Find the length of the segment indicated. Round to the nearest tenth if necessary.
1 answer:
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3x + 4y = - 8
The equation of a line in standard form is Ax + By = C
where A is a positive integer and B, C are integers
Express the line in ' slope- intercept form '
y = mx + c → (m is the slope and c is the y-intercept)
here m = - and c = - 2
hence y = - x - 2 → equation in slope- intercept form
multiply all terms by 4
4y = - 3x - 8
add 3x to both sides
3x + 4y = - 8 → in standard form
Answer:
Step-by-step explanation:
Given that:
population mean = 10
standard deviation = 0.1
sample mean = 9.8 < x > 10.2
The z score can be computed as:
if x > 10.2
z = 2
If x < 9.8
z = -2
The p-value = P (z ≤ 2) + P (z ≥ 2)
The p-value = P (z ≤ 2) + ( 1 - P (z ≥ 2)
p-value = 0.022750 +(1 - 0.97725)
p-value = 0.022750 + 0.022750
p-value = 0.0455
Therefore; the probability of defectives = 4.55%
the probability of acceptable = 1 - the probability of defectives
the probability of acceptable = 1 - 0.0455
the probability of acceptable = 0.9545
the probability of acceptable = 95.45%
4.55% are defective or 95.45% is acceptable.
sampling distribution of proportions:
sample size n=1000
p = 0.0455
The z - score for this distribution at most 5% of the items is;
z = 0.6828
The p-value = P(z ≤ 0.6828)
From the z tables
p-value = 0.7526
Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526
The z - score for this distribution for at least 85% of the items is;
z = −15.86
p-value = P(z ≥ -15.86)
p-value = 1 - P(z < -15.86)
p-value = 1 - 0
p-value = 1
Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1
Answer: Radius = 10 cm and Arc length = 5 cm
Step-by-step explanation:
The area of a sector with radius r and central angle (In radian) is given by :-
Given : A sector of a circle has area and central angle 0.5 radians.
Let r be the radius , then we have
Thus, radius = 10 cm
The length of arc is given by :-
Hence, the length of the arc = 5 cm