All categories

2 years ago

What is the length of the line?

Mathematics

1 answer:

Radda [10]2 years ago

8 0

Answer:

x= $\sqrt{169}$

x=13

Step-by-step explanation:

12*12+5*5=x*x

x*x=169

x= $\sqrt{169}$

x=13

You might be interested in

Help if good at math

Mariana [72]

Question 2 would be 6+3+n=12

3 0

3 years ago

Read 2 more answers

A student was given 32 problems he did 1/4 of them on monday and 1/2 of them on tuesday. find the unsolved problem.. PLEASE HELP

azamat

12 unsolved problems?

8 0

3 years ago

Read 2 more answers

Convert the expression 10-(-30) to an addition expression.

antoniya [11.8K]

Answer:

10 + 30

Step-by-step explanation:

if there are 2 negative signs they both cancel each other making it a positive, making the expression 10-(-30) into 10 + 30

Ps: Those 2 equations have the same answer

(could i have brainiest?)

4 0

3 years ago

HELP!!! This is so confusing

antoniya [11.8K]

What's your question?

8 0

3 years ago

An article suggests that substrate concentration (mg/cm^3) of influent to a reactor is normally distributed with μ = 0.60 and σ

defon

Answer:

a) $P(X>0.5)=P(\frac{X-\mu}{\sigma}>\frac{0.5-\mu}{\sigma})=P(Z>\frac{0.5-0.6}{0.08})=P(z>-1.25)$

And we can find this probability using the complement rule:

$P(z>-1.25)=1-P(z$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>-1.25)=1-0.106=0.894$

b) $P(X$

And we can use the z score formula given by:

$z = \frac{x- \mu}{\sigma}$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z$

c) $z=1.64$

And if we solve for a we got

$a=0.6 +1.64*0.08=0.7312$

So the value of height that separates the bottom 95% of data from the top 5% is 0.7312.

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".

Part a

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

$X \sim N(0.6,0.08)$

Where $\mu=0.6$ and $\sigma=0.08$

We are interested on this probability

$P(X>0.5)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>0.5)=P(\frac{X-\mu}{\sigma}>\frac{0.5-\mu}{\sigma})=P(Z>\frac{0.5-0.6}{0.08})=P(z>-1.25)$

And we can find this probability using the complement rule:

$P(z>-1.25)=1-P(z$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>-1.25)=1-0.1056=0.8944$

Part b

$P(X$

And we can use the z score formula given by:

$z = \frac{x- \mu}{\sigma}$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z$

Part c

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.05$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.64$

And if we solve for a we got

$a=0.6 +1.64*0.08=0.7312$

So the value of height that separates the bottom 95% of data from the top 5% is 0.7312.

4 0

3 years ago