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mario62 [17]
3 years ago
13

Question 8 (1 point)

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
6 0

Answer:

P_n=10+90n

Step-by-step explanation:

So it said it was linear and gave us two points on that line: (0,10) and (5,460).

y=mx+b is slope-intercept form where b is the y-intercept or the initial amount of beetles and m is the slope (or rate of change in population to number weeks) of the line.  Our variables (x,y) are really (n,P) here.

The slope of the line can be computed using \frac{y_2-y_1}{x_2-x_1} where (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }.

You can also just line up the points vertically and subtract, then put 2nd difference over first difference.

Like this:

(5  ,  460)

-(0  ,    10)

--------------

5       450

So the slope is 450/5=90.

The y-intercept is where the line crosses the y-axis.  A graph crosses the y-axis when it's x value is 0.  Luckily, they give us the y-intercept which is (0,10) so b=10.  Your problem gave us this as well and was just asking for the slope of the line.

Anyways the equation is

y=90x+10

or

y=10+90x

or since we are using P and n:

P_n=10+90n

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3. In determining food spending, it was found that the average meal in Albany is normally distributed, with a mean of $40 and a
Zarrin [17]

Answer:

a) P(X < 40) = 0.5

b) P(38 < X < 42) = 0.69143

c) P(X > 35) = 0.89435

d) P(X > 51) = 0.0029798

e) Find a meal cost which happen to be cheaper than 10% of the meals based on a given data. = $34.872

f) Find a meal cost which happen to be in the 5% of the most expensive based on a given data = $33.42

g) Find a meal costs which happen to be 40% symmetrically around the mean value based on a given data. = $38.988

Step-by-step explanation:

Z score formula = Z score = x - μ/σ

Mean = $40

Standard deviation = $4

a) P(X < 40)

Z score = x - μ/σ

= 40 - 40/4

= 0

Determining the Probability value from Z-Table:

P(X < 40) = 0.5

b) P(38 < X < 42)

For X = 38

Z score = x - μ/σ

= 38 - 40/4

= -0.5

Determining the Probability value from Z-Table:

P(X = 38) = 0.30854

For X = 42

Z score = x - μ/σ

= 42 - 40/4

= 4

Determining the Probability value from Z-Table:

P(x = 42) = 0.99997

Hence, P(38 < X < 42)

P(X = 42) - P(X = 38)

0.99997 - 0.30854

= 0.69143

c) P(X > 35)

Z score = x - μ/σ

= 35 - 40/4

= -1.25

Determining the Probability value from Z-Table:

P( X < 35) = 0.10565

P( X > 35) = 1 - P(X < 35)

1 - 0.10565

= 0.89435

d) P(X > 51)

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= 51 - 40/4

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Determining the Probability value from Z-Table:

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e) Find a meal cost which happen to be cheaper than 10% of the meals based on a given data.

z score for 10th percentile = -1.282

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$34.872

The meal cost which happen to be cheaper than 10% of the meals based on a given data is $34.872

f) Find a meal cost which happen to be in the 5% of the most expensive based on a given data

Z score for 5th percentile = -1.645

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Mean = $40

-1.645 = x - 40/4

-1.645 × 4 = x - 40

-6.58 + 40 = x

$33.42

The meal cost which happen to be in the 5% of the most expensive based on a given data is $33.42

g) Find a meal costs which happen to be 40% symmetrically around the mean value based on a given data.

Z score for 40th percentile = -0.253

Z score formula = Z score = x - μ/σ

Mean = $40

-0.253 = x - 40/4

-0.253 × 4 = x - 40

-1.012 + 40 = x

$38.988

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