Answer:
7614
Step-by-step explanation:
The exponential growth of the bacteria culture can be modeled by the equation ...
p = a·b^(t/c)
where 'a' is the initial population, 'b' is the growth factor, and 'c' is the period over which that growth factor applies.
__
modelIn the given scenario, we have ...
a = 6000 bacteriab = 6600/6000 = 1.1 . . . . growth factorc = 4 hoursSo, our model is ...
p = 6000·1.1^(t/4)
__
applicationAfter 10 hours, the population is predicted to be ...
p = 6000·1.1^(10/4) ≈ 7614
We predict 7614 bacteria will be present after 10 hours.
__
Additional comment
If we compare the form we used to the one suggested in the proglem statement, we see
p = 6000·1.1^(t/4)p = 6000·e^(kt)For the bases of the exponential term to be the same, we must have ...
1.1^(t/4) = e^(kt)
(1.1^(1/4))^t = (e^k)^t . . . . . factor t from the exponent
1.1^(1/4) = e^k . . . . . . . match the bases
k = ln(1.1)/4 . . . . . take natural logs
k ≈ 0.0238275
and the equation becomes ...
p = 6000·e^(0.0238275t)
__
In terms of 'a', 'b', and 'c' used above, we find ...
k = ln(b)/c
A motorcycle travels 20 miles west and then turns and goes 52° north of west another 38 miles. How far is the motorcycle from its starting point? Round to the nearest tenth.
Answer:52.7
Step-by-step explanation:
1) Find the angle inside the triangle by subtracting 52 from 180 getting you 128
2)Then we input everything into the law of cosines
Simplify cos^4x+(2cos^2x)(sin^2x)+sin^4x
Answer:
cos4(x)+2cos2(x)sin2(x)+sin4(x)
Step-by-step explanation:
If f(x)=3x−1 and f(a)=−43, what is the value of a ??
Answer:
a = -14
Step-by-step explanation:
f(a) = -43
3a - 1 = -43
3a = -43 + 1
3a = -42
a = -42/3
a = -14
A six-sided polygon is shown with sides labeled 12 cm, 10 cm, 10 cm, 8 cm, 6 cm, and 3 cm.
Lily decorated a poster with this polygon for school spirit week. What is the perimeter of Lily's polygon?
A.
149 cm
B.
120 cm
C.
86 cm
D.
49 cm
Answer:
49cm^2
Step-by-step explanation:
The perimeter is just a continuous line which forms the boundaries of a geometric figure.
The perimeter is just all the sides added up.
12cm+10cm+10cm+8cm+6cm+3cm = 49cm^2
Which set shows an average of 3?
A) A
B) B
C) A and B
D) none of the above
Answer:
B
Step-by-step explanation:
bbbbbb brainless me
Gabrielle's age is two times Mikhail's age. The sum of their ages is 81. What is Mikhail's age?
Answer:
27
Step-by-step explanation:
Let g be Gabrielle's age and m be Mikhail's age.
We can turn the statements the problem gives us into mathematical expressions to help us solve.
Gabrielle's age is two times Mikhail's age:
g = 2m
The sum of their ages is 81:
g + m = 81
This gives us a system of equations that will allow us to solve for Gabrielle's age.
g + m = 81
(2m) + m = 81
3m = 81
m = [tex]\frac{81}{3}[/tex]
m = 27
If we need to solve for Gabrielle's age, we can do the following.
g = 2m
2(27) = g
54 = g
g = 54
Mikhail's age is 27.
Gabrielle's age is 54.
Answer:
Mikhail is 27
Step-by-step explanation:
Use 'm' to represent Mikhail's ageUse g = 2m to represent Gabrielle's age (because Gabrielle's age is twice that of Mikhail's.You know that both of their ages combined must equal 81. This can be represented by g + m = 81Lastly, since we stated g=2m, substitute it into the equation to make: 2m + m = 81Combine like variables and divide to get Mikhail's age.**If you want to find Gabrielle's age, multiply Mikhail's age by two, as represented by the equation g=2m. Gabrielle is 57.
Hope this helps!
rounded to the nearest hundredth how many meters are in 32 ft (1 m = 3.28)
Answer:
9.76 M
Step-by-step explanation:
32/3.28
9.756097561
9.76
The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?
A. g(x) = (x − 7)2 − 3
B. g(x) = (x + 7)2 − 3
C. g(x) = (x − 3)2 − 7
D. g(x) = (x − 3)2 + 7
Answer:
B. g(x)=(x+7)^2-3
Step-by-step explanation:
Vertex form is F(x)= a(x-h)^2+k
a is the reflection
h and k are the vertex (x,y) = (h,k)
in this case there is no shrink or stretch (a)
if it is translating left or right it is "h". In this case it is translated left so its -7. However if you look at vertex form it is "x-h" so -7-7= +7
If it translating up or down it is "K". In this case it is translated down so its -3.
If it was translated up or right then its positive. If it was translated down or left its negative.
After you figure out what h and k are then you just plug it in. h=-7, k=-3
so the answer in vertex form is, g(x)=(x+7)^2-3
You walk along the edge of a park.
