Answer:
B.
y=2 · 3xy equals 2 times 3 superscript x baseline
Step-by-step explanation:
The bacteria culture starts with 500 bacteria and doubles size every half hour.= 2 hours
32,000
Thus, after three hours, the population of bacteria is 32,000.= 3 hours
A bacteria culture starts with 500 bacteria and doubles in size every half hour.1
(a) How many bacteria are there after 3 hours?
We are told “. . . doubles in size every half hour.” Let’s make a table of the time and population:
t 0 0.5 1.0 1.5 2.0 2.5 3.0
bacteria 500 1000 2000 4000 8000 16000 32000
Thus, after three hours, the population of bacteria is 32,000.
(b) How many bacteria are there after t hours?
In t hours, there are 2t doubling periods. (For example, after 4 hours, the population has doubled 8
times.) The initial value is 500, so the population P at time t is given by
P(t) = 500 · 2
2t
This is an acceptable response, but in calculus and all advanced mathematics and science, we will
almost always want to use the natural exponential base, e. Let’s redo the problem using the natural
exponential growth function
P(t) = P0e
rt
We are given that the initial population is 500 bacteria. So P0 = 500 and we have
P(t) = 500ert
We know that after 1 hour, there are 2000 bacteria. (We could’ve used any other pair from our table
that we wish.) Substituting into our function, we get
P(t) = 500ert
2000 = 500er·1
2000 = 500er
1
500
· 2000 =
1
500
· 500er
4 = er
and now we use the natural logarithm to solve for r
ln (4) = ln (er
)
ln (4) = r · ln (e)
ln (4) = r
1.3863 ≈ r
Thus the function P(t) = 500e1.3863t gives the number of bacteria after t hours.
(c) How many bacteria are there after 40 minutes?
The input t to our function is given in hours, so we must convert 40 minutes into hours. So (40 min)
1 hr
60 min
=
2
3
hr.
P(t) = 500e1.3863t
P
2
3
= 500e1.3863·(2/3)
P
2
3
≈ 1259.9258
Thus, after 40 minutes (2/3 of an hour), there are about 1260 bacteria.
(d) Graph the population function and estimate the time for the population to reach 100,000.
50000
100000
1 2 3 4 5
b
(3.8219, 100,000)
t
P
Using the calc:intersect on the TI-84, we get the point (3.8219, 100000), thus the population will
reach 100,000 in about 3.82 yrs
a shopkeeper sold 16 articles for a total of £400 and made a profit of £48.00 how much did each article cost him
In 3 years time Sarah will be twice as old as Emma was last year .Emma now 11 years how old is Sarah
Answer:
Sarah is 25 years old
Step-by-step explanation:
Answer:
Step-by-step explanation:
If the average annual CPI of a career goes from 124.0 to 130.7 what is the inflation rate (don't forget to put % in your answer).
Answer:
(new-old)/old * 100%
130.7-124/124 = .054 = 5.4%
Step-by-step explanation:
Can someone help me with questions 12 and 13 please I am very confused with this two I’ll appreciate it!
Answer:
12. (2, -3)
13. AH: +15 B: +721 CB: 0 N: +462 WB: -1200
Step-by-step explanation:
12.
When a point is reflected over the x-axis, the y coordinate becomes opposite because you are changing its y value, not its x-value. So (-2, 3) reflecting over the x-axis becomes (-2, -3).
The same concept goes for reflecting over the y-axis. The x coordinate becomes opposite because you are changing its x value. (It's like folding the graph in half and seeing where the point matches up with. So (-2, -3) reflecting over the y-axis becomes (2, -3).
13.
All you have to do is list each artifact and where they were found in relation the sea level (0). If it is above sea level then it is a positive number, below sea level is a negative number.
