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2 years ago

6. It took Juan 48 minutes to drive 12 miles, Calculate his speed in miles per hour,

Mathematics

1 answer:

GREYUIT [131]2 years ago

3 0

Answer:

15 miles per hour

Step-by-step explanation:

First, lets find the number of miles he goes in 1 minutes.

That would be found by dividing the number of miles (12) by the number of minutes (48), so we have:

12/48 = 0.25 miles per minute

We want the speed in miles PER HOUR.

So, how many minutes are in an hour??

That is 60 mins = 1 hr

So, we need to multiply this by 60.So,

0.25 miles per minute * 60 minutes (1 hr) = 15 miles per hour

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I strongly disagree bc it was an corporation for the public in 1995

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Inconsistent and dependent

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A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the pr

Gre4nikov [31]

Answer:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this: $P(-1.5 \leq Z \leq 1.5) = P(z$ Step-by-step explanation:

A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(50,12)$

Where $\mu=50$ and $\sigma=12$

Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We can find the probability required like this:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this:

$P(-1.5 \leq Z \leq 1.5) = P(z$

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2 years ago

Kyle collects rainwater in two barrels. Last week one barrel collected 1.46 gallons of rainwater. The other barrel collected 0.7

hram777 [196]

We’re given two numbers - 1.46 and 0.751 - and since we know that they were both collected last week (although from two separate barrels), we want to add these two numbers up. Aligning the numbers up ( for example, the 1 in 1.46 should align with the 0 in 0.751 because they’re both in the ones place, or the place before the decimal), we get

1.46
+0.751
————
-.—1
To fill in the blanks, we want to start by adding the 6 and 5, which is 11. Since the first digit of 11 is 1, we can carry the 1 into the space to the left to get

1
1.46
+ 0.751
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-.-11

For the next digit, we have 4+7=11, but we add the one on the top to get 12. 12-10=2, so we have
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Since 1+1+0=2, we have 2.211 as our answer.

Feel free to ask further questions!

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2 years ago

Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to neg

Mars2501 [29]

The function is $f(x)= x^{5} -9x ^{3}$

1. let's factorize the expression $x^{5} -9x ^{3}$ :

$f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)$

the zeros of f(x) are the values of x which make f(x) = 0.

from the factorized form of the function, we see that the roots are:

-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3

(the multiplicity of the roots is the power of each factor of f(x) )

2.
The end behavior of f(x), whose term of largest degree is $x^{5}$ , is the same as the end behavior of $x^{3}$ , which has a well known graph. Check the picture attached.

(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of $x^{2}$ )

so, like the graph of $x^{3}$ , the graph of $f(x)= x^{5} -9x ^{3}$ :

"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "

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