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Nataliya [291]
2 years ago
8

Solve for x.

Mathematics
2 answers:
Ostrovityanka [42]2 years ago
3 0

Answer:

C.  3, -7

Step-by-step explanation:

x^2 +4x-21 =0

Factor

What 2 numbers multiply to -21 and add to 4

7*-3 = -21

7-3 = 4

(x+7) (x-3) =0

Using the zero product property

x+7 =0       x-3=0

x+7-7=0-7     x-3+3=0+3

x = -7            x=3

Arada [10]2 years ago
3 0

Answer:

<h2>C. 3, -7</h2>

Step-by-step explanation:

x^2+4x-21=0\\\\x^2+7x-3x-21=0\\\\x(x+7)-3(x+7)=0\\\\(x+7)(x-3)=0\iff x+7=0\ \vee\ x-3=0\\\\x+7=0\qquad\text{subtract 7 from both sides}\\x=-7\\\\x-3=0\qquad\text{add 3 to both sides}\\x=3

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Weary of the low turnout in student elections, a college administration decides to choose an SRS of three students to form an ad
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Answer:

P(ABC) = 0.110592

P(ABC^c) = 0.119808

P(AB^cC) = 0.119808

P(A^cBC) = 0.119808

P(AB^cC^c)  = 0.129792

P(A^cBC^c)  = 0.129792

P(A^cB^cC)  = 0.129792

P(A^cB^cC^c)  = 0.140608

Step-by-step explanation:

Given

P(A) = P(B) = P(C) = 48\%

Convert the probability to decimal

P(A) = P(B) = P(C) = 0.48

Solving (a): P(ABC)

This is calculated as:

P(ABC) = P(A) * P(B) * P(C)

This gives:

P(ABC) = 0.48*0.48*0.48

P(ABC) = 0.110592

Solving (b): P(ABC^c)

This is calculated as:

P(ABC^c) = P(A) * P(B) * P(C^c)

In probability:

P(C^c) = 1 - P(C)

So, we have:

P(ABC^c) = P(A) * P(B) * (1 - P(C))

P(ABC^c) = 0.48 * 0.48 * (1 - 0.48)

P(ABC^c) = 0.48 * 0.48 * 0.52

P(ABC^c) = 0.119808

Solving (c): P(AB^cC)

This is calculated as:

P(AB^cC) = P(A) * P(B^c) * P(C)

P(AB^cC) = P(A) * [1 - P(B)] * P(C)

P(AB^cC) = 0.48 * (1 - 0.48)* 0.48

P(AB^cC) = 0.48 * 0.52* 0.48

P(AB^cC) = 0.119808

Solving (d): P(A^cBC)

This is calculated as:

P(A^cBC) = P(A^c) * P(B) * P(C)

P(A^cBC) = [1-P(A)] *P(B) * P(C)

P(A^cBC) = (1 - 0.48)* 0.48 * 0.48

P(A^cBC) = 0.52* 0.48 * 0.48

P(A^cBC) = 0.119808

Solving (e): P(AB^cC^c)

This is calculated as:

P(AB^cC^c)  = P(A) * P(B^c) * P(C^c)

P(AB^cC^c)  = P(A) * [1-P(B)] * [1-P(C)]

P(AB^cC^c)  = 0.48 * [1-0.48] * [1-0.48]

P(AB^cC^c)  = 0.48 * 0.52*0.52

P(AB^cC^c)  = 0.129792

Solving (f): P(A^cBC^c)

This is calculated as:

P(A^cBC^c)   = P(A^c) * P(B) * P(C^c)

P(A^cBC^c)   = [1-P(A)] * P(B) * [1-P(C)]

P(A^cBC^c)   = [1-0.48] * 0.48 * [1-0.48]

P(A^cBC^c)   = 0.52 * 0.48 * 0.52

P(A^cBC^c)  = 0.129792

Solving (g): P(A^cB^cC)

This is calculated as:

P(A^cB^cC)  = P(A^c) * P(B^c) * P(C)

P(A^cB^cC)  = [1-P(A)] * [1-P(B)] * P(C)

P(A^cB^cC)  = [1-0.48] * [1-0.48] * 0.48

P(A^cB^cC)  = 0.52 * 0.52 * 0.48

P(A^cB^cC)  = 0.129792

Solving (h): P(A^cB^cC^c)

This is calculated as:

P(A^cB^cC^c)  = P(A^c) * P(B^c) * P(C^c)

P(A^cB^cC^c)  = [1-P(A)] * [1-P(B)] * [1-P(C)]

P(A^cB^cC^c)  = [1-0.48] * [1-0.48] * [1-0.48]

P(A^cB^cC^c)  = 0.52*0.52*0.52

P(A^cB^cC^c)  = 0.140608

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Answer:

Step-by-step explanation:

5.

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Answer:

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