The equation p(h)=5,000 • 2^h represents a bacteria population as a function of time in hours.

Answers

Answer 1

Check the picture below.

[tex]p(h)=5000(2)^h\implies \stackrel{p(h)}{100000}~~ = ~~5000(2)^h\implies \cfrac{100000}{5000}=2^h \\\\\\ 20=2^h\implies \log(20)=\log(2^h)\implies \log(20)=h\log(2) \\\\\\ \stackrel{\textit{using the \underline{change of base rule}}}{\cfrac{\log(20)}{\log(2)}=h\implies \log_2(20)=h}\implies 4.3219\approx h[/tex]

Related Questions

The length of a rectangular garden is 2 m greater than the width. The area is 80 m^2. Find the dimensions of the garden.

The width of the garden is ___m.
The length of the garden is ___m.

Answers

Answer:

Length of rectangle = 10 mWidth of the Rectangle = 8 m

Step-by-step explanation:

Given :-

Length of a Rectangular garden is 2m greater than the width .Area of garden = 80 m²

To Find :-

Dimensions of the garden

Solution :-

Let's assume:

Width of the rectangle = xLength of the rectangle = x + 2

We know that,

Area of rectangle = Length × Width

↠ (x)(x + 2) = 80

↠ x² + 2x - 80 = 0

↠ x² + 10x - 8x - 80 = 0

↠ x(x +10) -8 (x + 10) = 0

↠ (x-8) (x + 10) = 0

↠ x = 8 or -10

↠ x = 8

Hence,

Width of the rectangle = x = 8 mLength of the rectangle = x + 2 = 10 m

Answer:

Given:-

Length of rectangular garden is 2m longer than its widthArea of Rectangular garden is 80m²

To Find :-

Dimensions of Rectangular garden

Solution:-

Let the width be x and length be x + 2

According to the question ,

Area = 80m²

putting the known values ,

(X)(X+2) = 80m

x² +2x - 80= 0

x² +10x-8x -80m= 0

x(x + 10) - 8(x+10) = 0

(x-8) = 0 ; (x+10) = 0

X = 8 ; X = -10

As dimensions can not be negative so , X = 8

Length = X + 2 ; 10 m

Width = X ; 8 m

Find the measure of the
exterior angle, x.
52°
Х I’m desperate please please please help me bc this is due soon

Answers

There is a picture attached refer to the picture as your answer and revise your question answering techniques

What do you think would be a good way to select a random sample of all the students at the 12 schools in the school district?

Answers

Step-by-step explanation:

At a birthday party, teams for a game are chosen by putting everyone's name into a jar, and then choosing the names at random for each team

Given: PO IPO
Prove:
(-o) (mat) = -1
m
PO
po
P'(-b, a)
P (a, b)
Y-Y
1.me=
PO X2-X
C-a
Q' (d.c)
Q (c,d)
Check

Answers

Answer: d-b

Step-by-step explanation:

What is the true solution to the equation below? l n e superscript l n x baseline l n e superscript l n x squared baseline = 2 l n 8

Answers

The true solution of the logarithmic equation [tex]\ln e^{\ln x} + \ln e^{\ln x^2} = 2\ln 8[/tex] will be 4.

What is a logarithm?

Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.

The logarithmic equation is given as

[tex]\ln e^{\ln x} + \ln e^{\ln x^2} = 2\ln 8[/tex]

We know that the formula

[tex]\ln e = 1\\\\\ln b^a = a \ln b\\\\\ln a + \ln b= \ln a +b[/tex]

Then we have

[tex]\begin{aligned} \ln x \times \ln e + \ln x^2 \times \ln e = \ln 8^2\\\\\ln x + \ln x^2 = \ln 64\\\\\ln x*x^2 = \ln 64 \end{aligned}[/tex]

Then take antilog, then we get

[tex]\rm x^3 = 64\\\\x^3 = 4^3 \\\\x \ =4[/tex]

More about the logarithm link is given below.

https://brainly.com/question/7302008

Answer:

b, x=4

Step-by-step explanation:

edge 2022

Solve for the formula for r. C=2πr Question 2 options:
r=C2π
r=2Cπ
r=2πC
r=2πC

Answers

Answer:

r = [tex]\frac{C}{2\pi }[/tex]

Step-by-step explanation:

C = 2πr ( isolate r by dividing both sides by 2π )

[tex]\frac{C}{2\pi }[/tex] = r

Does the table represent a linear or nonlinear function? Explain

Answers

Answer:

The table represents a nonlinear function.

