41/2 days is equivalent tο 492 hοurs.
What is divisiοn?Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.
We knοw that there are 24 hοurs in day therefοre,
Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:
41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs
Therefοre, 41/2 days is equal tο 492 hοurs.
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if someone knows the answer please tell me
Answer:
Step-by-step explanation:
first graph
y = 5x + 2
2 = y-intercept
5 = slope
the first graph is y = 5x+2 because the y-intercept is 2 and it rises 5 and goes over 1
second graph:
y = 2x + 3
third graph:
y = 3x + 3
Find the derivative of f(x)=−148x+1−−−−−√7
.
Answer: f(x) is -74(x+1/7)^(-1/2)
Step-by-step explanation:
To find the derivative of f(x), we can use the power rule and the chain rule.
First, let's rewrite f(x) as:
f(x) = -148(x+1/7)^(1/2)
Now, we can apply the power rule:
f'(x) = -148 * (1/2) * (x+1/7)^(-1/2)
Finally, we can use the chain rule:
f'(x) = -148 * (1/2) * (x+1/7)^(-1/2) * 1
f'(x) = -74(x+1/7)^(-1/2)
Therefore, the derivative of f(x) is -74(x+1/7)^(-1/2).
Quadrilateral MATH has coordinates M(-6,-3), A(-1,-3), 7(-2,-1), and H(-4,-1). The image of
quadrilateral MATH after the composition r x-axis °T 7,5 is quadrilateral M "A"T"H". State and
label the coordinates of M"A"T"H".
the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).
How to find?
The composition r x-axis ° T(7,5) first reflects the quadrilateral MATH about the x-axis and then translates it 7 units to the right and 5 units up.
To find the image of M(-6,-3) after reflection about the x-axis, we flip the sign of the y-coordinate to get M'(-6,3). Then, we translate M' 7 units to the right and 5 units up to get the coordinates of M":
M" = T(7,5) ∘ M' = (7 + (-6), 5 + 3) = (1, 8)
Similarly, we can find the coordinates of A", T", and H":
A' = (-1, 3) → A" = T(7,5) ∘ R(x-axis) ∘ A' = (7 + (-1), 5 - 3) = (6, 2)
T' = (-2, 1) → T" = T(7,5) ∘ R(x-axis) ∘ T' = (7 + (-2), 5 - 1) = (5, 4)
H' = (-4, 1) → H" = T(7,5) ∘ R(x-axis) ∘ H' = (7 + (-4), 5 - 1) = (3, 4)
Therefore, the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).
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Rieko is making bird houses for a craft fair she has 15 pounds of nails how many bird houses could rieko make if each bird house requires 1/4 pounds of nails
Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.
How many bird houses could rieko makeIf each bird house requires 1/4 pounds of nails and Rieko has 15 pounds of nails, we can use the following equation to determine the number of bird houses she can make:
number of bird houses = amount of nails / amount of nails per bird house
Plugging in the given values, we get:
number of bird houses = 15 / (1/4)
Simplifying the right-hand side by dividing 15 by 1/4, we get:
number of bird houses = 60
Therefore, Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
the values of x are 13 and 1.
Step-by-step explanation:
x - 7 = +√36 or x - 7 = -√36
Therefore,
x - 7 = +6 or x - 7 = -6
=> x = 7 + 6 or x = 7 - 6
=> x = 13 or x = 1
Therefore, the values of x are 13 and 1.
Answer: x = 25
Step-by-step explanation:
(x – 7)2 = 36 (Given)
2(x -- 7) = 36 (Associative Property)
2x - 14 = 36 (Distributive Property)
2x - 14 + 14 = 36 + 14 (Addition Property of Equality)
2x = 50 (Simplification)
2x/2 = 50/2 (Division Property of Equality)
x = 25 (Simplification)
help i forgot how to do this
1. The angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees. 2. the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.
Describe Cosine?In trigonometry, cosine (cos) is a trigonometric function that relates the adjacent side and the hypotenuse of a right triangle. It is defined as the ratio of the adjacent side to the hypotenuse. The cosine function is periodic with a period of 360 degrees or 2π radians, and it has a range of values between -1 and 1.
