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2 years ago

2. Express each of the following as a rational number in the form of p/q Where q≠0

Mathematics

1 answer:

ANTONII [103]2 years ago

4 0

Step-by-step explanation:

We need to find each of the following as a rational number in the form of p/q

(a) (3/7)² (b) (7/9)³ (c) (-2/3)⁴

Solution,

(a) (3/7)²

$(\dfrac{3}{7})^2=\dfrac{9}{49}$

(b) (7/9)³

$(\dfrac{7}{9})^3=\dfrac{7\times 7\times 7}{9\times 9\times 9}\\\\=\dfrac{343}{729}$

$(\dfrac{-2}{3})^4=\dfrac{-2\times -2\times -2\times -2}{3\times 3\times 3\times 3}\\\\=\dfrac{16}{81}$

Hence, this is the required solution.

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3) A jewelry store sells a popular line of charm

malfutka [58]

Answer:

Step-by-step explanation:

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1 year ago

What is the solution to the equation 1/4X-1/8=7/8+1/2x. X=-5 X=-4 X=4 X=5

zlopas [31]

Answer:

-8,-4,6

Step-by-step explanation:

Just answered it

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2 years ago

SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as

vovangra [49]

Answer:

a) $P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

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

b) $P(400$

$P(-1$

c) $z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

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

$X \sim N(500,100)$

Where $\mu=500$ and $\sigma=100$

We are interested on this probability

$P(X>625)$

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:

$P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

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

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

Part b

We are interested on this probability

$P(400$

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:

$P(400$

And we can find this probability with this difference:

$P(-1$

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

$P(-1$

Part c

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

$P(X>a)=0.8$ (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 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

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:

$z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

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2 years ago

5x-3y=12 what is the x-intercept

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Your x-intercept is (12/5,0) and your y-intercept is (0,-4)

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3 years ago

Select all numbers that are in the range. -3 -2 -1 0 1 2

Zepler [3.9K]

-2

Answered on edge

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3 years ago