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baherus [9]
3 years ago
8

9. Carla has $200 in her bank account.

Mathematics
1 answer:
Firdavs [7]3 years ago
4 0

(a) Linear Equation:   f(x) = 200 - 20x

(b) x-intercept : (10,0)

(c) y-intercept : (0,200)

(d) Domain : {0,1,2,3,4,5,6,7,8,9,10}

    Range : {0,1,2,...,200}

Step-by-step explanation:

Step 1: As we can see in graph, money in Carla is decreasing in multiples of 20 can be referred as 20x.

Every week $20 is getting deducted from the total amount of $200.

Step 2: (a) So we can quote it in equation as,

f(x) = 200 - 20x

where x represents number of weeks

Step 3: (b) x-intercept is where value of y becomes 0.

So, referring graph we can determine x intercept as x = 10. Point (10,0). which also means no money left in account.

Step 4: (c) y-intercept is where value of x becomes 0.

So, referring graph we can determine y intercept as y = 200. Point (0,200). which is starting value of money in account.

Step 5: (d) Domain : {0,1,2,3,4,5,6,7,8,9,10}

                  Range : {0,1,2,...,200}

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Here is dependence between scores and x-values:

Z_i=\dfrac{X_i-\mu}{\sigma},

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-0.25=\dfrac{57-\mu}{\sigma}.

2. When i=2, Z_2=1.25,\ X_2=87, then

1.25=\dfrac{87-\mu}{\sigma}.

Now solve the system of equations:

\left\{\begin{array}{l}-0.25=\dfrac{57-\mu}{\sigma}\\ \\1.25=\dfrac{87-\mu}{\sigma}.\end{array}\right.

\left\{\begin{array}{l}-0.25\sigma=57-\mu\\ \\1.25\sigma=87-\mu.\end{array}\right.

Subtract first equation from the second:

1.25\sigma-(-0.25\sigma)=87-57,\\ \\1.5\sigma=30,\\ \\\sigma=20.

Then

1.25=\dfrac{87-\mu}{20},\\ \\87-\mu=25,\\ \\\mu=87-25=62.

Answer: the mean is 62, the standard deviation is 20.

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Using the normal distribution, we have that:

a) The sketch of the situation is given at the end of this answer.

b) The probability is:

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In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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In this problem:

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Item a:

The part between 2.8 and 7 years is shaded on the sketch given at the end of this answer.

Item b:

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Z = \frac{2.8 - 4.1}{1.3}

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0.9871 - 0.1587 = 0.8284, thus:

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