In other words, if we have a right triangle with an angle x, then the cosine of x is equal to the length of the adjacent side of the triangle divided by the length of the hypotenuse.
1.In a right-angled triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. Therefore, cos(x) = adjacent/hypotenuse = 37/39.
Using inverse cosine function on a calculator, we get x ≈ 23.6 degrees.
Therefore, the angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees.
2. Again, using the definition of cosine, we have cos(x) = adjacent/hypotenuse = 8/17.
Using inverse cosine function on a calculator, we get x ≈ 62.3 degrees.
Therefore, the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.
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The circumference of the circular table is 72 π inches. What is the radius of the table
Answer: 36 inches
Step-by-step explanation:
The formula for the circumference of a circle is 2πr where r is the radius of the circle Therefore 2πr=72π so r=72/2 = 36 inches.
HELP PLEASE ! 10+ POINTS! Social networking sites make some very accurate suggestions for people that you might know. Explain how trees are used to make these suggestions.
A man went to a post office to buy some stamps. If he bought x, 50 cents stamps and y, 25 cents stamps, the total cost would have been $3.50. If, however, he bought twice as many 50 cents stamps and half as many 25 cents stamps, then the total cost would have been $4.75. Evaluate x and y.
sue sells rings for 6$ each. Her expenses are $2.50 per ring, plus $56 for supplies. How many rings does she need to sell for her revenue to equal her expenses? Show work to support your answer
Sue needs to sell 16 rings to make her revenue equal to her expenses
What is revenue?Revenue is the total income generated by a company or organization from its sales or operations. It is the amount of money that a business earns from selling its products or services, or from other sources such as investments or interest on deposits.
According to question:Let's assume that Sue sells x rings.
The revenue generated by selling x rings = $6x
The total expenses for selling x rings = $2.50x + $56
To find the number of rings that Sue needs to sell for her revenue to equal her expenses, we need to set the revenue equal to the expenses and solve for x.
6x = 2.5x + 56
Subtracting 2.5x from both sides, we get:
6x - 2.5x = 56
Simplifying the left side, we get:
3.5x = 56
Dividing both sides by 3.5, we get:
x = 16
Therefore, Sue needs to sell 16 rings to make her revenue equal to her expenses.
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Answer two questions about point
A
Astart color #9e034e, start text, A, end text, end color #9e034e on the number line below.
A vertical number line labeled 7.5 to 7.6 with tick marks every one hundredth unit. Point A appears slightly above tick mark 7.51.
A vertical number line labeled 7.5 to 7.6 with tick marks every one hundredth unit. Point A appears slightly above tick mark 7.51.
What is
A
Astart color #9e034e, start text, A, end text, end color #9e034e rounded to the nearest hundredth?
What is
A
Astart color #9e034e, start text, A, end text, end color #9e034e rounded to the nearest tenth?
the rounded color remains the original colour:: 9e034e
The color code #9e034e represents a shade of deep pink or magenta. To round this color to the nearest tenth, we need to convert the hexadecimal code to its corresponding RGB values and then round those values.
Converting #9e034e to RGB gives us (158, 3, 78).
Rounding each of these values to the nearest tenth gives us (158, 3, 78), which is the same as the original color. Therefore, the rounded color is still #9e034e.
As for the mention of "A" in the question, it's unclear what context it refers to. If it's related to the color, it might mean that the color is used to represent the letter "A" in a certain context. However,
The question doesn't provide enough information to determine the exact meaning of "A."n summary, the rounded color #9e034e remains the same as the original color, and the mention of "A" in the question is unclear.
Roger and Rohan are partners of R&R Biscuit Company. Given below is details of items that appeared in their current account for the year ended December 31, 2019:
The net profit before appropriation is (d). $1,889,000.
How to solveTo calculate net profit before appropriation to R&R biscuit company by adding all the appropriation expense to share of profit after appropriation and deducting appropriation income.
In this case, interest on capital, drawings and partner's salary are appropriation expense while interest on drawings is appropriation income.
