I need help on figuring out the two ways.

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

2 years ago

Why is the end behavior of a quadratic function different from a linear function?

inna [77]

A linear function can’t repeat but a quadratic function can

4 0

2 years ago

The function A(b) relates the area of a trapezoid with a given height of 10 and

Natali [406]

Answer:

$B(a)=\frac{a}{5} -7$

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height $*$ ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 $*$ ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 $*$ ( ( y + 7 ) / 2 ) or $b=\frac{\left(y+7\right)\cdot \:10}{2}$ - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

$y+7=\frac{a}{5}$ ,

$y^{-1}=\frac{a}{5}-7 = B(a)$

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

8 0

2 years ago

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 79.

xxMikexx [17]

<u>Answer:</u>

Price of the adult's ticket = $13

Price of a child's ticket = $ 10

<u>Step-by-step explanation:</u>

Given:

Cost of train fares for Three adults and four children = $79

Cost of train fares Two adults and three children = $ 56

To Find:

Price of the adult's ticket and the price of a child's ticket =?

Solution:

Let the cost of one adult's ticket be x and

Let the cost of one child's ticket be y

Then

Three adults and four children must pay $ 79 be

3x + 4y = 79-----------------------------------------------(1)

Two adults and three children must pay $56

2x + 3y = 56----------------------------------------------(2)

multiply eq(1) by 2, we get

6x + 8y = 158----------------------(3)

multiply eq(2) by 3, we get

6x + 9y = 168----------------------(4)

Subracting (3) from (4)

6x + 9y = 168

6x + 8y = 158

(-) (-) (-)

------------------------------

0x + y = 10

------------------------------

y=10

Now substitute the value of y in eq (1) to get the value of x

3x + 4(10)= 79

3x + 40 = 79

3x = 79 - 40

3x = 39

x = $\frac{39}{3}$

x= 13

3 0

2 years ago

Which is the simplified form of the expression ((p squared) (q Superscript 5 Baseline)) Superscript negative 4 Baseline times ((

oksano4ka [1.4K]

Answer:

1/q^30 (startfraction 1 over q subscript 30 baseline end fraction)

Step-by-step explanation:

just took quiz

5 0

2 years ago

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