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3 years ago

If a+b= -1 then the value of a^3+b^3 - 3ab= ?

Mathematics

1 answer:

Neporo4naja [7]3 years ago

5 0

Answer:

-1

Step-by-step explanation:

$(a + b)^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ ( - 1)^{3} = {a}^{3} + {b}^{3} + 3ab( - 1) \\ - 1 = {a}^{3} + {b}^{3} - 3ab\\ \\ \huge \red{ \boxed{{a}^{3} + {b}^{3} - 3ab = - 1}}$

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In a large population of college-educated adults, the mean IQ is 118 with a standard deviation of 20. Suppose 200 adults from th

cricket20 [7]

Answer: 0.0793

Step-by-step explanation:

Let the IQ of the educated adults be X then;

Assume X follows a normal distribution with mean 118 and standard deviation of 20.

This is a sampling question with sample size, n =200

To find the probability that the sample mean IQ is greater than 120:

P(X > 120) = 1 - P(X < 120)

Standardize the mean IQ using the sampling formula : Z = (X - μ) / σ/sqrt n

Where; X = sample mean IQ; μ =population mean IQ; σ = population standard deviation and n = sample size

Therefore, P(X>120) = 1 - P(Z < (120 - 118)/20/sqrt 200)

= 1 - P(Z< 1.41)

The P(Z<1.41) can then be obtained from the Z tables and the value is 0.9207

Thus; P(X< 120) = 1 - 0.9207

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3 years ago

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3 years ago

Joel is designing a ramp for a bike trick. He draws this diagram. What is the value of x?

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Answer:

x = -1

x = 5

Step-by-step explanation:

Use pythagorean theorem: a² + b² = c²

x² + (2x + 2)² = (2x + 3)²

Since these are quantities, you'll have to make them into quadratic equations.

(2x + 2)(2x + 2) = 4x² + 4x + 4x + 4

(2x + 3)(2x + 3) = 4x² + 6x + 6x + 9

x² + 4x² + 4x + 4x + 4 = 4x² + 6x + 6x + 9

Combine like terms

5x² + 8x + 4 = 4x² + 12x + 9

Move one side to set the equation equal to 0

x² - 4x - 5 = 0

Solve

x² - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x + 1)(x - 5) = 0

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We can check that these are correct by plugging them in for x and seeing if they are equal

For example

(-1)² + (2(-1) + 2)² = (2(-1) + 3)²

1 = 1

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