24x-12-43x-6 Simplify. Please help!! ASAP!!
2 answers:
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Answer:
(a) The probability that the thickness is less than 3.0 mm is 0.119.
(b) The probability that the thickness is more than 7.0 mm is 0.119.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is 0.762.
Step-by-step explanation:
We are given that thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm.
Let X = <u><em>thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village.</em></u>
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean thickness = 5.0 mm
= standard deviation = 1.7 mm
(a) The probability that the thickness is less than 3.0 mm is given by = P(X < 3.0 mm)
P(X < 3.0 mm) = P( <
) = P(Z < -1.18) = 1 - P(Z
1.18)
= 1 - 0.8810 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(b) The probability that the thickness is more than 7.0 mm is given by = P(X > 7.0 mm)
P(X > 7.0 mm) = P( >
) = P(Z > 1.18) = 1 - P(Z
1.18)
= 1 - 0.8810 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is given by = P(3.0 mm < X < 7.0 mm) = P(X < 7.0 mm) - P(X 3.0 mm)
P(X < 7.0 mm) = P( <
) = P(Z < 1.18) = 0.881
P(X 3.0 mm) = P(
) = P(Z
-1.18) = 1 - P(Z < 1.18)
= 1 - 0.8810 = 0.119
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
Therefore, P(3.0 mm < X < 7.0 mm) = 0.881 - 0.119 = 0.762.
Answer:
Step-by-step explanation:
{4x + y = 3
{x + y - z = 9 ←
{2x + 2y + z = 0 ←
{4x + y = 3
{3x + 3y = 9 >> Combined equation
−¾[4x + y = 3]
{−3x - ¾y = −2¼ >> New Equation
{3x + 3y = 9
_________
2¼y = 6¾
___ ___
2¼ 2¼
[Plug this back into all three equations to get the z-value of −6, and the x-value of 0];
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