Mathematics High School

Sam writes on a white board the positive integers from 1 to 6 inclusive, once each, She then writes p
additional fives and q sevens on the board. The mean of all the numbers on the board is then 5.3.
What is the smallest possible value of q?

Answers

Answer 1

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.

Related Questions

Joyce uses 3/10 bag of chocolate chips for each batch of cookies she makes. What is the least number of batches Joyce can make if she has to open a second bag of chocolate chips?

Answers

Answer:

6 batches is the least amount.

Step-by-step explanation:

What numbers are included in the set of integers? What numbers are not included

Answers

The integers are the set of whole numbers and their opposites. Fractions and decimals are not included in the set of integers. For example, 2,5,0,−12,244,−15 and 8 are all integers.

Answer:

sample response: Integers are the set of whole numbers and their opposites. Fractions and decimals are not included in this set.

Step-by-step explanation:

Which of the following expressions could be used to represent "the difference between -12 and 10"?

Answers

Answer:

-2

Step-by-step explanation:

I took the test :)

Answer:

-12-10

Step-by-step explanation:

difference means subtraction so it is saying subtract -12 and 10

can someone plz help i need it quick

Answers

Answer:

The correct answer is 70.

60+50=110

180-110=70

the angels x and y are equivalent

Step-by-step explanation:

hoped this helped

✩brainliest appreciated✩

Answer:

the answer is dododoodod

Step-by-step explanation:

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Answer:

-100

Step-by-step explanation:

-4 * 5 * 5

Answer:

-100

Step-by-step explanation:

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Answers

Answer:

6.04 inches

Step-by-step explanation:

1 in. = 100 Ft.

604 Ft / 100Ft = 6.04

Answer:

6.04 inches

Step-by-step explanation:

Given expression: 604 ÷ 100

The actual height of the building is 604 feet, and if Corbin wants to scale it down 1:100, then he would divide the height of the building by 100 to get the height in inches of the model.

PLEASE ANSWER ASAP !!!!! WILL GIVE BRAINLIEST

Answers

Answer:

f=-1/9

Step-by-step explanation:

Answer:

First, isolate the variable, f. Subtract 4 to both sides to result with 2f > -7f -1.

Then, add 7f to both sides to result with 9f > -1. Now, we can divide 9 to both sides to get f > -1/9.

y=3x + 4 Find the value of y when x=4

Answers

16

its 16 because you’d rewrite the equation as y=3x4+4

Need someone to help with this, Please and thanks

Answers

its 17 a, -4 b, 1 c, and -2 d

a = 4

b = -3

c = 8

d = 29

hope it's helpful ❤❤❤❤

THANK YOU.

Hiiii Can someone please help me please
A, B, C, or D
F, G, H, or J
Ill give lots of points because there's two Please help me thank you BRAINLIEST ANSWER btw ❤️

Answers

Answer:

B, H

Step-by-step explanation:

The electrician charges 45 dollars per hour and 30 at the beginning. We are multiplying the hours, h, by 45 to get 45h. We add 30 to get C=45h+30

Jerome will always earn 75 dollars, but he also gets 10 percent commission, which is 0.10.

Answer:

B and H are the correct answers

What is the length of AD? PLEASE HELP!!!

Answers

AD is equal to 15 do the answer is AD=15

Luke's parents hired a clown for his birthday party. The clown charges $100 plus an
additional $20 per hour. If h represents the hours, which expression represents how
much Luke's parents spent on the clown?
20h + 100
h
100 +
20
100h + 20
100 + h

Answers

Answer:

100+20h

Step-by-step explanation:

100 is fee plus 20h which is 20 per hour

You have 100 dollars and you give away 25% each week. How many weeks would it take to run out?

Answers

Answer:

1 day

Step-by-step explanation:

day if you're like mee because I will buy chips cards for games

Answer:

4

Step-by-step explanation:

what transformation is?​

Answers

Answer:

incomplete sentence More information At least please?

someone help me with this

Answers

Nine is the correct answer

-5(-y+5)+ 5y=-5
Solved by substitution

Answers

Answer:

5y(5) +5y=-5

25y+5y=-5

30y=-5

Step-by-step explanation:

There is a guitar that originally costs $249.99. It is on sale for 15% off. You also have to pay 6% sales tax. How much will you pay for the guitar? Please show work!!!

Answers

Answer:

225.24099

Step-by-step explanation:

249.99(0.15) = 37.4985

249.99 - 37.4985 = 212.4915

212.4915(0.06) = 12.74949

212.4915 + 12.74949 = 225.24099

What is the value of Y below?

