In a survey of school students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only by using Venn diagram.

Answer:

4, 14, 14, 16

Step-by-step explanation:

Key skills needed: Casework, Mean, Median, and Mode

1) We start with 4 numbers _ _ _ _

2) We can determine two of the numbers by using the fact that the median is 14 and the mode is 14.

3) The numbers would have to be:

The 2nd one does not work because the last number would have to be a 6 to have a mean of 12, but the range would not be 12.

4) So, our numbers are _ 14 14 _

5) The two numbers add up to 20 (in order to have a mean of 12. If you subtract the bigger one by the smaller one, it will be 12.

6) We can make a system: saying x is the bigger number and y is the smaller number.

x + y = 20

x - y = 12

Add both and you will get 2x = 32 (since the y values cancel out).

7) divide by on both sides, and x = 16.

8) To find y, we can plug x back in to one equation:

16 + y = 20

y = 4

Our smaller number is 4 and our bigger number is 16.

9) Therefore the numbers are: 4, 14, 14, 16

Hope you understood and have a nice day!! :D

Answer:

Never

Step-by-step explanation:

If two equations have the same slopes and the same y-intercepts they are equivalent to each other

Here's why:

The formula for a linear equation is y= mx +b

b= y- intercept

m= slope

m and b are only variable that have to be replaced by a number for the equation to be complete

Therefore, when m and b (or the slope and the y-intercept)  of both equations are the same, the two equations are the same

The answer would be allrealnumbers, not nosolutions

Hope this helps!!!

Answer:

22

Step-by-step explanation:

6×5 and 4×2 then subtract

Answer:

30-8=22

Step-by-step explanation:

6*5-4*2

30-8

22

Answer:

201.6

i think

Answer: I am pretty sure its A

Step-by-step explanation:

Answer:

[tex] \cos( \theta) \\ \cos(45) = \cos( \frac{\pi}{4} ) \\ = \frac{1}{ \sqrt{2} } \\ or \\ = \frac{ \sqrt{2} }{2} [/tex]

Answer:

its d

Step-by-step explanation:

Answer:

4 + 2t = m

Step-by-step explanation:

Answer:

i think it t=2m

so sorry if im wrong i tried

Step-by-step explanation:

9514 1404 393

Answer:

  B.  9 x 10^4

Step-by-step explanation:

The square number will be a square multiplied by 10 to an even power. Only one choice has an even power of 10.

  9 x 10^4

0.1 or 1/10 yards

So we know that Colton cut 1⁄2 of a yard of ribbon into equal pieces to make the decorations so what we can do is take that 1⁄2 and divided by 5 because we know that there are 5 dancers at his year end dance performance.

1⁄2 in a decimal form is 0.5 so 0.5 divided by 5 equals 0.1 or 1/10.

Step-by-step explanation:

A = 12x^3y^2

P = 2(4x^2y+3xy)

Answer:

V=9

Step-by-step explanation:

9 times 3 equals 27 and that's how I got 9

Answer:

$9

Step-by-step explanation:

DELTAMATH

1. There are 26 letters in the alphabet. Only one of those letters is A. Thus, the probability of picking A is 1/26.

2. Out of the 26 letters, two are either A or B. Thus, the probability would be 2/26, or 1/13.

3. 1/26 letters in the alphabet are Z thus there is a 1/26 probability in picking this letter.

4. There are 5 vowels in the alphabet. Thus, the probability would be 5/26.

5. There are 21 consonants in the alphabet, thus the probability of selecting a consonant fron the alphabet would be 21/26.

6. 4/26, as there are 4 unique letters from the alphabet in the name Bryn.

7. 8/26, as there are 8 letters before I in the alphabet.

8. 5/26 because there are 5 letters in the alphabet following the letter U

9. 11/26 because there are 11 letters between I and U.

10. 0/26 because there are no numbers in the alphabet.

Answer: 1+4(30)-12x

              1+4*30- 12*x X is  equal to 1 so 12x Will be 12

               1+4*30-12

                5*30-12

                150-12

                138    so not it dosen't equal 9

Step-by-step explanation: do PEMADS please excuse my dear ant saly

Answer:

9.40L

Step-by-step explanation:

Step-by-step explanation: To find the exponent, we look at the expression again and see how much of the same number or fraction is repeated. Since the main number is 1/9 and there are 3 fractions repeating it, the exponent is [tex]\frac{1}{9} ^3[/tex] or 1/9 to the 3rd power.

