NEED THE ANSWER ASAP PLEASE

A system of linear equations is graphed. which ordered pair is the best estimate for the solution to the system?

OLga [1]

Answer:

The answer that gives the best estimate is (1,1)

Step-by-step explanation:

i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y

intercept or $c_{1}$ = -1. Therefore the equation for this line can be written as

y = $m_{1}$ x + $c_{1}$ ⇒ y = $m_{1}$ x - 1 . It can also be seen from this graph that the

line passes through the point (2 , 2). Substituting these values for x and y

respectively we get 2 = 2 $m_{1}$ - 1 ∴ $m_{1}$ = $\frac{3}{2}$ . The equation of the first line

can be written as y = $\frac{3}{2}$ x - 1 ⇒ 2y - 3x = -2

ii) As can be seen on the other line the intercept on the y axis is at (0,2). So

the y intercept or $c_{2}$ = 2. Therefore the equation for this line can be

written as y = $m_{2}$ x + $c_{2}$ ⇒ y = $m_{2}$ x + 2 . It can also be seen from this

graph that the line passes through the point (1 , -1). Substituting these

values for x and y respectively we get 1 = 1 $m_{2}$ + 2 ∴ $m_{2}$ = -1 . The

equation of the second line can be written as y = - x + 2 or x + y = 2

iii) Solving the two equations of the two lines respectively as found in i) and

ii) we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and

when we add this to equation in i) we get 5y = 4 which means that y = 0.8.

If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.

iv) Therefore we get the solution of the two lines, which is the intersection

of the two lines as (1.2, 0.8). So the answer that gives the best estimate

is (1,1)

6 0

3 years ago

Two of the 240 passengers are chosen at random. Find the probability that

hjlf

Step-by-step explanation:

there are in total 240 passengers.

out of these 240, there are 150+30=180 passengers that are in holiday.

and 240-180 = 60 passengers are not.

if we pick one passenger then the probability is 180/240 = 3/4 = 0.75 that he/she is on holiday.

remember : desired "events" over total "events".

i)

now we pick 2 passengers.

the probabilty for the first one to be on holiday is again

3/4 or 0.75.

if that event happens, then we have only 179 passengers out of now 239 to be on holiday.

and to pick one out of that pool to be on holiday is then

179/239 = 0.748953975...

and for both events to happen in one scenario we need to multiply both probabilities (it is an "and" relation, while an addition would be for an "exclusive or" relation).

the probabilty that we pick 2 passengers on holiday is

3/4 × 179/239 = 0.561715481... ≈ 0.5617

we cannot simply square the basic probability of 0.75 (0.75² = 0.5625), because that would mean we pick one passenger, then put him back into the crowd, and then pick a second time (with a chance to pick the same person again). like with rolling a die.

but that is not the scenario as I understand it. it is to pick a passenger, then keep that person singled out and pick a second passenger. hence the difference.

ii)

exactly one of the two is in holiday.

that means

either the first one is on holiday and the second one is not, or the the second one is and the first one is not.

now we model this logic statement in probabilty arithmetic.

please note that after the first pull we need to update the numbers for the remaining pool depending on the result of the first pull.

the total remaining is in both cases 239. but either the remaining people on holiday go down to 179 (and not in holiday stays 60), or the remaining people not on holiday go down to 59 (and on holiday stays 180).

so, the first one is on holiday, and the second one is not :

3/4 × 60/239 (remember : "and" relation)

= 3 × 15/239 = 45/239 = 0.188284519...

the first one is not on holiday, and the second one is :

60/240 × 180/239 = 1/4 × 180/239 = 45/239 =

= 0.188284519...

since there is no overlap of the potential events (there is no event that could be in both cases), this is an exclusive or relation, and we can add the probabilities.

so, the probability for exactly one of the picked passengers to be on holiday is

2×0.188284519... = 0.376569038... ≈ 0.3766

8 0

2 years ago

How would you write this in simplest form 4p-5 (p+6)=

pychu [463]

Answer:

the answer is -p-30

Step-by-step explanation:

first you would distribute -5 to p and 6 = 4p-5p-30

second combine the like terms = -p-30

lastly it cannot be factored down any farther so the answer is just -p-30

7 0

3 years ago

Given the venn diagram, find P(brother and sister)

LUCKY_DIMON [66]

Based on the venn diagram of siblings, the probability of having a brother and sister is c. 0.33.

<h3>What is the probability of brother and sister?</h3>

The probability of having a brother and sister can be found as:

= Number of those with brother and sister / Total number of people in poll

Solving gives:

= 10 / (8 + 10 + 5 + 7)

= 10 / 30

= 0.33

In conclusion, the probability of having a brother and sister is 0.33.

Find out more on Venn diagrams at brainly.com/question/9085273

#SPJ1

6 0

1 year ago

What point in the feasible region maximizes the objective function, 3x + y ≤ 12, x+y ≤5, x ≥0,y ≥0

forsale [732]

Step-by-step explanation:

We have to find the point in the feasible region which maximizes the objective function. To find that point first we need to graph the given inequalities to find the feasible region.

Steps to graph 3x + y ≤ 12:

First we graph 3x + y = 12 then shade the graph for ≤.

plug any value of x say x=0 and x=2 into 3x + y = 12 to find points.

plug x=0

3x + y = 12

3(0) + y = 12

0 + y = 12

y = 12

Hence first point is (0,12)

Similarly plugging x=2 will give y=6

Hence second point is (2,6)

Now graph both points and joint them by a straight line.

test for shading.

plug any test point which is not on the graph of line like (0,0) into original inequality 3x + y ≤ 12:

3(0) + (0) ≤ 12

0 + 0 ≤ 12

0 ≤ 12

Which is true so shading will be in the direction of test point (0,0)

We can repeat same procedure to graph other inequalities.

From graph we see that ABCD is feasible region whose corner points will result into maximum or minimu for objective function.

Since objective function is not given in the question so i will explain the process.

To find the maximum value of objective function we plug each corner point of feasible region into objective function. Whichever point gives maximum value will be the answer

7 0

3 years ago