MATHEMATICS
MIDDLE SCHOOL

Answer: Total of 7 packs. 12 pencils in a pack. 7x12 = 84

HIGH SCHOOL

What is the angle of rotation of the minute hand clock moving from 6:10 to 7:00

-300 degrees , hope this helps

MIDDLE SCHOOL

8:20 am to 4:20 pm how many hours and minutes are there?

8 hours separate the two times. 8 times 60 get your total in minutes which is 480

8 hours exactly because the minutes are the same.

MIDDLE SCHOOL

The ratio of cars to trucks is 7:3-there are 16 more cars than trucks

There's an easy way to solve this.

The ratio is 7:3 as cars:trucks

The difference is that it starts off with 4 more cars than trucks.

We want to find how many of each are there when there are 16 more cars than trucks.

16÷4

4

Let's multiply each side of the ratio by 4.

7×4

28

3×4

12

28-12=16

So there will be 28 cars and 12 trucks.

The ratio is 7:3 as cars:trucks

The difference is that it starts off with 4 more cars than trucks.

We want to find how many of each are there when there are 16 more cars than trucks.

16÷4

4

Let's multiply each side of the ratio by 4.

7×4

28

3×4

12

28-12=16

So there will be 28 cars and 12 trucks.

HIGH SCHOOL

If cosine of x equals 1 over 2, and tan (x) > 0. In which quadrant is x located? Explain how you know. What is sin(x) and tan(x)? Show all work for full credit.

Answers:

x is in quadrant I (first quadrant) in the upper right hand corner

sin(x) = sqrt(3)/2

tan(x) = sqrt(3)

where 'sqrt' is shorthand for 'square root'

============================================

Explanation:

cos(x) = 1/2 shows us that cos(x) > 0. At the same time, we're told that tan(x) > 0. Both cosine and tangent are positive. This only happens when we're in the first quadrant. The first quadrant is to the right of the vertical y axis, and it is above the horizontal x axis. In short, the first quadrant is in the upper right hand corner. Tangent is positive in quadrant III; however, cosine is negative here. Similarly, cosine is positive in Q4, but tangent is negative here.

Use the pythagorean trig identity to determine the value of sin(x)

sin^2(x) + cos^2(x) = 1

sin^2(x) + (1/2)^2 = 1

sin^2(x) + 1/4 = 1

sin^2(x) = 1 - 1/4

sin^2(x) = 3/4

sin(x) = sqrt(3/4)

sin(x) = sqrt(3)/sqrt(4)

sin(x) = sqrt(3)/2 ... sine is positive in quadrant I

Now divide the values of sine and cosine to get tangent

tan(x) = sin(x)/cos(x)

tan(x) = sin(x) divided by cos(x)

tan(x) = sqrt(3)/2 divided by 1/2

tan(x) = sqrt(3)/2 times 2/1

tan(x) = sqrt(3) .... note how the '2's cancel

we see that tangent is positive, so that helps confirm the answer.

MIDDLE SCHOOL

1. 12 is 20% of what number?

20% * 5 = 100%

So multiply the number by 5.

12 * 5 = 60.

12 is 20% of 60.

Heres a little chart:

12 = 20%

24 = 40%

36 = 60%

48 = 80%

60 = 100%

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Answer: 5.6

Step-by-step explanation:

Multiply 1.12 times 100 and you get 112 then divide that by 20 which is the 20% and the answer is 5.6

COLLEGE

The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 267 days and standard deviation 19 days. Use the 68-95-99.7 rule to answer the following questions. (a) Between what values do the lengths of the middle 95% of all pregnancies fall?_____________and___________days

(b) How short are the shortest 2.5% of all pregnancies?______days or less

c) How long do the longest 2.5% of pregnancies last?________days or more

Answer:

a) 229 and 305 days

b) 229 days or less

c) 305 days or more

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 267

Standard deviation = 19

(a) Between what values do the lengths of the middle 95% of all pregnancies fall?_____________and___________days

By the Empirical rule, 95% of all pregnancies fall within 2 standard deviations of the mean.

So

267 - 2*19 = 229 days

to

267 + 2*19 = 305 days

(b) How short are the shortest 2.5% of all pregnancies?______days or less

95% of all pregnancies fall within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. Since the distribution is symmetric, 2.5% is more than 2 standard deviations below the mean(shortest 2.5%) and 2.5% is more than 2 standard deviations above the mean(longest 2.5%). So

267 - 2*19 = 229 days

c) How long do the longest 2.5% of pregnancies last?________days or more

Explanation in b)

267 + 2*19 = 305 days

MIDDLE SCHOOL

Which best explains why this relation is not a function of x

What relation? Is not a function to x

MIDDLE SCHOOL

An arc of a circle is 3πm long, and it subtends an angle of 72° at the center of the circle. Find the radius of the circle. The radius of circle is______m

that is how it should be put as answer.

The radius of the circle is 7.5 m

From the question,

We are to determine the value of the radius of the circle

Using the formula

Where

is the length of arc

θ is the angle subtended

and r is the radius

From the given information,

Putting the parameters into the equation, we get

This becomes

Therefore,

Hence, the radius of the circle is 7.5 m

Learn more on arc of a circle here: brainly.com/question/4174930

Using the arc length equation x 2πr, you can solve for the radius. So, the radius of the circle is 7.5m.

MIDDLE SCHOOL

When do sky divers use decimals

In a tenths situation

The tenth situation