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3 years ago

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The expression −50x+100 represents the balance, in dollars, of a bank account after x months. What is the rate of change, in dol

lars per month, of the bank account balance? Enter your answer in the box.

1 answer:

Rom4ik [11]3 years ago

5 0

Given expression = −50x+100.

Let us understand the structure of the above expression.

Actually above expression is written in slope-intercept form.

y= mx+b, where m is the slope and in other words we call a slope " rate of change", and b is the y-intercept, we take b as fix value.

If we compare −50x+100 by slope-intercept form mx+b, we can see that coefficent of x is -50 there,

Therefore, m=-50.

So, the rate of change of the bank account balance(in dollars per month) = $50/month.

And because it is a negative 50, so we could say the rate of decrease per month is $50.

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There is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi

Step-by-step explanation:

From the question we are told that

The data is

Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8

Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4

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the alternative hypothesis is $H_a : \mu_1 - \mu_2 > 0$

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=> $\= x_1 = 5.56$

Generally the standard deviation of age of cars

$\sigma _1 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }$

=> $\sigma _1 = \sqrt{\frac{(4 - 5.56)^2 + (0 - 5.56)^2+ (8 - 5.56)^2 + \cdots + 8}{ 27} }$

=> $\sigma _1 = 3.88$

Generally the sample mean for the age of taxi is mathematically represented as

$\= x_2 = \frac{\sum x_i }{n}$

=> $\= x_2 = \frac{8 +8 +0 + \cdots + 4
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=> $\= x_2 = 5.85$

Generally the standard deviation of age of taxi

$\sigma _2 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }$

=> $\sigma _2 = \sqrt{\frac{(8 - 5.85)^2 + (8 - 5.85)^2+ (0 - 5.85)^2 + \cdots + 8}{ 20} }$

=> $\sigma _2 = 2.83$

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$t = \frac{(\= x_ 1 - \= x_2 ) - 0}{\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2} } }$

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=> $t = -0.30$

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$df = n_1 + n_2 -2$

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So the p-value is

$p-value = P(t > T) = 0.61722067$

From the obtained values we see that the p-value > $\alpha$ hence we fail to reject the null hypothesis

Hence the there is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi

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