Step-by-step explanation:

A linear function has a constant rate of change. However, the y values in the table do not have a constant rate of change. 4pi - pi = 3 pi, 9pi - 4pi = 5pi and so on. The values change each time, so it is a nonlinear function.

This is the answer that I got, hopefully I am correct on this one.

Monique goes to a party that starts at 10 minutes to 6.
The party lasts 3 and a half hours.
What time does the party end?

Answers

Starts at 5:50, ends at 9:20
Total 3-1/2 hrs

Julian scored 24 points over the first 12 games of the basketball season. Disappointed with his performance, he started spending extra time after practice working on his shot. He scored 112 points over the last 16 games of the season. How many more points per game did Julian score in the last 16 games of the season

Answers

Answer:

5 more points

Step-by-step explanation:

To find the ppg of the first 12 games you do 24/12

for the 16 games: 112/16

24/12=2

112/16=7

7-2=5

Rounded to the nearest tenth of a centimeter, what is the length of arc lmn? 7.9 cm 10.2 cm 12.6 cm 14.2 cm

Answers

The length of arc LMN is the number of units on the arc

The length of arc LMN is 14.2 cm

How to calculate the length of the arc?

The given parameters are:

Arc LM = 6.3 cmRadius, r = 6 cmAngle MON = 75 degrees

Start by calculating the length of arc MN using:

[tex]MN = \frac{\theta}{360} * 2\pi r[/tex]

So, we have:

[tex]MN = \frac{75}{360} * 2 * 3.14 * 6[/tex]

Evaluate the product

MN = 7.85

The length of arc LMN is then calculated using:

LMN = LM + MN

This gives

LMN = 6.3 + 7.85

Evaluate the sum

LMN = 14.15

Approximate

LMN = 14.2

Hence, the length of arc LMN is 14.2 cm

Answers

Step-by-step explanation:

the indicated point in the middle is the center point of the circle.

the line perpendicular to a chord going through that center solid the chord in half.

so,

x = 9

Pythagoras

c² = a² + b²

13.5² = x² + 10.4²

182.25 = x² + 108.16

x² = 74.09

x = 8.607554821...

Intersecting Chords Theorem

(part one of chord 1)×(part two of chord 1) =

= (part one of chord 2)×(part two of chord 2)

6x = 10×9 = 90

x = 90/6 = 30/2 = 15

Intersecting Chords Theorem again

x(x+3) = 4×10 = 40

x² + 3x = 40

x² + 3x - 40 = 0

generation solution to a quadratic equation

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 3

c = -40

x = (-3 ± sqrt(3² - 4×1×-40))/(2×1) =

= (-3 ± sqrt(9 + 160))/2 = (-3 ± sqrt(169))/2 =

= (-3 ± 13)/2

x1 = (-3 + 13)/2 = 10/2 = 5

x2 = (-3 - 13)/2 = -16/2 = -8

negative values for a length do not make sense, so x = 5 is our solution

Intersecting Chords Theorem

(x+1)×4 = (x-1)×5

4x + 4 = 5x - 5

9 = x

SOLVE THIS!!!! CAUSE...WELL BRAINLY
please fill in the blanks

Time is an illusion~

that helps things make ____

so we're always living in the present tense

it is unforgiving when a good thing ____

Answers

Answer: sense happens

Step-by-step explanation:

Brandon recorded which donut his nephew picked for breakfast the past few months.
cake donuts 2
chocolate frosted donuts 2
jelly-filled donuts 5
glazed donuts 3
Considering this data, how many of the next 20 donuts Brandon's nephew picks for breakfast would you expect to be glazed donuts?

