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egoroff_w [7]
3 years ago
13

Given the following three arithmetic sequences : 1, 3, ... and 1, 4, ... and 1, 5, ... A number is randomly selected from 1 to 1

000, inclusive. What is the probability that the selected number is not a term of any of the given sequences?
Mathematics
1 answer:
ladessa [460]3 years ago
8 0

Answer:

  0.333

Step-by-step explanation:

The first sequence starts at 1 and has a common difference of 2. It will include every odd number in the range.

__

The second sequence starts at 1 and has a common difference of 3. It will include odd numbers and the even numbers 4, 10, 16, .... That is, all even numbers of the form 6n -2 will be included. The last one corresponds to the largest value of n such that ...

  6n -2 ≤ 1000

  6n ≤ 1002

  n ≤ 167

That is, 167 even numbers will also be excluded.

__

The third sequence starts at 1 and has a common difference of 4. Every number in this sequence is also a number in the first sequence.

__

So the numbers in these sequences include all 500 odd numbers and 167 even numbers, for a total of 667 numbers. The probability that a randomly chosen number is not in one of these sequences is ...

  (1000 -667)/(1000) = 333/1000 = 0.333 . . . . p(not a sequence term)

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The length of the den in Nellie's house is 18 feet. The area of the room is 216 square feet. How wide is the room?
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Tim and Tom are painters. Tim and Tom are painting a crate. Tom paints 10 sq ft per minute. They painted a particular crate in 1
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Tom-------------- >10 sq ft per minute

Tim------------------- >3.5*10=35 sq ft per minute

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Therefore

If Tim and Tom----------------------- > take 1 day----------- > to paint a crate V1

For the crate V2------------- > take 1.5874 days 

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6 0
3 years ago
I am trying to graduate HS please help me out!!!
vichka [17]
1. To solve this exercise, you must apply the formula for calculate the area of a trapezoid, which is shown below:
<span> 
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6 0
3 years ago
Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,
MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

       $=0-0+6$

       $=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

   It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴  x coordinate = $\frac{-(-7)}{2 \times 1} $

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Now substituting to find f(x),

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Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get   $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts  are the points where the parabola crosses the x-axis, which is the height $h(x)=0$. The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$.

Thus Kendra dives out of the water surface at 6 feet from the board.

3 0
2 years ago
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