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igor_vitrenko [27]
3 years ago
11

Compare and contrast qualitative and quantitative observations and give an example of each

Mathematics
1 answer:
Elanso [62]3 years ago
8 0
Think of quantitative observations as the quantity.

Quantitative observations involve measurements, numbers, or things you can count.
Example: The book is 12 inches long.

Qualitative observations are details about something NOT including numbers. Such as describing what it looks like with your senses.
Example: This book is blue.
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Step-by-step explanation:

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3 years ago
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In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b
madam [21]

Answer:

a = 2, b = 3.5

Step-by-step explanation:

Expanding (ax+by)^7 using Binomial expansion, we have that:

(ax+by)^7 =

(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7

= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> a^7 = 128

=> a = \sqrt[7]{128}\\ \\\\a = 2

For the second term:

a^6b = -224

b = \frac{-224}{a^6}

b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5

Therefore, a = 2, b = 3.5

5 0
3 years ago
For the values a = 3.4 and b = 2.6, which are legs of a right triangle, find c, the hypotenuse, to the nearest tenth.
sammy [17]
C^2 = a^2 + b^2
c^2 = 3.4^2 + 2.6^2
c^2 = 11.56 + 6.76
c^2 = 18.32
c = 4.3

answer
c = 4.3
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Solve the following equation: -2|3-4x|=10x
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