MATHEMATICS
MIDDLE SCHOOL

Answer: 40

3* 9 is 27 and then add 13

3* 9 is 27 and then add 13

HIGH SCHOOL

Given the value of cos 50° ? 0.6428, enter the sine of a complementary angle. Use an expression relating trigonometric ratios of complementary angles.

ANSWER

EXPLANATION

The sine and cosine ratios are complementary.

This means that:

We were given that,

cos(50°)=0.6428

We want to find the sine of the complement of this angle.

This implies that,

HIGH SCHOOL

Jody, a statistics major, grows tomatoes in her spare time. She keeps a record of the weight of each tomato she grows. One tomato is 2 standard deviations heavier than the mean weight. Assume a Normal model is appropriate. What percentile is it in?

Answer:

97.7%

Step-by-step explanation:

Given that Jody keeps a record of the weight of each tomato she grows. One tomato is 2 standard deviations heavier than the mean weight

Assuming normal model, we see that a normal distribution is symmetrical about the mean and hence we have this tomato weight is to the right side of mean. Hence we add with 0.5

i.e. This tomato is 97.7% above the others

Percentile = 97.7%

HIGH SCHOOL

How many times does 64 go into 343?

It will go in 343, 5 times

64 goes into 343 a total of 5.359375 times

MIDDLE SCHOOL

Find (5) for f(x) = (3)

a.9

b.3

c.27

d.81

Answer:

c, 27

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

f(x) = 3 is a constant function. It always equals 3 regardless of the x value.

Double-check to ensure that you have typed in the question correctly.

HIGH SCHOOL

Archie completed the 0.33 meter course in 2 minutes. What was Archie's average rate of speed, in meters per second?

We are given

Archie completed the 0.33 meter course in 2 minutes

total distance is 0.33 meter

so,

total time is 2 minutes

Firstly, we will change it into seconds

so,

seconds

now, we can find speed

now, we can plug values

and we get

meters per seconds

so, Archie's average rate of speed, in meters per second is 0.00275 meters per seconds............Answer

Answer: 0.00275 m/sec

Explanation:

2 x 60 = 120 seconds

0.33 ÷ 120 = 0.00275 m

Explanation:

2 x 60 = 120 seconds

0.33 ÷ 120 = 0.00275 m

HIGH SCHOOL

Which is bigger 80% of 150 or 3/4 of 200

80% of 150 means :

80/100 x 150 = 120

3/4 of 200 means :

3/4 x 200 = 150

The bigger number is 3/4 of 200

80/100 x 150 = 120

3/4 of 200 means :

3/4 x 200 = 150

The bigger number is 3/4 of 200

MIDDLE SCHOOL

A boy purchased (bought) a party-length sandwich 54 in. long. He wants to cut it into three pieces so that the middle piece is 6 in. longer than the shortest piece and the shortest piece is 9 in. shorter than the longest piece. How long should the three pieces be?

Answer:

length of shortest piece = 13 in

length of middle piece = 19 in

length of longest piece = 22 in

Step-by-step explanation:

Total length of sandwich = 54 inch

Let shortest piece = x

Middle piece = x+6

Longest piece = x+9

Add this pieces will make complete sandwich

x+(x+6)+(x+9) = 54

Solving

x+x+6+x+9 = 54

Combining like terms

x+x+x+6+9 = 54

3x + 15 = 54

3x = 54 -15

3x = 39

x = 13

So, length of shortest piece = x = 13 in

length of middle piece = x+6 = 13+6 = 19 in

length of longest piece = x+9 = 13+9 = 22 in

Answer:

The three pieces should be 13 , 19 , 22 inches

Step-by-step explanation:

* Lets study the information to solve the problem

- The length of the sandwich is 54 in

- The sandwich will cut into three pieces

- The middle piece is 6 inches longer than the shortest piece

- The shortest piece is 9 inches shorter than the longest piece

* Lets change the above statements to equations

∵ The shortest piece is common in the two statements

∴ Let the length of the shortest piece is x ⇒ (1)

∵ The middle piece is 6 inches longer than the shortest piece

∴ The length of the middle piece = x + 6 ⇒ (2)

∵ The shortest piece is 9 inches shorter than the longest piece

∴ The longest piece is 9 inches longer than the shortest piece

∴ The longest piece = x + 9 ⇒ (3)

∵ the length of the three pieces = 54 inches

- Add the length of the three pieces and equate them by 54

∴ Add (1) , (2) , (3)

∴ x + (x + 6) + (x + 9) = 54 ⇒ add the like terms

∴ 3x + 15 = 54 ⇒ subtract 15 from both sides

∴ 3x = 39 ⇒ divide both sides by 3

∴ x = 13

* The length of the shortest piece is 13 inches

∵ The length of the middle piece = x + 6

∴ The length of the middle piece = 13 + 6 = 19 inches

* The length of the middle piece is 19 inches

∵ The length of the longest piece = x + 9

∴ The length of the longest piece = 13 + 9 = 22 inches

* The length of the longest piece is 22 inches

* The lengths of the three pieces are 13 , 19 , 22 inches

MIDDLE SCHOOL

What percent of 140 is (n+94)

Answer:

46%

Step-by-step explanation:

MIDDLE SCHOOL

Dave can complete a sales route by himself in 4 hours. James can do the same job in 5 hours. How long will it take them to do it working together?

X/4 + x/5 = 1

5x/20 + 4x/20=1

9x/20 =1

9x = 20

x = 2.22 hours

5x/20 + 4x/20=1

9x/20 =1

9x = 20

x = 2.22 hours