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spin [16.1K]
3 years ago
5

Find the sum of X -4+ 2X -7

Mathematics
1 answer:
olasank [31]3 years ago
5 0

Answer:

3x-11

Step-by-step explanation:

first of all add the variables=X+2X=3X

THEN ADD CONSTANTS= (-4)+(-7)= -4-7= -11

THEN ADD BOTH CONSTANT AND VARIABLE

3x+(-11)so answer is 3x-11

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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
2 years ago
Members of the drama club spend $795 on t-shirts and sweatshirts for a play.They purchase 20 more tshirts than sweatshirts.They
Anika [276]

Answer:

The drama club bought 35 t-shirt

Step-by-step explanation:

Let

t-shirt = x

Sweatshirt = y

Total cost = $795

They purchase 20 more tshirts than sweatshirts

x = y + 20

The equation is:

12x + 25y = 795

12(y + 20) + 25y = 795

12y + 240 + 25y = 795

37y = 795 - 240

37y = 555

y = 15

Substitute y = 15 into

x = y + 20

x = 15 + 20

x = 35

t-shirt = 35

Sweatshirt = 15

The drama club bought 35 t-shirt

8 0
3 years ago
anonymous anonymous 2 years ago Math Help Please!! :) Crystal earns $5.25 per hour mowing lawns. Write a rule to describe how th
aivan3 [116]
It should be B or D. B because in 2 hours you make $10.50 and then add 15 minutes and you get B. It could also be D because that's doing $5.25 an hour which is true it's just deleting the extra 45 minutes so it can be either B or D.
8 0
2 years ago
Find the Total Surface area of a Pyramid. Its base is a regular hexagon 4cm on a side. its height is 8 cm. Round off to nearest
oksano4ka [1.4K]

Answer:

The total surface area of a regular hexagonal pyramid is 146.2 cm².

Step-by-step explanation:

The base is a regular hexagon 4cm on a side. its height is 8 cm.

The total surface area of a pyramid with regular hexagon base

A=\frac{3\sqrt{3}}{2}a^2+3a\sqrt{h^2+\frac{3a^2}{4}

Where, a represents the base edge and h represents the height of the pyramid.

The area of given regular hexagonal pyramid is

A=\frac{3\sqrt{3}}{2}(4)^2+3(4)\sqrt{(8)^2+\frac{3(4)^2}{4}

A=\frac{3\sqrt{3}}{2}(16)+12\sqrt{64+12}

A=24\sqrt{3}+12\sqrt{76}

A=146.182794027

A=146.2

The total surface area of a regular hexagonal pyramid is 146.2 cm².

8 0
3 years ago
9+g+6g–3<br><br> a<br> n<br> s<br> w<br> e<br> r<br><br> p<br> l<br> e<br> a<br> s<br> e
Alex_Xolod [135]
If you are being asked to simplify, just combine like terms; such as, all the g’s and all the numbers so, your answer should look something like: 7g+6
4 0
2 years ago
Read 2 more answers
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