Given a 13-card bridge hand has been dealt from a standard deck of 52 cards, what is the probability of having exactly 6 hearts

WILL MARK BRAINLEST

Ivenika [448]

Answer:

Part A) The system has one solution

Part B) The solution is the point (4,4)

Step-by-step explanation:

step 1

Find the equation of the line A

we have

(0,6) and (6,3)

Find the slope

m=(3-6)/(6-0)

m=-0.5

Find the equation of the line into slope intercept form

y=mx+b

we have

m=-0.5

b=6 -----> the point (0,6) is the y-intercept

substitute

y=-0.5x+6 ------> equation A

step 2

Find the equation of the line B

we have

(0,0) and (6,6)

Find the slope

m=(6-0)/(6-0)

m=1

Find the equation of the line into slope intercept form

y=mx+b

we have

m=1

b=0 -----> the line represent a direct variation

substitute

y=x ------> equation B

step 3

Find how many solutions does the pair of equations for lines A and B have

we have

y=-0.5x+6 ------> equation A

y=x ------> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both lines

using a graphing tool

There is one point of intersection

therefore

The system has one solution

see the attached figure

step 4

What is the solution to the equations of lines A and B?

we know that

The solution of the system of equations is the intersection point both lines

The intersection point is (4,4)

therefore

The solution is the point (4,4)

so

x=4,y=4

4 0

3 years ago

Dee is at an average speed of 50 miles per hour.Write a linear equation for the relationship that gives the distance y in for mi

Yuliya22 [10]

Answer:

Step-by-step explanation:

6 0

4 years ago

I need the answer to this plzzzz

4vir4ik [10]

Gianna worked for 5 hours
Matthew work for 6 hours

7 0

3 years ago

What is x and y -6x+8y=26

jek_recluse [69]

Answer:

x=-13/3

y=13/4

Step-by-step explanation:

6 0

3 years ago

According to a recent study, 1 in every 10 women has been a victim of domestic abuse at some point in her life. Suppose we have

vitfil [10]

Answer:

The probability that more than 22 of the women sampled have not been the victim of domestic abuse is P=0.537.

Step-by-step explanation:

This problem can be modeled by a binomial random variable.

The probability p can be calculated as the proportion of women that has not been a victim of domestic abuse at some point in her life:

$p=1-\dfrac{X}{n}=1-\dfrac{1}{10}=1-0.1=0.9$

The sample size is n=25.

We want to calculate the probability that more than 22 of the women of the sample have not been victim of domestic abuse.

The probability that exactly k women have not been victim of domestic abuse can be calculated as:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{25}{k} 0.9^{k} 0.1^{25-k}\\\\\\$

Then, the probability that more than 22 of the women sampled have not been the victim of domestic abuse is:

$P(x>22)=P(x=23)+P(x=24)+P(x=25)\\\\\\P(x=23) = \dbinom{25}{23} p^{23}(1-p)^{2}=300*0.089*0.01=0.266\\\\\\P(x=24) = \dbinom{25}{24} p^{24}(1-p)^{1}=25*0.08*0.1=0.199\\\\\\P(x=25) = \dbinom{25}{25} p^{25}(1-p)^{0}=1*0.072*1=0.072\\\\\\\\P(x>22)=0.266+0.199+0.072=0.537$

4 0

3 years ago