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Alisiya [41]
3 years ago
6

I need to know these new coordinates

Mathematics
1 answer:
hammer [34]3 years ago
3 0
P(-1, 1)
G(2,1)
R(1,-3)
S(-2,-3)
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.954 grams and a standard devia
olga_2 [115]

Let <em>X</em> be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

P(<em>X</em> ≤ 0.37) = P((<em>X</em> - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(<em>Z</em> ≤ -2)

where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform <em>X</em> to <em>Z</em> using the rule <em>Z</em> = (<em>X</em> - mean(<em>X</em>))/sd(<em>X</em>).)

Given the required precision for this probability, you should consult a calculator or appropriate <em>z</em>-score table. You would find that

P(<em>Z</em> ≤ -2) ≈ 0.0228

You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,

P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95

which means

P(<em>Z</em> ≤ -2 or <em>Z</em> ≥ 2) ≈ 1 - 0.95 = 0.05

The normal distribution is symmetric, so this means

P(<em>Z</em> ≤ -2) ≈ 1/2 × 0.05 = 0.025

which is indeed pretty close to what we found earlier.

4 0
3 years ago
Arianna claims that the rectangles shown below are similar, while Miguel claims that they are not similar.
yaroslaw [1]

Answer:

D

Step-by-step explanation:

5 0
3 years ago
A certain math teachers likes to keep a box of prizes to distribute to students. The math teacher likes to keep at least twice a
Law Incorporation [45]

Option C

Math teacher would need to buy 130 prizes

<em><u>Solution:</u></em>

Given that,

Math teacher currently has 109 students and the box has 88 prizes in it

The math teacher likes to keep at least twice as many prizes in the box as she has students

So, she wants the number of prizes to be twice the number of students

Therefore,

number of prizes = 2 x 109 students

number of prizes = 2 x 109 = 218 prizes

The box has 88 prizes in it

Therefore, number of prizes she would need to buy is:

⇒ 218 - 88 = 130

Thus she would need to buy 130 prizes

3 0
2 years ago
Bill and Joe leave their house at the same time heading in opposite directions. If Bill is driving three times faster than Joe a
Arisa [49]

The problem statement gives you the relationship between their speeds, and it gives you information you can use to find their total speed. You solve this by finding the total speed, then the proportion of that belonging to Bill.

The total speed is (120 mi)/(3 h) = 40 mi/h.

The speed ratio is ...

... Bill : Joe = 3 : 1

so the speed ratio Bill : Total is ...

... 3 : (3+1) = 3:4.

Bill's speed is (3/4)×(40 mi/h) = 30 mi/h.

4 0
3 years ago
Liz simplified the expression 5x - 3(4 - x) and got 2x -12. Did she simplify the expression correctly? Explain how you know.
Orlov [11]

Answer:

Step-by-step explanation:

Incorrect. She forgot to change the sign while distributing.

5x - 3(4-x) = 5x - 12 + 3x = 8x - 12

5 0
3 years ago
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