if a bacteria population starts with 100 bacteria and doubles every four hours, then the number of bacteria after t hours is n = f(t) = 100 · 2t⁄4. (a) find the inverse of this function.

Answers

Answer 1

The inverse of the given function,f(t) = 100 . 2^(t/4) is 4 * log2(x/100).

What is the inverse of a function?

An inverse of a function f(x), is defined as another function that undoes the operations performed on the function. It is denoted by f^(-1).

Calculation of the inverse of a function

We are given a function,

f(t) = 100 . 2^(t/4)

Let us assume that f^(-1) represents the inverse of a function

Replacing f(t) with y, we get,

y = 100 . 2^(t/4)

Now, replace further t with y and y with x

x = 100 . 2^(y/4)

Rearranging, we have,

2^(y/4) = x / 100

Taking log both sides, we get,

(y/4) log 2 = log (x/100)

y/4 = log2(x/100)

y = 4 * log2(x/100)

Further, replace x with t and y with f^(-1), i.e.

f^(-1) = 4 * log2(t/100)

Hence, the inverse of the given function, f(t) = 100 . 2^(t/4) is 4 * log2(x/100).

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Related Questions

I need help with introduction to probability lesson. Photo is attached below.

Answers

The probability of getting heads is 31/50.

How to calculate the probability?

Number of tosses = 50

Number of heads = 31

The probability of getting heads will be:

= Number of heads / Total number of tosses

= 31/50

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66 between numbers 4 and 39 put in four numbers, such that arithmetic sequence would be done. what is the third term of this arithmetic sequence?

Answers

The third term of the arithmetic sequence is 18.

How to solve arithmetic sequence?

The arithmetic sequence formula can be represented as follows:

nth term = a + (n - 1)d

where

a = first termd = common differencen = number of terms

Therefore, 4 numbers are inserted between 4 and 39.

Hence,

a = 4

39 = 4 + 5d

39 - 4 = 5d

35 = 5d

d = 35 / 5

d = 7

Hence, the common difference of the arithmetic sequence is 7.

Therefore, the sequence of the arithmetic sequence is as follows:

4, 11, 18, 25, 32, 39

Therefore, the third term of the arithmetic sequence is  18

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while standing in front of the school, jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.

Answers

This is an observational study because this is taken as observing all possible ways.

What is observational study?

An observational review is utilized to respond to an exploration question dependent simply upon what the scientist notices. There is no impedance or control of the examination subjects, and no control and treatment gatherings. These examinations are much of the time subjective in nature and can be utilized for both exploratory and logical examination purposes. In observational examinations, the analyst isn't permitted to control anything. They just notice and gather patterns inside the set up and hypothesize from those outcomes. Observational examination takes into consideration more precise information assortment, eliminating predispositions and inspecting blunders. Notwithstanding, it tends to be tedious because of extended periods of time of dormancy.

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Select the correct answer.
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been transformed to produce figure 2.
-00
55-
N
2
N
ON
6
80
Which notation describes this transformation?
OA. (x,y) = (x,-)
OB. (x,y)=(x-4,y - 8)
OC. (x,y) = (x - 8,y - 8)
OD. (x,y)= (-2,-y)
9.
8.

Answers

Using translation concepts, the notation that describes this transformation is:

C. (x,y) -> (x - 8, y - 8).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

To generate figure 2 from figure 1, these following translations happened:

8 units left, hence x -> x - 8.8 units down, hence y -> y - 8.

Thus the rule is given by:

C. (x,y) -> (x - 8, y - 8).

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Answer: (x',y') = (x - 4,y - 8)

Step-by-step explanation:

The width of a rectangle is the length minus 5 units. The area of the rectangle is 24
units. What is the length, in units, of the rectangle?

