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Vladimir [108]
3 years ago
8

When 36 is added to a certain two-digit number, the results is the number with the digits reversed. The units' digit is one more

than twice the tens' digit. Find the number​.
Mathematics
1 answer:
AnnZ [28]3 years ago
3 0

Answer:

37

Step-by-step explanation:

T = two digit number

X = first digit

Y = second digit

T = XY where XY are two numbers placed next to eachother rather than multiplied.

36 + XY = YX

The units' digit is one more than twice the tens' digit.

Y = 1 + 2X

Since Y is a 1 digit number it can't be greater than 9.

9 ≥ 1 + 2X

This means X can't be greater than 4.

9 - 1 ≥ 2X

8 ≥ 2X

8/2 ≥ X

4 ≥ X

If X = 1, Y = 3

36 + 13 = 48

If X = 2, Y = 5

36 + 25 = 58

If X = 3, Y = 7

36 + 37 = 73

If X = 4, Y = 9

36 + 49 = 88

37 is the reverse of 73

Therefore the number is 37

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A consumer organization estimates that over a​ 1-year period 20​% of cars will need to be repaired​ once, 5​% will need repairs​
gtnhenbr [62]

Answer:

a) 0.5476

b) 0.0676

c) 0.4524

Step-by-step explanation:

Given this information, we can conclude that 74% of the cars won't need any repairs over a 1-year period (100 - 20 - 5 - 1 = 74%). And 26% will need at least 1 repair over a 1-year period.

P(car doesn't need repair) = 0.74

P (car needs repair) = 0.26

If you own two cars, the probability that:

<u>a) Neither will need repair:</u>

We need that car 1 won't need repair AND car 2 won't need repair.

=P(Car 1 doesn't need repair) x P(Car 2 doesn't need repair)

= 0.74 x 0.74 = 0.5476

The probability that neither will need repair is 0.5476.

<u>b) Both will need repair:</u>

We need that car 1 needs repair AND car 2 needs repair.

P(Car 1 needs repair) x P(Car 2 needs repair)

= 0.26 x 0.26 = 0.0676

The probability that both will need repair is 0.0676

<u>c) At least one car will need repair</u>

Car 1 needs repair or Car 2 needs repair or both need repair.

To solve this one, it's easier to use the complement of P(neither needs repair)

1 - P(neither needs repair)

1 - (0.74)(0.74)  = 1 - 0.5476 = 0.4524

The probability that at least one car will need repair is 0.4524

4 0
3 years ago
A right rectangular prism has a length of 214 cm, width of 8 cm, and height of 2012 cm.
Amiraneli [1.4K]
The volume is 214*8*2012
=3,444,544
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3 years ago
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