Answers

Answer:

Step-by-step explanation:

2+2+3+5=12

12/3=4

4 divided by 20 =5 glazed donuts

y+4=-12/7(x-1) in standard form

Answers

Answer: y + [tex]\frac{12}{7}[/tex]x = -[tex]\frac{16}{7}[/tex]

Step-by-step explanation:

Standard form is Ay + Bx = C,

Given:

y+4=-12/7(x-1)

Rewrite:

y + 4 = [tex]\frac{-12}{7}[/tex](x - 1)

Distribute:

y + 4 = [tex]\frac{-12}{7}[/tex]x + [tex]\frac{12}{7}[/tex]

Subtract 4 from both sides:

y = [tex]\frac{-12}{7}[/tex]x + [tex]\frac{12}{7}[/tex] - 4

Add [tex]\frac{12}{7}[/tex]x to both sides:

y + [tex]\frac{12}{7}[/tex]x = + [tex]\frac{12}{7}[/tex] - 4

Combine like terms:

y + [tex]\frac{12}{7}[/tex]x = -[tex]\frac{16}{7}[/tex]

A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the screen to the height of the screen, is16: 9.
What is the length of the diagonal of the screen, to the nearest whole inch?
Enter your answer in the box

Answers

Answer

Step-by-step explanation

16/9=width/height

20 is the width of the computer monitor so you would put width as 20

20/x then you would cross multiply to find the height which is x.

20 x 9=180

Then you would divide 180 by 16.

180/16=11.25

So now you have the width and the height 20/11.25=width/height

Then you do the pythagorean theorem a^2+b^2=c^2=20^2+11.25^2=526.5.6^2.Then you would round you answer to get 526.6 Then you would find the square root of 526.6 which is 22.9. Then you would round the answer to get 23.

( Find the Mean Absolute Deviation and the Mean with an explanation )
How many siblings do the students in my math class have?
3,2,2,5,4,1,3,4,1,0,3,2,1,1,6,3

Answers

The mean of the data is 1.31, while the mean absolute deviation is 2.56.

What is the Mean Absolute Deviation?

The mean is the average of a data set, while the mean absolute deviation is the average distance of the each data point from the mean.

Given the data:

3,2,2,5,4,1,3,4,1,0,3,2,1,1,6,3

Find the Mean:

Mean = (3 + 2 + 2 + 5 + 4 + 1 + 3 + 4 + 1 + 0 + 3 + 2 + 1 + 1 + 6 + 3)/16 = 41/16 Mean = 2.5625

Find the Mean Absolute Deviation:

Mean abosolute deviation = (3 - 2.5625) + (2 - 2.5625) + (2 - 2.5625) + (5 - 2.5625) + (4 - 2.5625) + (1 - 2.5625) + (3 - 2.5625) + (4 - 2.5625) + (1 - 2.5625) + (0 - 2.5625) + (3 - 2.5625) + (2 - 2.5625) + (1 - 2.5625) + (1 - 2.5625) + (6 - 2.5625) + (3 - 2.5625) / 16

Mean abosolute deviation = 21/16 = 1.3125

Therefore, the mean of the data is 1.31, while the mean absolute deviation is 2.56.

Learn more about the mean absolute deviation on:

https://brainly.com/question/447169

Complete the work to find the dimensions of the rectangle. w(2w 4) = 240 2w2 4w = 240 2w2 4w – 240 = 0 2(w 12)(w – 10) = 0 what is the width of the rectangle? what is the length of the rectangle?

