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3 years ago

What rule will represent the function, (0,0), (1,1), (2,4), (3,9), (4,16)

Mathematics

2 answers:

marissa [1.9K]3 years ago

8 0

Answer:

y = x²

Step-by-step explanation:

y = x × x

y = x²

1 = 1²

4 = 2²

9 = 3²

VARVARA [1.3K]3 years ago

5 0

Answer:

a(n) = (n-1)^2

Step-by-step explanation:

Notice that each of the y-values {0, 1, 4, 9, 16, ... } is a perfect square. Thus,

the rule is a(n) = (n-1)^2.

Check: if n = 0, is (n-1)^2 = 0? yes

if n = 3, is (3-1)^2 = 4? yes

You might be interested in

The average amount parents and children spent per child on back-to-school clothes in Autumn 2010 was $527. Assume the standard d

Ad libitum [116K]

Answer: a. 0.14085

b. 3.826 x $10^{-3}$

c. 0.5437

d. 0.0811

Step-by-step explanation:

Given average amount parents and children spent per child on back-to-school clothes in Autumn 2010 , $\mu$ = $527

Given standard deviation , $\sigma$ = $160

Let X = amount spent on a randomly selected child

Also Z = $\frac{X-\mu}{\sigma}$

a. Probability(X>$700) = P( $\frac{X-\mu}{\sigma}$ > $\frac{700-527}{160}$ ) = P(Z>1.08125) = 0.14085 {Using Z % table}

b. P(X<100) = P( Z < $\frac{100-527}{160}$ ) = P(Z< -2.66875) = P(Z > 2.66875) = 3.826 x $10^{-3}$

c. P(450<X<700) = P(X<700) - P(X<=450)

P(X<700) = 1 - P(X>=700) = 1 - 0.14085 = 0.8592

P(X<=450) = P(Z<= $\frac{450-527}{160}$ ) = P(Z<= -0.48125) = P(Z<=0.48125) = 0.3155

So final P(450<X<700) = 0.8592 - 0.3155 = 0.5437

d. P(X<=300) = P(Z<= $\frac{300-527}{160}$ ) = P(Z<= -1.4188) = P(Z>=1.4188) = 0.0811

All the above probabilities are calculated using Z % table along with interpolation between two values.

7 0

3 years ago

Need help with courseReplace 250 with 575 and -3 with -5.

Svetlanka [38]

Given

The demand function

$p(x)=\frac{250}{\sqrt{x}}-5$

To determine:

a) The revenue function.

b) The marginal revenue.

c) The marginal revenue when x=200.

d) The equation of tangent, and its derivation.

Explanation:

It is given that,

$p(x)=\frac{250}{\sqrt{x}}-5$

a) The revenue function is given by,

$\begin{gathered} R(x)=x\cdot p(x) \\ R(x)=x\times(\frac{250}{\sqrt{x}}-5) \\ R(x)=250\sqrt{x}-5x \end{gathered}$

b) The marginal revenue function is,

$\begin{gathered} R^{\prime}(x)=\frac{d}{dx}(R(x)) \\ =\frac{d}{dx}(250\sqrt{x}-5x) \\ =250\times(\frac{1}{2}\times x^{-\frac{1}{2}})-5 \\ =\frac{125}{\sqrt{x}}-5 \end{gathered}$

c) The marginal revenue when x=200 is,

$\begin{gathered} R^{\prime}(200)=\frac{125}{\sqrt{200}}-5 \\ =\frac{125}{10\sqrt{2}}-5 \\ =8.8388-5 \\ =3.8388 \\ =3.84 \end{gathered}$

Hence, the marginal revenue is 3.84.

d) Let y=mx+c is the tangent.

Then,

$y=3.84x+c$

That implies, for y=12.68, and x=200,

$\begin{gathered} 12.68=3.84\times200+c \\ 12.68=768+c \\ c=12.68-768 \\ c=-755.32 \end{gathered}$

Hence, the equation of tangent is,

$y=3.84x-755.32$

8 0

1 year ago

Write an<br> i explicit formula for an, the nth term of the sequence 200, 40, 8, ....

Ugo [173]

Answer:

$T_n = 200 * (\frac{1}{5})^{n-1$

Step-by-step explanation:

Given

$Sequence: 200,40,8$

Required

The nth term

The given sequence is a geometric sequence.

So, first we identify the first term

$a = 200$

Calculate common ration

$r = \frac{40}{200}$ or $r = \frac{8}{40}$

$r = \frac{1}{5}$

So, the nth term is:

$T_n = ar^{n-1$

$T_n = 200 * (\frac{1}{5})^{n-1$

5 0

2 years ago

SAMPLE QUESTION 2

Arlecino [84]

Answer:

4 rth answer is correct if it is wrong plz comment

Step-by-step explanation:

=14-3/21

=11/21

2-1/6

1/6

4-3/12

1/12

5 0

3 years ago

Given the formula b=rs/t solve for s

Gekata [30.6K]

Answer:

$s = \frac{bt}{r}$

Step-by-step explanation:

To solve for s, you need to follow these steps.

First multiply by t both sides of the equation.

$b = \frac{rs}{t}$

$bt = \frac{rst}{t}$

We get $bt = rs$

Now we divide by r, both sides of the equation.

$\frac{bt}{r} = \frac{rs}{r}$

Finallly we obtain:

$\frac{bt}{r} = s$ or

$s = \frac{bt}{r}$

7 0

3 years ago