Now,
Net profit before appropriation
= ($650,000+$200,000+$100,000+$30,000-$20,000) + ($650,000+$150,000+$130,000+$25,000-$26,000)
= $960,000 + $929,000
= $1,889,000
So, the correct answer is (d). $1,889,000.
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Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.01q2 +5q-39, where q
is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in
thousands of dollars, from selling and producing a pairs of sunglasses.
A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your
answer.)
Answer: MP(q)
B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your
answer to three decimal places.)
Answer:
thousand pairs of sunglasses need to be sold.
C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your
answer to three decimal places.)
=
Answer:
thousand dollars of maximum profits can be expected.
Solving the quadratic equation, we get the maximum profit is 2451 thousand dollars.
What are quadratic equations?A second-degree algebraic equation in x is known as a quadratic equation. The quadratic equation is written as Ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
For an equation to be categorised as a quadratic equation, the coefficient of x2 must be a non-zero term (a 0).
The function is given as
P(q) = -0.01q2 +5q-39
We have
P(q) = -0.01q2 +5q-39
Differentiate
So, we have
P'(q) = -0.01q + 5
Set to 0
So, we have
-0.01q + 5
This gives:
-0.01q = -5
Evaluate
q = 500
Hence, 500 thousand pairs of sunglasses should be sold to maximize profits.
What is the maximum profit?
In (a), we have
q = 500
This gives:
P (500) = (-0.01)500×2 +5×500-39
Evaluating:
P (500) = -10 + 2500 -39
= 2451
Hence, the maximum profit is 2451 thousand dollars.
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When we solve the quadratic equation, we discover that the utmost profit is $2451 thousand dollars.
What are quadratic equations?A quadratic equation is an x-dependent second-degree algebraic problem. [tex]ax^{2} +bx+c=0[/tex], where x is the variable, a and b are the coefficients, and c is the constant element, is how the quadratic equation is expressed.
The coefficient of [tex]x^{2}[/tex] must not be negative for an equation to be categorized as a quadratic equation (a, 0).
The function is given as
P(q) = [tex]-0.01q^2[/tex] +5q-39
We have
P(q) = [tex]-0.01q^2[/tex] +5q-39
Differentiate
So, we have
P'(q) = -0.01q + 5
Set to 0
So, we have
-0.01q + 5
This gives:
-0.01q = -5
Evaluate
q = 500
So, in order to make the most money 500 000 sets of sunglasses should be sold.
In (a), we have
q = 500
This gives:
P (500) = (-0.01)500×2 +5×500-39
Evaluating:
P (500) = -10 + 2500 -39
= 2451
Therefore, the highest profit is $2451 thousand dollars.
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Find the polynomial that represents the area of the square
The polynomial expression that represents the area of the given square is: 4x² + 28x + 49
What is the area of the square?The formula for the area of a square is expressed as:
Area = side * side
Now, we are given the dimensions of the square and we have:
Side length = x + 7 + x = 2x + 7
Thus:
Area of square = (2x + 7) * (2x + 7)
= 4x² + 14x + 14x + 49
= 4x² + 28x + 49
Thus, we conclude that expression represents the area of the square.
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X follows Poisson distribution. This distribution was randomly sampled 40 times. The sum of these 40 numbers follows
a) Poisson distribution
b) Exponential distribution
c) Weibull distribution
d) Normal distribution
The sum of these 40 sampled numbers follows option D: normal distribution, if X follows Poisson distribution.
The likelihood that a certain number of events will occur in a specific period of time or space, provided that they do so with a known constant mean rate and the Poisson distribution describes the distribution of events, regardless of the time since the previous event. When the mean is high, the sum of the Poisson distribution resembles a normal distribution.
The "normal distribution," a continuous probability distribution that is symmetrical at the mean and has a bell-shaped curve. It is also known as the bell curve or the Gaussian distribution. Several natural phenomena, including height, weight, blood pressure, and others, have a normal distribution.
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A cone has a base area of 24 square inches and a height of 8 inches. What is the area of a cross-section of the cone
that is parallel to the base and 3 inches from the vertex?
The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is
Square inches.