Then you take a shortcut,
represented by PQ on the graph.
What is the length of the shortcut in
meters? Round your answer to the
nearest whole meter, if necessary.
The distance between the two points is 93.9 units
How to calculate the distance between two pointsThe formula for calculating the distance between two points is expressed as:
[tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Given the coordinate points (0, 0) and (40, 85). The distance between the points is expressed as:
[tex]D=\sqrt{(85-0)^2+(40-0)^2}\\D=\sqrt{7225+1600}\\D=93.9 units[/tex]
Hence the distance between the two points is 93.9 units
Learn more on distance between two points here: https://brainly.com/question/23848540
Answer:89.4
Step-by-step explanation:
x
3
+5x
2
−32x−7 divided by x-4x−4 is x^2+9x+4+\frac{9}{x+4}x
2
+9x+4+
x+4
9
(LOOK CAREFULLY!)
badddddddiesssssssss hmuuuuuuuu lulllllllllllllllllllllllllllllllllll
Answer:
The answer is 52x1100=21plus 23= 50010
Step-by-step explanation:
A crate of a apples that usually cost 40$ is on sale for 20$ off. what is the sale price for the crate of apples?
Step-by-step explanation:
We are trying to find $40 on sale for 20$ off.
40*20/100
40*0.2
You save=$8
40-8
Final Price=$32
Write and equivalent expression for 88 + 16x + 8.
X = 4
Answer:
8+88+16x
4=x
Step-by-step explanation:
just reverse it lol
Necesito saber cual funcion es
Answer:
A function is defined as a relation between a set of inputs having one output each..
Step-by-step explanation:
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
¿Qué es la función explicar?
Una función se define como una relación entre un conjunto de entradas que tienen una salida cada una. En palabras simples, una función es una relación entre entradas donde cada entrada está relacionada exactamente con una salida. Cada función tiene un dominio y un codominio o rango. Una función generalmente se denota por f(x) donde x es la entrada.
31
33
34
35
= 36
37
38
39
A certain loan program offers an interest rate of 8%, compounded continuously. Assuming no payments are made, how much would be owed after four years on
a loan of S2900?
Answer:
no sure about the answer
how do i solve and graph -5x+2y=10
Answer:
at first write the equation in correct order y=Mx+b. 2y=5x=10
y= 5x/2+5.
Step-by-step explanation:
the slope is 5/2. as we know slope is rise over run. so you go up 5 units and go right 2 unit.
the graph picture is added below click on the PNG. hope it helps. have a great day.
Which number is bigger: 0.135 or 0.14?
The number 0.14 is bigger than 0.135.
To compare the two numbers, you can look at their digits after the decimal point. In both numbers, the digit in the tenths place is 1. The next digit in 0.14 is 4, which is greater than the corresponding digit in 0.135, which is 3.
Since the digit in the hundredths place (4) is greater than the digit in the hundredths place (3), the number 0.14 is bigger than 0.135.
In summary, the order of the numbers from smallest to largest is:
0.135 < 0.14.
To know more about number:
https://brainly.com/question/3589540
#SPJ2
Find the diameter of a circle with an
area of 99 yd?. Use your calculator's
value of pi and round your answer to
the nearest tenth
Answer: 832
Step-by-step explanation:
trust i got correct
solve for x : -30 < -x/4
x > 120
Step-by-step explanation:
-30 < -x / 4
-30 x 4 < -x
x > 120
Answer:
ight so first you multiply by 4 to isolate x so you get -120<-x next you divide by -1 to get the x so the answer is 120 cause a negative and a negative cancel out and turns to a positive
Step-by-step explanation:
Ciara, an ornithologist, has 444 bird feeders at separate locations. She wonders if birds are equally likely to visit each of the feeders. She recorded data for a sample of 350350350 recent visits. Here are the results: Feeder \#1#1\#, 1 \#2#2\#, 2 \#3#3\#, 3 \#4#4\#, 4 Observed visits 808080 909090 929292 888888 Ciara wants to perform a \chi^2χ 2 \chi, squared goodness-of-fit test to determine if these results suggest that birds visit one specific feeder more often than the other feeders. What is the expected count of visits to the third feeder? You may round your answer to the nearest hundredth.
The expected count of visits is the mean or average visits to each feeder
The expected count of visits to the third feeder is 87.5
How to determine the expected count of visit?The table of values is given as:
Feeder 1 2 3 4
Observed visits 80 90 92 88
In this case, the null hypothesis implies that the visits to each feeder are uniformly distributed
So, the expected count is calculated using:
Expected count =Visits/Feeders
This gives
Expected count = 350/4
Evaluate the quotient
Expected count = 87.50
Hence, the expected count of visits to the third feeder is 87.5
Read more about chi square goodness of fit test at:
https://brainly.com/question/4543358
a retail owner can but a certain clock at an average price of $53 per clock and sell them for an average price of $84 per clock. his fixed costs are $8000 per month and his variable cost is $5 per clock. (A) how many clocks must he sell each month to break even? (B) how many clocks must he sell to have a profit of $3000?
