Answer: There will 486 bacteria in 31 hours.
Step-by-step explanation:
The population decay in bacteria is exponential.
Exponential function : [tex]y=Ab^x[/tex], where A = initial population, b multiplication decay factor, t= time:
As per given:
Initial population: [tex]A=120,000[/tex]
After 36 hours, population = [tex]120000(b^{36})=200[/tex]
Divide both sides by 120,000 we get
[tex]b^{36}= 0.00167[/tex]
Taking natural log on both sides , we get
[tex]36\ln b=\ln 0.00167\\\\\Rightarrow\ b=e^{\left(\frac{\ln0.00167}{36}\right)}=0.83724629\approx0.8372[/tex]
At x= 31,
[tex]y=120000(0.8372)^{31}=120000\times0.00405234\approx486[/tex]
Hence, there will 486 bacteria in 31 hours.
Write 11 numbers in a row so that the sum of any 3 consecutive numbers is negative, while the sum of all the numbers is positive.
Answer:
Step-by-step explanation:
Hello, if I take the following
2, 2, -5, 2, 2, -5, 2, 2, -5, 2, 2
The sum is 8*2-5*3=16-15=1 > 0
and
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
nishan bought 7 marbles Rs.x per each. if he gave Rs.100 to the shop keeper. what is the balance he would receive?
Find the surface area of the figure. ft
Answer:
486
Step-by-step explanation:
Hello!
To find the surface area of a cube we use the equation
[tex]S = 6a^{2}[/tex]
S is the surface area
a is the side length
Put what we know into the equation
[tex]S = 6*9^{2}[/tex]
Solve
S = 6 * 81
S = 486
Hope this Helps!
Answer:486[tex]ft^{2}[/tex]
Step-by-step explanation:
surface area= 6[tex]l^{2}[/tex]
l=9
sa=6 ([tex]9^{2}[/tex])= 6 x 81=486[tex]ft^{2}[/tex]
If the length of the legs of a right triangle are 13 and 13,what is the length of the hypotenuse? Round your answer to the nearest tenth,if necessary.
Answer:
a² + b² = c²
13² + 13² = c²
169 + 169 = c²
338 = c²
c = √338 or 18.385 or 13√2
Answer:
18.4
Step-by-step explanation:
13² + 13² = x²
169 + 169 = x²
338 = x²
x = 18.38477....
Use the set of ordered pairs to determine whether the relation is a one-to-one function. {(−6,21),(−23,21),(−12,9),(−24,−10),(−2,22),(−22,−22)}
Answer:
the relation is not one-to-one.
Step-by-step explanation:
it can't because every number is in the 4th quadrant.
(3.5x10^8)x(4.0x10^-12)=
Answer:
Below
Step-by-step explanation:
● (3.5× 10^8) × (4×10^(-12))
● (3.5×4) × (10^8 × 10^(-12) )
● 14 × 10^ (-12+8)
● 14 × 10^(-4)
● 14/10^4
estimate the number 4576
Nearest 1000: 5000
Nearest 100: 4600
Nearest 10: 4580
Hope that helped!!! k
------------------------------------------------------------------------------------------
which expression have a value of 2/3
A: 8+(24 divided by 12) X 4
B:8+24 divided by (12X4)
C: 8+24 divided 12X4
D: (8+24) divided (12X4)
Which statements are true?
Answer:
Step-by-step explanation:
The first statement is true. We use 4 as the base and 3.33 as the exponent, obtaining 101.
The second statement is true. Using 2 as the base and 6.15 as the exponent, we get 71.01, or approximately 71.
Third statement: 3^4.14 = 94.47, which is NOT equal to 24. False
Fourth statement: Raise the base (5) to the power 2.60, obtaining 65.66, or approximately 66. True
Fifth statement: Raise the base (6) to the power 0.17, obtaining 1.36. This does not match the '11' given. False
An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses. H0: The product does not change the height of the plant. Ha: The product makes the plant grow taller. Is the following an example of a type I or type II error? The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.
Answer:
hi
Step-by-step explanation:
hji
A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.
Answer: a=24
Step-by-step explanation:
Lets find the line's formula (equation of the line).
As known the general formula of any straight line (linear function) is
y=kx+b
Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7
(Xb;Yb)- are the coordinates of point B
(Xa;Ya) are the coordinates of point A
Now lets find the coefficient b. For this purpose we gonna use the coordinates of any point A or B.
