There are 42 students in a school lunch , 25 eat rice, 15 eat spaghetti and 11 eat neither rice nor spaghetti. (a) Draw a venn diagram to illustrate this information. (b) How many students eat both rice and spaghetti? (c) How many students eat at most one of the two types of food?

Answer: The mean is 87

84+ 85 + 85+ 86 +90+ 92 = 522/6 = 87

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

To find the mean of the a set of numbers, we first need to add all the numbers and divide by the number of terms in the set.

84 + 85 + 85 + 86 + 90 + 92 = 522

There are 6 terms so we divide by 6

522/6 = 87

Answer:

C

Step-by-step explanation:

think of a random K number (like 3 for example)

1/2(3) = 3/2

this equals k/2 = 3/2

Answer:

The associative property of multiplication

 8 . ( 5. b ) = ( 8. 5) . b

Step-by-step explanation:

Explanation

The associative property of multiplication

 a . ( b. c ) = ( a. b) . c

Given numbers are  8, 5 and b

The associative property of multiplication

 8 . ( 5. b ) = ( 8. 5) . b

 8 . ( 5. b ) = ( 8. 5) . b = 40 b

Answer:

12.5 inches

Step-by-step explanation:

3/8 of 20 = 3/8 * 20 = 60/8 = 15/2 = 7.5

20 - 7.5 = 12.5

Answer:

12.5 inches

Step-by-step explanation:

20/8=2.5

2.5*3=7.5

20-7.5=12.5

Answer:

V≈565.5cm³ is the answer

Answer:

The answer is (61/3), (-23/3)

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Hoped this helped!

Answer:

There is no solution

Step-by-step explanation:

-4(x+3)=16-4x

expand

−4x−12=16−4x

cancel out

−12=16

because −12=16 is false there is no solution.

Hope this helps :)

Answer: [tex]\angle B=79^{\circ}.[/tex]

Step-by-step explanation:

When two lines cross each other , then the opposite angles are known  as vertical angles.

Vertical angles are equal.

Here, ∠A and ∠B are vertical angles.

So, ∠A = ∠B

If [tex]\angle A=(6x-11)^{\circ}[/tex] and [tex]\angle B=(5x+4)^{\circ}[/tex]

Then , [tex]6x-11=5x+4[/tex]

Subtract 5x from both sides, we get

[tex]x-11=4[/tex]

Add 11 on both sides, we get

[tex]x=15[/tex]

Now , [tex]\angle B=(5(15)+4)^{\circ}=79^{\circ}[/tex]

Hence, the measure of [tex]\angle B=79^{\circ}.[/tex]

Answer: The smallest possible value of q is 9.

Step-by-step explanation:

If we have the set of N numbers:

{x₁, x₂, x₃, ..., xₙ}

The mean of this set is:

M = (x₁ + x₂ + x₃ + ... + xₙ)/N

Now, in this case our set is:

{1, 2, 3, 4, 5, 6, p times 5, q times 7}

Then we have a total of:

6 + q + p numbers.

The mean of this set will be:

Mean = 5.3 = (1 + 2 + 3 + 4 + 5 + 6 + p*5 + q*7)/(6 + p + q)

This is the equation that we will use now.

First, we can simplify this as:

5.3 = (21 + p*5 + q*7)/(6 + p + q)

Now we can pass the denominator in the right to the other side as:

5.3*(6 + p + q) = (21 + p*5 + q*7)

31.8 + p*5.3 + q*5.3 = 21 + p*5 + q*7

Now we want to isolate the variable p in one side of the equation.

p*5.3 - p*5 = 21 - 31.8 + q*7 - q*5.3

p*0.3 = q*1.7 - 10.8

p = (q*1.7 - 10.8)/0.3 = q*(1.7/0.3) - 36

p = q*(1.7/0.3) - 36

p = q*(17/10)*(10/3) - 36

p = q*(17/3) - 36

Now we can see that the denominator is 3, so q should be a multiple of 3.

We want to start with the smallest multiples of 3, but if we use q = 3, then we will have a negative value of p (the same happens if we use 1 = 6)

We do not want that, then we need to use q = 9

p = 9*(17/3) - 36

p = 3*17 - 36

p = 15

Then we have;

9 times the number 7

15 times the number 5 (plus one, because it was already on the first 6 numbers that Sam wrote)

The smallest possible value of q is 9.

Now we want to get the smallest possible value of q.

Remember, p and q need to be positive numbers.

