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3 years ago

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Linda makes booklets using 2 sheets of paper she has 17 sheets of paper how many more of these booklets can she make will she ha

ve any extra paper how many sheets

2 answers:

Vsevolod [243]3 years ago

8 0

8 books with 2 sheets each and 1 extra sheet as leftover

Nookie1986 [14]3 years ago

6 0

Hello!

OK, so Linda uses 2 sheets of paper per booklet.
She has 17 sheets of paper.
Will she have left over? How many?

Solve:

17 ÷ 2 = 8.5
2 × 8 = 16
17 - 16 = 1

This shows us that there will be ONE extra sheet.

Hope I helped! :)

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Exercise 5.2. Suppose that X has moment generating function

soldi70 [24.7K]

Answer:

a) Mean, E(X) = - 0.5

Variance = = 9.25

b) $M_{X}(t)=E(e^{tX})$

or

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Step-by-step explanation:

Given:

moment generating function of X as:

MX(t) = $\frac{1}{2} + \frac{1}{3}e^{-4t} + \frac{1}{6} e^{5t}$

a) Now

Mean, E(X) = $M_{X}'(t=0)$

Thus,

$M_{X}'(t)=\frac{1}{3}(-4)e^{-4t}+\frac{1}{6}(5)e^{5t}$

or

$M_{X}'(t)=\frac{-4}{3}e^{-4t}+\frac{5}{6}e^{5t}$

also,

$E(X^{2})=M_{X}''(t=0)$

Thus,

$M_{X}''(t)=\frac{-4}{3}(-4)e^{-4t}+\frac{5}{6}(5)e^{5t}$

or

$M_{X}''(t)=\frac{16}{3}e^{-4t}+\frac{25}{6}e^{5t}$

Therefore,

Mean, E(X) = $M_{X}'(t=0)=\frac{-4}{3}e^{-4(0)}+\frac{5}{6}e^{5(0)}$

or

Mean, E(X) = - 0.5

and

$E(X^{2})=M_{X}''(t=0)=\frac{16}{3}e^{-4(0)}+\frac{25}{6}e^{5(0)}$

or

$E(X^{2})$ = 9.5

also,

Variance(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

b) Now,

Let f(x) be the PMF of X

Thus,

$M_{X}(t)=E(e^{tX})$

or

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Therefore,

at x = 0, P(x) = $\frac{1}{2}$

at x= - 4 ,P(x) = $\frac{1}{3}$

at x = 5, P(x) = $\frac{1}{6}$

Thus,

E(X) = $\sum xP(x)=0(\frac{1}{2})+(-4)(\frac{1}{3})+5(\frac{1}{6})$

or

E(X) = - 0.5

also, $E(X^{2})=\sum x^{2}P(x)=0^{2}(\frac{1}{2})+(-4)^{2}(\frac{1}{3})+5^{2}(\frac{1}{6})$

$E(X^{2})$ = 9.5

Hence,

Var(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

4 0

4 years ago

What method(s) would you choose to solve the equation: x2 + 2x - 6 = 0

Nataly_w [17]

Complete the square since can't factor
2/2=1
add 1 to both sides
x²+2x+1-6=1
factor perfect square
(x+1)²-6=1
add 6 to both sides
(x+1)²=7
sqrt both sides
x+1=+/-√7
minus 1 both sides
x=-1+/-√7

so x=-1+√7 or x=-1-√7

7 0

3 years ago

Read 2 more answers

In the supermarket there is a scale that measures the weight of fruit and vegtsbles. The nedle is 24 cm long and it roatated 96d

Galina-37 [17]

Answer:

The distance of needle cover as it rotate is 0.700688 cm

Step-by-step explanation:

Given as :

The length of the needle = r = 24 cm

The needle is rotated at angle = Ф = 96°

The distance of needle cover as it rotate = length of arc made = l cm

The radius of arc = length of needle = r cm

<u>Now, According to question</u>

The distance of needle cover as it rotate = $\dfrac{\Pi \times radius\times \Theta }{180^{\circ}}$

where , π = 3.14

Or, l = $\dfrac{\Pi \times r\times \Theta }{180^{\circ}}$

Or, I = $\dfrac{3.14 \times 24 cm\times 96^{\circ} }{180^{\circ}}$

Or, l = 75.36 × 0.533°

∵ 180° = 3.14 radian

So, 0.533° = 0.0092978

So, l = 75.36 × 0.0092978

∴ l = 0.700688 cm

So,The distance of needle cover as it rotate = l = 0.700688 cm

Hence, The distance of needle cover as it rotate is 0.700688 cm Answer

8 0

3 years ago

angle a and b are both supplementary to angle c if the measure of angle a is 12 less than 2 times the measure of c find the meas

castortr0y [4]

Answer:

The measure of a = b = 116 degrees

Step-by-step explanation:

Here, we have value of angles to calculate.

If a and b are both supplementary to c, what this means is that when we add either a or b to c, we get 180

Hence; Mathematically;

a + c = 180 and b + c = 180

What we have here is that a and b must be equal since they are both supplementary to the same angle value

Now, we are told further in the question that the measure of angle a is 12 less than 2 times the measure of c;

Mathematically, this means that;

a = 2c - 12

So we now want to find the measure of b

Let’s substitute for a

2c -12 + c = 180

3c -12 = 180

3c = 180 + 12

3c =192

c = 192/3

c = 64

Thus; a = 2c - 12 = 2(64) -12 = 128 -12 = 116

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3 years ago

Expand and simplify: (x + 6)2

Sloan [31]

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3 years ago