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Alex
3 years ago
10

What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squ

ared over 6 times x to the fourth power ?
Mathematics
1 answer:
Sonbull [250]3 years ago
6 0
If we convert the given in its mathematical form, we have,

                      (30x⁶/14y⁵)(7y²/6x⁴)
It can be observed that the numerator of the first and the denominator of the second have a common factor of 6x⁴. Also, the denominator of the first and the numerator of the second expression have a common factor of 7y².

                      ((6x⁴)(5x²)/(7y²)(2y³))(7y²/6x⁴)

Cancellation of the common terms will give us an answer of,
  
                               <em>5x²/2y³

</em>
<em />Therefore, the simplified version of the involved operation is 5x²/2y³. <em>
</em>
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A veterinarian weighed a sample of 666 puppies. Here are each of their weights (in kilograms): 1, 2, 7, 7, 10, 151,2,7,7,10,151,
rjkz [21]

Answer:

The standard deviation of the weight, σ, is approximately 4.73 kg

Step-by-step explanation:

The weights of the six puppies are;

x_i = 1, 2, 7, 7, 10, and 15

The number of puppies, n = 6

Therefore, we have;

The mean = μ = ∑x/n = (1 + 2 + 7 + 7 + 10 + 15)/6 = 7

The standard deviation, σ, is given as follows;

\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu  \right )^{2} }{n}}

By substituting, we have;

\sigma =\sqrt{\dfrac{ \left (1-7  \right )^{2} + \left (2-7  \right )^{2} + \left (7-7  \right )^{2} + \left (7-7  \right )^{2} + \left (10-7  \right )^{2} + \left (15-7  \right )^{2} }{6}}

Simplifying gives;

\sigma =\sqrt{\dfrac{ \left (-6  \right )^{2} + \left (-5  \right )^{2} + \left (0  \right )^{2} + \left (0  \right )^{2} + \left (3 \right )^{2} + \left (8  \right )^{2} }{6}} =\sqrt{\dfrac{ 36 + 25 + 0 +0+ 9 + 64 }{6}}

\sigma =\sqrt{\dfrac{ 134 }{6}} = \sqrt{\dfrac{67}{3} } \approx 4.72582

The standard deviation of the weight, σ ≈ 4.73 kg to two decimal places.

4 0
3 years ago
Read 2 more answers
How would you graph the following systems of equations ? <br><br> y= -3x -7<br> x- 2y=-14
andrey2020 [161]
Solve both formulas to y=mx+b (slope intercept formula) where m=slope and b=y-intercept

y=-3/1x+-7

x-2y=-14
-2y=-14-x
y=7+1/2x

Start with the b variable so for problem 1 put a dot on 0,-7 and for problem 2 put a dot on 0,7

Then from -7 for problem 1 depending on whether the slope is negative or positive go down 3 and over right 1 therefore another point for problem one is marked, at 1,-10; for problem 2 up 1 and to the right 2; 2,8

For problem one connect the dots of 0,-7 and 1,-10

For problem two connect the dots of 0,7 and 2,8
7 0
3 years ago
What is the y-intercept of the equation y=6 - 7x
ipn [44]

Answer:

6

Step-by-step explanation:

change it around:

y=-7x+6

6 is the y

Hope this helps plz hit the crown :D

6 0
3 years ago
A question on my test:
Andre45 [30]

Answer:

180degrees

Step-by-step explanation:

Given the expression cos^2x - cos x - 2 = 0

Let P = cos x

P^2 - P - 2 = 0

Factorize

P^2 - 2P + P - 2 =0

P(P-2)+1(P-2) = 0

P-2 = 0 and P + 1 = 0

P = 2 and P = -1

Since P = cos x

cos x = -1

x = arccos(-1)

x = 180degrees

Hence the require angle is 180degrees

8 0
3 years ago
Find the volume of a rectangular prism if the length is 2x, the width is 4x2, and the height is 2x2 + x + 7. Use the formula V =
Wewaii [24]
2x*(4x^2)*(2x^2+x+7)
8x^3*(2x^2+x+7)
16x^5+8x^4+56x^3

Hope this helps :)
7 0
3 years ago
Read 2 more answers
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