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Paul [167]
3 years ago
6

I'm doing simplifying expressions with exponents

Mathematics
1 answer:
VladimirAG [237]3 years ago
7 0

Answer:

Expressing a number in a power of 2 means that you have to figure out how many times you should multiply 2 by itself so the product will be that number.

The number is expressed as 2^n

For example:

Express 16 as a power of 2:

To get 16, you have to multiply 2 by 4 times.

2 × 2 × 2 × 2 = 16

16 = 2^4

Then the answer is 2^4

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Two trains leave two different stations 300 km apart; the first starts at noon and the second at 12 15 h. Travelling on parallel
alexgriva [62]

Answer:

See below

Step-by-step explanation:

From noon to 1500  is three hours

  train A    then travels  <u> 3x</u>   where x = speed in km/hr

  train B   only travels for 2.45 hours and covers

                  <u>   2.45 ( x + 15)  </u>        where x + 15 is its speed in km/hr

       these two values sum to the 300 km distance

3x     +     2.45 ( x + 15) = 300

3x + 2.45 x  + 36.75 = 300

x = 48.3 km/hr       x+15= 63.3 km / hr

8 0
2 years ago
Susie has a bag of marbles containing 3 Red, 7 Green, and 10 Blue marbles.
morpeh [17]

Answer:

1) a) 0.0945

b) 0.1062

2) a) 0.0138

b) 0.00081

3) a) 0.00094

b) 0.00083

4) 301.68 cents

5) 0.0056

Step-by-step explanation:

Since there are 3 Red, 7 Green, and 10 Blue marbles.

Total number of marbles N = 20

Probability (Red) = 3/20

Probability (Green) = 7/20

Probability (Blue) = 10/20

1) the probability of picking 5 marbles and getting at least one red marble

A) with replacement

P(at least 1 red of 5)= (3/20 * 17/20 * 17/20 * 17/20 * 17/20) + (3/20 * 3/20 * 17/20 * 17/20 * 17/20) + (3/20 * 3/20 * 3/20 * 17/20 * 17/20)

P(at least 1 red of 5) = 0.0783 +0.0138 + 0.0024 = 0.0945

B) without replacement

P(at least 1 red of 5) = ( 3/20 * 17/19* 16/18 * 15/17 * 14/16) + (3/20 * 2/19 * 17/18 * 16/17 * 15/16) + (3/20 * 2/19 * 1/18 * 17/17 * 16/16)

P(at least 1 red of 5) = 0.0921 + 0.01316 + 0.0009 = 0.1062

2) the probability of picking 6 marbles having 2 of each color

A) with replacement

P( 6, 2 of each) = 3/20 * 3/20 * 7/20 * 7/20 * 10/20 * 10/20

P( 6, 2 of each) = 0.0138

B) without replacement

P( 6, 2 of each) = 3/20 * 2/19 * 7/18 * 6/17 * 10/16 * 9/15

P( 6, 2 of each) = 0.00081

3) Pick 8 marbles: 4 green and 4 blue

A) with replacement

P(8, 4G and 4 B) = 7/20*7/20*7/20*7/20*10/20*10/20*10/20

P(8, 4G and 4 B) = 0.00094

B) without replacement

P(8, 4G and 4 B) = 7/20*6/19*5/18*4/17*10/16*9/15*8/14*7/13 = 0.00083

4) getting at least 6 marbles of the same color

Only Green and Blue marbles are more than 6

P(at least 6 marbles of the same color) = (7/20*6/19*5/18*4/17*3/16*2/15) + (10/20*9/19*8/18*7/17*6/16*5/15)

= 0.00018 + 0.00542

P(at least 6 marbles of the same color) = 0.0056

Cost of 6 .marbles= 6* 50 cents

C = 300 cents

Therefore, You will have to pay

(1 + 0.0056) 300 cent = 301.68 cents to be sure of getting at least 6 marbles of the same color

5) getting at least 6 marbles of the same color

Only Green and Blue marbles are more than 6

P(at least 6 marbles of the same color) = (7/20*6/19*5/18*4/17*3/16*2/15) + (10/20*9/19*8/18*7/17*6/16*5/15)

= 0.00018 + 0.00542

P(at least 6 marbles of the same color) = 0.0056

6 0
3 years ago
A candle is 6 in tall after burning for 1 hour. After 3 hours it is 5 1/2 in tall. Write a linear equation to model the height y
wel

6-x=y it will take 22 hours

4 0
3 years ago
Antonio is a biologist studying life in a pond. He needs to know how deep the water is. He notices a water lily sticking straigh
quester [9]
For this problem we can represent the situation as a rectangle triangle.
 x: depth of water.
 40: Base. "Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot"
 x + 8: Hypotenuse. "He notices water lily sticking straight up from the water, whose blossom is 8 cm above the water's surface." Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot".
 By the Pythagorean theorem we have:
 x ^ 2 + 40 ^ 2 = (x + 8) ^ 2
 Clearing x:
 x ^ 2 + 1600 = x ^ 2 + 16x + 64
 x ^ 2 - x ^ 2 = 16x + 64 - 1600
 0 = 16x -1536
 1536 = 16x
 1536/16 = x
 x = 96
 answer:
 1) x ^ 2 + 40 ^ 2 = (x + 8) ^ 2
 2) the depth of the water is
 x = 96
6 0
3 years ago
Which expression will give the closest estimate to the answer for 1900 × 17
creativ13 [48]
--------------------------------------------32300
8 0
3 years ago
Read 2 more answers
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