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4 years ago

9

Translate the sentence into an inequality. Twice the difference of a number and 4 is at most -21. Use the variable x for the unk

nown number.

1 answer:

GREYUIT [131]4 years ago

6 0

Answer:

$2x-8\leq -21$

Step-by-step explanation:

At Most= $\leq$

Twice the difference of a number and 4:

$2(x-4)$

$2x-8$

There you have it!

P.S. Might be wrong. A bit late for me.

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We are drawing a 5-card hand from a standard 52-card deck a. What is the probability that all the cards are spades? (5pts)

Solnce55 [7]

Answer:

0.0005 = 0.05% probability that all the cards are spades.

Step-by-step explanation:

The cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

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

In this question:

52 cards means that N = 52.

13 of the cards are spades, which means that k = 13.

5 card hand means that n = 5.

What is the probability that all the cards are spades?

This is P(X = 5). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 5) = h(5,52,5,13) = \frac{C_{13,5}*C_{39,0}}{C_{52,5}} = 0.0005$

0.0005 = 0.05% probability that all the cards are spades.

7 0

3 years ago

Find the volume of the following

Alex_Xolod [135]

Answer: 3200

Step-by-step explanation:

4 0

3 years ago

If z^2 is directly proportional to W and Z=4 when W=8

NARA [144]

Answer:

The constant of proportionality is 2.

Step-by-step explanation:

z^2 = kW where k is a constant.

When z = 4 , W = 8 so

4^2 = 8k

k = 4^2/8

= 16/8

= 2.

3 0

3 years ago

Read 2 more answers

Please i need the step-by-step solution please thank you

Sergio [31]

Answer:

Question 6: -8

Question 7: C

Step-by-step explanation:

Question 6:

The reason question 6 is -8 is because of the distance in between each number, e.g -7 and -15. This is not to be confused with + 8 each time that would make the sequence 9, 18, 27.

Question 7:

The way we solve this question is using the nth term rule, whatever is before the n is the times tables we follow. So if it is 2n the sequence would be 2, 4, 6, 8 etc. However when we add something like the -2 we do the 2 times tables but this time we -2 for each one. Example: 2 - 2 = 0 so the first number of the sequence is 0, Example 2: 4-2 = 2 so the second number of the sequence is 2.

3 0

3 years ago

Read 2 more answers

Who Washes? Erica and Aaron, who are siblings, have decided to use a lottery system to decide who will wash dishes every night.

Anestetic [448]

Given that Erica and AAron,are using lottery system to decide who will wash dishes every night.

They put some red and blue power chips and draw each one. If same colour, Aaron will wash and if not same colours Erica will wash

If the game is to be fair, then both should have equal chances of opportunity for washing.

i.e. Probability for Erica washing = Prob of Aaron washing

i.e. P(different chips) = P(same colour chips)

Say there are m red colours and n blue colours.

Both are drawing at the same time.

Hence Prob (getting same colour) = (mC2+nC2)/(m+n)C2

Probfor different colour = mC1+nC1/(m+n)C2

The two would be equal is mC2 +nC2 = m+n

This is possible if mC2 =m and nC2 = n.

Or m = 2+1 =3 and n =3

That for a fair game we must have both colours to be 3.

3 0

3 years ago