We will use A
7=-2/7*3+b
7=-6/7+b
b=7 6/7
So the line' s equation is y= -2/7*x+7 6/7
Now we gonna find the value of a usingcoordinates of point C.
Yc=1, Xc=a
1=-2/7*a+7 6/7
2/7*a= 7 6/7-1
2/7*a=6 6/7
(2/7)*a=48/7
a=48/7: (2/7)
a=24
Answer:
a=24
Step-by-step explanation:
Select the correct answer. If , which statement is true? if g(x) = f(1/3x)
A. The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function f is compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function f is compressed vertically by a scale factor of to create the graph of function g.
Answer:
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
Step-by-step explanation:
The rules for linear transformations are that
g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factor of "a" (before the shift)
compresses the graph horizontally by a factor of "b" (before the shift)
shifts it to the right by amount "c"
shifts it up by amount "d".
Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.
The appropriate choice of description is ...
b) the graph of g(x) is horizontally stretched by a factor of 3
Answer:
B
Step-by-step explanation:
Correct on Plato
Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}
Answer:
The answer is 55, -275, 1375, -6875......
Step-by-step explanation:
A population of bacteria P is changing at a rate of dP/dt = 3000/1+0.25t where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t. Then find the population when t = 3 days.
Answer:
- At any time t, the population is:
P = 375t² + 3000t + 1000
- At time t = 3 days, the population is:
P = 13,375
Step-by-step explanation:
Given the rate of change of the population of bacteria as:
dP/dt = 3000/(1 + 0.25t)
we need to rewrite the given differential equation, and solve.
Rewriting, we have:
dP/3000 = (1 + 0.25t)dt
Integrating both sides, we have
P/3000 = t + (0.25/2)t² + C
P/3000 = t + 0.125t² + C
When t = 0, P = 1000
So,
1000/3000 = C
C = 1/3
Therefore, at any time t, the population is:
P/3000 = 0.125t² + t + 1/3
P = 375t² + 3000t + 1000
At time t = 3 days, the population is :
P = 375(3²) + 3000(3) + 1000
= 3375 + 9000 + 1000
P = 13,375
There are two pitchers of lemonade in the fridge there are 1.5 gallons of lemonade in 1 pitcher and 9 quarts of lemonade in the other pitcher how many cups of lemonade are there in the fridge
Answer:
52 cups
Step-by-step explanation:
1 gallon = 4 quarts
1.5 gallons = 6 quarts
6 + 9 = 13 quarts of lemonade in the fridge.
1 quart = 4 cups
13 quarts = 4 × 13 = 52 cups
52 cups of lemonade are in the fridge.
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
60 cups
Step-by-step explanation:
1 gal = 16 cups
1 quart = 4 cups
16 cups
1.5 gal x ------------- = 24 cups
1 gal.
4 cups
9 quarts x ----------- = 36 cups
1 quart
number of cups of lemonade in the fridge = 24 cups + 36 cups = 60 cups
Hi I need help with 800×200= 8 × ______ hundreds=_____ Hundreds = _______ plz help me
Answer:
800×200= 8 × 200 hundreds= 1600 Hundreds = 160000
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answer:
Step-by-step explanation:
Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods
1/PV (FV) = (PV(1 + r^n)1/PV divide by PV
ln(FV/PV) = ln(1 + r^n) convert to natural log function
ln(FV/PV) = n[ln(1 + r)] by simplifying
n = ln(FV/PV) / ln(1 + r) solve for n
n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually
n = 9
n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly
n = 104 months or 8.69 years
n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily
n = 3163 days or 8.67 years
Alternatively
A = P e ^(rt)
Given that r = 8%
= 8/100
= 0.08
2 = e^(0.08t)
ln(2)/0.08 = t
0.6931/0.08 = t
t= 8.664yrs
t = 8.67yrs
Which ever approach you choose to use,you will still arrive at the same answer.
6x+6+9x+9=? Please help
Answer:
15x + 15
Step-by-step explanation:
Combine like terms. Like terms are terms with the same amount of variables. Set the equation so that the terms are grouped:
6x + 9x + 6 + 9
Combine like terms:
(6x + 9x) = 15x
(6 + 9) = 15
15x + 15 is your answer.
