After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The number of bacteria decays by a factor of \dfrac{1}{15} 15 1 start fraction, 1, divided by, 15, end fraction every 6.76.76, point, 7 minutes, and can be modeled by a function, NNN, which depends on the amount of time, ttt (in minutes). Before the medicine was introduced, there were 90{,}00090,00090, comma, 000 bacteria in the Petri dish. Write a function that models the number of bacteria ttt minutes since the medicine was introduced.
Complete Question
After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The number of bacteria decays by a factor of 1/15, every 6.76minutes, and can be modeled by a function, N, which depends on the amount of time, t (in minutes). Before the medicine was introduced, there were 90,000 bacteria in the Petri dish. Write a function that models the number of bacteria t minutes since the medicine was introduced.
Answer:
Nt = 90,000 × e^t/15
Step-by-step explanation:
The function that models the number of bacteria t minutes since the medicine was introduced is written as
Nt = No×e^λt
Where:
No = The initial number of the bacteria after time t
Nt = The current number of the bacteria after time t
λ = Decay constant or factor
t = Time in years
From the question,
No = 90,000 bacteria
Nt = The current number of the bacteria after time t
λ = 1/15
t = Time in years
Therefore, our function is written as:
Nt = 90,000×e^1/15 × t
Nt = 90,000 × e^t/15
Answer:
90,000*(1/15)^t/6.7
Step-by-step explanation:
Khan told me it's correct.
I’m really confused on how to do this anyone good with geometry?
hii please help asap ill give brainliest thanks
Answer:
The answer should be C) Job category
sorry if I’m wrong
Plz help me. Giving branliest
Answer: im not sure about this but I’ll try
24 because if you look at the side that says 12mi And then look at the side withe the x where they are both standing which says 48 and 72 are really similar wand looks like they have the same distance so you can add 12 + 12 and is 24 miles
Step-by-step explanation:
HELP ME PLS!!! ANSWER QUICKLY!!!
Cindy's car used 15 gallons to travel 390 miles. How many gallons of gas would she need to travel 156 miles?
Answer: 6 gallons
Step-by-step explanation: 15/390 then answer x 156
Sally averaged that she spent about 6.8×10^4 seconds training for her weight lifting competition in the month of May. Write this time in standard notation.
Answer:
t = 68000 s
Step-by-step explanation:
Given that,
The average time Sally spent for training for her weight lifting competition in the month of May is [tex]6.8\times 10^4\ s[/tex].
We need to write this time in standard notation.
The power of 10 is 4. 10⁴ can be written as 10000.
[tex]6.8\times 10^4=\dfrac{68}{10}\times 10000\\\\=68000[/tex]
So, the standard time is equal to 68000 s.
Marris decides to bake his parents a cookie in the shape of a regular dodecagon (12‑gon) for their 12-day anniversary.
A.) If the edge of the dodecagon is 6 cm, what is the area of the top of the cookie?
B.) His parents decides to divide the cookie into 12 congruent pieces.
After 9 of the pieces have been eaten, what area of the cookie is left?
Answer:
The answer to each question is:
A.) 403.2 [tex]cm^{2}[/tex] B.) 100. 8 [tex]cm^{2}[/tex]Step-by-step explanation:
A.) To obtain the area of the dodecagon, you can use the next formula:
Area of a dodecagon = 6 * apothem * edgeIn the exercise, we have the edge (6 cm), but, to find the apothem of a dodecagon, that is the distance between the center of the polygon, and the middle point of each side, you can use the next formula:
Apothem = Edge * [tex]\frac{2+\sqrt{3}}{2}[/tex]If we replace the value of the edge, we obtain:
Apothem = 6 cm * [tex]\frac{2+\sqrt{3}}{2}[/tex]Apothem = 11.2 cm (approximately).With this data, we can find the area:
Area of a dodecagon = 6 * apothem * edgeArea of a dodecagon = 6 * 11.2 cm * 6 cmArea of a dodecagon = 403.2 [tex]cm^{2}[/tex]Then, the area of the dodecagon is 403.2 [tex]cm^{2}[/tex] approximately.
B.) As the area obtained is for 12 pieces, when the parents ate 9 pieces, just left 3 pieces, with these values you can make a rule of three.
If:
12 pieces = 403.2 [tex]cm^{2}[/tex]3 pieces = XThen:
X = (3 * 403.2 [tex]cm^{2}[/tex]) / 12X = 1209.6 [tex]cm^{2}[/tex] / 12X = 100. 8 [tex]cm^{2}[/tex]In this form, when the cookie has 3 pieces, its area is 100. 8 [tex]cm^{2}[/tex] approximately.
