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3 years ago

5

Fiona has a job at a garage.

1 answer:

Stolb23 [73]3 years ago

4 0

Yes.

8 + 1 + 1 = 10, so there are 10 parts to the ratio.
3.5 litres divided by 10 would mean that each part of the ratio is worth 0.35 litres.
The colour is worth 8 parts of the ratio. 0.35 litres multiplied by 8 would give 2.8 litres, meaning 2.8 litres of colour are required.
Fiona has 2.9 litres of colour, which is more than enough to make 3.5 litres of paint mix.

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You can eliminate one of the variable terms in an ___ by adding or subtracting another equation

MakcuM [25]

Answer:

system of equations

Step-by-step explanation:

You can eliminate one of the variable terms in a <u>system of equations</u> by adding or subtracting another equation.

8 0

2 years ago

Explain the meaning of F(30) = 8,950 in this situation

dexar [7]

Answer:

when you have something like f(x)=... that means

f means function

and every time you see an x or the variable in the parenthesis you plug in for that so it's f(x) =3x+1 then f(2)= 3x+1 every time you see x you plug in 2

4 0

3 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

3 years ago

A 9-pack of coffee mugs costs $14.04. What is the unit price?

Nat2105 [25]

Answer:

$\frac{14.4}{9} = 1.6$

8 0

2 years ago

Read 2 more answers

Jane travels7 mph less than2 times as fast as Mike. Starting at the same point and traveling in the same direction, they are198

Sphinxa [80]

Let:

Vj = Speed of jane

Vm = Speed of mike

d = distance

t = time

Jane travels 7 mph less than 2 times as fast as Mike, therefore:

Vj = 2Vm - 7

Remeber:

distance = speed*time

Distance traveled by mike:

d=Vm*t = Vm*6

Distance traveled by jane:

d + 198 = Vj*6

where:

Vj = 2Vm - 7

d + 198 = (2Vm-7)*6

Now, let:

d=Vm*6 (1)

d + 198 = (2Vm-7)*6 (2)

Replace (1) into (2)

6Vm + 198 = 12Vm - 42

Subtract 6Vm from both sides:

6Vm + 198 - 6Vm = 12Vm - 42 - 6Vm

198 = 6Vm - 42

Add 42 to both sides:

198 + 42 = 6Vm - 42 + 42

240 = 6Vm

Divide both sides by 6:

240/6 = 6Vm/6

40 = Vm

Vm = 40mph

Replace Vm into this equation Vj = 2Vm - 7 :

Vj = 2(40) - 7 = 80 - 7 = 73mph

4 0

1 year ago