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

how is the following written with only one exponent?
a^3 . a^5

Answers

Answer:

The expression 103 is called the exponential expression. ... The exponent applies only to the number that it is next to. ... If −3 is to be the base, it must be written as (−3)4, which means −3 • −3 • −3 ... From row 1 to row 2, the exponential form goes from 105 to 104. ... Following the pattern, you see that 100 is equal to 1.

Step-by-step explanation:

Work out the area of a rectangle with base, b = 20mm and perimeter, P = 42mm.

Answers

Answer:

20mm

Step-by-step explanation:

base=20mm

base x 2 because there are two long lines

20 x 2 = 40

42-40=2

amount needed on either side to balance

height=1mm

20 x 1 = 20mm

area = 20mm

Answer:

Let the length of the rectangle be 'l'

We have,

Perimeter of rectangle, P = 42mm.

[tex]or, 2(l+b) = 42\\or, l +b = \frac{42}{2} = 21\\or, l + 20 = 21\\or, l = 1mm\\[/tex]

Area of rectangle = [tex]lb = 1(20) = 20mm^{2}[/tex]

A and B are two mutually exclusive events.
P(A) = 0.3 and P(A or B) = 0.7
Work out the value of P(B).

Answers

If the events are mutually exclusive, then P(B)=P(A or B)-P(A). This is 0.7-0.3, which is 0.4.

Calculate the perimeter of this shape.
12 cm
18 cm

Answers

Answer:

Step-by-step explanation:

P = 2l + 2w

= 2(12) + 2(18)

= 24 + 36 = 60

plz help me
(a²-b²)²+a²b²
factorise
plzz

Answers

Answer:

a^4+b^4−a^2b^2

Step-by-step explanation:

you have to subtract first

Enter a formula using k to connect the two variables.
F is proportional to a.

Please help

Answers

Answer:

Weres The Formula?

Step-by-step explanation:

Answer:

f=ka

Step-by-step explanation:

which of the following graphs represents the equation y -2 = 3x-1

Answers

Answer:

y=3x+1

Step-by-step explanation:

PLEASE HELP ME ON THIS THE ANSWERS ARE 1/3 cm/s, 1/2 cm/s, 2/3 cm/s, and 3/2 cm/s

Answers

Answer: 3/2 cm per second

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

Explanation:

We could compute the slope of this line to get the answer, or we could simply compute y/x. This shortcut only works because the line goes through the origin. If the line didn't go through the origin, then we would have to use the slope formula.

The unit rate is y/x = 9/6 = 3/2 cm per second. I used the point (9,6) to compute the unit rate.

We can think of the fraction 3/2 as 1.5, so the unit rate is equivalent to 1.5 cm/sec.

25,002,000 in scientific notation

Answers

Answer:

2.5002 × 10^3 i think, dont quote me on that

Step-by-step explanation:

5x + 4x - 4x plz help me

Answers

the answer is 5x
hipe that helps

5x is the answer because 4x-4x=0 and 5x+0=5x.

WILL GIVE BRAINLIEST

A line has a slope of 2 and a y-intercept of 9, what is the equation of the line

Answers

Answer:

y=2x+9

Step-by-step explanation:

Slope intercept form is y=mx+b

m is the slope (2)

b is the y-intercept (9)

Plug the slope and intercept you were given in and you get the equation of the line in slope intercept form

y=2x+9

evaluate 11.5x + 10.7y when x = 3 and y = 4

Answers

Answer: 77.3

Step-by-step explanation:

11.5(3)+10.7(4)

11.5 times 3 equals 34.5

and 10.7 times 4 equals 42.8

34.5 plus 42.8 equals 77.3

Answer:

77.3 (see below)

Step-by-step explanation:

To solve, plug in the values given into the expression given and simplify:

11.5x + 10.7y

11.5 (3) + 10.7 (4)

34.5 + 42.8

77.3

Week 15
1. Sue wants to solve the following equation:
+5 = 12
What step should she take first?
A Multiply both sides by 6.
B. Subtract 12 by both sides.
C. Subtract 5 by both sides,
D. Add 5 to both sides.
MS7 12-1

Answers

I’m assuming the equation is something like x+5 = 12, so it would be C but if the equation is something like (x+5)/6 = 12 then its A

Answer:

huh what i dont get it huh lol this is what you get for stealing my points :)

Step-by-step explanation:

Type the missing number in this sequence:

47, 51, 55, 59, ,

PLEASE HELP

Answers

the answer would be 62

Find the 10th term in the
following sequence:
-21, -27, -33, -39,

Answers

-75 is the answer for the tenth term

Which is a true statement?
A. 7/4 is a rational number but not a whole number
B. 7/4 is a whole number but not a rational number
C. 7/4 is a whole number and a rational number
D. 7/4 is not a rational number, and is not a whole number

