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3 years ago

What is the numerical value of the following

1 answer:

6 0

1) 1

2)
${4}^{ - 3} = \frac{1}{64}$
3)
${ - 5}^{3} = - 125$
4)
${ \frac{4}{5} }^{3} = \frac{64}{125}$
5) 3² × 3³ = 9 x 27 = 243

6)
${7}^{5} \div {7}^{2} = {7}^{3 } = 343$
7)
$( {1}^{3} )^{4} = 1$
8)
${3}^{3} \div {3}^{5} = {3}^{ - 2} = \frac{1}{9}$

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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 X be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

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

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

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

P(Z ≤ -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 ≤ Z ≤ 2) ≈ 0.95

which means

P(Z ≤ -2 or Z ≥ 2) ≈ 1 - 0.95 = 0.05

The normal distribution is symmetric, so this means

P(Z ≤ -2) ≈ 1/2 × 0.05 = 0.025

which is indeed pretty close to what we found earlier.

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2 years ago

In the diagram, how many angles are supplementary but not adjacent angles with angle 7?

sweet [91]

Answer:

The answer is zero

Step-by-step explanation:

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2 years ago

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Find the area of the circle. Round to the nearest whole number

GuDViN [60]

Hello!

$\mathcal{GIVEN:}$

Diameter of the circle = 12 cm

$\mathcal{TO\:FIND:}$

Area of the Circle

$\mathcal{SOLUTION:}$

A=πr²

Hey! We have the diameter, not the radius.

Don't panic. In order to find the radius, we should divide the diameter by 2.

So, the radius is 6.

Plug it into the formula:

A=π(6)²

A=π(36)

A≈113 cm

Hope it helps!

Good luck and enjoy your day!

-SnowFlake

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2 years ago

-3 5/12 divided 2 please help

finlep [7]

Answer:

on the file:

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2 years ago

Dakota’s parents are creating her practice ballet studio and want to install baseboards around the perimeter of the rectangular

kherson [118]

1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet

2. 3ft 8in = 3 8/12 or reduced to 3 2/3 12ft 3in = 12 3/12 or reduced to 12 1/4 The fractional part is referring to a fraction of a foot.

3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3 P= 31 5/6 feet

4. The estimate and the actual are very close. They are 1/6 of a foot apart.

5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.

5b. Take the total and divide it by 8ft = 29 7/12 divided by 8= 3.7 You are not buying a fraction of a board so you would need 4 boards.

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2 years ago