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3 years ago

Please see attachment

Mathematics

1 answer:

Inga [223]3 years ago

8 0

The surface area of a regular tetrahedron with edge length s is

... A = (√3)s²

For your edge length of 4 inches, the surface area is

... A = (√3)(4 in)² = 16√3 in²

You might be interested in

A hand of 5-card draw poker is a simple random sample from the standard deck of 52 cards. How many 5 draw poker hands are there?

kupik [55]

Answer:

There are 2,598,960 5 draw poker hands are there.

There are 311,875,200 5-stud poker hands.

Step-by-step explanation:

When the order is not important, we use the combinations formula:

For example, eating an apple and an orange is the same as eating an orange and an apple.

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

When the order is important, we use the permutations formula:

For example, a 3 digit credit card password, 123 is different than 213.

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!)}$

A hand of 5-card draw poker is a simple random sample from the standard deck of 52 cards. How many 5 draw poker hands are there?

Here, the ordering is not important, so we use the combinations formula.

$C_{52,5} = \frac{52!}{5!47!} = 2598960$

There are 2,598,960 5 draw poker hands are there.

In 5-card stud poker, the cards are dealt sequentially and the order of appearance is important. How many 5-stud poker hands are there?

The ordering is important, so we use the combinations formula.

$P_{(52,5} = \frac{52!}{47!)} = 311875200$

There are 311,875,200 5-stud poker hands.

7 0

4 years ago

Factor 9x^2+6x+1 completely

Savatey [412]

Answer:

$(3x+1)^2$

Step-by-step explanation:

$9x^2+6x+1=\\(3x+1)^2$

You can confirm this by working and expanding backwards:

$(3x+1)^2=\\(3x+1)(3x+1)=\\9x^2+3x+3x+1=\\9x^2+6x+1$

Hope this helps!

7 0

3 years ago

Read 2 more answers

Help my paper is almost ripped and I don't now 12 and 14

choli [55]

The word missing in 12 is fraction and field
the missing word in 14 is dividing

5 0

3 years ago

In a recent year, the ACT scores for the math portion of the test were normally distributed, with a mean of 21.1 and a standard

Natali5045456 [20]

Answer:

a) $P(X$

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

$P(z$

b) $P(19$

And we can find this probability with this difference:

$P(-0.396$

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

$P(-0.396$

c) $P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)$

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

$P(z>0.925)=1- P(Z$

d) We can consider unusual events values above or below 2 deviations from the mean

$Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5$

A value below 10.5 can be consider as unusual

$Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7$

A value abovr 31.7 can be consider as unusual

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

$X \sim N(21.1,5.3)$

Where $\mu=21.1$ and $\sigma=5.3$

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 b

$P(19$

And we can find this probability with this difference:

$P(-0.396$

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

$P(-0.396$

Part c

$P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)$

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

$P(z>0.925)=1- P(Z$

Part d

We can consider unusual events values above or below 2 deviations from the mean

$Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5$

A value below 10.5 can be consider as unusual

$Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7$

A value abovr 31.7 can be consider as unusual

6 0

3 years ago

The polynomial 4x^3 - 6x^2 + 8x – 12 can be grouped in different ways to factor by

zubka84 [21]

Answer:

(4x3-6x) + (8x-12)= 2x

(4x3+8x) + (-6x2-12)= 2(2x-3) (x^2+2)

Step-by-step explanation:

All you have to do is simplify.

8 0

4 years ago