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rosijanka [135]
2 years ago
10

Which expressions are equal to

Mathematics
1 answer:
Jobisdone [24]2 years ago
6 0

Answer:

b,c,e

Step-by-step explanation:

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MCR3U1 Culminating 2021.pdf
11111nata11111 [884]

Answer:

(a) y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is 607,325

(ii) The population after 24 hours is 1,828,643

(c) The rate of increase of the population as a percentage per hour is 7.132%

(d) The doubling time of the population is approximately, 10.06 hours

Step-by-step explanation:

(a) The initial population of the bacteria, y₁ = a = 350,000

The time the colony grows, t = 12 hours

The final population of bacteria in the colony, y₂ = 800,000

The exponential growth model, can be written as follows;

y = a \cdot (1 + r)^t

Plugging in the values, we get;

800,000 = 350,000 \times (1 + r)^{12}

Therefore;

(1 + r)¹² = 800,000/350,000 = 16/7

12·㏑(1 + r) = ㏑(16/7)

㏑(1 + r) = (㏑(16/7))/12

r = e^((㏑(16/7))/12) - 1 ≈ 0.07132

The  model is therefore;

y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is given as follows;

y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82

By rounding down, we have;

The population after 8 hours, y = 607,325

(ii) The population after 24 hours is given as follows;

y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571

By rounding down, we have;

The population after 24 hours, y = 1,828,643

(c) The rate of increase of the population as a percentage per hour =  r × 100

∴   The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%

(d) The doubling time of the population is the time it takes the population to double, which is given as follows;

Initial population = y

Final population = 2·y

The doubling time of the population is therefore;

2 \cdot y = y \times (1 + 0.07132)^t

Therefore, we have;

2·y/y =2 = (1 + 0.07132)^t

t = ln2/(ln(1 + 0.07132)) ≈ 10.06

The doubling time of the population is approximately, 10.06 hours.

8 0
3 years ago
Solve Quadratic Equations by Factoring:
mr_godi [17]

Answer:

  1. x = 0 or 1
  2. x = ±i/4
  3. x = -5 (twice)

Step-by-step explanation:

Factoring is aided by having the equations in standard form. The first step in each case is to put the equations in that form. The zero product property tells you that a product is zero when a factor is zero. The solutions are the values of x that make the factors zero.

1. x^2 -x = 0

  x(x -1) = 0 . . . . . x = 0 or 1

__

2. 16x^2 +1 = 0

This is the "difference of squares" ...

  (4x)^2 - (i)^2 = 0

  (4x -i)(4x +i) = 0 . . . . . x = -i/4 or i/4 (zeros are complex)

__

3. x^2 +10x +25 = 0

  (x +5)(x +5) = 0 . . . . . x = -5 with multiplicity 2

5 0
3 years ago
Can anyone help me please? It’s urgent. Worth 20 points!
Arturiano [62]
6% chance he is certified
Molly has a 54%chance
60% chance

If you do them out of 100%
6 0
3 years ago
(10 POINTS AND BRAINLIEST)
bekas [8.4K]

Answer:

A.) 15.60=11.40+10x

Step-by-step explanation:

okay we know kathy spent 15.60 in total at the post office

so we know 15.60 will be after the equal sign.

she paid 11.40 only on the package

and rest of money was on stamps.

15.60-11.40= 4.20

so she used 4 dollars and 20 cents for stamps if she bought 10 we need to divied 4.20/10=0.42

0.42 cents for each stamps so we need a equation that will give us this answer.

Me i go thru each one and solve for x

lucky for me i just need to solve one

because equation A solves it correctly.

15.60=11.40+10x

subtract 11.40 on both sides

15.60-11.40

4.20=10x

now we divide 10 on each side

4.20/10=0.42

x=0.42

 

5 0
3 years ago
Read 2 more answers
Brad can bicycle at a rate of 55km/h. What is his speed in feet per second?
Brrunno [24]
55km/60minuess=0.916km per min. 0.916/60second=0.01527km per sec. convert km to feet. which is 50 feet. your answer is 50 feet per second
3 0
3 years ago
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