MATHEMATICS COLLEGE

What is 37/40 in simplest form

Answers

Answer 1
Answer:

Answer:

It is already explained in simplest form

Step-by-step explanation:

It can be written as 0.925 in decimal form (rounded to 6 decimal places).

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Sin(5x)cos(9x)-cos(5x)sin(9x)=-.75X=
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A lightning bolt is graphed on the coordinate plane below. A rotation of this lightning bolt 270° clockwise would place it in which quadrant?A. Quadrant I (x, y)B. Quadrant II (-x, y)C. Quadrant III (-x, -y)D. Quadrant IV (x, -y)

Answers

Explanation

From the image, it can be seen that the initial position of the lightning bolt is in the first quadrant.

After it has been rotated 270 degrees clockwise, it moves by three quadrants and stays in the second quadrant

Answer: Option B

A particular salad contains 4 units of vitamin A, 5 units of vitamin B complex, and 2 mg of fat per serving. A nutritious soup contains 6 units of vitamin A, 2 units of vitamin B complex, and 3 mg of fat per serving. If a lunch consisting of these two foods is to have at least 10 units of vitamin A and at least 10 units of vitamin B complex, how many servings of each should be used to minimize the total number of milligrams of fat

Answers

Answer:

2 servings of salad and 1 serving of soup

Step-by-step explanation:

In the given scenario the aim is to minimise the fat content of the food combination.

Fat content of soup is 3mg while fat content of salad is 2 mg.

Using Soup as 0 and Salad as 2 will not give the required vitamin content

The logical step will be to keep servings of soup to the minimum.

Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1

1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.

This will not work because amount of vitamin B complex is not up to 10 mg

2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat

This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.

Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving

In how many ways can a subcommittee of 6 students be chosen from a committee which consists of 10 senior members and 12 junior members if the team must consist of 4 senior members and 2 junior members?

Answers

Answer:

The number of ways is 13860 ways

Step-by-step explanation:

Given

Senior Members = 10

Junior Members = 12

Required

Number of ways of selecting 6 students students

The question lay emphasis on the keyword selection; this implies combination

From the question, we understand that

4 students are to be selected from senior members while 2 from junior members;

The number of ways is calculated as thus;

Ways = Ways of Selecting Senior Members * Ways of Selecting Junior Members

Ways = ^(10)C_4 * ^(12)C2

Ways = (10!)/((10-4)!4!)) * (12!)/((12-2)!2!))

Ways = (10!)/((6)!4!)) * (12!)/((10)!2!))

Ways = (10 * 9 * 8 * 7 *6!)/((6! * 4*3*2*1)) * (12*11*10!)/((10!*2*1))

Ways = (10 * 9 * 8 * 7)/(4*3*2*1) * (12*11)/(2*1)

Ways = (5040)/(24) * (132)/(2)

Ways = 210 * 66

Ways = 13860

Hence, the number of ways is 13860 ways

Express M=cos3A + cos A and N = sin3A + sin A as a product form​

Answers

Answer:

2cosAcos2A, 4sinAcos^2A

Step-by-step explanation:

cos3A+cosA

2cos((3A+A)/2)cos((3A-A)/2)

2cos(4A/2)cos(2A/2)

2cosAcos2A

sin3A+sinA

2sin((3A+A)/2)cos((3A-A)/2)

2sin(4A/2)cos(2A/2)

2sin2AcosA

4sinAcos^2A

9,16,25,36 arithmetic or geometric?24,18,12,arithmetic or geometric?
500,100,20 ,4 arithmetic or geometric?

Answers

Answer:

9,16,25,36 neither, 24,18,12 arithmetic, 500,100,20 ,4 geometric

Step-by-step explanation:

1. has no common number

2. goes down by 6 each time

3. is divided by 5 each time

If on a scale drawing 100 feet are represented by 15 inches, then a scale of 1/2 inches represents how many feet

Answers

Answer:

3(1)/(3) feet

Step-by-step explanation:

Inches : Feet = 15 : 100

Let 'x' be the feet required to find

15 : 100 :: 1/2 : x

Product of extremes  = product of means

          15 * x = 100 * (1/2)

          15 * x = 50

                  x = 50/15

                 x  =  10/3

                 x = 3(1)/(3)

                 

Answer:

3 1/3 feet

Step-by-step explanation:

100 feet : 15 inches

3 1/3 feet : 1/2 inch
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