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musickatia [10]
3 years ago
9

Marie pays $2.50 for 5 pecils. Use the drop down menu to explain how to determine and use constant of proportionality, in dollar

s per pencil, that relates these values
Mathematics
1 answer:
stiks02 [169]3 years ago
5 0

Answer:

$0.5

Step-by-step explanation:

Given data

Cost of 5 pencils= $2.50

Required

The cost per pencil

The cost per pencil is

Cost of 5 pencils divided by 5

=2.5/5

=$0.5

This is the constant of proportionality

For any number of pencils x

The cost is

Cost =0.5x

Hence the cost of one pencil is $0.5

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The answer is B. 34.281
22.854 + 5(22.954) = 137.124
137.124 divided by 4 = 34.281 = 34.2810
7 0
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What is -3 over 10 plus -1 7 over 10?
shusha [124]
-3/10 + -17/10 = -20/10 = -2

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8 0
4 years ago
. Let X and Y be random variables of possible percent returns (0%, 10%,
bazaltina [42]

(a) The marginal distribution of <em>X</em> is

Pr(<em>X</em> = <em>x</em>) = ∑ Pr(<em>X</em> = <em>x</em>, <em>Y</em> = <em>y</em>)

… = 0.0625 + 0.0625 + 0.0625 + 0.0625

… = 0.25

That is, the first equality follows from the law of total probability, with the sum taken over <em>y</em> from {0, 5, 10, 15}. Each probability Pr(<em>X</em> = <em>x</em>, <em>Y</em> = <em>y</em>) is given in the table to be 0.0625.

Similarly, the marginal distribution of <em>Y</em> is

Pr(<em>Y</em> = <em>y</em>) = 0.25

(b) Yes, they're independent because

Pr(<em>X</em> = <em>x</em>, <em>Y</em> = <em>y</em>) = 0.0625,

and

Pr(<em>X</em> = <em>x</em>) Pr(<em>Y</em> = <em>y</em>) = 0.25 • 0.25 = 0.0625.

(c) The mean of <em>X</em> is

E[<em>X</em>] = ∑ <em>x</em> Pr(<em>X</em> = <em>x</em>)

… = 0.25 ∑ <em>x</em>

<em>… </em>= 0.25 (0 + 5 + 10 + 15)

… = 7.5

and you would find the same mean for <em>Y</em>,

E[<em>Y</em>] = 7.5

The variance of <em>X</em> is

V[<em>X</em>] = E[<em>X</em>^2] - E[<em>X</em>]^2

… = (∑ <em>x</em>^2 Pr(<em>X</em> = <em>x</em>)) - 7.5^2

… = 0.25 (∑ <em>x</em>^2) - 56.25

… = 0.25 (0^2 + 5^2 + 10^2 + 15^2) - 56.25

… = 31.25

and similarly,

V[<em>Y</em>] = 31.25

(each sum is taken with <em>x</em> and <em>y</em> from {0, 5, 10, 15})

7 0
3 years ago
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?
beks73 [17]

Answer:

Option B.

Step-by-step explanation:

It is given that the sides of an equilateral triangle are 8 units long.

Draw an altitude of the triangle.

Altitude of an equilateral triangle is perpendicular bisector.

Let x be the length of the altitude of the triangle.

According to the Pythagoras theorem

hypotenuse^2=base^2+perpendicular^2

Using Pythagoras theorem we get

8^2=4^2+x^2

64=16+x^2

64-16=x^2

48=x^2

Taking square root on both sides.

\sqrt{48}=x

4\sqrt{3}=x

The length of the altitude of the triangle is 4√3 units.

Therefore, the correct option is B.

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