MATHEMATICS HIGH SCHOOL

9. If the area of a rectangle measures 20 square inches, the side lengthsmust be 4 inches and 5 inches.

Answers

Answer 1
Answer:

Answer:

True

Step-by-step explanation:

The given statement is true.

Area of a rectangle is length times width.

A rectangle with the side length of 4 and 5 inches would have an area of 20 square inches.

A=l*w\n\nA=4*5\n\nA=20

Hope this helps.
Answer 2
Answer:

Answer:

False

Step-by-step explanation:

There can be two sets of side lengths 4, 5 inches and 2, 10 inches.

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16500 rounded to the nearest whole numberrrr

Answers

? it’s already rounded, is there supposed to be a decimal?

State whether the given measurements determine zero, one, or two triangles. A=35°, a=6, b=13

Answers

If we were to use the sine law we would get 

sin(B) / b = sin(A) / a ----> sin(B) = b*sin(A)/a = 13*sin(35)/6 = 1.24275 to 5 d.p.., 

so since this is greater than 1 there can be 0 triangles with these dimensions, 

as the range of the sine function is [-1,1].

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In the fifth grade at Lenape Elementary School, there are 3/4
as many girls as there are boys. There are 63 students in the fifth grade. How many students are girls?

Answers

Answer:

47 girls

Step-by-step explanation:

63÷4=15.75

15.75×3=47.25

Brad and Wes are building a tree house. They cut a 12 1/2 foot piece of wood into 5 of the same length. how long is each piece of wood? show your work

Answers

Answer:

2(1)/(2) foot

Step-by-step explanation:

Brad and Wes cut a 12(1)/(2) foot piece of wood into 5 of the same length.

Let length of 1 piece be x

So, Length of 5 pieces = 5x

Total length of wood= 12(1)/(2)=(25)/(2)

So, 5x=(25)/(2)

x=(5)/(2)

x=2(1)/(2)

Hence Length of each piece is 2(1)/(2) foot
This is what I did
I divided 12.5/5=2.5 and each pieces of wood would be 2.5 FT.

You and your friend are rolling number cubes. Each cube has 6 sides with the numbers 1 to 6. If a sum of 7 is rolled, your friend gets 1 point. If a 2, 3, or 4 is rolled, you get 1 point. After 108 rolls each, what scores should you expect? Friend: 54; You: 54

Friend: 18; You: 18

Friend: 54; You: 18

Friend: 18; You: 54

Answers

Answer:

Friend: 18; You: 54

Step-by-step explanation:

You and your friend are rolling number cubes.

Each cube has 6 sides with the numbers 1 to 6.

Total Outcomes=36

{1,1};{1,2};{1,3}{1,4};{1,5};{1,6}

{2,1};{2,2};{2,3}{2,4};{2,5};{2,6}

{3,1};{3,2};{3,3}{3,4};{3,5};{3,6}

{4,1};{4,2};{4,3}{4,4};{4,5};{4,6}

{5,1};{5,2};{5,3}{5,4};{5,5};{5,6}

{6,1};{6,2};{6,3}{6,4};{6,5};{6,6}

If a sum of 7 is rolled, your friend gets 1 point.

Favorable outcomes for friend = {1,6};{2,5};{3,4};{4,3};{5,2};{6,1}=6

Total outcomes = 36

So, probability of getting a sum of 7 =(6)/(36)=(1)/(6)

Since there are 108 rolls

So, expected score of friend = 108 * (1)/(6)=18

If a 2, 3, or 4 is rolled, you get 1 point.

So, probability of getting 2 = (1)/(6)

So, probability of getting 3 = (1)/(6)

So, probability of getting 4 = (1)/(6)

So, So, probability of getting 2,3 or 4 = (1)/(6)+(1)/(6)+(1)/(6) =(3)/(6) =(1)/(2)

So, your expected score = 108 * (1)/(2)=54

So, option D is correct.

Hence expected score of friend is 18 and yours expected score is 54
Friend: 18; you: 54
Because you have much bigger chance

Write 42 and 63 as products of their prime factors

Answers

We perform prime factorization on both numbers.
Prime factors are prime numbers. These numbers can only be divided by 1 and itself.

42 ÷ 2 = 21
21 ÷ 3 = 7

2, 3, and 7 are prime factors: 2 * 3 * 7 = 42

63 ÷ 7 = 9
  9 ÷ 3 = 3 

3 * 3 * 7 = 63  OR 3² * 7 = 63
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