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4 years ago

For each question (a–e) below, choose one of the answers (i–viii); explain your choice.

Mathematics

1 answer:

Natasha2012 [34]4 years ago

5 0

Answer:

Step-by-step explanation:

given that a deck of cards is shuffled.

we know in a deck there are 52 cards, 13 cards of each variety spade, clubs hearts and dice. Red are 26 and black are 26. kings, will be 4.

(a) the top card is the king of spades and the bottom card is the queen of spades?

(iii) 1/52 × 1/52

Top has 1/52 and bottom has 1/52 and these are independent.

(b) the top card is the king of spades and the bottom card is the king of spades?

(viii) None of the above

Because it is impossible.

(iv) 1/52 + 1/52

This is the sum of probabilities because there is no common event for these two.

(d) the top card is the king of spades or the bottom card is the queen of spades?

(ii) 1/52 + 1/51 (once king of spades is there, then probability is 1/51 for bottom card)

(e) of the top and bottom cards, one is the king of spades and the other is the queen of spades?

(vii) 2/52 × 1/51

Because this is twice of probability d.

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A machine, when working properly, produces 5% or less defective items. Whenever the machine produces significantly greater than

vovikov84 [41]

Answer:

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

Step-by-step explanation:

A machine, when working properly, produces 5% or less defective items.

This means that the null hypothesis is:

$H_0: p \leq 0.05$

Test if the percentage of defective items produced by this machine is greater than 5%.

This means that the alternate hypothesis is:

$H_a: p > 0.05$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.05 is tested at the null hypothesis:

This means that $\mu = 0.05, \sigma = \sqrt{0.05*0.95}$

A random sample of 300 items taken from the production line contained 27 defective items.

This means that $n = 300, X = \frac{27}{300} = 0.09$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}$

$z = 3.18$

Pvalue of the test:

Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.

Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993

1 - 0.9993 = 0.0007

5 0

3 years ago

Carlos has six cards in a bag, numbered 2, 2, 3, 6, 8, and 9. What is the probability Carlos will randomly select a 2 or a 9

AfilCa [17]

Answer:

50 percent

Step-by-step explanation:

100 percent divided by 6 (the amount of data) is 16 2/3.

Each number represents 16 2/3 percent.

3 of the numbers are either 2 or 9.

16 2/3x3=50.001

The final answer is a 50% probability.

I think

8 0

3 years ago

Photo attached A. -2 B. -1 C. 1/-2 D. 1/2

kifflom [539]

Step-by-step explanation:

(X1,Y1) = (-2,2)

(X2,Y2) = (0,1)

• Find slope.

m = (Y2 - Y1)/(X2 - X1)

m = (1 - 2)/(0 - (-2))

m = -1/2

The answer is C.

6 0

2 years ago

1. Which represents the type of sequence: -99, -96, -92, -87, -81, …?

Juli2301 [7.4K]

So here are the answers for the given questions above:
1. Based on the given values above, the correct answer would be option B. NEITHER ARITHMETIC NOR GEOMETRIC. Why? When we say arithmetic sequence, the values should have a common difference which remains constant all throughout the sequence, and this sequence does not qualify. On the other hand, a geometric sequence should have a common ratio, and these numbers do not have one.
2. The correct answer for this problem would be option C. 121,520.
Based on the given values above, the values have a common ratio of 1.1. So what we are going to do is just to multiply 1.1 each time and by 2016, we will get 121,520.
Hope these answers help.

8 0

3 years ago

To convert 345 millimeters to liters,which proportion should I use?

Usimov [2.4K]

I think number 2 not sure tho

3 0

3 years ago