Answers

Answer:

y=2

Step-by-step explanation:

2 3/5 x 5/6 plz help​

Answers

Answer:

2 1/6

Step-by-step explanation:

2 3/5 x 5/6

convert the 2 3/5 to an improper fraction so it can be easier to multiply

2 3/5 = 13/5

13/5 * 5/6

All you need to do is multiply across. Both denominators, and both numerators.  

13 * 5 = 65 (numerator)

5 * 6 = 30 (denominator)

65/30 and that is in an improper form

2 5/30 = 2 1/6 = In a simplified mixed number

2 1/6

Hope this helped!

Have a supercalifragilisticexpialidocious day!

PLEASE PLEASE HOW MANY TIMES CAN I SAY PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer like
Answer 1.___________
Answer 2.___________
Answer 3.___________
Answer 4.___________
Answer 5.___________

Answers

1. C
2. A
3. B
4. D
6. B
I think these are right

Find the product. Enter the product in simplest form. 8 x 1/3 =

Answers

8x1/3 is in the simplest form. 8x1/3=7 3/3x1/3=8 3/9. 8 3/9=8 1/3.

Simplest Form: 8 1/3

It’s 8 1/3 that’s simplest form

SOMEONE DO THESE QUESTIONS FOR ME ASAP!! - GIVING BRAINLIEST

Answers

Answer:

1 Question= 26

2 Question=41

3 Question= 57

4 Question= 15

5 Question = 20

Step-by-step explanation:


Graph the line with the equation y = 22 - 2.
y
10
9
8
7
6
5
4
3
2
-10 -9
-8
-7 -6
-5
-4
-3
-2
-
1
2
3
4
5 6
7
8
9 10
-1

Answers

Ok I uploaded a picture of the graph I hope it helps :)
The slope is 0 and the y-int is (0,20)

- The discount is $4.40 off for each mug. - The club is able to order 24 mugs if they choose this company The club has a budget of $120 for the mugs. There is a set-up fee for each order, but the company decides to waive the fee for the science club. What is the regular price per mug at this company?​

Answers

Answer:

The answer is $9.40

it would be $9.40, hope this helped

An ipod shuffle costs $99.00. The sales tax rate is 8%. What is the total cost of the ipod shuffle including tax?

Answers

I believe the answer is 106.92! Hope this helps <3

One less than five times a number is fewer
than twenty-four.

Answers

Answer:

x < 5

Step-by-step explanation:

[tex]5x - 1 < 24\\5x < 25\\x < 5[/tex]

Answer:

any number under 5

Step-by-step explanation:

5(5) -1 =24

so anything under that would equal fewer than 24

Is this what you're asking?

Which ordered pair uses the rule used in the table?

Answers

Pretty sure it’s B but I don’t rlly know

Answer:

8,17    Answer B.

Step-by-step explanation:

If a line passes through (4,13) and (6,19) what is the slope? And can you please explain how you got your answer

Answers

Answer:

The slope is 3.

Step-by-step explanation:

The equation for slope is either [tex]\frac{y2-y1}{x2-x1}[/tex] or [tex]\frac{y1-y2}{x1-x2}[/tex]. So this should be [tex]\frac{19-13}{6-4}[/tex], which is 3.

Answer:

Slope =

6

—

2

Step-by-step explanation:

First find the rise over run

Second use the format

Y2-y1

———-

X2-x1

Using the format you will get this

19-13

——

6-4

Next solve

Which then you get

6

—

2

Solve by completing the square x^2-10x-24=0

Answers

Step-by-step explanation:

=x²-10x-24

=x²-4x+6x-24

=x(x-4)+6(x-4)

=(x-4)(x+6)

hope it helps.

What is the slope of the line

Answers

The answer is B or 4
This is because the line is positive line. And you have to do rise/run
The rise is 4 and the run is 1.
4/1=4
Hope this helps have a good day! :)

Answer:

B) 4

Step-by-step explanation:

Use the slope formula:

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

Let:

[tex](x_1 , y_1) = (1 , -2)\\(x_2 , y_2) = (2 , 2)\\[/tex]

Plug in the corresponding numbers to the corresponding variables:

slope:

[tex]m = \frac{2 - (-2)}{2 - 1} \\m = \frac{2 + 2}{2 - 1}\\m = \frac{4}{1} = 4[/tex]

B) 4 is your answer.

~

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