Complete Question
Bacteria culture A culture of the bacterium Rhodobacter sphaeroids initially had 30 bacteria and t hours later increases at a rate of 2e^2t 1 bacteria per hour. Find the population size after four hours
Answer:
3010
Step-by-step explanation:
We were given the rate: 2e^2t
Step 1
We would integrate
P = Population
dP/dt = 2e^2t
dP =( 2e^2t) dt
∫dP = ∫ 2e^2t dt
P(t) = (2e^2t)/2 + C
P(t) = e^2t + C
Step 2
We solve for C
The culture initially has 30 bacteria
When t = 0
P(0) = 30
P(0) = e^2t + C
30 = e^2× 0 + C
30 = 1 + C
C = 30 - 1
C = 29
Step 3
Find the population size after four hours
t = 4, C = 29
P(t) = e^2t + C
P(4) = e^2 × 4 + 29
P(4) = e^8 + 29
P(4) = 3009.957987
Approximately = 3010 bacteria
Which of these is a solution to the equation ⅛ = ⅖ x? Use inverse operations to solve.
2/40
5/16
11/40
17/40
Ok so these are the answers that I can choose~ (Please and thank you <3)
A.44°
B.134°
C.90°
D.34°
Answer:
44 degrees, or A is your answer.
Step-by-step explanation:
You know angle A which is 46 and angle C which is 90, now all you have to do is solve to find angle B.
90+46=136
All the sides have to add up to 180 so simply do 180 - 136.
That will get you 44.
The set of all real numbers between 2 and 5, including 2
Answer:
3
Step-by-step explanation:
A soft drink company wants to increase the volume of the cylindrical can they sell soft drinks in by 25%. The company wants to keep the 5-inch height of the can the same. The radius of the can is currently 2.5 inches. Approximately how much should the radius of the can be increased
Answer:
The radius should be increased by 0.295 inches.
Step-by-step explanation:
Volume of a cylinder:
In a cylinder, in which the base has radius [tex]r[/tex], and the height is [tex]h[/tex], the volume is given by:
[tex]V = \pi r^{2}h[/tex]
In this question:
5 inch height, radius of 2.5 inches. So the volume is given by:
[tex]V = \pi (2.5)^2(5) = 31.25\pi[/tex]
We want to increase the volume by 25%.
So, the new volume is given by:
[tex]1.25*31.25\pi = 39.0625\pi[/tex]
With this volume, keeping the height, the radius should be of:
[tex]V = \pi r^{2}h[/tex]
[tex]39.0625\pi = 5\pi r^{2}[/tex]
[tex]r^{2} = \frac{39.0625}{5}[/tex]
[tex]r^{2} = 7.8125[/tex]
[tex]r = \sqrt{7.8125}[/tex]
[tex]r = 2.795[/tex]
The radius should be of 2.795 inches, which is an increase of 2.795 - 2.5 = 0.295 inches.
Answer:
https://slideplayer.com/slide/14286858/ copy paste the link it has a bunch of the answers but sadly no work on it.
Step-by-step explanation:
The ratio of girls to boys in Mr. Freda's class is
3:4. If Mr. Freda has 15 girls in his class, how
many students does Mr. Freda have altogether
in his class?
Please will give brainiest to who ever answers
Answer:
he has 35 students all together
Step-by-step explanation:
15 divided by 3(the girls)=5. 5 x 4(the boys)=20. 20 + 15 =35.
Answer:
35
Step-by-step explanation:
Three pizzas are shared equally among 12 people.what fraction of pizza will each person get
Answer:
1/4
Step-by-step explanation:
3/12 =0.25
0.25 = 1/4
Answer:
there are three pizzas
it has to be shared among 12 peoples
so, 3/12 = 1/4.
1
Select the correct answer.
What is the range of the function x) = 12 - 3x for the domain (-4,-2, 0, 2,4}?
OA.
{24, 18, 12, 6, 20}
OB. {6, 12, 18, 24, 30}
OC. {-12, -6, 0,6,12}
OD.
{0, 6, 12, 18, 24}
Reset
Next
Answer:
so the right answer is of option D
Step-by-step explanation:
Have a great day and hope this helps!!!
Pls help me
What is the awners
Step-by-step explanation:
I didn't understand the question.
Do u want the function?
if so
[tex]y = ax + b[/tex]
at 0=0
at 1= 3
[tex]b = 0[/tex]
at 1=3
3=a
[tex]y = 3x[/tex]
if ur looking for something else, please tell me.
Hello! I need help thanks!
Answer:
On brainly we help each other what need help with
Step-by-step explanation:
Answer:
There shouldn't be any divison with this problem. If one gallon gets you thirty miles, then 13 gallons would get you 13 x 30 miles. There's no need for fractions. (He'd drive 390 miles on 13 gallons, by the way)
Step-by-step explanation:
Evaluate the expression 8x for x=2
Answer:
16
Step-by-step explanation:
8x2
8x = 16
8 * 2 = 16
If "x" is equal 2.
