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Alchen [17]
3 years ago
8

Eric has two number cubes each labeled 1 to 6. Eric is going to conduct an experiment by tossing the cubes a total of 180 times.

He will find the product of the two numbers in each roll.
a) How many possible outcomes are there? ____________
b) How many times should Eric toss a product of 12? ____________
c) How many times should Eric toss a product greater than 20? ___________
d) How many times should Eric toss a product less than 10? _________
Mathematics
1 answer:
Lera25 [3.4K]3 years ago
7 0
The possible outcomes are:
1,1~~1,2~~1,3~~1,4~~1,5~~1,6
2,1~~2,2~~2,3~~2,4~~2,5~~2,6
3,1~~3,2~~3,3~~3,4~~3,5~~3,6
4,1~~4,2~~4,3~~4,4~~4,5~~4,6
5,1~~5,2~~5,3~~5,4~~5,5~~5,6
6,1~~6,2~~6,3~~6,4~~6,5~~6,6

The possible products are:
1~~2~~3~~4~~5~~6
2~~4~~6~~8~~10~~12
3~~6~~9~~12~~15~~18
4~~8~~12~~16~~20~~24
5~~10~~15~~20~~25~~30
6~~12~~18~~24~~30~~36


a) There are 36 outcomes.

b) 5/36 * 180 = 25

c) 6/36 * 180 = 30

d) 16/36 * 180 = 80

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8x² - 4 = 28
8x² = 28 + 4
8x² = 32
x² = 32/8
x² = 4
x = <span>±2


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2 years ago
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.8 parts
Alexxandr [17]

Answer:

The value of the test statistic is t = 2.67

Step-by-step explanation:

The null hypothesis is:

H_{0} = 7.8

The alternate hypotesis is:

H_{1} \neq 7.8

Our test statistic is:

t = \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.

In this problem, we have that:

X = 8.2, \mu = 7.8, \sigma = 0.6, n = 16

Then

t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

t = \frac{8.2 - 7.8}{\frac{0.6}{\sqrt{16}}}

t = 2.67

The value of the test statistic is t = 2.67

5 0
3 years ago
The perimeter of a rectangular garden is 108 meters. The length is 6 meters longer than twice the width. Find the dimensions of
faltersainse [42]

The answer is that the width is 16 m

7 0
3 years ago
Work out the volume of the shape​
pashok25 [27]

Answer:

\large\boxed{V=\dfrac{1,421\pi}{3}\ cm^3}

Step-by-step explanation:

We have the cone and the half-sphere.

The formula of a volume of a cone:

V_c=\dfrac{1}{3}\pi r^2H

r - radius

H - height

We have r = 7cm and H = (22-7)cm=15cm. Substitute:

V_c=\dfrac{1}{3}\pi(7^2)(15)=\dfrac{1}{3}\pi(49)(15)=\dfrac{735\pi}{3}\ cm^3

The formula of a volume of a sphere:

V_s=\dfrac{4}{3}\pi R^3

R - radius

Therefore the formula of a volume of a half-sphere:

V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3

We have R = 7cm. Substitute:

V_{hs}=\dfrac{2}{3}\pi(7^3)=\dfrac{2}{3}\pi(343)=\dfrac{686\pi}{3}\ cm^3

The volume of the given shape:

V=V_c+V_{hs}

Substitute:

V=\dfrac{735\pi}{3}+\dfrac{686\pi}{3}=\dfrac{1,421\pi}{3}\ cm^3

7 0
3 years ago
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