Arrow head: +15 (since it is 15 feet above sea level)
Woven basket: -1200 (since it is 1200 feet below sea level)
The difference between high and low tides along the Maine coast one week is 19 feet on Monday and x feet on Tuesday. Write an expression to show the average difference between the tides for Monday and Tuesday. (will give brainliest,)
Answer: 19 + × / 2
Step-by-step explanation:
Look for the key words:
Rise AND fall of the tide = Addition (19+x)
To show the AVERAGE = Division (Divide it by 2 because there is Monday and Tuesday)
The average difference between the tides for Monday and Tuesday Expression is 1/2×(19 + x)
Average difference Expression = 1/2 ×(19 + x)
Where:
19 represent the Difference between high and low tides on Monday
x represent Difference between high and low tides on Tuesday
Inconclusion The Average difference Expression is 1/2 ×(19 + x)
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PLS HELP WILL MAKE FIRST RIGHT ANSWER BRAINLIEST
Answer:
OPTION A:
SEE IMAGE FOR SOLUTION
write an expression that means the same as the sentence. "the sum of sixteen and g is equal to seventy divided by seven. "
an elevator in a tall building goes up 7 floors, then down 9 floors, down 4 floors, up 8 floors, anddown 2 floors. now it is on floor 14 on what floor did the elevator start
Answer:
It started on the same floor, floor 14
Step-by-step explanation:
if it went up 7 then down 9, so negative 2 kinda, then down another 4, so negative 6, then up 8 so positive 2, then down 2, it would've started on floor 14
Answer:
14
Step-by-step explanation:
Let the floor started be 'x'
Equation:-
=> x + 7 - 9 - 4 + 8 - 2= 14
x + (+7) + (-9) + (-4) + (+8) + (-2) = 14
x + 7 - 9 - 4 + 8 - 2 = 14
x + 15 - 15 = 14
x = 14
Therefore, elevator started from 14th level.
What is 127 divided by 4
The value of expression 127 divided by 4 would be; 31.5
When 'a' is divided by 'b', then we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the expression of 127 divided by 4.
A negative divided by a negative is positive, then;
Therefore, 127 ÷ 4 = 31.5
Therefore, The value of expression 127 divided by 4 would be; 31.5
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The cost of renting the Party Barn is $150 flat fee plus an additional $50 per hour. Manny can spend up to $325 to rent
the Party Barn for his birthday party. What are the possible hours that Manny could rent the Party Barn?
Form a linear equation for the given statement and draw its graph:
Taxi fare for the first km is charged at Rs 20 and Rs 10 is charged for another extra
1 km.
Step-by-step explanation:
See the image for solution
Hope it helps
Have a great day
BRAINIEST AWNSER 100 points PLEASE HELP
The number 1 is the identity for multiplication. Do you think
that division has an identity? Explain your reasoning.
Answer:
Yes, because if the multiplication identity is 1, the division identity may be -1 because it is the opposite.
Step-by-step explanation:
Evaluate the expression. Will choose brainliest
Answer:
-213
Step-by-step explanation:
3|3-5|^2-(-15)^2
3(4)-225
=12-225= -213
Answer:
-213
Step-by-step explanation:
=3|x+y|²-(xy)²
Subtitute value of x and y above:
=3(|3+-5|)²-(3×-5)²
=3(|-2|)²-(-15)²
=3(2)²-(225)
=3(4)-225
=12-225
=-213
Note: If you need to ask question,I'll gladly give you answee.Thanks
A 5×12 rectangle is inscribed in a circle. What is the radius of the circle need help with this
Answer:
6.5
Step-by-step explanation:
Im not 100% sure because I may have overcomplicated this but im going to submit this anyway.
pls hurrryyyyyyy #42 only and show work
Answer:
x = 70
Step-by-step explanation:
50 + x + 2x + 100 = 360
Combine like terms
3x + 150 = 360
Subtract 150 from both sides
3x = 210
Divide both sides by 3 to isolate x
x = 70
If ST= 16 and RT= 69, find RS.
Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2 Find F{G[H(2)]}. 27 71 121
Answer:
27
Step-by-step explanation:
H(2)=2^2=4
G(H(2))= 3(4) +2=14
F(G(H(2)))=2(14)-1=27
List all the intercepts for the graph shown and determine whether the graph is symmetric with respect to he x-axis, y-axis, origin, or none of these.
X-int: (___,0).
Y-int: (0,___).
Is it symmetric about the x-axis: yes/no
Is it symmetric about the y-axis: yes/no
Is it symmetric about the origin: yes/no
A force of 125 newtons stretches a spring 0.15 meters. What force is required to stretch it 0.25 meters??
show procedure
Answer:
Step-by-step explanation:
A spring has a force formula of F = k*x
f = 125 N
x = 0.15 m
125 = k*0.15
k =833.33
F = ?
k = 833.33
x = 0.25 m
F = 833.33 * 0.25
F = 208.33 N
You could do this without solving for k
F1/F2 = x1/x2
F1 = 125 N
F2 = ?
x1 = 0.15
x2 =0.25
125 / F2 = 0.15 / 0.25 Cross multiply
125 * 0.25 = 0.15 * F2 Divide by 0.15
125*0.25 /0.15 = F2
F2 = 208.33 just as you got above
PLEASE HELP ASAPPPPPPPPPPPPPPP
Answers:
a) -3b) 7/3c) -1/2d) 1/11e) undefinedf) 0d) 2/3========================================================
Explanation:
If the original slope is a/b, then the perpendicular slope is -b/a
We flip the fraction and we flip the sign from positive to negative, or vice versa.