Answer:
(A) 308 clocks
(B) 423 clocks
Step-by-step explanation:
The contribution margin is the amount by which the selling price of the clock exceeds the cost of the clock. The contribution margin is used to figure the break-even point, and the amount of profit from sales.
contribution margin = selling price - variable cost - purchase price
contribution margin = $84 -5 -53 = $26
__
(A)To break even, the contribution margin from 'b' clocks must equal or exceed the owner's fixed cost:
26b ≥ 8000
b ≥ 8000/26
b ≥ 307.7
The owner must sell 308 clocks each month to break even.
__
(B)To make a profit of $3000, the owner must sell enough clocks to cover the $8000 fixed cost and contribute an additional $3000. That is, the total contribution margin from selling p clocks must be about $3000+8000 = $11000.
26p ≈ 11000
p ≈ 11000/26 ≈ 423.08
The owner must sell about 423 clocks each month to earn a profit of about $3000.
__
Additional comment
Selling 423 clocks will yield a profit of $2998.
use multiplication to show how many twelfths equal 2/3.
you can get 74 points
[tex]\\ \rm\rightarrowtail \dfrac{2}{3}[/tex]
We need. the denominator as 12
So
[tex]\\ \rm\rightarrowtail \dfrac{2(4)}{3(4)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{8}{12}[/tex]
Answer is 4Answer:
[tex]\sf \dfrac23=\dfrac{2 \times 4}{3 \times 4}=\dfrac{8}{12}[/tex]
Step-by-step explanation:
To get from 3 to 12, we must multiply 3 by 4 since 3 x 4 = 12
Therefore, multiply both the numerator and denominator by 4:
[tex]\sf \dfrac23=\dfrac{2 \times 4}{3 \times 4}=\dfrac{8}{12}[/tex]
An ice cream shop sold 352 scoops of ice cream.25% of the scoops sold were strawberry ice cream.how many scoops of strawberry ice cream were sold
Answer:
88 scoops
Step-by-step explanation:
Hello!
If 25% of 352 scoops were strawberry, we find 25% of 352
Solve:
25% of 3520.25 * 35288This means 88 scoops of strawberry were sold.
Image attatched for conversion of decimals, percents, and fractions.
What would be the formula for this?
Answer:
ba/2+bd/2+cd, in this case the area is 46
Step-by-step explanation:
The formula for this would simply be the area of the trapazoid plus the area of the rectangle.
The area of a trapazoid(in this case) is b(a+d)/2
The area of the rectangle is cd
Adding these you get ba/2+bd/2+cd
In this case the area is 46
What is the measure of angle x?
Enter your answer in the box.
+
1470
x =
1 2 3 4 5 6 7
5.
Answer:
x=43 degrees
Step-by-step explanation:
Subtract 47 from 90 to get the angle next to 47 degrees which is 43 degrees and x is also 43 degrees because they form vertical angles with each other
Which pair shows equivalent expressions?
2x + 10 = -2(x-5)
-2(x+5) = 2x-10
-2x-10 = -2(x+5)
-2(x-5) = -2x-10
Answer:
The 3rd equation, -2x-10 = -2(x+5)
Step-by-step explanation:
Equivalent expressions means both sides of the equal sign equal the same thing
To find which ones are equivalent expressions, we must solve/simplify both sides of each equation to see if they're actually equal to each other
We will use PEMDAS for this
1. 2x + 10 = -2(x - 5)
Start with Parentheses, and distribute the -2 to what's inside said parentheses
2x + 10 = -2x + 10
Not equal
2. -2(x+5) = 2x-10
Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses
-2x - 10 = 2x - 10
Not equal
3. -2x-10 = -2(x+5)
Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses
-2x - 10 = -2x - 10
Equal
4. -2(x-5) = -2x-10
Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses
-2x + 10 = -2x - 10
Not equal
Find the Sum.
29, 8 67
+ 14, 938
Answer:
44805
Step-by-step explanation:
i just added them together lol
Answer:
the answer is 44805
Step-by-step explanation:
just add them together
Giving brainliest to people who get this right
Answer:
A
Step-by-step explanation:
If y is a function of x, then the equation for y would be y=Ix(+or-or*or%) to nI
For this specific event, the proper equation would be y=Ix-0.5I
Breaking down this equation, y equals the absolute value of x-0.5.
So if x was 2, it would go as y=I2-0.5I where y equals 1.5.
What is the equation of a circle with center (−8, 3) and radius 8?
(x + 8)2 + (y − 3)2 = 64
(x − 8)2 + (y + 3)2 = 64
(x − 8)2 + (y + 3)2 = 8
(x + 8)2 + (y − 3)2 = 8
Answer:
(x + 8)² + (y - 3)² = 64
Step-by-step explanation:
(x - (-8))² + (y - 3)² = 8²
(x + 8)² + (y - 3)² = 64
Find the equation for the circle with center (-2,4) and passing through (-1,- 4).
Answer:
(x+2)^2 + (y-4)^2 = 65
Step-by-step explanation:
r^2 = (4-(-4))^2 + (-1-(-2))^2 = 65
center = (-2, 4) so you add 2 to x and subtract 4 from y
help. will give brainliest. please hurry!!! <3
also, please explain how to get my answer. need to show work.