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2 years ago

9

Paula used different amounts of red paint mixed with white paint to make samples of pink paint. The table shows the amount of wh

ite paint, in teaspoons, and the amount of red paint, in teaspoons, used for each sample.
Create a line plot that shows the amount of red paint Paula used in each sample. For each amount that is used, start on the bottom dot and click to select a dot.

If Paula took all the red paint and used the same amount in each of the samples, how much would she use for each sample?

2 answers:

motikmotik2 years ago

5 0

Ur mum isand cute she is good at doing

alexgriva [62]2 years ago

4 0

5Step-by-step explanation:8+7-7+9-7=lan

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Any 10th grader solve it <br>for 50 points

kkurt [141]

Answer:

$\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0$ is proved for the sum of pth, qth and rth terms of an arithmetic progression are a, b,and c respectively.

Step-by-step explanation:

Given that the sum of pth, qth and rth terms of an arithmetic progression are a, b and c respectively.

First term of given arithmetic progression is A

and common difference is D

ie., $a_{1}=A$ and common difference=D

The nth term can be written as

$a_{n}=A+(n-1)D$

pth term of given arithmetic progression is a

$a_{p}=A+(p-1)D=a$

qth term of given arithmetic progression is b

$a_{q}=A+(q-1)D=b$ and

rth term of given arithmetic progression is c

$a_{r}=A+(r-1)D=c$

We have to prove that

$\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)=0$

Now to prove LHS=RHS

Now take LHS

$\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)$

$=\frac{A+(p-1)D}{p}\times (q-r)+\frac{A+(q-1)D}{q}\times (r-p)+\frac{A+(r-1)D}{r}\times (p-q)$

$=\frac{A+pD-D}{p}\times (q-r)+\frac{A+qD-D}{q}\times (r-p)+\frac{A+rD-D}{r}\times (p-q)$

$=\frac{Aq+pqD-Dq-Ar-prD+rD}{p}+\frac{Ar+rqD-Dr-Ap-pqD+pD}{q}+\frac{Ap+prD-Dp-Aq-qrD+qD}{r}$

$=\frac{[Aq+pqD-Dq-Ar-prD+rD]\times qr+[Ar+rqD-Dr-Ap-pqD+pD]\times pr+[Ap+prD-Dp-Aq-qrD+qD]\times pq}{pqr}$

$=\frac{Arq^{2}+pq^{2} rD-Dq^{2} r-Aqr^{2}-pqr^{2} D+qr^{2} D+Apr^{2}+pr^{2} qD-pDr^{2} -Ap^{2}r-p^{2} rqD+p^{2} rD+Ap^{2} q+p^{2} qrD-Dp^{2} q-Aq^{2} p-q^{2} prD+q^{2}pD}{pqr}$

$=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2}-pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}$

$=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2} -pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}$

$\neq 0$

ie., $RHS\neq 0$

Therefore $LHS\neq RHS$

ie., $\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0$

Hence proved

5 0

3 years ago

Is the DIAMETER of a circle proportional to its circumference???

Elodia [21]

Answer:

Is the DIAMETER of a circle proportional to its circumference??

1. One of the unique qualities of a circle is that its diameter and circumference have a proportional relationship.

2. This means that no matter what size the circle is, the proportional relationship, or ratio, between its circumference and diameter is always the same.

Is the RADIUS of a circle proportional to its area??

1. Yes, the circumference of a circle is proportional to its radius.

2. Double the radius and you double the circumference.

3 0

3 years ago

A rectangle has a perimeter of 26 cm and one of its sides has length of 5 cm

otez555 [7]

Answer:5 by 8 by 5 by 8

Step-by-step explanation: the perimeter is 26 and one side if 5 so you know that another side is also 5. So add 5 and 5 together you get 10. Then subtract 10 from the perimeter(witch we know is 26) and you end up with 16. we know that the last two side lengths are the same so divide 16 by two and the sidle length is 8.

8 0

3 years ago

What is the percentage decrease if an item has dropped from $115 to $46

Sav [38]

Answer: 60% decrease

Step-by-step explanation:

Look at the attachment

4 0

4 years ago

You are planning to work in the summer (13 weeks). You

Llana [10]

Answer:

(a) Equations for both

$y = 500 + 12x$ --- lifeguard

$y = 15x$ --- camp counselor

(b) Total pay for 5 days

Lifeguard pays $800

Camp counselor pays $375

(c) Which pays more

Lifeguard job pays more

Step-by-step explanation:

Let

$x \to hours$

$y \to total\ pay$

Given

Lifeguard job

$Signing\ bonus = \$500$

$Rate = \$12/hr$

Camp counselor job

$Signing\ bonus =\$0$

$Rate = \$15/hr$

Solving (a): The equation for both

The total pay for each job is calculated as:

Total Pay = Signing Bonus + Rate * Hours

So, we have:

Lifeguard

$y = 500 + 12*x$

$y = 500 + 12x$

Camp counselor

$y = 0 + 15 * x$

$y = 15x$

Solving (b): Total pay for 5 days

First, we calculate the total hours worked in 5 days

$x = 5hrs/day * 5days$

$x = 25hrs$

So, the pay for each is:

$y = 500 + 12x$

$y =500 + 12*25$

$y =800$ --- Lifeguard

$y = 15x$

$y = 15 * 25$

$y = 375$ --- camp counselor

Solving (c): Which job pays more

By comparing the solution in (b)

$800 > 375$

<em>Hence, lifeguard job pays more</em>

6 0

3 years ago