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3 years ago

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Ray is a contestant on a quiz show. Every time Ray answers a question correctly,his winnings double. If he answers the first que

stion correctly his winnings are $1,000; if he answers the second question correctly, his winnings increase $2,000;for the third correct answer he earns $4,000, & so on.
Write an equation for the relationship between the number of correct answers c and the winnings w

1 answer:

Andru [333]3 years ago

8 0

The equation will be b=1000*2^(c-1).

You might be interested in

ANSWER QUICKLY..

astra-53 [7]

Answer:

10 weeks

Step-by-step explanation:

Let's set an equation for you and your brother.

You have $90 plus $18 for every week you save (x).

90+18x

And your brother has $120 plus $15 dollars per week that he saves (x)

120+15x

You want to have the sum of the money equal so combine the two concluded statements

90+18x=120+15x

Arrange them so that you have like terms on each side

90+18x-15x=12+15x-15x

90+3x=120

90-90+3x=120-90

3x=30

x=10

"x" is our number of weeks you and your brother save so the answer is 10 weeks

Just to be sure you can use our equation and plug 10 for every time you see x to make sure our answer is right.

6 0

3 years ago

Write five names for 64 .

Natali [406]

In word form: Sixty four
in expanded form: 6x10 + 4x1
in place value form: 6 tens + 4 ones
in Roman numeral form: LXIV
in Arabic numeral form: ٦٤

4 0

3 years ago

Read 2 more answers

Determine the combined surface area of a cube with an edge that is 3.5 cm long and a cube with an edge that is 2 cm long.

Elis [28]

Answer:

97.5

Step-by-step explanation:

3.5cm cube surface area:

3.5*3.5*6 (the 6 faces of the cube) =

73.5

2cm cube surface area:

2*2*6 =

24

combined surface area:

73.5+24=

97.5

5 0

3 years ago

Binomial Expansion/Pascal's triangle. Please help with all of number 5.

Mandarinka [93]

$\begin{matrix}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\end{bmatrix}$

The rows add up to $1,2,4,8,16$ , respectively. (Notice they're all powers of 2)

The sum of the numbers in row $n$ is $2^{n-1}$ .

The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When $n=1$ ,

$(1+x)^1=1+x=\dbinom10+\dbinom11x$

so the base case holds. Assume the claim holds for $n=k$ , so that

$(1+x)^k=\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k$

Use this to show that it holds for $n=k+1$ .

$(1+x)^{k+1}=(1+x)(1+x)^k$
$(1+x)^{k+1}=(1+x)\left(\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k\right)$
$(1+x)^{k+1}=1+\left(\dbinom k0+\dbinom k1\right)x+\left(\dbinom k1+\dbinom k2\right)x^2+\cdots+\left(\dbinom k{k-2}+\dbinom k{k-1}\right)x^{k-1}+\left(\dbinom k{k-1}+\dbinom kk\right)x^k+x^{k+1}$

Notice that

$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!}{\ell!(k-\ell)!}+\dfrac{k!}{(\ell+1)!(k-\ell-1)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)}{(\ell+1)!(k-\ell)!}+\dfrac{k!(k-\ell)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)+k!(k-\ell)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(k+1)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{(k+1)!}{(\ell+1)!((k+1)-(\ell+1))!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dbinom{k+1}{\ell+1}$

So you can write the expansion for $n=k+1$ as

$(1+x)^{k+1}=1+\dbinom{k+1}1x+\dbinom{k+1}2x^2+\cdots+\dbinom{k+1}{k-1}x^{k-1}+\dbinom{k+1}kx^k+x^{k+1}$

and since $\dbinom{k+1}0=\dbinom{k+1}{k+1}=1$ , you have

$(1+x)^{k+1}=\dbinom{k+1}0+\dbinom{k+1}1x+\cdots+\dbinom{k+1}kx^k+\dbinom{k+1}{k+1}x^{k+1}$

and so the claim holds for $n=k+1$ , thus proving the claim overall that

$(1+x)^n=\dbinom n0+\dbinom n1x+\cdots+\dbinom n{n-1}x^{n-1}+\dbinom nnx^n$

Setting $x=1$ gives

$(1+1)^n=\dbinom n0+\dbinom n1+\cdots+\dbinom n{n-1}+\dbinom nn=2^n$

which agrees with the result obtained for part (c).

4 0

3 years ago

Use the box method to distribute and simplify (3x – 1)(-5x + 1)

Softa [21]

Answer:

-15x^2 +8x -1

Step-by-step explanation:

(3x – 1)(-5x + 1)=

3x(-5x) + 3x(1) - 1(-5x) -1 =

-15x^2 +3x +5x -1 =

-15x^2 +8x -1

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4 0

3 years ago