MATHEMATICS COLLEGE

1.) The island shown has a population of 12,175 people. Find the populationdensity in people per square kilometer.

18.5 km

11.1 km

Answers

Answer 1
Answer:

Answer:

Population density = 148.22\ \text{people per square kilometer}

Step-by-step explanation:

The attached figure shows the dimension of an island.

Population density is equal to total population per unit land area.

Firstly we will find the area of the triangle using Pythagoras theorem as follows :

H^2=B^2+P^2

H is Hypotenuse, B is base and P is perpendicular

B=√(H^2-P^2) \n\nB=√((18.5)^2-(11.1)^2) \n\nB=14.8\ km

Area of triangle is given by :

A=(1)/(2)* b* P\n\nA=(1)/(2)* 14.8* 11.1\n\nA=82.14\ km^2

\text{Population density}=\frac{\text{Total population}}{\text{land area}}\n\n=(12175 )/(82.14)\n\n=148.22\ \text{people per square kilometer}

Hence, the population density is 148.22\ \text{people per square kilometer}.

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There are 9 girls and 11 boys in a class, and two students will be chosen one after another. Find the probability that both are boys.

Answers

Answer:

11/20

Step-by-step explanation:

total=20

11=boys

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you drink a beverage with 120 mg of caffeine. Each hour, the amount m of caffine in a persons system decreases by 12%. About how much caffeine will be in your system after 3 hours? Round your answer to the nearest milligram

Answers

Answer:43.2

Step-by-step explanation: multiply 120 x 0.12 and you get 14.4, since it’s 3 hours multiply 14.4 3 times and u get 43.2

Please answer this correctly without making mistakes

Answers

Answer:

\boxed{\sf 319:3388}

Step-by-step explanation:

Total number of tickets sold = 3388

Total number of coach tickets = 3069

Total number of first-class tickets = Total number of tickets sold - Total number of coach tickets

= 3388 - 3069

= 319

\therefore

Ratio of the number of first-class tickets to the total number of tickets = 319:3388

Answer:

  • \boxed{ 319 : 3388}

Step-by-step explanation:

Given, Total no. of tickets sold = 3388

Total no. of coach tickets = 3069

Then, No. of first class ticket:

= 3388 - 3069

= 319

We need to find the ratio of first-class tickets to the total number of tickets: 319:3388

Find the next three terms in the geometric sequence. 2,-16,128,-1024,...

Answers

Answer:8192,-65536,524288

Step-by-step explanation:

2,-16,128,-1024,....

First term=a=2

Common ratio=r=-16/2=-8

Using the formula

Tn=a x r^(n-1)

T5=2 x (-8)^(5-1)

T5=2x (-8)^4

T5=2x4096

T5=8192

T6=2x(-8)^(6-1)

T6=2x(-8)^5

T6=2x-32768

T6=-65536

T7=2x(-8)^(7-1)

T7=2x(-8)^6

T7=2x262144

T7=524288

A math student has a plan to solve the following system by the elimination method. to eliminate the x-term , he wants to multiply the top equation by 7. what should he multiply the second equation by so that when he adds the equation, the x-term are eliminated ? -3x-7y=-56-7x+10y=-1

Answers

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Answer:

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Step-by-step explanation:

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The problem statement tells us the multiplier of the first equation is 7, so the multiplier of the second equation needs to be -3.

Match the vocabvulary

Answers

Answer: The answers are in the steps I numbered it as a question from 1 to 12 hopes it helps.Read it carefully.

Step-by-step explanation:

(1)  Answer is RATIONAL NUMBERS.

(2) Answer is  Fraction  

(3) Answer is Terminating decimal

(4) Answer  is  Decimal

(5)  Answer is Integer  

(6) Answer  is Repeating Decimal

(7)  Answer is  Perfect Square  

(8) Answer   is CLASSIFY

(9) Answer is Real Numbers  

(10) Answer is Percent

(11) Answer   Whole numbers

(12) Answer is Irrational numbers

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