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Nastasia [14]
2 years ago
12

Find the constant of variation when t varies directly as the square of s, and t = 64 when S = 4.

Mathematics
1 answer:
UkoKoshka [18]2 years ago
7 0

Answer:

The constant of variation is 4

Step-by-step explanation:

We are looking for the constant of variation when t varies directly as the square of s

t = k s^2  where k is the constant of variation

t = 64 and s = 4

64 = k  4^2

64 = k * 16

Divide each side by 16

64/16 = k * 16/16

4 = k

The constant of variation is 4

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A coordinate system, or ____________________, is used to locate points in a 2-dimensional plane.
andreev551 [17]

Answer:

A coordinate system,or Coordinate plain ,is used to locate points in a 2-dimensional plane.

explanation:

A coordinate plain is formed by the intersection of two lines.One line is vertical and the other is horizontal.The vertical line is called y- axis and the horizontal line is called x-axis. It is two dimensional plane,which means it has length and breadth but no depth.The point where both the lines intersect is called the point of origin.Any point can be located on the coordinate plain by numbers(x,y). These pair of numbers are called coordinates.

It is used to plot points and lines.This system explains algebraic concepts .it has four equal divisions called quadrants namely I ,II,III,IV.

6 0
3 years ago
The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?
Amanda [17]

Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.

First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.

Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:

         1, 3, 5, 7, 9, 11, 13, 15 .

Number of items in the set . . . 8
Sum of all the items in the set . . . 64

Hmmm.  That's interesting.  64 happens to be the square of 8 . 
Do you think that might be all there is to it ?

Let's check it out:

Even-numbered lists of odd numbers:

1, 3                                   Items = 2, Sum = 4
1, 3, 5, 7                           Items = 4, Sum = 16
1, 3, 5, 7, 9, 11                 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .

Amazing !  The sum is always the square of the number of items in the set !

For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.

I slogged through it on my calculator, and it's true.

I never knew this before.  It seems to be something valuable
to keep in my tool-box (and cherish always).


3 0
3 years ago
The weights of 67 randomly selected axles were found to have a variance of 3.85. Construct the 80% confidence interval for the p
VLD [36.1K]

Answer:

3.13

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 67

Variance = 3.85

We have to find 80% confidence interval for the population variance of the weights.

Degree of freedom = 67 - 1 = 66

Level of significance = 0.2

Chi square critical value for lower tail =

\chi^2_{1-\frac{\alpha}{2}}= 51.770

Chi square critical value for upper tail =

\chi^2_{\frac{\alpha}{2}}= 81.085

80% confidence interval:

\dfrac{(n-1)S^2}{\chi^2_{\frac{\alpha}{2}}} < \sigma^2 < \dfrac{(n-1)S^2}{\chi^2_{1-\frac{\alpha}{2}}}

Putting values, we get,

=\dfrac{(67-1)3.85}{81.085} < \sigma^2 < \dfrac{(67-1)3.85}{51.770}\\\\=3.13

Thus, (3.13,4.91) is the required 80% confidence interval for the population variance of the weights.

8 0
3 years ago
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the verbal descriptions with the co
Daniel [21]

Answer:

Step-by-step explanation:

6 more than a number is 36: x+6=36

36 more than a number is 6: x+36=6

6 times a number is 36: 6x=36

4 0
3 years ago
Gene paid a deposit on a leased car. The deposit earns 2.8 percent simple annual interest. At the end of the year, the interest
Lapatulllka [165]

Answer:

it would be <u>800</u> because 2.8% of <u>800</u> is 22.40 and that is your answer.

hope i helped :)

6 0
3 years ago
Read 2 more answers
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