Answers

Answer:

10 units wide; 24 units long

Step-by-step explanation:

The width is represented by the variable w in the given equation ...

w(2w +4) = 240

This is conveniently divided by 2. Writing in standard form lets us see potential factoring.

w(w +2) = 120

w² +2w -120 = 0

(w +12)(w -10) = 0 . . . . . . factor

w = -12 or w = 10 . . . . . width

2w+4 = 2(10) +4 = 24 . . . length

The positive solution to this equation is the one of interest here.

The width of the rectangle is 10 units; its length is 24 units.

State reasons why these two triangles are congruent

Answers

Both the same size lengths and have the same angles.

If m=5, evaluate m^18 divide by m^11

Answers

Answer:

78125

Step-by-step explanation:

Using a rule of powers, a^x / a^y = a^(x-y)This gives you m^(18 - 11) = m^7M is 5, so it would be 5^7 or 78125

9x10^2 is how many times as much as 3x10^-2

Answers

Answer:

3 times

Step-by-step explanation:

divide both numbers Which will give you 3

Is there any way for my to view my full highschool transcript online

Answers

sorry brain ly won't let me tell you I'm sorry

a 2014 mustang originally costs $25000.00 and depreciates at a rate of 8% per year. What is the cost of the car after 7 years?

Answers

$11,000 will bet the cost in 7 years

Given:

Original cost: $25,000

Depreciation rate: 8%

Term: 7 years

Formula for Depreciation:

A = C ( 1 - ( r ) (t) )

A = Future Value

C = Original Cost

r = rate

t = term

Solution:

Substitute the given values to the formula for depreciation.

A = $25,000( 1 - ( 0.08)(7))

A = $25,000( 1 - .56 )

A = $25,000(0.44 )

A = $11,000

While cleaning out the garage, Nelson discovers some containers of oil that need to be taken in for recycling. The containers hold 25 fluid ounces, 2 cups, and 7 quarts, respectively. Find the total amount of oil ready to be recycled (in fluid ounces)

Answers

Answer:265

Step-by-step explanation: 2 cups is 16fluid Ounce, 7quaryz is 224 fluid ounce

Total will 265 fluid ounce (225+16+224)

100 POINTS PLEASE ANSWER

What do you think? How do superheroes help teach us about the world we live in? What values should superheroes represent?

Respond in a cohesive paragraph that includes the following:
- provide 3 values and elaborate their importance
- address what your superhero would teach society
- provide a name and superpower

Answers

Answer:

Superheroes are meant to inspire. They represent someone we are not, or someone that can do things that we can't. They can provide an escape into a world where someone is there for us even when our protectors or our medical and social institutions have let us down.

Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x − p)2 = q?
[p and q are integers] (5 points)

Select one:
a.
Step 1 x2 + 10x + 24 − 1 = 0 − 1
Step 2 x2 + 10x + 23 = −1
Step 3 (x + 5)2 = −1
b.
Step 1 x2 + 10x + 24 − 2 = 0 − 2
Step 2 x2 + 10x + 22 = −2
Step 3 (x + 5)2 = −2
c.
Step 1 x2 + 10x + 24 + 2 = 0 + 2
Step 2 x2 + 10x + 26 = 2
Step 3 (x + 5)2 = 2
d.
Step 1 x2 + 10x + 24 + 1 = 0 + 1
Step 2 x2 + 10x + 25 = 1
Step 3 (x + 5)2 = 1

Answers

The correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is

Step 1: x² + 10x + 24 + 1 = 0 + 1

Step 2: x² + 10x + 25 = 1

Step 3: (x + 5)² = 1

To transform x² + 10x + 24 = 0 into the form (x − p)² = q where [p and q are integers], we perform the following steps of transformation.

What is transformation?

This is process of converting one expression to the other by performing some mathematical operations.

