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nekit [7.7K]
3 years ago
10

Which expression is equivalent to 1/4(8- 6x + 12 ) ?

Mathematics
1 answer:
Bogdan [553]3 years ago
6 0
-3x/2 + 5 would be equivalent.
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#1. What is 15% of 60?
Sati [7]

Answer:

9

Step-by-step explanation:

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3 years ago
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What point in the feasible region maximizes P for the objective function P = 2x + 3y? Constraints
Bond [772]
<span>Suppose 2x + y = 15 -----eq 1 . x + 3y = 20 -----eq 2. Multiplying eq (1) by 1 and (2) by 2 and subtracting the result We have: 2x + y = 15 and 2x +6y =40.If we subtract, we have y - 6y = 15 - 40. So we have -5y = -25. y is 5. Substiting into eq (1), we have 2x + 5 = 15. 2x = 15-5 =10 Hence X =5.Hence option B is the correct option.</span>
4 0
3 years ago
Among persons donating blood to a clinic, 85% have Rh+ blood (that is, the Rhesus factor is present in their blood.) Six people
Leona [35]

Answer:

a) There is a 62.29% probability that at least one of the five does not have the Rh factor.

b) There is a 22.36% probability that at most four of the six have Rh+ blood.

c) There need to be at least 8 people to have the probability of obtaining blood from at least six Rh+ donors over 0.95.

Step-by-step explanation:

For each person donating blood, there are only two possible outcomes. Either they have Rh+ blood, or they do not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

p = 0.85, n = 6.

a) fine the probability that at least one of the five does not have the Rh factor.

Either all six have the factor, or at least one of them do not. The sum of the probabilities of these events is decimal 1. So:

P(X < 6) + P(X = 6) = 1

P(X < 6) = 1 - P(X = 6)

In which:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} = 0.3771

So

P(X < 6) = 1 - P(X = 6) = 1 - 0.3771 = 0.6229

There is a 62.29% probability that at least one of the five does not have the Rh factor.

b) find the probability that at most four of the six have Rh+ blood.

Either more than four have Rh+ blood, or at most four have. So

P(X \leq 4) + P(X > 4) = 1

P(X \leq 4) = 1 - P(X > 4)

In which

P(X > 4) = P(X = 5) + P(X = 6)

P(X = 5) = C_{6,5}.(0.85)^{5}.(0.15)^{1} = 0.3993

P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} = 0.3771

P(X > 4) = P(X = 5) + P(X = 6) = 0.3993 + 0.3771 = 0.7764

P(X \leq 4) = 1 - P(X > 4) = 1 - 0.7764 = 0.2236

There is a 22.36% probability that at most four of the six have Rh+ blood.

c) The clinic needs six Rh+ donors on a certain day. How many people must donate blood to have the probability of obtaining blood from at least six Rh+ donors over 0.95?

With 6 donors:

P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} = 0.3771

37.71% probability of obtaining blood from at least six Rh+ donors over 0.95.

With 7 donors:

P(X = 6) = C_{7,6}.(0.85)^{6}.(0.15)^{1} = 0.3960

0.3771 + 0.3960 = 0.7764 = 77.64% probability of obtaining blood from at least six Rh+ donors over 0.95.

With 8 donors

P(X = 6) = C_{8,6}.(0.85)^{6}.(0.15)^{2} = 0.2376

0.3771 + 0.3960 + 0.2376 = 1.01 = 101% probability of obtaining blood from at least six Rh+ donors over 0.95.

There need to be at least 8 people to have the probability of obtaining blood from at least six Rh+ donors over 0.95.

5 0
3 years ago
Celeste wants to have a haircut and permed and also go to lunch. she knows she will need $77. the perm will cost twice as much a
Elza [17]
$48 is the cost of the perm
4 0
2 years ago
Given f(x)=1/x+5 and g(x)=x-2
vladimir1956 [14]

For this case we have the following functions:

f (x) = \frac {1} {x + 5}\\g (x) = x-2

We must find f (g (x)). So:

f (g (x)) = \frac {1} {(x-2) +5} = \frac {1} {x-2 + 5} = \frac {1} {x + 3}

Finally we have to:

f (g (x)) = \frac {1} {x + 3}

For the function to be defined the denominator must be different from 0. That is x different from -3.

Answer:

Option B

3 0
3 years ago
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