 or 2/3. So, it has to be 1,008.
Kenwood High School sold t-shirts for a school fundraiser. The principal rounded the number of shirts sold to 3,000. Which number might be the exact number of t-shirts Kenwood sold?
Answers
The weights of 3 puppies at one week old were 6.5 ounces, 7.3 ounces, and 6.4 ounces. If each
puppy gained 2.1 ounces, how much would the puppies weigh?
The first puppy would weigh ounces, the second puppy would weigh ounces, and the third
puppy would weigh ounces.
(Type integers or decimals.)
Answers
The answers are 8.6 ounces, 9.4 ounces, and 8.5 ounces
Explanation:
To find how much each puppy weights simply add the weight they gained (2.1 ounces) to the weight of each puppy at one week old. The process to add the weights is shown below:
First Puppy
6.5 ounces (weight at one week old) + 2.1 ounces (weight gained)
Align both numbers using the period as the reference and add
6.5
+ 2.1
8.6
The weigh of the first puppy is 8.6 ounces which can be rounded as 9 ounces (integer)
Second Puppy
Now, repeat the process
7.3 ounces + 2.1 ounces
7.3
+ 2.1
9.4
The weigh of this puppy is 9.4 ounces or 9 ounces (integer) if rounded
Third Puppy
6.4 ounces + 2.1 ounces
6.4
+ 2.1
8.5
The weight of the third puppy is 8.5 ounces which can be rounded as 8 ounces or 9 ounces (integers) depending on the rounding method.
Answer:
The answer to this questions is 8.6
Step-by-step explanation:
How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 20% antifreeze to get a mixture that is 60% antifreeze?
gallons
The number of gallons that must be mixed is
(Round to the nearest whole number.)
Answers
Answer:
360
Step-by-step explanation:
If x is gallons of 70% antifreeze solution, then:
0.70x + 0.20(90) = 0.60(x + 90)
0.70x + 18 = 0.60x + 54
0.10x = 36
x = 360
In a linear cost function, the marginal cost is the (additional, abstract or fixed) cost per item.
Answers
Answer:
Does this help
Step-by-step explanation:
included in the fixed cost are, for instance, mortgage payments, salaries, and insurance. This allows us to interpret the marginal cost, m = $3.50, as the cost to print each additional books.In general, the marginal cost is the cost per additional item.
abstractAnswer:
additional
Step-by-step explanation:
10-mg Atorvastatin Placebo Headache 15 65 No headache 17 3 3. If two different subjects are randomly selected, find the probability that they both had a headache.
Answers
Answer:
0.6384
Step-by-step explanation:
Given that:
10-mg Atorvastatin Placebo Headache 15 65 No headache 17 3
Hence the total of number of patients = 15 + 65 + 17 + 3 = 100 patients
The number of patients with headache = 15 + 65 = 80 patients
Also, C(n, x) is the number of combinations in which n items can be chosen taken x at a time it is given by the formula:
[tex]C(n,x)=\frac{n!}{(n-x)!x!}[/tex]
The the probability that if two different subjects they both had a headache = [tex]\frac{C(80,2)}{C(100,2)}=\frac{\frac{80!}{(80-2)!2!} }{\frac{100!}{(100-2)!2!} } =\frac{3160}{4950}=0.6384[/tex]
The area of an 20 -cm-wide rectangle is 440 cm. What is its length?