How to transform x² + 10x + 24 = 0 into the form (x − p)² = q

x² + 10x + 24 = 0

We add 1 to both sides.So,

Step 1: x² + 10x + 24 + 1 = 0 + 1

Thus, we have

Step 2: x² + 10x + 25 = 1

Since the left-hand-side x² + 10x + 25 = (x + 5)²

So, we have

x² + 10x + 25 = 1

Step 3: (x + 5)² = 1

So, the correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is

Step 1: x² + 10x + 24 + 1 = 0 + 1

Step 2: x² + 10x + 25 = 1

Step 3: (x + 5)² = 1

Learn more about transformation here:

https://brainly.com/question/27224339

What is the difference? startfraction x over x squared minus 2 x minus 15 endfraction minus startfraction 4 over x squared 2 x minus 35 endfraction startfraction x squared 3 x 12 over (x minus 3) (x minus 5) (x 7) endfraction startfraction x (x 3 minus 12) over (x 3) (x minus 5) (x 7) endfraction startfraction x squared 3 x 12 over (x 3) (x minus 5) (x 7) endfraction startfraction x squared 3 x minus 12 over (x 3) (x minus 5) (x 7) endfraction

Answers

The difference is StartFraction x squared + 3 x minus 12 Over (x + 3) (x minus 5) (x + 7) EndFraction.

What is a quadratic equation?

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given expression is

[tex]\frac{x}{x^{2} -2x-15} -\frac{4}{x^{2} +2x-35}[/tex]

[tex]\frac{x}{x^{2} -5x+3x-15} -\frac{4}{x^{2} +7x-5x-35}\\\frac{x}{(x-5)(x+3)} -\frac{4}{(x-5)(x+7)}[/tex]

by Taking LCM

[tex]\frac{x(x+7)-4(x+3)}{(x-5)(x+3)(x+7)} \\[/tex]

[tex]\frac{x^{2} +3x -12}{(x-5)(x+3)(x+7)} \\[/tex]

Learn more about a quadratic equation;

https://brainly.com/question/2263981

Answer: The correct answer is D on edge

Step-by-step explanation:

got it right on the pretest

Decide whether y is a function of x.
x2 + y2 = 1

Answers

Answer:

Not a function.

Explanation:

x² + y² = 1 is not a function.

Here's the breakdown!

Looking at the type of equation, It is a circle equation.

In a circle equation, y value is not completely determined by the x value.

Shown:

x² + y² = 1y² = 1 -x²y = ±√1 -x²

There are multiple values of x for each value of y

Answer:

A function can be described as one-to-one or many-to-one, i.e. each value in the domain ([tex]x[/tex]-values) is mapped to a single value in f(x).

An example of a one-to-one function is a linear function. For every value of x there is one value of y.

An example of a many-to-one function is a quadratic function, where 2 different x-values map to one y-value.

[tex]x^2+y^2=1[/tex] is not a function as some values of [tex]x[/tex] are mapped to two different values of f(x).

For example, let x = 0.5

[tex]\implies (0.5)^2+y^2=1[/tex]

[tex]\implies y^2=0.75[/tex]

[tex]\implies y=\pm\sqrt{0.75}[/tex]

So as x = 0.5 maps to √0.75 and -√0.75, it is one-to-many, and is therefore not a function.

what numbers are missing from.the pattern below 108,5,43,63 ???? 108,5,43,63

Answers

Answer:

108,5,43,63

Step-by-step explanation:

108,5,43,63,_,_,_,_,108,5,43,63

groups of 4

Also just to add on the the answer it’s a pattern you got this

The radius of a circle is 3 meters. What is the circle's circumference?
r=3 m
Use 3. 14 for .

Answers

Answer: The circle's circumfrence is 18.84

Step-by-step explanation:

When you are finding the circumference of a circle you use the formula

[tex]C=2\pi r[/tex]

[tex]C=2*3.14*3[/tex]

[tex]C=18.84[/tex]

HELPEHEGEDHGDGXCCVCCXVV

Answers

Step-by-step explanation:

1) 7x+3y=19

2)2x-7y=12

3) x=5, y=0

4) x=15/2, y=(-63/4)

5) x=9, y=92

6) x=(-2) , y=(-9)

7) x=5, y=(-2)

8) x=2, y=2

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