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2 years ago

What is the solution to the system? 5x-y+z=4 x+2y-z=5 2x+3y-3z=5

1 answer:

6 0

Eliminate one variable at a time. We have three equations so we can solve for three variables.

(5x-y+z=4)-5(x+2y-z=5)=-11y+6z=-21

-2(x+2y-z=5)+(2x+3y-3z=5)=-y-z=-5

Now using the two yz equations above to cancel out z

(-11y+6z=-21)+6(-y-z=-5)=-17y=-51

-17y=-51 divide both sides by -17

y=3, making -y-z=-5 become:

-3-z=-5, z=2, making 5x-y+z=4 become:

5x-3+2=4

5x-1=4

5x=5

x=1

So the solution to the system of equations, (x,y,z) is (1,3,2)

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Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round y

tino4ka555 [31]

Answer:

0.8762 or 87.62%

Step-by-step explanation:

Since our mean is μ=14.3 and our standard deviation is σ=3.7. If we're trying to figure out what percentage is P(10 ≤ x ≤ 26) equal to we must first calculate our z values as such:

$z=\frac{x-\mu}{\sigma}$

Our x value ranges from 10 to 26 therefore let x=10 and we obtain:

$z=\frac{10-14.3}{3.7} =-1.16\\$

If we look at our z-table we find that the probability associated with a z value of -1.16 is 0.1230 meaning 12.30%.

Now let's calculate the z value when x = 26 and so:

$z=\frac{26-14.3}{3.7}=3.16\\$

Similarly, we use the z-table again and find that the probability associated with a z value of 3.16 is 0.9992 meaning 99.92%.

Now we want to find the probability in between 10 and 26 so we will now subtract the upper limit minus the lower limit in P(10 ≤ x ≤ 26) therefore:

0.9992 - 0.1230 = 0.8762

or 87.62%

7 0

2 years ago

The pizza shown has a radius of 12 cm. What is the approximate area of the pizza?

yan [13]

Answer:

Step-by-step explanation:

Area=πr²

area= π(12)²

area=452.4cm²

7 0

2 years ago

The constant of ________ is the value that relates two variables that are directly proportional or inversely proportional.

krok68 [10]

The constant of proportion is the value that relates two variables that are directly proportional or inversely proportional.

Option B is correct!!~

6 0

1 year ago

A bag contains 5 white marbles and 5 blue marbles. You randomly select one marble from the bag and put it back. Then, you random

Schach [20]

1/5 this shows that each can be picked up at Least 1/5 or 2/10

3 0

2 years ago

Read 2 more answers

Choose the correct simplification of a5b6/a4b4

NemiM [27]

The Answer is a b¹⁰

Simplify the following:
(a^5 b^6 b^4)/a^4

Combine powers. (a^5 b^6 b^4)/a^4 = a^(5 - 4) b^(6 + 4):
a^(5 - 4) b^(6 + 4)

5 - 4 = 1:
a b^(6 + 4)

6 + 4 = 10:
Answer: a b^10

6 0

2 years ago