the line plot below shows how many points fewer trevor scored in 20 games. In how many games did trevor score 18 points fewer?

John was given a math equation. He completed it in 5 seconds. Is his answer correct? If it is, show how he got the answer. Show

Maru [420]

Yes; his answer is correct.

John can do this by multiple ways, but most likely he just remembered this one. Here are some ways.

1. He used his fingers; he put 1 finger, then another finger, and got 2 fingers up. The answer is 2.

2. He remembered it; usually Kindergarteners learn this and this is very easy to remember.

3. He used the things around him; I have 1 crayon then add another, how many do I have? 2.

7 0

3 years ago

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and

Firdavs [7]

Answer:

1a

$P(39 < X < 48 ) = 0.8767$

1b

95% of all sample means will fall between $40.1 < \mu < 49.9$

1c

$\= x = 41. 795$

2

$n = 25$

Step-by-step explanation:

From the question we are told that

The mean is $n = 45$

The population standard deviation is $\sigma = 10$

The sample size is n = 16

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{ \sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 10 }{\sqrt{16 } }$

=> $\sigma_{x} = 2.5$

Generally the probability that the sample mean will be between 39 and 48 minutes is

$P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )$

=> $P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )$

=> $P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)$

From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is

=> $P( Z< 1.2 ) = 0.88493$

and

$P( Z< - 2.4 ) = 0.0081975$

So

$P(39 < X < 48 ) = 0.88493 -0.0081975$

=> $P(39 < X < 48 ) = 0.8767$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * 2.5$

=> $E =4.9$

Generally the 95% of all sample means will fall between

$\mu -E < and \mu +E$

=> $45 -4.9\ and \ 45 + 4.9$

Generally the value which 90% of sample means is greater than is mathematically represented

$P( \= X > \= x ) = 0.90$

=> $P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90$

=> $P( \= X > \= x ) = P( Z > z ) = 0.90$

Generally from the z-table the critical value of 0.90 is

$z = -1.282$

$\frac{\= x -45 }{ 2.5} = -1.282$

=> $\= x = 41. 795$

Considering question 2

Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

$s = \frac{1}{5} \sigma$

Generally the standard deviation of the sample mean is mathematically represented as

$s = \frac{\sigma }{ \sqrt{n} }$

=> $\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }$

=> $n = 5^2$

=> $n = 25$

5 0

2 years ago

Find the average rate of change of k(x)=5x–19 over the interval [<br> -<br> 14,<br> -<br> 4].

rusak2 [61]

The rate of change of a function can be modeled with the following expression:

$\frac{\Delta{k{x)}}{\Delta{x}}$

Where Δx is the change in x value, and Δk(x) is the corresponding change in k(x). We're given the two extremes of x, so we can calculate the change in x to be

$\Delta{x}=-4-(-14)=10$

To find the change in k(x), we can calculate the values of k(x) at x = -14 and x = -4 and find the difference between them:

$k(-14)=5(-14)-19=-70-19=-89\\ k(-4)=5(-4)-19=-20-19=-39\\ \Delta{y}=k(-14)-k(-4)=-89-(-39)=-50$

So, the rate of change for the function from x = -14 to x = -4 is

$\frac{\Delta{y}}{\Delta{x}}= \frac{-50}{10}=-5$

7 0

3 years ago

Tom works at an aquarium shop cleaning reef tanks. His job is to drain the tank. How much water is initally in

insens350 [35]

Answer is 175

_________

5 0

2 years ago

I need help which letter is it?

aniked [119]

Answer:

D. -2n - 6 = 9

Step-by-step explanation:

The first step you have to do is the distributive property in the given equation. So, you multiply n and 3 by -2. The resulting equation is -2n - 6 = 9.

7 0

2 years ago

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