Write the answer in friction
Answer:
Step-by-step explanation:
Cone height h = 8
Cone base r = sqrt( 24/pi) = 2.764
AB = h - 3 = 5
BC = 5 / tan(β) = 1.727
FB = FC - BC = 1.036482449 ( FB is the radius of cross-section circle)
Area of a cross-section is: (FB)2 * pi = 3.375 in2
An observer views a rocket take off from a distance of N miles from the launch pad, and tracks the angle of elevation.
a) Express the height of the rocket as a function of the angle of elevation, Θ.
b) Express the angle of elevation as a function of the height, h, of the rocket.
c) When the angle of elevation is A degrees, find the height of the rocket.
N=Any given number
A=Any given angle
(My Open Math question)
Short Answers:
a)N*tan(Θ)
b)arctan(h/N)
c)N*tan(A)
Let * stand for multiplication
Hope this is helpful to someone:)
Rewrite 300-4 in a different way, using the Commutative Law of Multiplication.
A) 30-40
B) 1200
C) 4.300
D) 3.100-4
Answer:
3x100-4
Step-by-step explanation:
3x100=300
(3x100)-4
300-4
Pleas help, Will mark brainliest and if you don't know then don't answer
Answer: 10 pigs and 3 chickens
Step-by-step explanation:
So the farmer has seen 40 legs
Pigs have 4 legs & Chickens have 2
Pigs: 40/4= 10 pigs
Chickens: 40/2= 20 chickens
So with us know which answer is correct we choose 10 pigs
Then if we have 10 pigs we have 3 chickens
13-10= 3 chickens
In conclusion we have the 10 pigs & 3 chickens
The perimeter of a rectangle is
360cm. find the breadth if its
length is 80cm.
Answer:
4.5 cm.
Step-by-step explanation:
Divide the length by the width to get the perimeter: 360 / 80 = 4.5 cm.
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In the triangle, x = 3. Find y.
Responses
A y = 3√
y = 3
B y = 6y = 6
C y = 7y = 7
D y = 32√
y = 3 2
E y = 62√
y = 6 2
Answer:
3√2
Step-by-step explanation:
9 + 9 = 18
square root of 18 is
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Mr Lim, Mr Bell and Mrs Walker paid for a meal. Mr Lim paid 1/5 of the amount Mr Bell and Mrs Walker paid together. Mr Bell paid 1/4 of the amount Mr Lim and Mrs Walker paid. A) What fraction of the total cost of the meal did Mrs Walker pay?
As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C)
what is fraction ?A fraction is a number that in mathematics represents a portion of a whole. It consists of a horizontal line between the numerator and denominator of two numbers. The denominator is the total number of equally sized components that make up the whole, whereas the numerator is the number of parts that are being taken into account. As an illustration, the fraction 3/4 denotes three of the four equal pieces. The denominator, 4, indicates that the entire is divided into four equal parts, while the numerator, 3, indicates that three parts are being taken into consideration.
given
Payment to Mr. Lim:
1/5(B + W) = (B + W)/5
Payment to Mr. Bell:
1/4(L + W) = (L + W)/4
These equations can be combined to find the value of W, or the amount Mrs. Walker paid:
(L + W)/4 + W + (B + W)/5 = C
To get rid of the fractions, multiply both sides by 20, which is the least common multiple of 5 and 4. This gives us:
20W + 4(B + W) + 5(L + W) = 20C
By enlarging and condensing, we obtain:
20C = 4B + 4W + 5L + 5W + 20W
9W + 4B + 5L = 20C
Now, we may change the expressions for the payments made to Mr. Lim and Mr. Bell to:
9W plus 4 (1/5 B + W) plus 5 (1/4 L + W) equals 20C.
If we simplify, we get:
9W + 4B + 4W + 4W + 4W + 5L + 5W = 20C.
