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zvonat [6]
3 years ago
5

The sum of the digits of a two-digit number is 9. If the digits are reversed,the new number is 9 more than the original number.F

ind the original number.
Mathematics
1 answer:
hodyreva [135]3 years ago
4 0

Answer:

45

Step-by-step explanation:

Let the original number be xy where y is unit and x is tens hence original number is 10x+y When reversed, the new number is yz hence 10y+x

We know that the original number plus 9 is the reversed number hence

10x+y+9=10y+x

9y-9x=9 which when simplified we obtain that

y-x=1 equation 1

Originally, we are told that the sum of x and y is 9 hence

y+x=9 equation 2

Solving equation 1, it means y=x+1

Substituting the above into equation 2

x+1+x=9

2x=9-1

2x=8

x=8/2=4

Since y=x+1 then y=4+1=5

Therefore, the original number, xy is 45

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Natasha2012 [34]

Answer:

The other dimension of the sandbox must be (4x+3).

Hope this helps! Have a good day!

6 0
2 years ago
An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What
galina1969 [7]

Answer:

Part A:

The probability that all of the balls selected are white:

P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\      P(A)=\frac{5}{66}=0.075757576

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

P(D_i)=\frac{1}{6} for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}

P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}

P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}

P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}

P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}

P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0

Part A:

The probability that all of the balls selected are white:

P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)

P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\      P(A)=\frac{5}{66}=0.075757576

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find P(D_3|A)

The data required is calculated above:

P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516

7 0
3 years ago
Julianne earned $296 working at a grocery store last week. She earned $8 per hour. How many hours did Julianne work?
hram777 [196]
37 hours
You divide 296 by 8 and then you get your answer


4 0
2 years ago
Read 2 more answers
The legs of a right triangle are 5 and 7 cm long, respectively. What is the length of the hypotenuse? If necessary, round your a
valentinak56 [21]
A squared plus B squared equals C squared, so what you need to do it square 5 and 7. 5 = 25 7 = 48 Then add then and square root your answer. 48 + 25 = 73. 73 square rooted equals an rounded amount of 8.6. SO the answer is D
4 0
3 years ago
A newspaper article states that 90% of drivers in Iowa wear their seatbelt. Suppose we are interested in estimating the proporti
konstantin123 [22]

Answer:

The sample size is  n  = 3457

Step-by-step explanation:

From the we are told that

  The population proportion is  p =  0.90

  The margin of error is  E =  0.01  

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally the sample size is mathematically represented as

       n  =[  \frac{ Z_{\frac{\alpha }{2} }  }{E} ]^2 * p(1-p)

=>  n  =[  \frac{ 1.96  }{0.01} ]^2 * 0.90(1-0.90)

=>   n  = 3457

8 0
3 years ago
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