Answers
Answer:
22cm
Step-by-step explanation:
440÷20
I need the domain range and function. With an explanation
Answers
Problem 1
Domain = [tex]-3 < x \le 3[/tex], interval notation (-3, 3]Range = [tex]-3 \le y < 3[/tex], interval notation [-3, 3)Is it a function? YesProblem 2
Domain = [tex]x \ge -2[/tex], interval notation [tex][-2, \infty)[/tex]Range = All real numbers, interval notation [tex](-\infty, \infty)[/tex]Is it a function? NoProblem 3
Domain = [tex]-4 \le x < 3[/tex], interval notation [-4, 3)Range = [tex]-4 < y \le 3[/tex], interval notation (-4, 3]Is it a function? YesProblem 4
Domain = All real numbers, interval notation [tex](-\infty, \infty)[/tex]Range = [tex]y \le 4[/tex], interval notation [tex](-\infty, 4][/tex]Is it a function? Yes==================================================
Explanations:
The left most point is when x = -3, and we are not including this value due to the open hole. The other endpoint is included because it is a filled in circle. The domain is therefore [tex]-3 < x \le 3[/tex] which in interval notation is (-3, 3]. We have the curved parenthesis meaning "exclude endpoint" and the square bracket says "include endpoint". The range is a similar story but we're looking at the smallest and largest y values. Though be careful about which endpoint is open/closed. We have a function because it passes the vertical line test.The smallest x value is x = -2. There is no largest x value because the arrows say to go on forever to the right. We can say the domain is [tex]x \ge -2[/tex] which in interval notation is [tex][-2, \infty)[/tex]. The range is [tex](-\infty, \infty)[/tex] to indicate "all real numbers". This graph fails the vertical line test, so it is not a function. The vertical line test is where we check to see if we can pass a vertical line through more than one point on the curve. In this case, such a thing is possible which is why it fails the test.This is the same idea as problem 1, though note the endpoints are flipped in terms of which has an open circle and which doesn't. It is not possible to draw a single vertical line to have it pass through more than one point on the curve, so it passes the vertical line test and we have a function.This is a function because it passes the vertical line test. The domain is the set of all real numbers due to the arrows in both directions. Any x value is a possible input. The range is [tex]y \le 4[/tex] which is the same as saying [tex](-\infty, 4][/tex] in interval notation. This is because y = 4 is the largest y value possible. There is no smallest y value due to the arrows.desperate i need help on this
Answers
Complementary angles are two angles which sum is equal to 90 degrees
angle DFG and angle JKL are complementary angles
DFG = x + 3
JKL = x - 5
x-5 +x + 3 = 90
Add like terms
2x - 2 = 90
Add 2 to each side
2x = 92
Divide each side by 2
x = 46
Let's plug 46 into x for angle DFG
46 + 3 = 49
Since they add up to 90, we can subtract 49 from 90 to get angle JKL
90 - 49 = 41
DFG = 49
JKL = 41
For question 5, bisecting means cutting something in half. Angles LMO and NMO are equal to each other.
6x - 21 = 2x + 31
Let's subtract 2x from both sides and add 21 to both sides
4x = 52
Divide each side by 4
x = 13
Let's plug 13 in for x
LMO = 6(13) - 21 = 57
Since LMO and NMO are equal, we can multiply 57 by 2
57 * 2 = 114
The measure of LMN is 114
What is the greatest common
factor) of 105 and 75
Answer: 15
Answers
Answer:
What?
Step-by-step explanation:
x2 + 10x + 89 = 0
what are the roots of the equation in the simplest a+bi form?
Answers
Answer:
The answer is
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]Step-by-step explanation:
x² + 10x + 89 = 0
Using the quadratic formula
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]From the question
a = 1 , b = 10 , c = 89
Substitute the values into the above formula and solve
We have
[tex]x = \frac{ - 10\pm \sqrt{ {10}^{2} - 4(1)(89)} }{2(1)} \\ = \frac{ - 10\pm \sqrt{100 - 356} }{2} \\ = \frac{ - 10\pm \sqrt{ - 256} }{2} \\ = \frac{10\pm 16 \: i}{2} [/tex]Separate the real and imaginary part
That's
[tex]x = - \frac{10}{2} \pm \frac{16}{2} \: i \\ x = - 5\pm8 \: i[/tex]We have the final answer as
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]Hope this helps you
Sandi had the following problem on her math test:6•4+2÷2-7
Answers
Explanation:
24+1-7
1. On the number line, plot and label all numbers with an absolute value of 3/2
Answers
Answer:
1 1/3
Step-by-step explanation:
it's unporore
Points [tex]\frac{3}{2} , \frac{-3}{2} , 1.5 , -1.5 , 1 \frac{1}{2} , -1 \frac{1}{2}[/tex] have same absolute value as 3/2
What is an absolute value?The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign.
For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.
According to the question
numbers with an absolute value of 3/2 are
[tex]absolute value of |\frac{-3}{2}| = \frac{3}{2} \\absolute value of |1.5| = 1.5 or \frac{3}{2} \\\\absolute value of |-1.5| = 1.5 or \frac{3}{2} \\\\absolute value of |1\frac{1}{2} | = \frac{3}{2} \\\\\\[/tex]
[tex]absolute value of |-1\frac{1}{2} | = \frac{3}{2}[/tex]
Number line is attached below
Hence, Points [tex]\frac{3}{2} , \frac{-3}{2} , 1.5 , -1.5 , 1 \frac{1}{2} , -1 \frac{1}{2}[/tex] have same absolute value as 3/2 .
