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marishachu [46]
3 years ago
9

Examine the following system of inequalities.

Mathematics
1 answer:
lubasha [3.4K]3 years ago
7 0

Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

y > -x+4 ----> inequality A

The solution of the inequality A is the shaded area above the dotted line y=-x+4

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

y \leq -(1/2)^{x} +6 -----> inequality B

The solution of the inequality B is the shaded area above the solid line y=-(1/2)^{x} +6

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

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What is the measure of angle 7?
umka2103 [35]

Answer:

<7 = 47, 2x - 5 + 47 = 180, x = 69

Step-by-step explanation:

<5 and <7 are vertical angles, which means that they have the same degree.

<7 + <6 = 180. <6 = 2x - 5. 2x - 5 + 47 = 180.

Solve

2x - 5 + 47 = 180

2x + 42 = 180

2x = 138

x = 69

6 0
2 years ago
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In the division problem, what does the 8 represent in the quotient?<br> 3653÷13=281
yan [13]

Answer:

The eight represents a tenth/ten

Step-by-step explanation:

The 2 represents a two hundred, the 8 a eight tenth/eighty and the 1 a one

5 0
3 years ago
What value of x makes this proportion true?
Trava [24]
The answer is 5:) you first have to cross multiply then divide both sides from x
8 0
3 years ago
What makes this a binomial distribution and what is the probability?
kati45 [8]

Answer:

Probability at least one car will get punctured: 0.39347

Step-by-step explanation:

B(10,000 , 0.00005)

P(X ≥ 1) = 1 - P(X = 0)

            = 1 - (1 - 0.00005)^10,000

            = 1 - (0.99995)^10,000

            = 1 - 0.60652...

            = 0.39347 (probability that at least one car will get punctured)

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3 0
3 years ago
Read 2 more answers
A fair die is rolled 12 times. the number of times an even number occurs on the 12 rolls has
bonufazy [111]

Answer:

Step-by-step explanation:

For a fair die, there are six likely options; 1, 2, 3, 4, 5, and 6

the probability of a even number is 3/6 = 0.5

Since the results of the die roll is independent and each trial is mutually exclusive, the distribution to explain the probability of occurrence will follow a binomial distribution such that n is the number of trials

x = number of successful throws

therefore for a Binomial distribution where

P(X =x) = nCx . P^x . (1-P)^ (n-x)

since p = 0.5, and n = 12, the distribution follows

P(X = x) = 12Cx . 0.5^x . (1 - 0.5)^(12- x)

= 12Cx . 0.5^x . 0.5)^(12- x)

where x = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)

since we are interested in the probability of the number of times an even number occurs

it can occur either as P(X = 0), P(X =1), P(X =2), P(X =3), P(X =4), P(X =5), P(X =6), P(X =7), P(X =8), P(X =9), P(X =10), P(X =11), and P(X =12)

For no even number in 12 rolls,

P(X = 0) = 12C0 . 0.5^0 . 0.5^(12- 0) = 0.000244

For one even number in 12 rolls,

P(X = 1) = 12C1 . 0.5^1 . 0.5^(12- 1) = 0.002930

For two even number in 12 rolls,

P(X = 2) = 12C2 . 0.5^2 . 0.5^(12- 2) = 0.016113  

For three even number in 12 rolls,

P(X = 3) = 12C3 . 0.5^3 . 0.5^(12- 3) = 0.053711  

For four even number in 12 rolls,

P(X = 4) = 12C4 . 0.5^4 . 0.5^(12- 4) = 0.120850

For five even number in 12 rolls,

P(X = 5) = 12C5 . 0.5^5 . 0.5^(12- 5) = 0.193359

For six even number in 12 rolls,

P(X = 6) = 12C6 . 0.5^6 . 0.5^(12- 6) = 0.225586

For seven even number in 12 rolls,

P(X = 7) = 12C7 . 0.5^7 . 0.5^(12- 7) = 0.193359

For eight even number in 12 rolls,

P(X = 8) = 12C8 . 0.5^8 . 0.5^(12- 8) = 0.120850

For nine even number in 12 rolls,

P(X = 9) = 12C9 . 0.5^9 . 0.5^(12- 9) = 0.053711

For ten even number in 12 rolls,

P(X = 10) = 12C10 . 0.5^10 . 0.5^(12- 10) = 0.016113

For eleven even number in 12 rolls,

P(X = 11) = 12C11 . 0.5^11 . 0.5^(12- 11) = 0.002930

For twelve even number in 12 rolls,

P(X = 12) = 12C12 . 0.5^12 . 0.5^(12- 12) = 0.000244

Final test summation[P(X)] =  1

i.e.

P(X = 0) + P(X =1) + P(X =2) + P(X =3) + P(X =4) + P(X =5) + P(X =6) + P(X =7) + P(X =8) + P(X =9) + P(X =10) + P(X =11) + P(X =12) = 1

Hence since 0.000244 + 0.002930 + 0.016113 + 0.053711 + 0.120850 + 0.193359 + 0.225586 + 0.193359 + 0.120850 + 0.053711 + 0.016113 + 0.002930 + 0.000244 = 1.000000,

the probability value stands

7 0
3 years ago
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