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2 years ago

Write without the absolute value sign. |x-3| if x>4

1 answer:

lisabon 2012 [21]2 years ago

6 0

If x>4, then the quantity x-3 inside the absolute value symbol is already positive. So, in this case, |x-3| => x-3, and x-3 is all you need to write.

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Solve the simultaneous equations 2x + y = 5 and 2y = x – 10.

Black_prince [1.1K]

X = 4
The first equation can be substituted into the second one. It would be: 2(-2x+5)=x-10 and after solving it, x = 4

7 0

2 years ago

Read 2 more answers

A certain industrial process yields a large number of steel cylinder whose lengths are distributed normally with mean 3.25 inche

Taya2010 [7]

Answer:

$Y = X_1 + X_2$

If we find the expected value of Y we got:

$E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5$

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

$Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005$

And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

$Y \sim N (\mu =6,5 , \sigma = 0.0707)$

And we want to find this probability:

$P(Y$

And we can use the z score formula given by:

$z=\frac{y -\mu_y}{\sigma_y}$

And if we use the z score formula we got:

$P(Y$

Step-by-step explanation:

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 lenghts of a population, and for this case we know the distribution for X is given by:

$X \sim N(3.25,0.05)$

Where $\mu=3.25$ and $\sigma=0.05$

We slect two observations $X_1, X_2$

And let denote the combined lenght as:

$Y = X_1 + X_2$

If we find the expected value of Y we got:

$E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5$

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

$Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005$

And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

$Y \sim N (\mu =6,5 , \sigma = 0.0707)$

And we want to find this probability:

$P(Y$

And we can use the z score formula given by:

$z=\frac{y -\mu_y}{\sigma_y}$

And if we use the z score formula we got:

$P(Y$

3 0

2 years ago

If the price of an object dropped 25% down to $101.25, what was the original price?

AveGali [126]

$135------------------------

3 0

3 years ago

Find 3 ordered pairs which are Solutions to the equation 2x - 3y = 12

KonstantinChe [14]

2x-3(0)=12
2x=12
x=6
(6,0)

2(0)-3y=12
-3y=12
y=-4
(0,-4)

2x-3(2)=12
2x-6=12
2x=18
x=9
(9,2)

ANSWERS: (6,0) (0,-4) (9,2)

7 0

3 years ago

A kennel is moving 160 dogs to a new facility. Each dog has its own crate. The facility manager rents 17 trucks. Each truck hold

Galina-37 [17]

Answer:

17.7 = 18 (when rounded)

Step-by-step explanation:

160 divided by 9 = the amount of trucks.

8 0

3 years ago