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Pie
2 years ago
14

A spinner and 4 cards are shown below:

Mathematics
2 answers:
elena55 [62]2 years ago
7 0

Answer:

1 over 20

Step-by-step explanation:

<u><em>Given that:</em></u>

<em>a spinner and 4 cards</em>

<u><em>A Spinner ⇒ 5 equal sectors;Color: Blue,Purple,Yellow,Red,Green</em></u>

<em>Arrow point at purple </em>

<u><em>Four cards ⇒ Color : Red,Yellow,Blue,Pink</em></u>

<em>Jane spins the spinner & selects card without looking.</em>

<em>To Find - Probability spinner stops at purple & select pink card.</em>

<u><em>Solve:</em></u>

<em>Multiply 4 (the number of cards) with 5 (The number of equal sectors)</em>

<em />\frac{1}{5}\times\frac{1}{4}=\frac{1}{20}          {1 × 1 = 1}    {5×4=20}

<u><em>~lenvy~</em></u>

Mama L [17]2 years ago
7 0

Answer:

1 over 20

Step-by-step explanation:

Given the following:

1 spinner and 4 cards

A Spinner which has 5 equal sectors;Color: Green, Blue,Purple,Yellow,Red.

{Arrow point at purple}

Four cards ⇒ which color are Red,Yellow,Blue,Pink

Jane spins the spinner & selects card without looking.

To Find →  Probability spinner stops at purple & select pink card.

Since, purple and pink only has one in each of Spinner/card

Thus,

Spinner (5 equal sectors - 1/5}

Card {4 cards - 1/4}

1/4 × 1/5 = 1/20

Hence, probability spinner stops at purple & select pink card is [A] 1/20

[RevyBreeze]

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Answer:

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And replacing we got:

E(Y) =0*0.60 +1*0.25 +2*0.1 +3*0.05 = 0.60

b) E(Y^2) =0^2*0.60 +1^2*0.25 +2^2*0.1 +3^2*0.05 = 1.1

And then the expected value would be:

E(100Y^2) = 100*1.1= 110

Step-by-step explanation:

We assume the following distribution given:

Y       0       1        2        3

P(Y) 0.60 0.25  0.10  0.05

Part a

We can find the expected value with this formula:

E(Y) = \sum_{i=1}^n Y_i P(Y_i)

And replacing we got:

E(Y) =0*0.60 +1*0.25 +2*0.1 +3*0.05 = 0.60

Part b

If we want to find the expected value of 100 Y^2 we need to find the expected value of Y^2 and we have:

E(Y^2) = \sum_{i=1}^n Y^2_i P(Y_i)

And replacing we got:

E(Y^2) =0^2*0.60 +1^2*0.25 +2^2*0.1 +3^2*0.05 = 1.1

And then the expected value would be:

E(100Y^2) = 100*1.1= 110

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What is the coefficient of x2y3 in the expansion of (2x + y)5?
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Option C:

The coefficient of x^{2} y^{3} is 40.

Solution:

Given expression:

(2 x+y)^{5}

Using binomial theorem:

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here a=2 x, b=y

Substitute in the binomial formula, we get

(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}

                                                            $+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}

Let us solve the term one by one.

$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}

$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y

$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}

$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}

$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}

$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}

Substitute these into the above expansion.

(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}

The coefficient of x^{2} y^{3} is 40.

Option C is the correct answer.

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For this case we must find a linear equation of the form:

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Where,

m: slope of the line

b: cutting point with vertical axis.

For the slope we have the following equation:

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Substituting values we have:

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Answer:

The equation of the line is given by:

x = 1

8 0
3 years ago
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