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qwelly [4]
2 years ago
9

Five double-digit numbers We have five consecutive positive double-digit integers. If we swap places on the numbers in the large

st number, the sum of the five numbers increases by 1 more than the mean of the original numbers. What is the lowest number?
Mathematics
1 answer:
barxatty [35]2 years ago
3 0

Answer:

  • 33

Step-by-step explanation:

<u>Let the numbers are:</u>

  • x, x + 1, x + 2, x + 3 and x + 4
  • Their sum is 5x + 10
  • Their mean is (5x + 10)/2 = x + 2

If we swap the digits on the largest number, the sum increases by 1 more than x + 2

<u>We are looking for the number x + 4 = ab such that:</u>

  • ba - ab = ab - 2 + 1
  • ba = 2ab - 1
  • 10b + a = 2(10a + b) - 1
  • 10b + a = 20a + 2b - 1
  • 8b = 19a - 1
  • 19a = 8b + 1

<u>By trial method we get the solution:</u>

  • a = 3, b = 7

<u>Since x + 4 = 37, the lowest number is:</u>

  • x = 37 - 4 = 33

<u>Lets verify:</u>

  • 33, 34, 35, 36, 37

<u>The sum is:</u>

  • 5*33 + 10 = 175

<u>The mean is:</u>

  • 35

<u>Change the largest number tp 73 and find the sum again:</u>

  • 175 + (73 - 37) = 175 + 36 = 175 + 35 + 1

The sum has increased by 1 more than 35

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Levart [38]
The correct choice is B 
x is greater than equals to -4.25
8 0
3 years ago
20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability
erik [133]

Answer:

First choice:

               \large\boxed{\large\boxed{5/19}}

Explanation:

<em>The probability that the first is a man's card and the second, a woman's card</em> is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards  in the hat has changed.

In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.

<u>1. Probability that the first is a man's card</u>

  • Number of cards in the hat = 20 (the 20 business card)

  • Number of man's card in the hat: 10

  • Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.

<u />

<u>2. Probability that the second is a woman's card</u>

  • Number of cards in the hat = 19 (there is one less card in the hat)

  • Number of wonan's card in the hat: 10

  • Probability = favorable oucomes / possible outcomes = 10/19.

<u>3. Probability that the first is a man's card and the second, a woman's card</u>

<u />

  • (1/2) × (10/19) = 5/19

That is the first choice.

5 0
3 years ago
Read 2 more answers
Write and solve an equation to find the number n. The difference of three times a number and 4 is -19.
Law Incorporation [45]

Answer:

-5

Step-by-step explanation:

Let n be the unknown number

difference is subtraction

3n -4 = -19

Add 4 to each side

3n-4+4 = -19+4

3n = -15

Divide by 3

3n/3 = -15/3

n = -5

4 0
3 years ago
1. The area of a circle is 60 square units. What is the area of ...
AVprozaik [17]

Multiply the area of the circle by the percentage:

60 square units x 50% = 60 x 0.50 = 30

50% 0f the circle id 30 square units.

3 0
2 years ago
The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
Ann [662]

Answer:

h=30

Step-by-step explanation:

Volume of a cone=1540cm^{3}, Radius=7cm.

The height of a cone=h

When we need to find the height of a cone, we can use the formula of the volume of a cone, which is \frac{1}{3} \pi r^{2} h to find the height of a cone.

1540cm^{3} =\frac{1}{3}\pi r^{2}  h

Put the pi value=22/7 and the value of radius which is 7 cm into the formula.

1540cm^{3}=\frac{1}{3}*\frac{22}{7}  7^{2}h

1540cm^{3} =\frac{154}{3}h

Move \frac{154}{3} to another side. 1540 divided by  \frac{154}{3} to calculate what is the value of h, h is the height of a cone. Like this.

\frac{1540cm^{3} }{\frac{154}{3} } =h

30=h

Rearrange the h.

h=30

I hope you will understand my solution and explanation. If you still cannot get the point, you can ask me anytime! Thank you!

4 0
3 years ago
Read 2 more answers
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