~
Answer:
15x+15
Step-by-step explanation:
6x+9x=15x
9+6=15
6x+6+9x+9=15x+15
A sequence of 1 million iid symbols(+1 and +2), Xi, are transmitted through a channel and summed to produce a new random variable W. Assume that the probability of transmitting a +1 is 0.4. Show your work
a) Determine the expected value for W
b) Determine the variance of W
Answer:
E(w) = 1600000
v(w) = 240000
Step-by-step explanation:
given data
sequence = 1 million iid (+1 and +2)
probability of transmitting a +1 = 0.4
solution
sequence will be here as
P{Xi = k } = 0.4 for k = +1
0.6 for k = +2
and define is
x1 + x2 + ................ + X1000000
so for expected value for W
E(w) = E( x1 + x2 + ................ + X1000000 ) ......................1
as per the linear probability of expectation
E(w) = 1000000 ( 0.4 × 1 + 0.6 × 2)
E(w) = 1600000
and
for variance of W
v(w) = V ( x1 + x2 + ................ + X1000000 ) ..........................2
v(w) = V x1 + V x2 + ................ + V X1000000
here also same as that xi are i.e d so cov(xi, xj ) = 0 and i ≠ j
so
v(w) = 1000000 ( v(x) )
v(w) = 1000000 ( 0.24)
v(w) = 240000
simplest form 2 3/4 x 4/5 *
Answer:
2 1/5
Step-by-step explanation:
2 3/4 * 4/5
Change the mixed number to an improper fraction
( 4*2+3)/4 * 4/5
11/4 * 4/5
The 4 in the numerator and denominator cancel
11/5
Changing back to a mixed number
5 goes into 11 2 times with 1 left over
2 1/5
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]2\frac{3}{4}*\frac{4}{5}\\\frac{11}{4}*\frac{4}{5}\\\frac{11}{5}\\ 2\frac{1}{5}[/tex]
Solve for x: 7 > x/4
Answer: x < 28
Step-by-step explanation:
How many feet are in 26 miles, 1, 155 feet? Enter only the number. Do not include units
The solution is
Answer:
137, 280 feet
Step-by-step explanation:
There are 5,280 feet in a mile.
26 * 5,280 = 137,280
There are 137, 280 feet in 26 miles.
There are 137,280 feet in 26 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We know that there are 5,280 feet in a mile.
So, the solution would be;
26 x 5,280 = 137,280
Thus, There are 137,280 feet in 26 miles.
Learn more about the unitary method;
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One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
A small company is creating a new product to sell to buyers. They have estimated that it will cost them $25 to produce each item and they will have start-up costs of $116000. This leads to the following expression, which gives the total cost, in dollars, to produce q of these new products: 25q+116000 Use this expression to predict how much it will cost them to produce 8900 items.
Answer:
[tex]Cost = 338500[/tex]
Step-by-step explanation:
Given
Startup = $116000
Cost per item = $25
Equation: 25q + 116000
Required
Determine the cost of producing 8900 items
The question implies that q = 8900
To solve further, we have to substitute 8900 for q in the given equation
Equation = 25q + 116000 becomes
[tex]Cost = 25 * 8900 + 116000[/tex]
[tex]Cost = 222500 + 116000[/tex]
[tex]Cost = 338500[/tex]
Hence, the cost of producing 8900 items is $338500
Please help with this
Answer:
B) x=80°
Step-by-step explanation:
This is a hexagon, so it has interior angles equaling 720°. (N-2)*180
So the equation would be
78+134+136+132+2x+x=720
480+3x=720
3x=720-480
3x=240
x=80°
To find ∫ (x − y) dx + (x + y) dy directly, we must parameterize C. Since C is a circle with radius 2 centered at the origin, then a parameterization is the following. (Use t as the independent variable.)
x = 2 cos(t)
y = 2 sin(t)
0 ≤ t ≤ 2π
With this parameterization, find the followings
dy=_____
dx=_____
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x=x(t)=2cos(t)\\\\dx=\dfrac{dx}{dt}dt=x'(t)dt=-2sin(t)dt[/tex]
and
[tex]y=y(t)=2sin(t)\\\\dy=\dfrac{dy}{dt}dt=y'(t)dt=2cos(t)dt[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The values of dx and dy are give as -2sin(t)dt and 2cos(t)dt respectively. The answer to the given problem can be stated as,
dy = 2cos(t)dt
And, dx = -2sin(t)dt.
