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Fiesta28 [93]
2 years ago
8

Julia is saving money for the down payment on a car. She plans to save for one year. Her parents have offered to contribute $50

a month to her savings. How much does Julia need to save each month in addition to her parents' contribution if she wants to have a $2700 down payment on a car at the end of the year? Define a variable and write an equation to represent this situation.
Mathematics
1 answer:
denis23 [38]2 years ago
4 0

Answer:

12x+600=2700

$175

Step-by-step explanation:

Let x represent money saved by her in one month.

So money saved by her in one year (12 months) would be 12x.

We can represent our given information as:

12x+600=2700\\12x=2700-600\\12x=2100\\x=\frac{2100}{12}\\x=175

Therefore, she needs to save $175 per month.

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3 years ago
Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars
GuDViN [60]

Answer:

Probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

Step-by-step explanation:

We are given that the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars. Also, incomes for the industry are distributed normally.

<em>Let X = incomes for the industry</em>

So, X ~ N(\mu=95,\sigma^{2}=5^{2})

Now, the z score probability distribution is given by;

         Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = mean income of firms in the industry = 95 million dollars

            \sigma = standard deviation = 5 million dollars

So, probability that a randomly selected firm will earn less than 100 million dollars is given by = P(X < 100 million dollars)

    P(X < 100) = P( \frac{X-\mu}{\sigma} < \frac{100-95}{5} ) = P(Z < 1) = 0.8413   {using z table]

                                                     

Therefore, probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

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2 years ago
Simplify the following expression.
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Answer:

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Step-by-step explanation:

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