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3 years ago

Simplify when it is possible. 10x² -y + x² =

Mathematics

2 answers:

mafiozo [28]3 years ago

3 0

Answer:

11x² - y

Step-by-step explanation:

Step 1: Write out expression

10x² - y + x²

Step 2: Combine like terms

11x² - y

That is simplest form.

masha68 [24]3 years ago

3 0

Answer:

$\huge \boxed{11x^2-y}$

Step-by-step explanation:

$10x^2 -y + x^2$

Grouping like terms.

$(10x^2 + x^2)-y$

Combining like terms.

$(11x^2)-y$

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Roman55 [17]

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2 years ago

You roll three die. what is the probability that 5 will not appear on the die?

castortr0y [4]

No of out comes =216
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3 years ago

Explain if you can please and thank you

svetlana [45]

Given:

Given that the angles of the kite.

The opposite angles of the kite measures (3y + 14)° and (y + 50)°

We need to determine the value of y.

Value of y:

We know the property that the opposite angles are equal.

Thus, applying the property, we have;

$3y+14=y+50$

Subtracting both sides of the equation by y, we have;

$2y+14=50$

Subtracting both sides of the equation by 14, we get;

$2y=36$

Dividing both sides of the equation by 2, we get;

$y=18$

Thus, the value of y is 18.

4 0

3 years ago

The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard

PtichkaEL [24]

Answer:

a) $X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

b) $P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

c) $P(X$

$P(Z$

d) $P(60$

$P(-0.167$

e) IQR = 75.13-50.87=24.26

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 amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

$X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

Part b

We are interested on this probability

$P(X>90)$

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:

$P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

Part c

We are interested on this probability

$P(X$

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:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(Z$

Part d

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

$P(60$

And we can find this probability with this difference:

$P(-0.167$

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

$P(-0.167$

Part e

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

$P(X>a)=0.75$ (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 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

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:

$z=-0.674$

And if we solve for a we got

$a=63 -0.674*18=50.87$

So the value of height that separates the bottom 25% of data from the top 75% is 50.87.

Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674

$z=0.674$

And if we solve for a we got

$a=63 +0.674*18=75.13$

And then the IQR = 75.13-50.87=24.26

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=2%20%2B%202%20-%203%20%2B%208%20%20%5Cdiv%203%20%3D%20" id="TexFormula1" title="2 + 2 - 3 + 8

Nataly [62]

If your using pemdas the answer would be roughly 3.6 because you divide 8 and 3 first to get 2.6 repeated then do 2+2=4 then 4-3=1 + the original 2.6 = 3.6

4 0

2 years ago