What is the integration of a function?The integration can be defined as the inverse operation of differentiation. If a function is the integration of some function f(x) , then differentiation of that function is f(x).
The given integral over C is ∫ (x − y) dx + (x + y) dy.
And, the parameters for C are as follows,
x = 2cos(t)
y = 2sin(t)
0 ≤ t ≤ 2π
Now, on the basis of these parameters dx and dy can be found as follows,
x = 2cos(t)
Differentiate both sides with respect to t as follows,
dx/dt = 2d(cos(t))/dt
=> dx/dt = -2sin(t)
=> dx = -2sin(t)dt
And, y = 2sin(t)
Differentiate both sides with respect to t as follows,
dy/dt = 2d(sin(t))/dt
=> dy/dt = 2cos(t)
=> dy = 2cos(t)dt
Hence, the value of dx and dy as per the given parameters is -2sin(t)dt and 2cos(t)dt respectively.
To know more about integration click on,
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A height is labeled on the triangle below.
Which line segment shows the base that corresponds to the given height of the triangle
Option A,B,C
Answer:
A
Step-by-step explanation:
The height is always perpinducular to the base. The height here is perpendicular to line segment A.
Answer:
A
Step-by-step explanation:
9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In general, what does mu Subscript d represent? Temperature (degrees Upper F )at 8 AM 98.1 98.8 97.3 97.5 97.9 Temperature (degrees Upper F )at 12 AM 98.7 99.4 97.7 97.1 98.0 Let the temperature at 8 AM be the first sample, and the temperature at 12 AM be the second sample. Find the values of d overbar and s Subscript d.
Answer:
[tex]\frac{}{d}[/tex] = −0.26
[tex]s_{d}[/tex] = 0.4219
Step-by-step explanation:
Given:
Sample1: 98.1 98.8 97.3 97.5 97.9
Sample2: 98.7 99.4 97.7 97.1 98.0
Sample 1 Sample 2 Difference d
98.1 98.7 -0.6
98.8 99.4 -0.6
97.3 97.7 -0.4
97.5 97.1 0.4
97.9 98.0 -0.1
To find:
Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]
d overbar ( [tex]\frac{}{d}[/tex]) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5
[tex]\frac{}{d}[/tex] = ∑d/n
= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5
= −1.3 / 5
[tex]\frac{}{d}[/tex] = −0.26
s Subscript d is the sample standard deviation of the difference which is calculated as following:
[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1
[tex]s_{d}[/tex] =
√ [tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]
= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −
(−0.26))² + (−0.1 − (−0.26))² / 5−1
= [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]
= [tex]\sqrt{\frac{0.712}{4} }[/tex]
= [tex]\sqrt{0.178}[/tex]
= 0.4219
[tex]s_{d}[/tex] = 0.4219
Subscript d represent
μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose is
Answer:
8
Step-by-step explanation:
Ham with or without cheese-2 choices
Bologna with or without cheese-2 choices
Bologna with cheese with water or juice-2 choices
Bologna without cheese with juice or water-2 choices
Ham with cheese with juice or water -2 choices
Ham without cheese with juice or water -2 choices
2+2+2+2=8
Kile has 8 choices for lunch
Find the derivative of the function f(x) = (x3 - 2x + 1)(x – 3) using the product rule.
then by distributing and make sure they are the same answer
Answer:
Step-by-step explanation:
Hello, first, let's use the product rule.
Derivative of uv is u'v + u v', so it gives:
[tex]f(x)=(x^3-2x+1)(x-3)=u(x) \cdot v(x)\\\\f'(x)=u'(x)v(x)+u(x)v'(x)\\\\ \text{ **** } u(x)=x^3-2x+1 \ \ \ so \ \ \ u'(x)=3x^2-2\\\\\text{ **** } v(x)=x-3 \ \ \ so \ \ \ v'(x)=1\\\\f'(x)=(3x^2-2)(x-3)+(x^3-2x+1)(1)\\\\f'(x)=3x^3-9x^2-2x+6 + x^3-2x+1\\\\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Now, we distribute the expression of f(x) and find the derivative afterwards.
[tex]f(x)=(x^3-2x+1)(x-3)\\\\=x^4-2x^2+x-3x^3+6x-4\\\\=x^4-3x^3-2x^2+7x-4 \ \ \ so\\ \\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