What is the volume of the triangular prism?
Answer:
Step-by-step explanation:
6x16
6x8 (don't divide)
6x8.5 (don't divide)
8.5x16 (don't divide)
(I THINK I HAVE NO IDEA)
cosβ=-√2/10. find the angle. plz help me
Answer:[tex]98.13\ \text{or}\ 261.87^{\circ}[/tex]
Step-by-step explanation:
Given
[tex]\cos \beta =-\dfrac{\sqrt{2}}{10}[/tex]
As the value of cosine is negative, therefore the angle must lie in II or III quadrant
[tex]\Rightarrow \beta =\cos^{-1}(-\dfrac{\sqrt{2}}{10})\\\Rightarrow \beta=\cos^{-1}(-0.14142)\\\Rightarrow \beta =98.13^{\circ}\ \text{or}\ 270^{\circ}-8.13\\\Rightarrow \beta=98.13^{\circ}\ \text{or}\ 261.87^{\circ}[/tex]
6 times the quotient of 3 and 5
Answer:
ten less the quotient of a number and 3 is 6. help needed with equation!Step-by-step explanation:
Answer: I’m not sure if you’re asking for me to solve this or how to set it up. But if you solve it you get 3.6. if you have to sit it up it would be 6 x 3/5
Step-by-step explanation:
What can it be solved by?
Write the equation of the line passing
through the point (2, -1) with a slope of -3.
Answer:
y = -3x + 5
Step-by-step explanation:
(2, -1); m = -3
y - y1 = m(x - x1)
y + 1 = -3(x - 2)
y + 1 = -3x + 6
y = -3x + 5
A sphere has a volume of 1,436 in3. What is its radius?
Answer:
7
Step-by-step explanation:
So first you would have to know the formula for the volume of a sphere to solve for the radius. The formula is:
V=4 /3πr3
so now we plug in the variables
1,436=4/3πr3
divide by pi
457.09=4/3r3
divide by 4/3 (multiply by the reciprocal which is 3/4)
342.82=r3
Take the third root to get r by itself
r=6.998 or 7 if you will.
What are the factors of 2x^2 - 10x + 12 ?
1) (x + 2) and (x + 3)
2) (x-2) and (x - 3)
3) (x + 6) and (x - 1)
4) (x - 6) and (x + 1)
Solve the following quadratic by
completing the square.
y = x2 – 8x + 5
Answer:
x = 4 ± √11
Step-by-step explanation:
hello :
x²-8x+5= x² -2(4 )(x)+5
x²-8x+5= x² -2(4 )(x)+5 = ( x² -2(4 )(x) +4²) -4²+5
= (x-4)²-11 .....( completing the square )
x²-8x+5= 0 means : (x-4)²-11 = 0
(x-4)²=11 but : 11 = (√11)² = ( - √11)²
x-4 =√11 or x-4 = -√11
x = 4 ± √11
Answer:
x = 4 ± [tex]\sqrt{11}[/tex]
Step-by-step explanation:
To solve the equation let y = 0 , that is
x² - 8x + 5 = 0 ( subtract 5 from both sides )
x² - 8x = - 5
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = - 5 + 16
(x - 4)² = 11 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{11}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{11}[/tex]
y is inversely proportional to x^2
When x = 4, y = 3.
Find y when x= 5.
Answer:
1.92
Step-by-step explanation:
y = k/x^2
k = yx^2
k = 3 * 4^2
k =3*16=48
y = 48/x^2
y = 48/ 5^2
y = 48/25
y=1.92
7. Matéd is 41 years old. Mateo's brother
is younger than him. Mateo writes
the inequality b > 41, where b equals
the number of years, to represent
his brother's age. Is Mateo correct?
Explain.
A clothing manufacturer offers 2 different styles of jeans, relaxed fit and regular fit, in 5 different colours. How many combinations of a style and a colour are possible?
Answer:
10 combinations
Step-by-step explanation:
We can solve the above question using the Fundamental Counting Principle.
This states that:
If an event has x possible outcomes and a other event has y possible outcomes, then there are x and y total possible outcomes for the two events together.
We are told in the above question that:
Styles of jeans = 2
Number of colors = 5
Hence,the number of combinations of a style and a colour that are possible is calculated as:
5 × 2 = 10 combinations
Please answer this question correctly
Answer: it is 6
Step-by-step explanation: because they are the same length.