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Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1
Answers
Answer:
[tex]\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]
Step-by-step explanation:
Given that:
The surface area (S.A) [tex]z = x^2 +y^2[/tex]
Hence the S.A is of form z = f(x,y)
Then the S.A can be represented with the equation
[tex]A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA[/tex]
where :
D = cylinder [tex]x^2 +y^2 =1[/tex]
In polar co-ordinates:
D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)
Similarly, [tex]\dfrac{\partial z}{\partial x} = 2x[/tex] and [tex]\dfrac{\partial z}{\partial y} = 2y[/tex]
Therefore;
[tex]S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA[/tex]
[tex]= \iint_D \sqrt{1+4(x^2+y^2)} \ dA[/tex]
[tex]= \int^{2 \pi}_{0} \int^{1}_{0} \sqrt{1+4r^2} \ r \ dr \d \theta[/tex]
[tex]= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0[/tex]
[tex]= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1][/tex]
[tex]\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]
The function h (x) = StartFraction 1 Over x squared + 1 EndFraction is the result of the composition f(g(x)). If g(x) = x2 + 1, what is f(x)? f (x) = StartFraction 1 Over StartRoot x EndRoot f (x) = StartFraction 1 Over x + 1 EndFraction f (x) = StartFraction 1 Over x squared + 1 EndFraction
Answers
Answer:
f(x) = 1/x
Step-by-step explanation:
Given h(x) = 1/(x²+ 1) and g(x) = x²+ 1. If h(x) = f(g(x)) then;
1/(x²+ 1) = f(x²+ 1)
f(x²+ 1) = 1/(x²+ 1)
This means that function of (x²+ 1) will give 1/(x²+ 1). To get f(x), we will simply replace x²+ 1 in the function f(x²+ 1) with x to give;
f(x) = 1/x
Hence the function of x i.e f(x) is 1/x
Answer:
B
Step-by-step explanation:
edge 2021
HELP! IT'S OVERDUE! An engineer is building a bridge that should be able to hold a maximum weight of 1 ton. He builds a model of the bridge that is exactly 4 times smaller than the actual bridge. 16 ounces = 1 pound. 2,000 pounds = 1 ton. If a test of the model shows that it holds 8,000 ounces, will the bridge hold 1 ton? 1. 8,000 ounces on the model is equal to (A.32,000 B.35,000 C.80,000) pounds on the actual bridge. 2. Convert ounces to pounds. The actual bridge can hold (A.1,500 B.2,000 C.2,500) pounds. 3. Therefore, the bridge (A.will B.will not) hold one ton. PLEASE READ EVERYTHING
Answers
Answer:
1. C
2. C
3. B
Step-by-step explanation:
This was hard but i tried
Answer:
1. 32,000
2. 2,000
3. will
Step-by-step explanation:
i got it wrong and it showed me the correct answer.
8a + 4 = 4 + 8a
Property bank
Answers
Answer:
x=x
Infinite solutions
Step-by-step explanation:
8a + 4 = 4 + 8a
subtract 4
8a=8a
Factor out the GCF (8)
x=x
when an equation simplifies to x=x, it has Infinite solutions
Answer:
Commutative Property of Addition
Step-by-step explanation:
Tom earns $15.50 per hour at the Yankee Bowling Alley. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 42 hours. What was his gross pay for the week?
Answers
Answer:
$666.50
Step-by-step explanation:
Tom worked only 2 hours of overtime, at (1.5)($15.50/hr) = $23.25/hr.
At the regular pay rate of $15.50/hr he earned:
($15.50/hr)(40 hrs) = $620
His overtime pay is (1.5)($15.50/hr)(2 hr) = ($23.25/hr)(2 hr) = $46.50
Additing these two amounts together, we get $666.50 (gross pay for the week).
A boat that is out in sea is 400m from the bottom of a cliff. A lighthouse is at the top of the cliff. The lighthouse is 52m tall. The distance from the boat to the top of the lighthouse is 610m. What is the height of the cliff?
Answers
Answer:
409m
Step-by-step explanation:
Please see attached picture for full solution.
