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2 years ago

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Latrell and his cousin, Tisha, met at a state park to go for an all-day hike. Latrell drove 122 miles to get to the park, and it

took him 2 hours. Tisha drove 96 miles to get to the park, and it took her 1.5 hours. On average, how much faster did Tisha drive than Latrell?

2 answers:

nikklg [1K]2 years ago

7 0

Answer:

Tisha is faster than Latrell by 3 miles/hour

just did the math

Naddika [18.5K]2 years ago

5 0

Answer:

3 miles

Step-by-step explanation:

122/2 is 61

64 plus 32 is 96. 96/1.5 is 64 meaning that she goes 64 miles an hour.

so she goes 3 miles faster on average than latrell, with latrell going 61 an hour average and her going 64 an hour average

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3 years ago

Factor completely 2x3 + x2 - 18x - 9

melisa1 [442]

Factor the following:
2 x^3 + x^2 - 18 x - 9

Factor terms by grouping. 2 x^3 + x^2 - 18 x - 9 = (2 x^3 + x^2) + (-18 x - 9) = x^2 (2 x + 1) - 9 (2 x + 1):
x^2 (2 x + 1) - 9 (2 x + 1)

Factor 2 x + 1 from x^2 (2 x + 1) - 9 (2 x + 1):
(2 x + 1) (x^2 - 9)

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3 years ago

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Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105 and a standard deviation sigma equa

Sindrei [870]

Answer:

0.7698

Step-by-step explanation:

If you call your random variable $X$ , then what you are looking for is

$P(87 \leq X \leq 123)$

because you want the probability of $X$ being <em>between 87 and 123.</em>

We need a table with of the normal distribution. But we can only find the table with $\mu = 0$ and $\sigma = 1$ . Because of that, first we need to <em>normalize </em>our random variable:

$Z = \frac{X - \mu}{\sigma} = \frac{X - 105}{15}$

(you can always normalize your variable following the same formula!)

now we can do something similar to our limits, to get a better expression:

$\frac{87 - 105}{15} = \frac{-18}{15} = -1.2$

$\frac{123 - 105}{15} = \frac{18}{15} = 1.2$

And we transform our problem to a simpler one:

$P(87 \leq X \leq 123) = P(-1.2 \leq Z \leq 1.2) = P(Z \leq 1.2) - P(Z \leq -1.2)$

(see Figure 1)

From our table we can see that $P(Z \leq 1.2) = 0.8849$ (this is represented in figure 2).

Remember that the whole area below the curve is exactly 1. So we can conclude that $P(Z \geq 1.2) = 0.1151$ (because 0.8849 + 0.1151 = 1). We also know the normal distribution is symmetric, then

$P(Z \leq -1.2)= P(Z \geq 1.2) = 0.1151$ .

FINALLY:

$P(Z \leq 1.2) - P(Z \leq -1.2) = 0.8849 - 0.1151 = 0.7698$

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3 years ago

An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce p

ludmilkaskok [199]

Answer:

a) $y=-0.317 x +46.02$

b) Figure attached

c) $S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

a) Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

b) Plot the points and graph the line as a check on your calculations.

For this case we can use excel and we got the figure attached as the result.

c) Calculate S^2

In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

$MSE=\frac{SSE}{df_{E}}$

The degred of freedom for the error are given by:

$df_{E}=n-2=12-2=10$

We can calculate:

$S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792$

And now we can calculate the sum of squares for the regression given by:

$SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67$

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

$S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

5 0

3 years ago

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belka [17]

Answer:

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Step-by-step explanation:

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3 years ago

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