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3 years ago

12

On a coordinate plane, triangle L M N has points (negative 1, 2), (negative 1, negative 4), and (3, negative 4). What is the are

a of triangle LMN?

1 answer:

frozen [14]3 years ago

8 0

Answer:

The base length (which is the length on MN) is 4 and the height (which is LM) is 6 so the area is 4 * 6 / 2 = 12 sq. units.

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The scatter plot shows the relationship between pages read per week and age. What is the range of the cluster shown in the scatt

Katen [24]

Answer:

part 1 of the question is d ,and part 2 of the question is b.

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3 years ago

Read 2 more answers

A poker hand is a set of 5 cards randomly chosen from a deck of 52 cards. Find the probability of a (a) royal flush (ten, jack,

zysi [14]

Answer:

a) 0.000001539

b) 0.00001385

c) 0.0002401

d) 0.001441

e) 0.001966

Step-by-step explanation:

Since there are 52 deck of cards, and the hand of the poker is 5 set, then the total number of hands achievable would be

T = 52! / 5!(52 - 5)!

T = 52! / 5! 47 !

T = 2598560 possibilities.

a) There are 4 ways of getting a royal flush. So the probability of getting a royal flush is

4 / 2598560 =

0.000001539

b) There are 9 hands from the 5 card hands, and also, there are 4 possible suits. So then, the probability is

9 * 4 / 2598560 =

36 / 2598560 =

0.00001385

c) There are 13 possible ways to get a four of a kind, since there are 5 cards with the poker, the remaining would be taken from the 48 remaining cards, thus

13 * 48 / 2598560 =

624 / 2598560 =

0.0002401

d) 3 of a kind in conjunction with a pair is needed to form a full house. This 3 of a kind can be gotten from any 4 suits. Then again, the pair has two cards with the same face value. So,

4! / 2! (4 - 2)! =

4! / 2! 2! = 6

That means, there are 6 possible ways to get our needed suits. Then, the probability of getting a full house is

13 * 4 * 12 * 6 / 2598560 =

3744 / 2598560 =

0.001441

e) To get a flush, all the 5 cards in the hand needs to have the same suit. Now, there are 13 different types of cards with only 5 cards being in the hand, thus

13! / 5! (13 - 5)! =

13! / 5! 8! = 1287

Now, recall that the question specifically asked us not to include any straight. There are 10 straights that can be gotten, and thus, we subtract it.

1287 - 10 = 1277

Since there are 4 suits, the probability of getting a flush is

1277 * 4 / 2598560 =

5108 / 2598560 = 0.001966

5 0

4 years ago

Mark and his three friend's ate at Applebee's. Their bill totaled $52.35. if they left the server a 20% tip, how much would each

kompoz [17]

Check the attachment.

6 0

4 years ago

Round 14.603 to the nearest hundredth

Finger [1]

The answer is 14.60. Hope this helps!

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4 years ago

Read 2 more answers

A researcher wants to test whether a certain sound will make rats do worse on learning tasks. It is known that an ordinary rat c

AveGali [126]

Answer:

So we reject the null hypothesis and accept the alternate hypothesis that rats learn slower with sound.

Step-by-step explanation:

In this data we have

Mean= u = 18

X= 38

Standard deviation = s= 6

1) We formulate the null and alternate hypothesis as

H0: u = 18 against Ha : u > 18 One tailed test .

2) The significance level alpha = ∝= 0.05 and Z alpha has a value ± 1.645 for one tailed test.

3)The test statistics used is

Z= X- u / s

z= 38-18/6= 3.333

4) The calculated value of z = 3.33 is greater than the z∝ = 1.645

5) So we reject the null hypothesis and accept the alternate hypothesis that rats learn slower with sound.

First we set the criteria for determining the true of value of the variable. That whether the rats learn in less or more than 18 trials.

Then we find the value of z for the given significance value given and the test about to be checked.

Then the test statistic is determined and calculated.

Then both value of z and z alpha re compared. If the test statistics falls in the rejection region reject the null hypothesis and conclude alternate hypothesis is true.

The figure shows that the calulated z value lies outside the given z values

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3 years ago