As an example, the slope 1/3 flips its fraction to 3/1 or just 3. Then we flip the sign to -3. So if the original slope is 1/3, then its perpendicular counterpart is -3.
Notice how the two slopes multiply to -1
(1/3)*(-3) = -1
This applies to any pair of perpendicular lines such that neither line is horizontal and neither line is vertical either.
------------------------
If the original slope is some whole number, then rewrite it as a fraction over 1
Example: 2 becomes 2/1
That way we can flip the fraction and the sign
-------------------------
If we had an original slope of 0, then it's the same as 0/1
Flipping the fraction leads to 1/0, but that's undefined. We cannot divide by zero. So that explains the answer to part e).
Going in reverse of this process, any line with undefined slope will be perpendicular to lines of slope 0.
horizontal lines have slope of 0
vertical lines have undefined slopes
-------------------------
For part g), you'll need to convert from a mixed number to an improper fraction
Use this formula
a & b/c = (a*c + b)/c
So this means,
1 & 1/2 = (1*2 + 1)/2 = 3/2
which leads to
-1 & 1/2 = -3/2
Then applying the rule "flip the fraction flip the sign" gets us from -3/2 to 2/3.
What do you start with?
6(3+8n)=210
Answer:
PEMDAS
a
r
e
n
t
h
e
s
e
s
Step-by-step explanation:
in pemdas parenthesis are always first so start with the parenthesis and you should get an answer of N=4
What type of number is the square root of 5?
Answer:
That is called an 'irrational algebraic number'
Hope this helps!! :)
Question 2
Which results in a net value of 0?
O John has $25 and spends $10
O John gives away 4 out of 5 of his canned sodas
O John buys a shirt for $20 and returns it for a refund of $20
O John makes $8 but owes Tracie $5
A bakery van has an original value of $40,000. The van is depreciating at a rate of 9% each year. About
how much will this van be worth 5 years later?
Answer:
$22,000
Step-by-step explanation:
9 percent of 40000 is 3600
it depreciates for 5 years so times 5 which gives us 18000
now subtract this amount from its original value and you get 22,000
Select the equivalent expression.
5
23
=?
42
Choose 1 answer:
A
44
215
410
46
47
Answer:
The choose B.
[tex] \frac{2^{15} }{ {4}^{10} } [/tex]
I hope I helped you^_^
simplify ( -12) x ( 13) x (-15)
Please give explanation
fast please
Answer:
2340
Step-by-step explanation:
(-12)×(13)×(-15)
=(-156)×(-15)[ (+) × (-) = (-)]
=2340[(-) × (-) = (+)]
How can the word "LEO MESSI" be arranged so that the vowels do not stay together?
Answer:
"ELO MESSI"
Step-by-step explanation:
Hope it helps
which of the following functions is graphed below?
The correct answer is option (D).
To find from graph below which functions.
What is co-ordinate geometry?Coordinate geometry is defined as the study of geometry using the coordinate points.
First at the left side of the graph. The shape that it is an [tex]x^{3}[/tex] function. also the filled in circle means inclusive. so that when x <= (whatever number). It is impossible to tell for sure with this graph if it is on 1. for the first part. the only answer that has less than or equal to is the last one, D. To look at the right side that it is open circle. It is >.
So, the answer is Option (D).
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Solve the equation. Provide your answer as a simplified fraction or round to the nearest hundredth, if necessary.
(-3/2)(4x + 2) + 2x = -30
x = _______ ?
Answer:
[tex] \frac{ - 3}{2} (4x + 2) + 2x = - 30 \\ \frac{ - 3 \times 4x}{2} + \frac{ - 3 \times 2}{2} + 2x = - 30 \\ - 6x + - 3 + 2x = - 30 \\ - 4x - 3 = -30 \\ - 4x = -27\\ x = \frac{-27}{ - 4} \\ = 6.75 = 7 \\ thank \: you[/tex]
Please no links because they dont work :).
Answer:
C
Step-by-step explanation:
Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7x(y+3) has three factors: 7 , x , and (y+3) .