Down is a formula I made!

Main number: 1/9

Repeating how many times: 3

Expression: [tex]\frac{1}{9} ^3[/tex]

Therefore, 1/9 to the 3rd power is 1/729.

[tex]\frac{1}{9}^3=\frac{1}{729}[/tex]

Note: The questioner did not ask for the answer. I wanted to add it anyway for future reasons.

According to the biologist's estimates, there will be 9.25 million ladybugs in the region after the swarm arrives.

To find the total population of ladybugs in the region after the swarm arrives, we need to add the number of ladybugs in the region before the swarm arrives to the number of ladybugs in the swarm:

Total ladybugs = 8.3 x 10⁶ + 950,000

Total ladybugs = 8,300,000 + 950,000

Total ladybugs = 9,250,000

Therefore, according to the biologist's estimates, there will be 9.25 million ladybugs in the region after the swarm arrives.

Learn more about total population here: https://brainly.com/question/13902749

#SPJ1

Answer: 2 feet tall

Step-by-step explanation: 5*6=30/60=2

Answer:

339.7705

Step-by-step explanation:

Answer:

=2x - 21y

Step-by-step explanation:

One step at a time

-3(x + 4y) = -3x - 12y

2(x - 2y) =2x - 4y

=-3x - 12y + 2x - 4y + 3x -5y

=2x - 21y

Answer:

Rotated then reflected.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. multiplication property of equality.

2.division property of equality.

Answer:

Perimeter with brackets is: [tex]\mathbf{Perimeter = (t+7)+(t+7)+(t+7)+(t+7)}[/tex]

perimeter without brackets is:

[tex]\mathbf{Perimeter = 4t+28}[/tex]

Step-by-step explanation:

We need to write two expressions for the perimeter of given shape, one with brackets and one without.

Length of side of shape = t+7

The formula used to find perimeter is: [tex]Perimeter = Sum\: of\: all\: sides[/tex]

Since the shape has 4 sides, we get:

[tex]Perimeter = Sum\: of\: all\: sides\\Perimeter = (t+7)+(t+7)+(t+7)+(t+7)[/tex]

So, perimeter with brackets is: [tex]\mathbf{Perimeter = (t+7)+(t+7)+(t+7)+(t+7)}[/tex]

Now, finding perimeter without brackets:

[tex]Perimeter = (t+7)+(t+7)+(t+7)+(t+7)\\Perimeter = t+7+t+7+t+7+t+7\\Combining\:like\:terms:\\Perimeter=t+t+t+t+7+7+7+7\\Perimeter=4t+28[/tex]

So, perimeter without brackets is:

[tex]\mathbf{Perimeter = 4t+28}[/tex]

Answer:

[tex]7x - 4y = 42[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (6,0)[/tex]

[tex](x_2,y_2) = (2,-7)[/tex]

Required

Determine the equation in standard form

First, calculate the slope (m) using:

[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{-7 -0}{2 - 6}[/tex]

[tex]m = \frac{-7}{-4}[/tex]

[tex]m = \frac{7}{4}[/tex]

The equation in standard form is calculated using:

[tex]y - y_1 = m(x - x_1 )[/tex]

This gives:

[tex]y - 0 = \frac{7}{4}(x - 6)[/tex]

[tex]y = \frac{7}{4}(x - 6)[/tex]

Cross Multiply

[tex]4y = 7(x - 6)[/tex]

Open bracket

[tex]4y = 7x - 42[/tex]

Subtract 7x from both sides

[tex]-7x + 4y = 7x - 7x - 42[/tex]

[tex]-7x + 4y = - 42[/tex]

Multiply through by -1

[tex]-1(-7x + 4y) = - 42*-1[/tex]

[tex]7x - 4y = 42[/tex]

Answer:

2 litres of water

Step-by-step explanation:

If Ryan drinks 1 1/2 liters of water every 3/4 of an hour at a constant rate, this can also be expressed as;

1 1/2 litres = 3/4 hour

To get the amount of litres Ryan drank for 1 hour

x = 1 hour

Divide both equations

(3/2)/x = (3/4)/1

3/2x = 3/4

2x * 3 = 3 * 4

6x = 12

x = 12/6

x = 2

Hence Ryan drinks 2 litres of water in an hour

Answer:

3 x 3/12 x 2/11 x 9/10

Step-by-step explanation: