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3 years ago

1. What is the solution of the system of equations shown below? y = 3x + 7 y = x-9

Mathematics

2 answers:

juin [17]3 years ago

6 0

Answer:

x= -8

y= -17

Step-by-step explanation:

elena55 [62]3 years ago

3 0

Answer:

If you trying to find x and y is the answer is:

x=-8 and y=-17

(-8,-17)

Step-by-step explanation:

First you need to subtract the two equations which becomes 2x+16=0

Now you move the 16 to the other side by subtracting 16 on both sides:

2x=-16

Now divide 2 on both sides to eliminate the 2 on 2x

x=-8

Now that you got -8 as x you can replace x on the two equations any one of them you only need to get one but I am going to use both of them to show you that it is the same:

y= 3(-8)+7

y=-17

y=-8-9

y=-17

Hope this helps!

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3 years ago

On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4 , she doe

Troyanec [42]

Answer:

(a) The value of fₓ (9.5) is 0.125.

(b) The value of fₓ (10.5) is 0.50.

Step-by-step explanation:

Let X denote delivery time of the mail delivered by Alice and Y denote delivery time of the mail delivered by Bob.

It i provided that:

$X\sim U(9, 11)\\Y\sim U(10, 12)$

The probability that Alice delivers the mail is, p = 1/4.

The probability that Bob delivers the mail is, q = 3/4.

The probability density function of a Uniform distribution with parameters [a, b] is:

$f(x)=\left \{ {{\frac{1}{b-a};\ a, b>0} \atop {0;\ otherwise}} \right.$

The probability density function of the delivery time of Alice is:

$f(X_{A})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[9, 11]} \atop {0;\ otherwise}} \right.$

The probability density function of the delivery time of Bob is:

$f(X_{B})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[10, 12]} \atop {0;\ otherwise}} \right.$

(a)

Compute the value of fₓ (9.5) as follows:

For delivery time 9.5, only Alice can do the delivery because Bob delivers the mail in the time interval 10 to 12.

The value of fₓ (9.5) is:

$f_{X}(9.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times0)\\=\frac{1}{8}\\=0.125$

Thus, the value of fₓ (9.5) is 0.125.

(b)

Compute the value of fₓ (10.5) as follows:

For delivery time 10.5, both Alice and Bob can do the delivery because Alice's delivery time is in the interval 9 to 11 and that of Bob's is in the time interval 10 to 12.

The value of fₓ (10.5) is:

$f_{X}(10.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times\frac{1}{2})\\=\frac{1}{8}+\frac{3}{8}\\=0.50$

Thus, the value of fₓ (10.5) is 0.50.

5 0

3 years ago

397 students went on a field trip. Eight

lbvjy [14]

Answer:48

Step-by-step explanation:

Total number of students=397

Students that travelled in a car=29

Let the students that travelled in a bus be represented by y.

Since 8 buses were filled, it will be 8y for total students

8y + 29= 397

8y= 397-29

8y= 368

Divide both side by 8

8y/8=368/8

y = 46

Number of students in each bus is 46

8 0

3 years ago