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rosijanka
6 days ago
12

The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers

Mathematics
2 answers:
Inessa [9K]6 days ago
6 0

Greetings!

Let's denote the larger integer as L and the smaller one as s.

The relationship can be expressed as L=s+1

The sum of the integers can be described by the equation L+s=3s-1

Now, substituting L into the second equation allows us to isolate s.

s+1+s=3s-1

Combining like terms results in.

2s+1=3s-1

Subtracting 3s from both sides gives us.

-s+1=-1

Next, we can eliminate 1 from both sides.

-s=-2

Dividing both sides by -1 yields.

s=2

Hence, since these numbers are consecutive, the larger integer must be 3.

Thus, the integers we found are 2 and 3.

I hope this response is useful!


Inessa [9K]6 days ago
4 0

The two integers are 2 and 3n+n+1=3n-1\\\\
2n+1=3n-1\\\\
3n-2n=1+1\\\\
n=2\\
n+1=3

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A parcel delivery company delivered 103,000 packages last year, when its average employment was 84 drivers. This year the firm h
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Answer: 4.85%

Step-by-step explanation: productivity = parcels delivered / count of drivers.

When the parcels delivered totaled 103,000, the average driver count was 84, resulting in productivity of

103,000 / 84 = 1226.19

In the instance when the parcels delivered amounted to 112,800, the mean number of drivers was 96, leading to a productivity of

112,800 / 96 = 1166.67

Consequently, the change in productivity is calculated as 1226.19 - 1166.67 = 59.52.

The initial productivity stands at 1226.19

the final productivity is 1166.67

The percentage change in productivity can be expressed as the change in productivity divided by initial productivity, multiplied by 100

% change in productivity = 59.52 / 1226 * 100

% change in productivity = 4.85%

8 0
3 days ago
There were 567 people at a concert when a band started playing. After each song, only one-third of the people stayed to hear the
Leona [9271]
When formulating the function accurately, it is crucial to properly designate the variables and comprehend the problem's context. Here, we will define y as the number of individuals and x as the number of songs performed.

At x = 0, y = 567
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At x = 2, y = 567 - 567(1/3)(1/3)
At x = 3, y = 567 - 567(1/3)(1/3)(1/3)

Thus, the equation representing the number of individuals remaining after x songs is:

y = 567 - 567(1/3)x
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7 0
9 days ago
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Farmer John walks his pet pig around his barn every day. The barn is 25
Zina [9171]

Answer:

900m

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A=wl

W=25

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4 0
2 days ago
Is the line y = 3x – 7 parallel or perpendicular to 3x + 9y = 9? Explain your answer.
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Y = 3x - 7...the slope here is 3 while the y-intercept is -7

3x + 9y = 9
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4 days ago
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A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly,
PIT_PIT [9117]

Answer:

P(valid) = 1 * 10^{-8}

Step-by-step explanation:

First, we need to calculate how many potential credit card numbers can be created using the digits 0 through 9.

We aim to create a number that consists of 16 digits from a total of 10 digits, therefore:

N = 10^{16}

The total count of possible numbers formed is 10^{16}. However, only 100 million of these are valid (100 * 10^6 = 10^8). Let n represent the valid number of combinations.

This leads us to the probability of selecting a valid number:

P(valid) = n / N

P(valid) = 10^{8} / 10^{16}\\\\P(valid) = 1 * 10^{-8}

8 0
1 month ago
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