When we multiply both sides by 20 to once more get rid of the fractions, we get:
400C = 180W + 16B + 16W + 25L + 25W
20C = 4B + 4W + 5L + 5W + 20W
9W + 4B + 5L = 20C
Now, we may change the expressions for the payments made to Mr. Lim
If we simplify, we get:
61W + 16B + 25L = 400C
We may now determine W:
W = (400C - 16B - 25L) / 61
We can divide W by the overall cost C to determine the portion of the cost of the lunch that Mrs. Walker covered:
W/C = (400C - 16B - 25L) / (61C)
W/C = 400/61 - (16B + 25L) / (simplified) (61C)
As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C) .
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1+1 I don’t know I’m in 7 th grade
Answer:
2
Step-by-step explanation:
no explanation needed.
x – 19 ≤ 81, if x = 110
The inequality x - 19 ≤ 81 is not satisfied when x = 110.
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The given inequality is X – 19 ≤ 81, and we are asked to evaluate it when X = 110. To do so, we substitute X with 110 and simplify the expression. In this case, we get 110 - 19 ≤ 81, which simplifies to 91 ≤ 81. Since this statement is false, we conclude that the inequality X – 19 ≤ 81 is not satisfied when X = 110.
we can substitute x = 110 and simplify:x - 19 ≤ 81
110 - 19 ≤ 81
91 ≤ 81
This statement is false, since 91 is not less than or equal to 81.
Therefore, the inequality x - 19 ≤ 81 is not satisfied when x = 110.
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I need help with this math problem. It’s from the course “Apply Math”.
The expected value of the gas grill is 6.50 million dollars if a development cost of $4 million is invested.
What is expected value?The expected value is the sum of all possible outcomes multiplied by their associated probabilities.
The expected value of the gas grill can be calculated as follows:
Expected value = (0.10 × 3) + (0.50 × 6) + (0.40 × 8)
= 0.30 + 3.00 + 3.20
= 6.50 million dollars
Therefore, the expected value of the gas grill is 6.50 million dollar.
This calculation allows investors to decide whether or not to invest in a specific project, as the expected return must be greater than the development cost.
In this case, the expected value of 6.50 million dollars is greater than the development cost of 4 million dollars, making the investment a viable option.
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or children between the ages of 5 and 13 years, the Ehrenberg equation ln � = ln 2.4 + 1.84 ℎ gives the relationship between the weight � (in kilograms) and the height ℎ (in meters) of the child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.1 m.
We can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
What is differential?A differential equatiοn is an equatiοn that includes an unknοwn functiοn and its derivative. A differential equatiοn describes a relatiοnship between a functiοn and changes in the functiοn.
The given equatiοn relating weight (W) and height (h) fοr children between 5 and 13 years οld is:
ln(W) = ln(2.4) + 1.84h
We want tο estimate the change in weight when a child grοws frοm a height οf 1 m tο 1.1 m.
First, we need tο calculate the weight at h = 1 m and h = 1.1 m.
At h = 1 m, we have:
ln(W1) = ln(2.4) + 1.84(1)
ln(W1) = ln(2.4) + 1.84
ln(W1) ≈ 2.684
Sο the weight at h = 1 m is apprοximately W1 ≈ e².684 ≈ 14.66 kg.
Similarly, at h = 1.1 m, we have:
ln(W2) = ln(2.4) + 1.84(1.1)
ln(W2) = ln(2.4) + 2.024
ln(W2) ≈ 2.807
Sο the weight at h = 1.1 m is apprοximately W2 ≈ e².807 ≈ 16.59 kg.
Tο estimate the change in weight when the height increases frοm 1 m tο 1.1 m, we can use the differential οf the equatiοn:
dln(W) = 1.84dh
Using differentials, we can apprοximate the change in weight as:
dW ≈ W2 - W1
dW ≈ e².807 - e².684
dW ≈ 1.93 kg
Therefοre, we can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
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Homeowners are installing a pollinator garden in
the corner of their backyard. The garden has the in
dimensions shown.
on
°538 = 33 feet
es
22 feet
104°
A
B
%
Part A
A fence will be installed along the entire edge, c,
of the area. What is the length of fence that will
be installed to the nearest tenth of a foot?
16
24
C
Part B
The homeowners will plant wildflowers to cover
the garden. If one packet of wildflower seeds covers
9 ft², how many packets of seeds will they need to
cover the entire garden?
