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sergeinik [125]
3 years ago
12

The sum of a two digit number and the number obtained by interchanging the digits is 132. If the two digits differ by 2, find th

e number​
Mathematics
1 answer:
damaskus [11]3 years ago
6 0

Answer:

A two-digit number can be written as:

a*10 + b*1

Where a and b are single-digit numbers, and a ≠ 0.

We know that:

"The sum of a two-digit number and the number obtained by interchanging the digits is 132."

then:

a*10 + b*1 + (b*10 + a*1) = 132

And we also know that the digits differ by 2.

then:

a = b + 2

or

a =  b - 2

So let's solve this:

We start with the equation:

a*10 + b*1 + (b*10 + a*1) = 132

(a*10 + a) + (b*10 + b) = 132

a*11 + b*11 = 132

(a + b)*11 = 132

(a + b) = 132/11 = 12

Then:

a + b = 12

And remember that:

a = b + 2

or

a = b - 2

Then if we select the first one, we get:

a + b = 12

(b + 2) + b = 12

2*b + 2 = 12

2*b = 12 -2 = 10

b = 10/2 = 5

b = 5

then a = b + 2= 5 + 2 = 7

The number is 75.

And if we selected:

a = b - 2, we would get the number 57.

Both are valid solutions because we are changing the order of the digits, so is the same:

75 + 57

than

57 + 75.

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Terri and Donna both sell crafts at two different craft shows each weekend. Terri is charged a 5% commission on the amount of mo
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T   = 0.05x + 35

D  = 0.03x + 55

Step-by-step explanation:

i) On the last weekend in November both Terri and Donna earned from sales the amount of x.

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iii) Donna pays the amount D  = 0.03x + 55

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3 years ago
A parallelogram has base (2x - 1) metres and height (4x - 7) metres.
Jobisdone [24]

Answer:

0.4069 ; 1.843

Step-by-step explanation:

Given:

Base of parallelogram, b = (2x - 1)

Height = (4x - 7)

Area = 1

Area of parallelogram = Base * height

Area of parallelogram = (2x - 1) * (4x - 7)

(2x - 1) * (4x - 7) = 1

8x² - 14x - 4x + 7 = 1

8x² - 18x + 7 - 1 = 0

8x² - 18x + 6 = 0

Divide through by 2

4x² - 9x + 3 = 0

Solving the quadratic equation :

Using the formula

-b ± √(b² - 4ac) / 2a

a = 4 ; b = - 9 ; c = 3

Plugging in the values :

-(-9) ± √((-9)² - 4(4)(3)) / 2(4)

9 ± √(81 - 48) / 8

9 ± √33 / 8

(9 ± 5.7445626) / 8

(9 - 5.7445626) / 8) = 0.4069

(9 + 5.7445626) / 8 = 1.843

4 0
3 years ago
A student believes that less than 50% of students at his college receive financial aid. A random sample of 120 students was take
marusya05 [52]

Answer:

p= 0.9995 and we can conclude that students receiving aid is more than 50% according to the sample results in 2% significance level.

Step-by-step explanation:

H_{0}: less than or equal 50% of students at his college receive financial aid

H_{a}: more than 50% of students receive financial aid.

According to the nul hypothesis we assume a normal distribution with proportion 50%.

z-score of sample proportion can be calculated using the formula:

z=\frac{X-M}{\frac{s}{\sqrt{N} } } where

  • X is the sample proportion (0.65)
  • M is the null hypothesis proportion (0.5)
  • s is the standard deviation of the sample (\sqrt{0.5*(1-0.5)})
  • N is the sample size (120)

then z=\frac{0.65-0.50}{\frac{\sqrt{0.25}}{\sqrt{120} } } ≈ 3,29

thus p= 0.9995 and since p<0.02 (2%), we reject the null hypothesis.

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3 years ago
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monitta
The answer would be 49.3
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