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kondor19780726 [428]
3 years ago
10

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4)

Mathematics
2 answers:
lions [1.4K]3 years ago
8 0
B: inverse property of addition
velikii [3]3 years ago
6 0
Inverse property of addition
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What is the volume, in cubic M, of a cylinder with a height of 13M and a base radius of 3M, to the nearest 10th Place?
irina [24]

Answer:

The volume of the cylinder is 367.6 M^3

Step-by-step explanation:

Mathematically, we have the volume of a cylinder calculated as follows;

V = pi * r^2 * h

r is the base radius given as 3 m

h is the height given as 13 m

So, we have the volume as;

V = 22/7 * 3^2 * 13 = 367.6 M^3

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What is the missing reason in the proof shown ?
vodomira [7]

Answer:

A symmetric property

Step-by-step explanation:

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3 years ago
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.

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1/10 of the thread is left because a connected to b is the thread and minus the 1/5 is 1/10 since 1/3 +total thread to begin wit.
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