MATHEMATICS HIGH SCHOOL

A nest of ants initially contains 500 individuals. The population is increasing by 12% each week.a) How many ants will be there after :
i. 10 weeks
ii. 20 weeks

b)How many weeks will it take for the ant population to reach 2000.

Answers

Answer 1
Answer:

Answer:

a) (i) 1553 ants

(ii) 4823 ants

b) 12 weeks

Step-by-step explanation:

Given,

The initial number of ants, P = 500,

Also, the rate of increasing per week, r = 12% = 0.12,

So, the number of ants after x weeks,

A=P(1+r)^x

\implies A=500(1+0.12)^x=500(1.12)^x

a) (i) If x = 10 weeks,

The number of ants would be,

A=500(1.12)^(10)=1552.92\approx 1553

(ii) If x = 20 weeks,

The number of ants would be,

A=500(1.12)^(20)=4823.15\approx 4823

b) If A = 2000

\implies 2000 = 500(1.12)^x

4=(1.12)^x

Taking log both sides,

log(4) = xlog(1.12)

⇒ x =  12.23 ≈ 12 weeks
Answer 2
Answer: A)4, 823
B)13 Weeks

A: 500 (1 + .12)^x (which is 500 (1 + .12)^20 now)
= 4823. 15 which is ≈ 4823.

B: 2000/ y1 =  500 (1 + .12)^x / y2

12.23 so 13 weeks

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From the top of a building, 40 feet above the ground, a construction worker locates a rock at a 12° angle of depression. How far is the rock from the building? ​

Answers

Answer:

188 m

Step-by-step explanation:

\tan(12) = (40)/(x) \n x = (40)/( \tan(12) ) \n x = 188

Answer:

I think that the other answer is WRONG

tan(12) = (x)/(40)

x = tan(12)*40 = 8.5

Step-by-step explanation:

(sin\left(78\right))/(40)=(sin\left(12\right))/(x) = 8.5

What is the slope of the line that passes through the points (-10,4) and (-10,8) ?

Answers

Answer:

0

Step-by-step explanation:

Slope is rise/run. The rise is 0, making the slope = 0 (any fraction with a numerator of 0 is equal to 0)

Casey bought 3/8 pound of plums and 5/12 pound of bananas. How many pounds of fruit did he buy?

Answers

Answer:

19/24 pounds

Step-by-step explanation:

To find the total number of pounds, we should add 3/8 and 5/12. They both have different denominators, so we have to find the least common multiple between 12 and 8. The least common multiple between 12 and 8 is 24. 12 should be multiplied by 2 to get 24 (5 too) and 8 should be multiplied by 3 to get 24 (3 too).

(3)/(8) + (5)/(12)

(3 * 3)/(8 * 3) + (5 * 2)/(12 * 2)

(9)/(24) + (10)/(24)

(19)/(24)

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Answers

1/4 foot =  how many inches ⇒ 3 inches
3/4 year = how many months ⇒ 9 months
3/5 meter = how many centimeter ⇒ 60 cm
 
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1 meter has 100 centimeter

3/5 meter * 100 cm/1m = (3*100cm)/5 = 300/5 = 60 centimeters.

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Answers

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What is 1037 by the power of 702

Answers