Answer:
1. There is a <u><em>1/5</em></u> chance you will get a blue one from both bags.
2. There is a <u><em>3/32</em></u> chance you will get a 1 and then a 2.
3. There is a <u><em>5/12</em></u> chance of rolling a factor of 12 and then an odd number.
Step-by-step explanation:
<u><em>Question 1</em></u>
Add all the marbles together.
3 + 2 = 5
4 + 2 = 6
Make a fraction.
blue/all
Use it on the numbers.
3/5
2/6
Multiply them together.
6/30
Simplify.
1/5
There is a <u><em>1/5</em></u> chance you will get a blue one from both bags.
<u><em>Question 2</em></u>
Add all the numbers together.
There are 8.
Make the two crucial fractions.
ones/all
twos/all
Use them.
3/8
2/8
Multiply them together.
6/64
Simplify.
3/32
There is a <u><em>3/32</em></u> chance you will get a 1 and then a 2.
<u><em>Question 3</em></u>
Find the factors of 12.
1, 2, 3, 4, 6
Make a fraction.
factors/all
Use the fraction.
5/6
Find the odd numbers.
1, 3, 5
Make a fraction.
odd/all
Use the fraction.
3/6
Multiply them together.
15/36
Simplify.
5/12
There is a <u><em>5/12</em></u> chance of rolling a factor of 12 and then an odd number.
Step-by-step explanation:
You have to use logarithms.
1) a = log_3 (1/27) = -log_3 (27) = -3
2) b = log_3 (9 * 3^(1/2)) = log_3 (3 ^ {5/2}) = 5/2
3) c = -log_3 (sqrt3) = -1/2
Answer:
Step-by-step explanation:
You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.
__
<h3>a)</h3>
Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.
__
<h3>c)</h3>
For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...
Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r
We want to find n such that ...
Sn ≥ 1,000,000
1 × (2^n -1)/(2 -1) ≥ 1,000,000
2^n ≥ 1,000,001 . . . . add 1
n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm
n ≥ 19.93
The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.
Coordinates of C ( 3, - 2 ). After the rotation for 90° clockwise new coordinates would be C ` ( - 2, - 3 ).
Answer:
B ) ( x , y ) → ( y, -x ) ; C`( -2, - 3 )
Answer:
-4y-2
Step-by-step explanation:
-4(y+1)+2
-4 times y is -4y
-4 times 1 is -4
-4y-4 plus 2
is 4y-2