Then 8 multiplied by 2 is equal to 16.
What operation is used to change a PERCENT to a DECIMAL?
Answer:
divide by 100 i think
What is the percent of decrease from 6 to 5.4?
Answer:
The percent decrease from 6 to 5.4 is 10%.
Step-by-step explanation:
Enter a number sentence with > or < to compare -- 5 1/2 and -- 3 and explain your answer.
Answer:
-5 1/2 < -3
Step-by-step explanation:
because the higher or bigger the number is as a negative the lower the number really is.
Hope this helps!
In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 1000 grams and mass was decreasing by 14% per day. Determine the mass of the radioactive sample at the beginning of the 10th day of the experiment. Round to the nearest tenth (if necessary).
Answer:
120.91 grams
Step-by-step explanation:
multiply the initial amount by the percent that will remain to the power of n-1, n being the term number, or how many days that have passed.
f(x)=1000(0.85)^14-1
The mass of the radioactive sample at the beginning of the 10th day of the experiment is 221.30 grams if the mass was decreasing by 14% per day.
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We have:
Mass of the substance = 1000 grams
Rate of decay = 14% per day = 0.14
Let's suppose the mass is m at the beginning of the 10th day of the experiment.
The equation for the exponential decay:
[tex]\rm E = m(1-r)^t[/tex]
[tex]\rm m = 1000(1-0.14)^1^0[/tex]
m = 1000×0.22130
m = 221.30 grams
Thus, the mass of the radioactive sample at the beginning of the 10th day of the experiment is 221.30 grams if the mass was decreasing by 14% per day.
Learn more about the exponential decay here:
https://brainly.com/question/14355665
#SPJ2
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) 1 2 , 1 4 , 1 6 , 1 8 , 1 10 , ...
Answer:
1•2n
Step-by-step explanation:
Given the sequence if numbers
1 2 , 1 4 , 1 6 , 1 8 , 1 10 , ...
You will see that 1 is common to all the numbers, the other part of the sequence are in arithmetic progression and they are
2,4,6,8,10...
The nth term of an AP is expressed as
Tn = a+(n-1)d
a is the first term
n is the number of terms
d is the common difference
a = 2
d = 4-2 = 6-4 = 8-6 = 2
Substitute into the formula
Tn = 2+(n-1)2
Tn = 2+2n-2
Tn = 2-2+2n
Tn = 2n
Hence the nth term of the sequence is 1•2n
A 12-ft ladder leans against the side of a house. The bottom of the ladder is 6 ft from the side of the house. How high is the top of the ladder from the gro
If necessary, round your answer to the nearest tenth.
Answer:
10.4 ft
Step-by-step explanation:
think of it like a right triangle like in the picture with 12ft ladder as the hypotenuse
a²+b²=c²
6²+b²=12²
b²= 12²-6² =108
b=√108 = 10.392≈ 10.4 ft
The table below shows the number of days that a meteorologist predicted it would be sunny and the number of days it was sunny. Based on the data in the table, what is the conditional probability that it will be sunny on a day when the meteorologist predicts it will be sunny? If necessary, round your answer to the nearest percent.
The probability that it will be sunny when the meteorologist predicts it will be sunny is approximately ____%.
Answer:
570
Step-by-step explanation:
The sum of two numbers is 50 and the difference is 16. what are the numbers ?
Answer:
33 and 17
Step-by-step explanation:
Answer:
Step-by-step explanation:
A rectangular prism has a length of 7 units, a width of 12 units, and a height of 8 units.
Enter your answers in the boxes to complete the formula.
V=l×w×h
What's 27.63 subtracted by 60
Answer:
-32.37
Step-by-step explanation:
Answer:
-32.37
Step-by-step explanation:
I need the simplified expression for this please
total bill for repairs is 329.00
parts were 125.00
labor was 68.00 per hour
how many hours did you spend on labor?
Answer:
3 hours was spent on labor
Step-by-step explanation:
Key skills needed: Creating an equation, Solving an equation
1) The total cost is 329.00 (or 329). The parts are 125.00 (or 125), and the labor is 68 per hour.
2) If we say h is the number of hours of labor, then we can create this equation --> [tex]68h[/tex] (or 68 multiplied by "h") 68h would be the cost of labor, and we need to find the number of hours (h) as a number.
3) We can create this equation --> [tex]329 = 125 + 68h[/tex]
--> This equation can be made as the total cost (329) is equal to the parts (125) and the labor (68h)
4) Subtract 125 from both sides to get 68h by itself
--> 329 - 125 = 204 so 204 = 68h
--> Divide by 68 on both sides (204 divided by 68 is 3)
--> This means that h is 3.
Therefore, the number of hours spent on labor is 3.
Hope you understood and have a nice day!! :D
The table and the graph show the height and weight of ten basketball players, Which
statement is true?
The data point for player G is an outlier.