Please help will give brainliest
Answer:
A
Step-by-step explanation:
Volume = lwh
Volume = (8/3) x (13/4) x (3)
Volume = 26 cubic meters
Shane hit the ball 3 out of times. How is this written as a ratio?
Question is incomplete as number of trials isn't given. We'll use an hypothetical value to make x plain the situation
Answer:
Kindly check explanation
Step-by-step explanation:
Given that the number of trials = x
If the number of tines the ball was hit out if 'x' trials = 3
The ratio of the number of hits to the number of trials is written as :
Number of hits : Number of trials
3 : x
Just put the exact value of x in the equation above and if possible, reduce to simplest form.
PLSSSSSSSS HELPPPPPPPP
URGENT - PLEASE HELP 25 POINTS AND BRAINIEST
A right triangle has legs that measure 5 and x - 1
Its hypotenuse measures x.
Solve for x
The power,
P
(watts)
, of a car engine is proportional to the square of its speed,
s
(
m
/
s
)
.
When
s
=
20
,
P
=
2000
.
Work out the speed (to 1 DP) when the power is
1960
watts
Answer:
30
Step-by-step explanation:
-4 (b + 2) = 20 answer
put it into greatest and least
Answer:
3, 1, 2
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
1.) 10.5
2.) 3[tex]\pi[/tex] + 1
3.) [tex]\sqrt{105}[/tex]
Step-by-step explanation:
Simplify each first
3[tex]\pi[/tex] + 1 ≈ 10.42
[tex]\sqrt{105}[/tex] ≈ 10.25
10.5
Order
1.) 10.5
2.) 3[tex]\pi[/tex] + 1
3.) [tex]\sqrt{105}[/tex]
Decide if each expression represents one third the sum of 5 and 4. choose yes or no for each expression.
Answer:
yes
no
yes
no
Step-by-step explanation:
pls mark brainliest
The value of x can be 2 or 5
The value of y can be 3 or 12
List the possible values of
XY
Step-by-step explanation:
[tex]when \: x = 2 \: and \: y = 3 \\ xy = (2 \times 3) = 6 \\ when \: x = 2 \: and \: y = 12 \\ xy = (2 \times 12) = 24 \\ when \: x = 5 \: and \: y = 12 \\ xy = (5 \times 12) = 60 \\ when \: x = 5 \: and \: y = 3 \\ xy = (5 \times 3) = 15 \\ values \: of \: xy \: are \: 6, \: 24, \: 60, \: 15[/tex]
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units
Answer:
We have a prism with a volume of 16y⁴ + 16y³ + 48y² cubic units.
Its volume is equal to the area of its base times its height.
Of course, for those to be the base area and height of this prism, they would have to multiply to 16y⁴ + 16y³ + 48y² cubic units.
Let's test each of these answers to see which gives us the correct volume.
--------------------------------------------------------------------------------------------------
a base area of 4y square units and height of 4y² + 4y + 12 units
We find the volume by multiplying the base area by the height...
4y(4y² + 4y + 12)
Distribute the 4y to each term inside the parentheses.
16y³ + 16y² + 48y
This is not the right volume, so these can not be dimensions of our prism.
--------------------------------------------------------------------------------------------------
a base area of 8y² square units and height of y² + 2y + 4 units
We find the volume by multiplying the base area by the height...
8y²(y² + 2y + 4)
Distribute the 8y² to each term inside the parentheses.
8y⁴ + 16y³ + 32y²
This is not the right volume, so these can not be dimensions of our prism.
--------------------------------------------------------------------------------------------------
a base area of 12y square units and height of 4y² + 4y + 36 units
We find the volume by multiplying the base area by the height...
12y(4y² + 4y + 36)
Distribute the 12y to each term inside the parentheses.
48y³ + 48y² + 432y
This is not the right volume, so these can not be dimensions of our prism.
--------------------------------------------------------------------------------------------------
a base area of 16y² square units and height of y² + y + 3 units
We find the volume by multiplying the base area by the height...
16y²(y² + y + 3)
Distribute the 16y² to each term inside the parentheses.
16y⁴ + 16y³ + 48y²
The volume fits, so these could be the base area and height of our prism.
--------------------------------------------------------------------------------------------------
D. a base area of 16y² square units and height of y² + y + 3 units
--------------------------------------------------------------------------------------------------
Step-by-step explanation: