Find the radius of the button

I’m not sure how to solve “system of equations”

natka813 [3]

Hey there! :)

Answer:

(2, -2)

Step-by-step explanation:

-2x + y = -6

4x + 3y = 2

We can begin by setting the first equation equal to y:

-2x + y = -6

Add 2x to both sides:

y = 2x - 6

Plug this equation for y into the second equation:

4x + 3(2x - 6) = 2

Distribute:

4x + 6x - 18 = 2

Combine like terms:

10x = 20

x = 2

Plug the value of 'x' into an equation to solve for 'y':

-2(2) + y = -6

-4 + y = -6

y = -2

Therefore, the solution is (2, -2)

7 0

3 years ago

Write the equation of the line that passes through the points (3,-2) and (5, -1).

steposvetlana [31]

Answer:

hi

Step-by-step explanation:

8 0

2 years ago

1) A family consisting of three persons—A, B, and C—goes to a medical clinic that always has a doctor at each of stations 1, 2,

crimeas [40]

Answer:

Step-by-step explanation:

Let us record the station number 1, 2 or 3 for each family member A, B or C.

I am attaching a table containing total outcomes. Outcomes are presented along rows while the assigned station to each member is written along columns. For ease of understanding, 1 3 2 in the table should be interpreted as family member A being assigned to station 1, member B to station 3 and member C to station number 2, respectively.

From table it is clear that the total outcomes possible are 27.

We know that, probability can be defined as,

$PROBABITILY = \frac{NUMBER\;OF\;DESIRED\;OUTCOMES}{TOTAL\;NUMBER\;OF\;OUTCOMES}$

a) All Members Assigned to the Same Station.

Cases for all members being assigned to same station are as follows:

[1 1 1], [2 2 2], [3 3 3] (outcome number 1, 14 and 27 in the table).

Therefore,

$PROBABILITY\;(Case\;a) = \frac{3}{27}\\\\PROBABILITY\;(Case\;a) = 0.111$

b) At Most Two Members Assigned to the Same Station.

It means that maximum of 2 members can have the same station. Cases for this situation are as follows:

[1 1 2], [1 1 3], [1 2 1], [1 2 2], [1 3 1], [1 3 3], [2 1 1], [2 1 2], [2 2 1], [2 2 3], [2 3 2],

[2 3 3], [3 1 1], [3 1 3], [3 2 2], [3 2 3], [3 3 1], [3 3 2]

(outcome number 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 25 and 26 in the table).

Therefore,

$PROBABILITY\;(Case\;b) = \frac{18}{27}\\\\PROBABILITY\;(Case\;b) = 0.666$

c) All Members Assigned to a Different Station.

For this scenario, we have the following results:

[1 2 3], [1 3 2], [2 1 3], [2 3 1], [3 1 2], [3 2 1] (outcome number 6, 8, 12, 16, 20 and 22 in the table).

Therefore,

$PROBABILITY\;(Case\;c) = \frac{6}{27}\\\\PROBABILITY\;(Case\;c) = 0.222$

3 0

3 years ago

Construct 3 linear equation starting with qiven solution z = 1/3

Andreyy89

Answer:

(a) $9z+2=5$

(b) $21z-11=-4$

(c) $4z=2-2z$

Step-by-step explanation:

We are required to construct 3 linear equations starting with the given solution z = 1/3.

Equation 1

$z=\frac{1}{3}$

Multiply both sides by 9

$9z=\frac{1}{3}\times 9\\9z=3$

Rewrite 3 as 5-2

9z=5-2

Add 2 to both sides

Our first equation is: $9z+2=5$

Equation 2

$z=\frac{1}{3}$

Multiply both sides by 21

$21z=\frac{1}{3}\times 21\\21z=7$

Rewrite 7 as 11-4

21z=11-4

Subtract 11 from both sides

Our second equation is: $21z-11=-4$

Equation 3

$z=\frac{1}{3}$

Multiply both sides by 6

$6z=\frac{1}{3}\times 6\\6z=2$

Rewrite 6z as 4z+2z

4z+2z=2

Subtract 2z from both sides

Our third equation is: $4z=2-2z$

4 0

3 years ago

A machining operation produces bearings with diameters that are normally distributed with mean 3.0005 inches and standard deviat

padilas [110]

Answer:

5%

Step-by-step explanation:

The 68-95-99.7 rule for the Normal distribution is an empirical rule that remind us the percentages of data that falls between the mean ± 1, ± 2 and ± 3 standard deviations.

That is to say, if the mean is m and the standard deviation s, roughly speaking 68% of the data falls between [m-s, m+s], 95% between [m-2s, m+2s] and 99.7% between [m-3s, m+3s].

Since the mean is 3.0005 and the standard deviation is s=0.0010, 2s=0.0020, 95% of the data should fall between [3.0005-0.0020, 3.0005+0.0020] and 5% outside this interval. So around 5% of total production will be scrap.

7 0

3 years ago