Answers

Answer:

L = 8

w = 3

Step-by-step explanation:

Givens

w = L - 5

L = x

Area = 24

Formula

Area = L * w

Solution

Area = (x) * (x - 5)

24 = x * (x - 5)                      Remove the brackets

24 = x^2 - 5x                       Subtract 24 from both sides

0 = x^2 - 5x - 24                  This will factor

0 = (x - 8)(x + 3)

x + 3 is an extraneous root. You cannot have a length of -3 units no matter what the units are.

x - 8 = 0  

x = 8

Answer

The length = 8

The width is = 8 - 5 = 3  

Solve 4∣x+5∣=24

A.x = –11 and x = –1
B.x = 11 and x = –1
C.x = –11 and x = 1
D.x = 11 and x = –11

Answers

Step-by-step explanation:

You first need to get the absolute vaule of x+5 by its self. So you need to divide 4 on yet sides

[tex] |x + 5| = 6[/tex]

Then set up two equations a negative and a postive on

[tex] |x + 5| = 6[/tex]

x=1

[tex] |x + 5| = - 6[/tex]

x=-11

Hope that helped!

Feel free to ask questions!

Sorry if that's hard to see, but I need ur help!

Answers

The control group is group B

The independent variable is the new sauce

Dependent variable is the amount of gas

Conclusion: the new sauce works because it curved the gas problems of a greater percentage of people tested

Help please!
I also need an explaination on how to do it.
Which expression is equivalent to −4 + 9 − 2x − 9x?


−11x + 5

−11x + 13

−11x − 5

11x + 13

Answers

Answer:

−11x    +    5

Step-by-step explanation:

−4  +  9  −   2x  −9x

−4  +   9  +  −  2x  +  −9x

Combine Like Terms:

−4  +  9  +  −2x  +−  9x

(   −2x+−9x   )+(   −4+9   )

−11x    +    5


28. Use the properties of the mean and median to determine which
are the correct mean and median for the following histogram.
(i) Mean is 3.6; median is 4.8
(ii) Mean is 4.8; median is 3.6
(iii) Mean is 3.5; median is 3.1
(iv) Mean is 4.2; median is 4.1

Answers

The properties of the mean and median to determine which

are the correct mean and median for the following histogram. The answer is Mean is 3.5; median is 3.1.

Mean

[tex]\mu=& \varepsilon x \cdot P(x)[/tex]

= 0(0.04)+1(0.08)+2(0.125)+3(0.24) +4(0.15)+5(0.14)+6(0.12)+7(0.05)

= 0+0.08+0.25+0.72+0.6+0.7+0.72+0.35

= 3.42 [Approx: 3.5]

Mean =3.5 of median 3.1.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data collection is called the mode.

The median is computed by sorting the scores into numerical order, dividing the total by 2, rounding the result up if the number of scores is odd to determine the median position, or by averaging the median position and the position after it, if the number of scores is even.

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Based on the what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of numbers y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number

Answers

The statements are:

x . y = m/n

substituting the values.

a/b . y = m/n

multiplication property of equality.

b/a . a.b . y  = m/n . b/a

simplify.

y = mb/na

The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.

Hence we made the required conclusion.

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The coordinate -1 has a weight of 1, the coordinate 4 has a weight of 2, and the coordinate 9 has a weight of 2. Find the
weighted average.

Answers

The weight average of the coordinates is 5

How to determine the weight average?

The given parameters are:

Coordinate -1 has a weight of 1Coordinate 4 has a weight of 2Coordinate 9 has a weight of 2

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

So, we have:

Weight average = (-1 * 1 + 4 * 2 + 9 * 2)/(1 + 2 + 2)

Evaluate the quotient

Weight average = 5

Hence, the weight average of the coordinates is 5

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i need help!! ……………….

Answers

Answer:

Step-by-step explanation:

The first one its easy

2 divided by $1.03 round to the nearest cent ?

Answers

Answer:

.05

Step-by-step explanation:

Find the mean of the data set: 9, 6, 7, 3, 10, 9
A. 6
B. 7
C. 8
D. 9

Answers

Answer: 7

Step-by-step explanation: add all the numbers up and divide them by how many numbers they are

A walking tour of Washington, D.C., costs $20 per person. Show that the relationship between the number of people in a tour group and the total cost is a proportional relationship. Write an equation for the relationship.

