What does it mean for a value to be non-negative?

The measure of angle 1 is 130°. 2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 4, 3, 2. Which o

NemiM [27]

Vertical angles are the same measurement and are opposite each other.

Angle 3 is opposite angle 1 and would also be 130 degrees.

5 0

3 years ago

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Suppose the expected tensile strength of type-A steel is 103 ksi and the standard deviation of tensile strength is 7 ksi. For ty

ExtremeBDS [4]

Answer:

a

i So the approximate distribution of $\= X$ is $\mu_{\= X} =103$ and $\sigma_{\= X} = 0.783$

ii So the approximate distribution of $\= Y$ is $\mu_{\= Y} =105$ and $\sigma_{\= Y} = 0.645$

b

the approximate distribution of $\=X - \= Y$ is $E (\= X - \= Y) = -2$ and $\sigma_{\= X - \=Y}=1.029$

Here we can see that the mean of the approximate distribution is negative which tell us that this negative value of the data for $\=X - \= Y$ sample are more and their frequency occurrence is higher than the positive values

c

the value of $P(-1 \le \=X - \= Y \le 1)$ is $= -0.1639$

Step-by-step explanation:

From the question we are given that

The expected tensile strength of the type A steel is $\mu_A = 103 ksi$

The standard deviation of type A steel is $\sigma_A = 7ksi$

The expected tensile strength of the type B steel is $\mu_B = 105\ ksi$

The standard deviation of type B steel is $\sigma_B = 5 \ ksi$

Also the assumptions are

Let $\= X$ be the sample average tensile strength of a random sample of 80 type-A specimens

Here $n_a =80$

Let $\= Y$ be the sample average tensile strength of a random sample of 60 type-B specimens.

Here $n_b = 60$

Let the sampling distribution of the mean be

$\mu _ {\= X} = \mu$

$=103$

Let the sampling distribution of the standard deviation be

$\sigma _{\= X} = \frac{\sigma }{\sqrt{n_a} }$

$= \frac{7}{\sqrt{80} }$

$=0.783$

So What this mean is that the approximate distribution of $\= X$ is $\mu_{\= X} =103$ and $\sigma_{\= X} = 0.783$

For $\= Y$

The sampling distribution of the sample mean is

$\mu_{\= Y} = \mu$

$= 105$

The sampling distribution of the standard deviation is

$\sigma _{\= Y} = \frac{\sigma }{\sqrt{n_b} }$

$= \frac{5}{\sqrt{60} }$

$= 0.645$

So What this mean is that the approximate distribution of $\= Y$ is $\mu_{\= Y} =105$ and $\sigma_{\= Y} = 0.645$

Now to obtain the approximate distribution for $\=X - \= Y$

$E (\= X - \= Y) = E (\= X) - E(\= Y)$

$= \mu_{\= X} - \mu_{\= Y}$

$= 103 -105$

$= -2$

The standard deviation of $\=X - \= Y$ is

$\sigma_{\= X - \=Y} = \sqrt{\sigma_{\= X}^2 - \sigma_{\= Y}^2}$

$= \sqrt{(0.783)^2 + (0.645)^2}$

$=1.029$

Now to find the value of $P(-1 \le \=X - \= Y \le 1)$

Let us assume that $F = \= X - \= Y$

$P(-1 \le F \le 1)$ $= P [\frac{-1 -E (F)}{\sigma_F} \le Z \le \frac{1-E(F)}{\sigma_F} ]$

$= P[\frac{-1-(-2)}{1.029} \le Z \le \frac{1-(-2)}{1.029} ]$

$= P[0.972 \le Z \le 2.95]$

$= P(Z \le 0.972) - P(Z \le 2.95)$

Using the z-table to obtain their z-score

$= 0.8345 - 0.9984$

$= -0.1639$

3 0

3 years ago

The night watchman in a factory cannot guard both the safe in back and the cash register in front. The safe contains $6000, whil

Zolol [24]

Answer:

The guard should be positioned at the safe

Step-by-step explanation:

The night watchmen should be positioned to guard whichever place gives the highest expected value to the thief.

The expected value of robbing the safe is:

$EV_{s} = \$ 6000*0.2\\EV_{s} = \$ 1200$

The expected value of robbing the cash register is:

$EV_{r} = \$ 1000*0.8\\EV_{r} = \$ 800$

Therefore, the guard should be positioned at the safe since it yields a higher expected value to the thief in case he tries to rob it.

7 0

3 years ago

Please help me I have been trying to do this problem

Semmy [17]

Answer:

14 42 in thirds is 14 so if he had to pay a third he paid 14 bucks

Step-by-step explanation:

42/3=14

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3 years ago

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A local water company charges a flat fee of $5 per month, plus $0.0007 per gallons, and $0.0009 per gallon for every gallon for

cestrela7 [59]

Answer:

Total cost= $51

Step-by-step explanation:

<u>Giving the following information: </u>

Fixed cost= $5

From 0 to 40,000 gallons= $0.0007 per gallon

From 40,001 to infinity= $0.0009

<u>We need to calculate the total cost for 60,000 gallons:</u>

Total cost= 5 + 40,000*0.0007 + 20,000*0.0009

Total cost= $51

7 0

3 years ago