36
(D) 48
Using sine and cosine rule, the length of fence is 19.84 feet and the number of packets to cover the garden is approximately 48
What is the length of fence c?To find the value of of the length of the fence, we can either use sine rule or cosine rule.
Since we have two sides and an angle, we sine rule first
a/sin A = b / sin B
[tex]\frac{33}{sin 104} = \frac{22}{sin B} \\sin B = 0.6469\\B = 40.31^0[/tex]
Using this, we can find the value of angle C
A + B + C = 180 degrees
Reason: Sum of angles in a triangle is equal to 180 degrees
104 + 40.31 + C = 180
C = 35.69 degrees
We can proceed to use cosine rule to find the length of the fence.
[tex]c^2 = a^2 + b^2 -2(a)(b)cosC\\c^2 = 33^2 + 22^2 - 2(33)(22)cos35.69\\c^2 = 393.71\\c = 19.84 ft[/tex]
Part B
Since one packet will cover 9ft², we need to know the total area of the field to determine the number of packets required.
Using heron's formula;
[tex]s = \frac{a + b + c}{2} \\s = \frac{33 + 22 + 29.84}{2} \\s = 42.42\\[/tex]
The area of the field is
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\A = \sqrt{42.42(42.42-33)(42.42-22)(42.42-19.84}\\A = 429.24ft^{2}[/tex]
The number of packets will be
x = 429.24 / 9
x = 47.69≅48 packets
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The count in a bacteria culture was 100 after 15 minutes and 1800 after 40 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Correct ___17.65___ bacteria
Find the doubling period.
____?_____ minutes
Find the population after 115 minutes.
____?_____ bacteria
When will the population reach 12000.
___?____ minutes
The population will reach 12000 bacteria after 56.4 minutes and other solutions are listed below
What was the initial size of the culture?We can use the formula for exponential growth, which is given by:
N = N0 * e^(kt)
where N is the final population, N0 is the initial population, k is the growth rate constant, and t is time.
To find the initial size of the culture, we can use the values given at 15 minutes and 40 minutes:
100 = N0 * e^(15k)
1800 = N0 * e^(40k)
Dividing the second equation by the first, we get:
18 = e^(25k)
Taking the natural logarithm of both sides, we get:
k = ln(18)/25
Solving for k, we get:
k = 0.1156
Substituting this value of k into the first equation, we can solve for N0:
100 = N0 * e^(15 * 0.1156)
N0 = 17.65
Therefore, the initial size of the culture was 17.65 bacteria.
The doubling periodTo find the doubling period, we use the fact that the population doubles when t increases by a certain amount, which we'll call T. That is:
N0 * e^(kT) = 2N0
Dividing by N0 and taking the natural logarithm of both sides, we get:
T = ln(2)/k
Solving for T, we get:
T = ln(2)/k ≈ 6.00 minutes
Therefore, the doubling period is approximately 6 minutes.
The population after 115 minutesTo find the population after 115 minutes, we can use the formula with the values of N0, k, and t:
N = N0 * e^(kt) = 17.65 * e^(0.1156 * 115) ≈ 10477448.92
Therefore, the population after 115 minutes is approximately 10477448.92 bacteria.
When the population reaches 12000To find when the population reaches 12000, we set N equal to 12000 and solve for t:
12000 = 17.65 * e^(0.1156t)
Dividing by 17.65 and taking the natural logarithm of both sides, we get:
ln(12000/17.65 ) = 0.1156t
Solving for t, we get:
t ≈ 56.42 minutes
Therefore, the population will reach 12000 bacteria after approximately 56.4 minutes.
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f(x) = x + 1, g(x) = 7x + 8 find (fog)(x)
Answer:
(fog)(x) = 7x + 9.
Step-by-step explanation:
To find (fog)(x), we need to first find the composition of f and g, which is given by f(g(x)).
So, we substitute g(x) into f(x) and simplify:
f(g(x)) = f(7x + 8)
= (7x + 8) + 1 (using the definition of f(x))
= 7x + 9
Therefore, (fog)(x) = 7x + 9.