Answers

The Total cost for a tour group consisting of n number of people is 20n

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let T represent the total cost if a tour group consisting of n people

Since A walking tour of Washington, D.C., costs $20 per person. Hence, for n number of people:

Total cost = $20 per person * n persons = 20n

The Total cost for a tour group consisting of n number of people is 20n

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Patrice is trying a low-calorie diet. She would like to keep her calories consumed between the levels shown in the following compound inequality: 2450 < 2x + 50 and 2x + 50 < 3250. Solve for x in the inequality, and explain what the answer represents.

Answers

The solution to the compound inequality is 1200 < x < 1600 and the meaning is she must keep her calories consumed between 1200 and 1600

How to solve for x in the inequality, and explain what the answer represents?

The compound inequality is given as

2450 < 2x + 50 and 2x + 50 < 3250

Subtract 50 from both sides of the inequality

So, we have

2400 < 2x and 2x < 3200

Divide through the inequality by 20

So, we have

1200 < x and x < 1600

Combine the inequalities

1200 < x < 1600

Hence, the solution to the compound inequality is 1200 < x < 1600 and the meaning is she must keep her calories consumed between 1200 and 1600

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The image represents what geometric construction?
A Parallel Lines Construction
B Copy an Angle Construction
C Angle Bisector Construction
D Perpendicular Bisector Construction

Answers

the answer is a parallel lines

What is the point-slope form of the equation for the line with a slope of 6/19 that passes through the point (−1, 7/5)?

Answers

The point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] is [tex]6x-19y=-\frac{163}{5}[/tex]

As per the question statement, we are supposed to find the point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] .

Before solving the question, we need to know about the point - slope form of the line i.e., [tex]y-y_{1} =m(x-x_{1} )[/tex]

where m = slope = [tex]\frac{6}{19}[/tex]

[tex]x_{1} =-1[/tex] and [tex]y_{1} = \frac{7}{5}[/tex]

Now substituting values, we get

[tex]y-\frac{7}{5} =\frac{6}{19} (x-[-1])[/tex]

[tex]y-\frac{7}{5} = \frac{6}{19} (x+1)[/tex]

[tex]19y - \frac{133}{5} = 6x+6[/tex]

Rearranging,

[tex]6x-19y+6+\frac{133}{5} =0[/tex]

[tex]6x-19y+\frac{163}{5} =0[/tex]

[tex]6x-19y=-\frac{163}{5}[/tex]

Hence our required equation is [tex]6x-19y=-\frac{163}{5}[/tex]

Point slope form of equation: The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

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how many groups of 1/5 are in 4​

Answers

Answer:

20

Step-by-step explanation:

To find this, we need to figure out what 1/5 is as a decimal

5/5 = 1, so 5 groups of 1/5 equals 1

Multiply this by 4, 20 groups of 1/5, or 20/5 = 4

Now we confirm this

1/5=0.2

4/0.2=20

So it is true

Hope this helps!^^

Mr. Wise is ordering a set of books for his class. Each book costs $6. There is a flat shipping fee of $5. The table below shows the relationship between the total cost, c, and the number of books, b. Fill in the blanks to complete the table. Number of Book, b 2 [a] 6 [b] 10 Total Cost ($), c 17 29 [c] 53 65

Answers

Filling the table to show the relationship between the total cost, c, and the number of books ordered is as follows:

Number of Books      Total Cost ($)

            2                     $17 ($6 x 2 + $5)

            6                     $41  ($6 x 6 + $5)

           10                    $65  ($6 x 2 + $5)

What is the total cost?

The total cost is a function of the number of units and the variable cost per unit plus the fixed costs.

For instance, the total cost of 9 books, in this scenario, is $59 ($6 x 9 + $5).

Data and Calculations:

Cost per book = $6

Shipping fee = $5

Number of Books      Total Cost ($)

            2                   $17 ($6 x 2 + $5)

            6                  $41  ($6 x 6 + $5)

           10                 $65  ($6 x 2 + $5)

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The principal is measuring the floor of the second-grade classroom.
What is the best estimate for the length of a classroom?

Answers

The best measure to do so will be is in feet that is the principal will measure it as 10 feet.

The principal has to measure the floor of the second grade classroom.

The best measure to do so will be is in feet

As centimeters and inches will be too short to measure it and can cause problems while further maintaining the records.

