answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vikentia [17]
2 years ago
5

A culture of yeast grows at a rate proportional to its size. If the initial population is 2000 cells and it doubles after 2 hour

s, answer the following questions. 1. Write an expression for the number of yeast cells after t hours. Answer: P(t)= 2. Find the number of yeast cells after 7 hours. Answer: 3. Find the rate at which the population of yeast cells is increasing at 7 hours. Answer (in cells per hour):
Mathematics
1 answer:
White raven [17]2 years ago
3 0

Answer:

Step-by-step explanation:

1) We would apply the formula,

y = ab^t

Where

a represents the initial amount of yeast.

t represents the doubling time.

From the information given

a = 2000

t = 2 hours

Since after 2 hours, the population of cells doubles, then

y = 2 × 2000 = 4000

Therefore

4000 = 2000 × b^2

Dividing through by 2000, it becomes

2 = b^2

Raising both sides of the equation by 1/2, it becomes

2^(1/2) = b^2/2

b = 1.414

The equation becomes

y = 2000(1.414)^t

2) when t = 7 hours,

y = 2000(1.414)^7

y = 22604 cells

3) the rate is 22604/7 = 3229 cells per hour

You might be interested in
The weights of cars passing over a bridge have a mean of 3,550 pounds and standard deviation of 870 pounds. Assume that the weig
Annette [7]

Answer:

0.24315

Step-by-step explanation:

Using the z score formula to solve this question

z = (x - μ) / σ,

Such that:

x = raw score

μ = population mean

σ = population standard deviation.

From the question:

x = 3000

μ = 3550

σ = 870

z = (3000 - 3550) / 870

z = -550/870

z = -0.6962

Using the z score table as well as probability calculator(as requested in the question to find the z score)

The probability of having less than 3000 is obtained as:

P(x<3000) = 0.24315

7 0
2 years ago
Expand (2x-3y)^4 using Pascal's Triangle. Show work
deff fn [24]
(2x+3y)⁴
1) let 2x = a   and 3y = b

(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle
     
                     0     |               1
                     1     |            1    1
                     2     |          1   2   1
                     3     |         1  3   3   1
                     4     |       1  4   6    4  1

0,1,2,3,4,.. represent the exponents of binomials 
Since our binomial has a 4th exponents, the coefficients are respectively:

(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):

2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)

16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴
3 0
2 years ago
at a restaurant, Trevor decides to tip the server 16% of the bill. If he leaves $4.00 tip, which proportion could be used to fin
Kazeer [188]
4\25 is the proportion of the percentage


5 0
2 years ago
Read 2 more answers
A study of immunizations among school‑age children in California found that some areas had rates of unvaccinated school‑age chil
Rom4ik [11]

Answer:

Probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.

Step-by-step explanation:

We are given that a classroom of 20 children in one such area where 13.5% of children are unvaccinated.

If there are no siblings in the classroom, we are willing to consider the vaccination status of the 2020 unrelated children to be independent.

The above situation can be represented through binomial distribution;

P(X=r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,......

where, n = number of trials (samples) taken = 20 children

            r = number of success = none of the 20 children

            p = probability of success which in our case is probability that

                   children are unvaccinated, i.e; p = 13.5%

<u><em>Let X = Number of children that are unvaccinated</em></u>

So, X ~ Binom(n = 20, p = 0.135)

Now, Probability that none of the 20 children in such a classroom would be unvaccinated is given by = P(X = 0)

           P(X = 0)  =  \binom{20}{0} \times 0.135^{0} \times (1-0.135)^{20-0}

                          =  1\times 1 \times 0.865^{20}

                          =  0.055

<em>Hence, the probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.</em>

8 0
2 years ago
Which number, when substituted for x, makes the equation 4x+8=164x+8=16 true?
ra1l [238]
X = 2

4x + 8 = 16
      -8     -8
----------------
4x= 8
--     --
4     4
------------
x=2
7 0
2 years ago
Read 2 more answers
Other questions:
  • In 2010, the population of Denver, Colorado, was 600,158. Denver's land area is about 153 square miles. To the nearest whole num
    15·2 answers
  • A health club charges a $130 yearly membership fee and $3 for each day a member uses the health facilities. If the member paid $
    5·1 answer
  • A vegetable store sold 3 tons of vegetables less on the first day than on the second, and on the third day it sold 5/9 of the am
    10·2 answers
  • The amphitheater has two types of tickets available, reserved seats and lawn seats. The maximum capacity of the venue is 20,000
    11·1 answer
  • For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation c
    6·2 answers
  • A coach drives 360 miles at a speed of 60mph how long did the journey take
    12·1 answer
  • A hiker travels 3 km due east then 2 km on a bearing of 110°. Find: a) how far south the hiker is from the starting point Hint:
    9·1 answer
  • The following are the hypotheses for a test of the claim that college graduation statue and cola preference are independent. H0:
    15·1 answer
  • Susie and Katie received candies on Valentine's Day. Susie received four less candies than Katie. Together, they received 16 tot
    15·1 answer
  • A local florist buys a dozen roses for x dollars. He plans to sell the roses at a 40% mark-up. What expression shows the selling
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!