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yulyashka [42]
3 years ago
15

The tens digit is twice the units digit. Reverse the digits, add 2 and the new number is 34 less than the original number. Find

the original number.

Mathematics
1 answer:
inna [77]3 years ago
3 0

Answer:

Step-by-step explanation: X and Y represent the digits.

The tens digit is twice the units digit.

The digit in the Tens place has 10× its base value, so we can set up equations to model the information given.

10x +y 10y +x are Original & Reversed numbers

X = 2y means the Tens digits is twice the units digit.

10y + x +2 = 10x +y - 34 models the statement: The reversed number plus two is 34 less than the original number.

Substitute 2y for x to solve for y

10y +2y +2= 10(2y) + y -34

Distribute and combine like terms

12y + 2 = 20y +y - 34

34 +2 = 21y -12y

36 = 9y Divide both sides to find the value of y.

4 = y

X = 2(4) Substitute 4 for y to find x

X = 8

Original number: 84 Reversed number: 48

Substitute into equation model

48 +2= 84 -34

50 = 50

True!

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Answer:

A=\$14,555.17

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

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in this problem we have  

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Answer: (0.465, 5.535)

Step-by-step explanation:

Formula to calculate the confidence interval (<em>when population standard deviation is unknown</em>) is given by :-

\overline{x}\pm t_{\alpha/2} \dfrac{s}{\sqrt{n}}

, where \overline{x} = sample mean.

s= sample standard deviation.

n= Sample size.

t_{\alpha/2} = critical value

By considering the given information , we have

\overline{x}=6

s=0.75

n= 9

Significance level = \alpha=0.1   [1-0.90=0.1]

By using students' t distribution -table , the critical value for 95% confidence level :

t_{\alpha/2 , n-1}=t_{0.1/2,\ 8}=1.86

[Note: degree of freedom = n-1]

Now, the 90% confidence interval for the true mean weight of these Southern California avocados will be :

6\pm (1.86) \dfrac{0.75}{\sqrt{9}}

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6\pm 0.465=(6-0.465,\ 6+0.465)=(0.465,\ 5.535)

Hence, the required confidence interval  =(0.465, 5.535)

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