Yards on the other hand is a too big unit of measurement to bthe length of the classroom.

Therefore, the best measure to do so will be is in feet that is the principal will measure it as 10 feet.

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Your question was incomplete. Please refer the content below

The principal is measuring the floor of the second-grade classroom.

What is the best estimate for the length of a classroom?

10 yards

10 centimeters.

10 feet

10 inches


Find the volume of a cube that has a total surface area of 54 square millimeters.

Answers

The volume of a cube that has a total surface area of 54 square millimeters is 27 cubic millimeters

How to determine the volume?

The surface area is given as

A = 54

This is calculated using

A = 6L^2

So, we have

6L^2 = 54

Divide

L^2 = 9

This gives

L = 3

The volume is

V = L^3

This gives

V = 3^3

Evaluate

V = 27

Hence, the volume of a cube that has a total surface area of 54 square millimeters is 27 cubic millimeters

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1: Find m (25x-5)
12X-
A
(15

Answers

Answer:

Step-by-step explanation:

(25x-5) 12X- Ax15

A group of friends wants to go to the amusement park. They have no more than $325
to spend on parking and admission. Parking is $13, and tickets cost $39 per person,
including tax. Write and solve an inequality which can be used to determine p, the
number of people who can go to the amusement park.

Answers

6 people can only go in

The second side of a triangular deck is 3 feet longer than the shortest side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 52 feet, what are the lengths of the three sides?​

Answers

The shortest side of the triangle measures 17 feet.The second side of the triangle measures 20 feet.The third side of the triangle measures 31 feet.What is the length of the three sides?The perimeter of a triangle is the sum of the length of the three sides of the triangle. Let the shortest side be represented with s.The second side = 3 + s The third side = 2s - 3 2s - 3 + 3 + s + s = 68 4s = 68s = 17The second side = 17 + 3 = 20 The third side = = (2 x 17) - 3 = 31

How do I solve this step by step

Answers

I’m pretty sure this is correct

its a data handling question can u guys please help

Answers

(i) Maximum students were watching T.V for 4-5 hours.

(ii) 34 students watched T.V for less than 4 hours.

(iii) 14 students spent more than 5 hours watching TV.

Given from the graph we can say that:

The process of acquiring, storing, and displaying data in a way that makes it easy for others to use (read or fetch data), such as in graphs or charts, is known as data handling. Statistics is another name for it. Additionally, it is employed for data comparison and mean, median, and mode extraction.

(i) maximum number of students watching TV  =32

Almost 32 students watched TV for 4-5 hours.

(ii) For students watching TV for less than 4 hours = ?

= 4 ₊ 8 ₊ 22

= 34

(iii) students who spent more than 5 hours watching  TV = ?

= 8 ₊ 6

= 14

Hence we get the desired answers.

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simplify (4a-3)(a-9)=4a² -39a+27

Answers

Answer:

Step-by-step explanation:

0=0

Please help me :3 please explain

Answers

Using a proportional relationship, the amounts are given as follows:

Tennis 3, Soccer 7.Tennis 36, Soccer 84.

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For this problem, we have that:

The input variable is the number of tennis players.The output variable is the number of soccer players.

From the first row of the table, the constant is given as follows:

k = 35/15 = 7/3.

Hence the relationship is:

y = 7/3x.

For the second row of the table, we have that x = 3, hence:

y = 7/3 x 3 = 7.

For the third row of the table, we have that y = 84, hence:

84 = 7/3x

x = 84 x 3/7

x = 36.

Then the amounts are given as follows:

Tennis 3, Soccer 7.Tennis 36, Soccer 84.

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The perimeter of Stephanie’s triangle is half the perimeter of Juan’s triangle. Juan’s triangle is shown. Write a numerical expression to describe the perimeter of Stephanie’s triangle

Answers

The perimeter of Stephanie’s triangle is half the perimeter of Juan’s triangle.Numerical expression to describe the perimeter of Stephanie’s triangle is S =(1/2) J;

Let as assume that

Stephanie's triangle has a perimeter (S)

And, Juan's triangle has a perimeter (J);

According to question, it implies:

S =(1/2) J;

The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.

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