All categories

3 years ago

1.) What is the best approximation of the solution to the system to the nearest integer values?

Mathematics

2 answers:

storchak [24]3 years ago

7 0

For number one, the answer is C. (2,3).

For number two, the answer is (-1, -1).

((Simply find the intersection between the two lines to get your solution.

melisa1 [442]3 years ago

5 0

Part 1) we have

$5x+2y=16$ ------> equation A

$x+3y=12$

$x=12-3y$ ------> equation B

Substitute the equation B in equation A

$5[12-3y]+2y=16$

$60-15y+2y=16$

$13y=44$

$y=44/13=3.38$

Find the value of x

$x=12-3(44/13)=1.85$

the best approximation is the point $(2.3)$

therefore

the answer Part 1) is the option C

$(2.3)$

Part 2) we have

$y=-x-2$ ------> equation A

$y=3x+2$ ------> equation B

equate equation A and equation B

$-x-2=3x+2$

$4x=-4$

$x=-1$

Find the value of y

$y=-(-1)-2=-1$

the solution is the point $(-1,-1)$

therefore

the answer Part 2) is

$(-1,-1)$

You might be interested in

What happens to the volume of a square pyramid if the base dimensions remain the same, but the height is cut to one third of the

Nadya [2.5K]

The volume becomes 1/3 of the original. With a rectangular base, volume of a pyramid is V=(length*width*height)/3. Cutting the height to 1/3 of the original length will make the total volume 1/3 of the original volume.

5 0

3 years ago

Accuracy in taking orders at a drive-through window is important for fast-food chains. Periodically, QSR Magazine publishes "The

pav-90 [236]

Answer:

a) 0.7412 = 74.12% probability that all the three orders will be filled correctly.

b) 0.0009 = 0.09% probability that none of the three will be filled correctly

c) 0.0245 = 2.45% probability that at least one of the three will be filled correctly.

d) 0.9991 = 99.91% probability that at least one of the three will be filled correctly

e) 0.0082 = 0.82% probability that only your order will be filled correctly

Step-by-step explanation:

For each order, there are only two possible outcomes. Either it is filled correctly, or it is not. Orders are independent. This means that we use the binomial probability distribution to solve this question.

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 combinations 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.

The percentage of orders filled correctly at Burger King was approximately 90.5%.

This means that $p = 0.905$

You and 2 friends:

So 3 people in total, which means that $n = 3$

a. What is the probability that all the three orders will be filled correctly?

This is P(X = 3).

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

$P(X = 3) = C_{3,3}.(0.905)^{3}.(0.095)^{0} = 0.7412$

0.7412 = 74.12% probability that all the three orders will be filled correctly.

b. What is the probability that none of the three will be filled correctly?

This is P(X = 0).

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

$P(X = 0) = C_{3,0}.(0.905)^{0}.(0.095)^{3} = 0.0009$

0.0009 = 0.09% probability that none of the three will be filled correctly.

c. What is the probability that one of the three will be filled correctly?

This is P(X = 1).

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

$P(X = 1) = C_{3,1}.(0.905)^{1}.(0.095)^{2} = 0.0245$

0.0245 = 2.45% probability that at least one of the three will be filled correctly.

d. What is the probability that at least one of the three will be filled correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

With what we found in b:

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0009 = 0.9991$

0.9991 = 99.91% probability that at least one of the three will be filled correctly.

e. What is the probability that only your order will be filled correctly?

Yours correctly with 90.5% probability, the other 2 wrong, each with 9.5% probability. So

$p = 0.905*0.095*0.095 = 0.0082$

0.0082 = 0.82% probability that only your order will be filled correctly

7 0

3 years ago

Help please number 4, 5, 6, and 7

FinnZ [79.3K]

Step-by-step explanation:

4. So, total time traveled is calculated by adding travel times in both directions.

From Detroit to Chicago, Charlie flew 300 miles at 150 miles per hour speed. That means that he traveled:

t1 = s / v1

t1 = 300 miles / 150 miles per hour

t1 = 2 hours

Now, let's do the same for the opposite direction. Since it's the same distance, he again flew 300 miles, but the speed this time was 100 miles per hour:

t2 = s / v2

t2 = 300 miles / 100 miles per hour

t2 = 3 hours

So, total time he traveled was t1 + t2 = 2 hours + 3 hours = 5 hours.

For the trip distance we need to add distances in both directions. We already said that the distance is the same, so the total trip distance is 300 miles + 300 miles = 600 miles.

Displacement shows how far are the ending and the starting point. Since Charlie started from Detroit, flew to Chicago, and then came back to Detroit, his ending point is the same as the starting, so the displacement is 0.

We can calculate average speed by dividing total distance with the total travel time. We already found that the total trip distance was 600 miles, and the total travel time was 5 hours. That means that:

v(average) = s(total) / t (total)

v(average) = 600 miles / 5 hours

v (average) = 120 miles per hour

As for the average velocity, we calculate it by dividing displacement by total travel time. Since the displacement was 0, average velocity will also be 0.

5. From the left graph we see that the object went from 0 to 2 meters (it moved 2 meters) in 1 second. That means that its speed was:

v1 = s1 / t1

v1 = 2 meters / 1 second

v1 = 2m/s

From there, it went from 2 to 4 meters (it moved 2 meters) in the next 4 seconds. That means that its speed, during that interval, was:

v2 = s2 / t2

v2 = 2 meters / 4 seconds

v2 = 0.5 m/s

So, our graph will show, for the first second, velocity of 2m/s, and for the next four seconds, the velocity of 0.5 m/s.

6. Again, when calculating speed, we use the equation:

v = s / t

In this case, the distance (s) is 325 miles and the time (t) is 5 hours. So, the speed will be:

v = 325 miles / 5 hours

v = 65 mph

7. Now, we have the same distance (s) of 325 miles ant the speed (v) of 70 mph. We want know how long will the drive take:

t = s / v

t = 325 miles / 70 mph

t = 4.64 hours.

6 0

3 years ago

Mrs carter manages a pizza parlor the average daily cost is 40 $ plus 52 $ to pay each employee it also cost 2$ to make each piz

Shtirlitz [24]

Total costs: 40 + (7*52) + (42*2) = 488

4 0

3 years ago

Find the equation of the line Use exact numbers

GaryK [48]

Your Y intercept is 5
Y= mx + 5
Rises -5 / runs 2.5 so
Y= -2x + 5

8 0

3 years ago