Answers

A. 7/4 is a rational number but not a whole number.

Some teenagers collected trash for a beach cleanup. The data for the number of pounds of trash collected by each teenager are shown below. 26, 26, 21, 22, 20, 25, 35 What is the standard deviation of the data? 0 pounds 4.66 pounds 5.03 pounds 25.33 pounds

Answers

Answer:

4.66

Step-by-step explanation:

We are given the following data

26, 26, 21, 22, 20, 25, 35

Step 1

We find the Mean

Mean = 26+ 26+ 21+ 22+20+25+ 35/7

= 175/7

= 25

Step 2

We find the Standard Deviation

The formula for Standard deviation that we would use is the Population Standard deviation, this is because the data given above is the data of the number of pounds of trash collected by each teenager

= √(x - Mean)²/n

= √(26 - 25)²+( 26 - 25)²+ (21 - 25)²+ (22 - 25)² +(20 - 25)²+(25 - 25)²+ (35 - 25)²/7

= √152/7

= √21.7142857

= 4.65985898

Approximately = 4.66

Answer:

5.03 Pounds (C)

ED2021

The person above me is right, but you gotta solve for sample data; not population.

!This is for standard deviation!

GIVING BRAINLIST!!!
The point (5, -6) is reflected over the x-axis. The coordinates of reflected point are (_______).
Group of answer choices

(5, 6)

(-5, 6)

(-5, -6)

(5, -6)

Answers

The correct answer is (5,-7) Hope that helps!

Answer:

it would be (-5,6)

Step-by-step explanation:

since it is just reflected and not moving anywhere it would just be the same coordinates but flipped values. if its positive then when its reflected it would be negative.

Question 7(Multiple Choice Worth 1 points)
(05.02 MC)

A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have?

Approximately 26–34 pounds
Approximately 24–36 pounds
Approximately 28–32 pounds
Approximately 29–31 pounds

Answers

Answer: C

Step-by-step explanation: I took the test and got it right

simplify
5p - 4p - 4p

Answers

Answer:

-3p

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

5p - 4p = 1p - 4p = -3p

If QRS is dilated by a scale factor of 6 through the origin, which of the following points represent the coordinates of R?
OA. (-12,-24)
OB. (-24,-12)
OC. (12.24)
OD. (24,12)

Answers

Answer:

OD. (24,12) This is the right answer ok

Answer:

oopp

Step-by-step explanation:

Please help it’s a test and I only have 50 minutes left

Find x. Round to the nearest hundredth if necessary.

Answers

Answer:

Step-by-step explanation:

X is equal to 60 degrees

y = 3x - 1
y = x - 7
Solve with Substitution

Answers

Y = 3x -1. Y = 3x - 1
(-3) Y = x - 7. -3y = -3x + 21

-2y = 20
-2. = -2
Y = - 10

Y = 3x - 1
-10 = 3x - 1
+ 1. + 1
-9. = 3x
3. 3

-3 = x

(-3,-10)

Solution : {y,x } = { -10 , -3 }
Solve the equation [2] for the variable of y
2 . Y = x-7
Plug this in for variable y in the equation [1]
1 (x -7 ) -3x = -1
1 -2x = 6
Solve the equation [1] for the variable x
1 2x =-6
1 x= -3
By now we know this much
Y = x-7
X =-3
Use the x value to solve for y
Y= ( -3 ) -7 = -10

please help with question 2! BRAINLIEST to correct answer!!!

Answers

Answer:

B: (-infinity, 4]

HELP PLS PLSSSSS

ASAP

Answers

Answer:

9(9d+4)

Step-by-step explanation:

Hope I helped!

Compared to last year the population of city had decreased by 15% the population is now 6800 what was the population last year?

Answers

Answer:

6800 x ( 100%-15% ) =5780 population

Step-by-step explanation:

HI WHAT IS 7/6 OF 456327=
PLEEEEAAASE HEEEELLLP ME!!!!!!!!

Answers

Answer:

532381.5

Step-by-step explanation:

456327 divided by 6 to get 1/6 = 76054.5

76054.5 x 7 to get 7/6 = 532381.5

or 456327 (6/6) + 76054.5 (1/6) =532381.5

Find the area of the figure.

Answers

Answer:

area = 164

Step-by-step explanation:

Divide the square into 2 pictures.

; Square 1 = 5×2 = 10

Square 2 = 14×11 (11 from 16-5 )

so, square 2 = 154

all of area = 154+10 = 164

hope it helps ☺️

3 of 8
The area of a circle is 16.71cm2.
Find the length of the radius rounded to 2 DP.

Answers

Answer:

Radius = 2.31 cm

Step-by-step explanation:

Area of circle = 16.71 square centimeters

[tex]\pi r^2 = 16.71 \\3.14r^2=16.71\\r^2=\frac{16.71}{3.14}\\r^2=5.32\\\sqrt{r^2}=\sqrt{5.32}\\r=2.306[/tex]

Radius of circle = 2.31 centimeter

What is the slope of this line

Answers

Answer:

K=2

Step-by-step explanation:

I es Smrt

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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

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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?