The equation p(h)=5,000 • 2^h represents a bacteria population as a function of time in hours.
Answers
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
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
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]
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
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 -x²There 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.
( 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
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]
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
23
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.
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.
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:
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
d.
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 = qx² + 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
d.
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
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:
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)
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.
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
State reasons why these two triangles are congruent
Answers
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:
5
Step-by-step explanation:
2+2+3+5=12
12/3=4
4 divided by 20 =5 glazed donuts
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
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 mStep-by-step explanation:
Given :-
Length of a Rectangular garden is 2m greater than the width .Area of garden = 80 m²To Find :-
Dimensions of the gardenSolution :-
Let's assume:
Width of the rectangle = xLength of the rectangle = x + 2We know that,
Area of rectangle = Length × Width↠ (x)(x + 2) = 80
↠ x² + 2x - 80 = 0
↠ 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 mAnswer:
Given:-
Length of rectangular garden is 2m longer than its widthArea of Rectangular garden is 80m²To Find :-
Dimensions of Rectangular gardenSolution:-
Let the width be x and length be x + 2According 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 = 8Length = 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
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
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
Can someone please give me the (Answers) to this? ... please ...
I need help….
Answers
Step-by-step explanation:
1.
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
2.
Pythagoras
c² = a² + b²
13.5² = x² + 10.4²
182.25 = x² + 108.16
x² = 74.09
x = 8.607554821...
3.
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
4.
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
5.
Intersecting Chords Theorem
(x+1)×4 = (x-1)×5
4x + 4 = 5x - 5
9 = x
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
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
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
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 degreesStart 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
Read more about arc lengths at:
https://brainly.com/question/15589041
Answer:
D ( 14.2 )
Step-by-step explanation:
edg 2022
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 78125Complete 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.
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
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
Total 3-1/2 hrs
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