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koban [17]
3 years ago
6

This question has 2 parts. Answer both parts. Sara started with 12 comic books in her collection. She collected the same number

of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.
Part A

Interpret the origin on the graph. Also, describe the scale of each axis by telling what does each unit on the x-axis and the y-axis represent.


Part B

Compare the slope and y-intercept for the graphs of each function in terms of the quantities.

Mathematics
1 answer:
dezoksy [38]3 years ago
8 0

Answer:

see the explanation

Step-by-step explanation:

Part A

<u>Sara</u>

Find out the equation of the line

The equation of the line in slope intercept  form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

x is the number of months

y is the number of comic books

we have

b=12\ comic\ books

<em>Find the slope m</em>

we have the points

(0,12) and (4,20)

m=(20-12)/(4-0)\\m=2\ comic/month

substitute

y=2x+12

Each unit on the x-axis represent 0.5 months and each unit  on the y-axis represent 4 comic books

The origin of the graph is the point (0,12), this point represent the y-intercept or the initial value (the value of y when the value of x is equal to zero)

<u>Ashton</u>

Find out the equation of the line

The equation of the line in slope intercept  form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

x is the number of months

y is the number of comic books

we have

b=2\ comic\ books

m=3\ comic/month

substitute

y=3x+2

The origin of the graph is the point (0,2), this point represent the y-intercept or the initial value (the value of y when the value of x is equal to zero)

Part B

Compare the slope and y-intercept for the graphs of each function in terms of the quantities

<em>Sara</em>

b=12\ comic\ books

m=2\ comic/month

<em>Ashton</em>

b=2\ comic\ books

m=3\ comic/month

therefore

Sara's graph has the greater y-intercept than Ashton's graph

Ashton's graph has the greater slope than Sara's graph

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Step-by-step explanation:

In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion

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6 0
3 years ago
uppose that​ Mary's utility function is​ U(W) = W0.5​, where W is wealth. She has an initial wealth of​ $100. How much of a risk
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Note that U(W) = W^{0.5}

Answer:

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Step-by-step explanation:

Mary's utility function,  U(W) = W^{0.5}

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The gamble has a 50% probability of  raising her wealth to $115 and a 50% probability of lowering it to $77

Expected wealth of Mary, E_w

E_{w} = (0.5 * $115) + (0.5 * $77)

E_{w} = 57.5 + 38.5

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The expected value of Mary's wealth is $96

Calculate the expected utility (EU) of Mary:-

E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75

The expected utility of Mary is $9.75

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Square root (94 - P) = 9.63

If Mary's risk premium is P, the expected utility will be given by the formula:

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Mary's risk premium is $0.9375

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