Answer:

3

Step-by-step explanation: set the two equations equal to each other. 5-2x=-4x+9 and you'd get x=2. insert 2 into the expression, and you'd get 1. to find the perimeter, a triangle has 3 sides. 1+1+1 =3

Answer:

2

Step-by-step explanation:

4 divided by 2

Answer:

2 oranges

Step-by-step explanation:

because half of 4 oranges is 2

plz follow me

Answer:

1) The probability that at least 2 support Green is 1 minus the probability that 0 people or 1 person supports Green

2) The probability that exactly 1 person supports Green

Step-by-step explanation:

9514 1404 393

Answer:

  41.7 nautical miles

Step-by-step explanation:

It can help to draw yourself a diagram. It will show you the desired distance is the hypotenuse of a right triangle with side lengths 36 and 21. The Pythagorean theorem can be used to find the distance of interest.

  d² = 36² +21²

  d² = 1296 +441 = 1737

  d = √1737 ≈ 41.6773

The ship is about 41.7 nautical miles from the starting point.

Answer:

hol up

x=-1/8  negative one over eight

Step-by-step explanation:

Answer: What grade work is this? I think I can help...

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

180 * .2 = 36

20% is the same thing as 1/5 of something, so read the question again,

"36 is 1/5 of what number?"

Multiply 36 by 5 to get 180

Double check yourself by finding 20% of 180

180 * .2 = 36

Hope this helped, queen!

9514 1404 393

Answer:

  x = 3/2

Step-by-step explanation:

Multiply by 3 and solve the resulting 2-step equation.

  5 = (1/3)(2x +12)

  15 = 2x +12 . . . . . . multiply by 3

  3 = 2x . . . . . . . . . . subtract 12

  3/2 = x . . . . . . . . . . divide by 2

Answer:

Step-by-step explanation:

I'm not sure about what the answer is for the last two questions. If somebody else does know please right it in the comment section. :)

Answer:

Step-by-step explanation:

disc.=b²-4ac=2²-4×1×5=4-20=-16<0

it has imaginary roots.

Answer:

a) b^4×b^5

hope it helps..,

Answer: 13.2

Step-by-step explanation:

the ratio between the given measurements (11 and 5) is 2.2 [5 x 2.2 = 11]

so, i just multiplied 6 by 2.2 , which equals 13.2 .

hope this helps! xoxo

Answer:

13.2

Step-by-step explanation:

6x2.2=13.2 The triangles are equal and its size is increased by 2.2

Answer:

Yes, Lin is correct.

Step-by-step explanation:

23 is a prime number because it has only two distinct divisors: 1 and itself (23).

Answer:

( 5 + s ) 4 = 20 + 4 s

Step-by-step explanation:

Distribution property

Let a, b and c are numbers then distribution property is defined by

a( b + c) = a b + a c

(a+ b) c = a c + b c

Given that

( 5 + s ) 4 = 5× 4 + s× 4

               = 20 + 4 s

Final answer:-

( 5 + s ) 4 = 20 + 4 s

Answer:

A and D

Step-by-step explanation:

It should be Sx2 + 2(S+ 1/2)

Which is equal to 4s+1

and 2(2s + 1/2) is equal to 4s+1 as well

Kindly check picture to the question below.

Answer:

150 minutes

Step-by-step explanation:

Volume of prism = height * base area

Height of prism = 1m

Base area = area of a trapezium

Area of trapezium = 0.5(a + b) h

a, b = parallel sides, h= height of trapezium

Area of trapezium = 0.5(1.4+0.6)*2

Area = 0.5(2)*2 = 2m²

Hence,

V of prism = area of trapezium * height of prism

Volume = 2m² * 1m = 2m³

Decrease in water level due to pumping

20cm decrease in 30minutes

(20/100)m in 30 minutes

0.2 m decrease in height of water

Hence, height of water in prism after 30 minutes pumping :

height - 0.2 = 1 - 0.2 = 0.8m

Volume after 30 minutes of pumping :

Base area * new height

2m² * 0.8m = 1.6m³

Decrease in volume over 30 minutes :

(Initial volume - volume after pumping)

2m³ - 1.6m³ = 0.4m³

If ;

0.4m³ = 30 minutes

1.6m³ = x

0.4x = 48

x = 48 / 0.4

x = 120

Hence, it takes 120 minutes for the remaining 1.6m³ to be emptied.

Hence, total wait time :

120 minutes + 30 minutes

= 150 minutes