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kaheart [24]
2 years ago
15

Solve 3x + 5 ⩾ x + 17

Mathematics
1 answer:
Ugo [173]2 years ago
5 0

Answer:

Step-by-step explanation:

Simplifying

3x + 5 = x + 17

Reorder the terms:

5 + 3x = x + 17

Reorder the terms:

5 + 3x = 17 + x

Solving

5 + 3x = 17 + x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

5 + 3x + -1x = 17 + x + -1x

Combine like terms: 3x + -1x = 2x

5 + 2x = 17 + x + -1x

Combine like terms: x + -1x = 0

5 + 2x = 17 + 0

5 + 2x = 17

Add '-5' to each side of the equation.

5 + -5 + 2x = 17 + -5

Combine like terms: 5 + -5 = 0

0 + 2x = 17 + -5

2x = 17 + -5

Combine like terms: 17 + -5 = 12

2x = 12

Divide each side by '2'.

x = 6

Simplifying

x = 6

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Suppose the number of radios in a household has a binomial distribution with parameters n=11 and p=40%. Find the probability of
Ivenika [448]

Answer:

Step-by-step explanation:

The formula for binomial distribution is expressed as

P(x=r) = nCr × q^(n-r) × p^r

From the information given,

n = 11

p = 40% = 40/100 = 0.4

q = 1 - 0.4 = 0.6

x represent the number of radios

a) P( x = 1) or P(x = 9)

P(x = 1) = 11C1 × 0.6^(11-1) × 0.4^1

P(x = 1) = 0.027

P(x = 9) = 11C9 × 0.6^(11-9) × 0.4^9

P(x = 9) = 0.0052

P( x = 1) or P(x = 9) = 0.027 + 0.0052 = 0.0322

b) P(x lesser than or equal to 7) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6)

P(x = 0) = 11C0 × 0.6^(11-0) × 0.4^0 = 0.004

P(x = 1) = 0.027

P(x = 2) = 11C2 × 0.6^(11-2) × 0.4^2 = 0.089

P(x = 3) = 11C3 × 0.6^(11-3) × 0.4^3 = 0.177

P(x = 4) = 11C4 × 0.6^(11-4) × 0.4^4 = 0.24

P(x = 5) = 11C5 × 0.6^(11-5) × 0.4^5 = 0.22

P(x = 6) = 11C6 × 0.6^(11-6) × 0.4^6 = 0.15

P(x = 7) = 11C7 × 0.6^(11-7) × 0.4^7 = 0.15

P(x lesser than or equal to 7) = 0.004 + 0.027 + 0.089 + 0.177 + 0.24 + 0.22 + 0.15 + 0.07 = 0.977

c) P(x greater than or equal to 5) = 1 - P(x lesser than or equal to 4) = 1 - (0.004 + 0.027 + 0.089 + 0.177 + 0.24) = 1 - 0.537 = 0.463

d) P(x lesser than 9) = P(x lesser than or equal to 7) + P(x = 8)

P(x = 8) = 11C8 × 0.6^(11-8) × 0.4^8 = 0.02

P(x lesser than 9) = 0.977 + 0.02 = 0.997

e. P(x greater than 7) = 1 - P(x lesser than or equal to 7) = 1 - 0.977 = 0.023

5 0
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pashok25 [27]

Answer:  g(f(0)) = 2 and  (f ° g)(2) = -3.

Step-by-step explanation:  We are given the following two functions in the form of ordered pairs :

f = {(-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)}

g = {(-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)} .

We are to find g(f(0))  and   (f ° g)(2).

We know that, for any two functions p(x) and q(x), the composition of functions is defined as

(p\circ q)(x)=p(q(x)).

From the given information, we note that

f(0) = 0,  g(0) = 2,  g(2) = 2  and  f(2) = -3.

So, we get

g(f(0))=g(0)=2,\\\\(f\circ g)(2)=f(g(2))=f(2)=-3.

Thus,  g(f(0)) = 2 and  (f ° g)(2) = -3.

8 0
3 years ago
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