Player
Basketball Players
Height and Weight
A
There is a slight negative association between
height and weight.
B
с
D
Height
Weight
(inches) (pounds)
77
205
83
255
84
250
80 225
83
265
80 250
85
325
69 180
82 240
76
220
y
340
320
300
280
260
240
220
200
180
160
The y-intercept for a line of best fit would be
about 240.
E
F
G
H
1
68 70 72 74 76 78 80 82 84 86
Height (inches)
A 72-inch player would probably weigh about
160 pounds.
Done
Answer:
a c 77
Step-by-step explanation:
There’s a picture about and you have to balance them.
Answer and Step-by-step explanation:
For these, you have to make sure the same amount of moles are on each side of the chemical equation.
[tex]1ZN + 2HCL[/tex] → [tex]1ZnCL_{2} + H_{2}[/tex]
[tex]1SiO_{2} + 4HF[/tex] → [tex]SiF_{4} + 2H_{2} O[/tex]
[tex]12HCIO_{4} + 1P_{4} O_{20}[/tex] → [tex]4H_{3}PO_{4} + 6Cl_{2} O_{7}[/tex]
These are the balanced equations.
#teamtrees #WAP (Water And Plant)
Someone plssss help
Find the sum of the first 38 terms: 9/2,5,11/2,6,13/2
Answer:
Ths sum of the first 38 terms is [tex]\frac{1,045}{2}=522.5[/tex]
Step-by-step explanation:
Arithmetic Sequences
They are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)r[/tex]
Where
an = nth term
a1 = first term
r = common difference
n = number of the term
The sum of n terms of the sequence is
[tex]S_n=\frac{n}{2}( a_1 + a_n)[/tex]
The common difference is found by subtracting two consecutive terms:
[tex]r=a_{n+1}-a_n[/tex]
Using the first two terms:
[tex]r=a_2-a_1=5-\frac{9}{2}=\frac{1}{2}[/tex]
Now we find the term n=38
[tex]\displaystyle a_{38}=\frac{9}{2}+(38-1)\frac{1}{2}[/tex]
[tex]\displaystyle a_{38}=\frac{9}{2}+\frac{37}{2}=\frac{46}{2}=23[/tex]
The sum is:
[tex]\displaystyle S_{38}=\frac{38}{2}( \frac{9}{2} + 23)[/tex]
[tex]\displaystyle S_{38}=19( \frac{9+46}{2})[/tex]
[tex]\displaystyle S_{38}=19( \frac{55}{2})= \frac{1,045}{2}=522.5[/tex]
Ths sum of the first 38 terms is [tex]\mathbf{\frac{1,045}{2}=522.5}[/tex]
Please help me guys I really need your help i'm stuck. Your help will be appreciated :)
If (5n^5)^3÷(n^2)^7=875, then n is equal to ....
Step-by-step explanation:
[tex] \frac{(5 {n}^{5} ) ^{3} }{( {n}^{2} ) ^{7} } = 875[/tex]
[tex] \frac{5 {n}^{15} }{ {n}^{14} } = 875[/tex]
[tex]5 {n}^{15 - 14} = 875[/tex]
[tex]5n \: = 875[/tex]
[tex]n \: = \frac{875}{5} [/tex]
Therefore n = 175
Hope it will help :)❤
i’m so confused i need to know the transformation but i don’t know what it is help may please
9514 1404 393
Answer:
2. K'(-1, -5)
3. (-3, 5), (3, 10), (-6, 8); translation left 2 and up 7
Step-by-step explanation:
2. The transformation is the one you have shown:
(x, y) ⇒ (x, -y) . . . . reflection over the x-axis
You are given the coordinates for K and asked for K', the reflected point. Use the x- and y-values in the transformation formula:
K(-1, 5) ⇒ K'(-1, -5) . . . . . . the y-coordinate is negated
It's that simple.
__
3. Same deal, different formula.
(x, y) ⇒ (x -2, y +7)
A(-1, -2) ⇒ A'(-1-2, -2+7) = A'(-3, 5)
B(5, 3) ⇒ B'(5 -2, 3 +7) = B'(3, 10)
C(-4, 1) ⇒ C'(-4 -2, 1 +7) = C'(-6, 8)
When constants are added to the coordinates, the transformation is a translation.
The x-values are decreased by 2, so that is a shift left by 2 units.
The y-values are increased by 7, so that is a shift up by 7 units.
The attachment shows the translated triangle (red). The translation vector (-2, 7) is shown as a black arrow. You will notice each triangle vertex is translated that length in that direction.
the 20% tip on a $8 sandwich
Answer:
$1.60 tip on a $8 sandwich
Step-by-step explanation:
SO to find percent
just multiply the number by the percent
Remeber the percent means x/100
SO in this case 20/100 or 1/5
So you can just multiply 1/5*8 and get 1 3/5.
If you convert 3/5 into a decimal
3 divided by 5
that is .6
SO add them up
1+0.6= $1.60