Answer: in 95% of races, his finishing time will be between 62 and 64 seconds.
Step-by-step explanation:
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 63 seconds and the standard deviation is 5 seconds.
2 standard deviations = 2 × 0.5 = 1
63 - 1 = 62 seconds
63 + 1 = 64 seconds
Therefore, in 95% of races, his finishing time will be between 62 and 64 seconds.
Answer:
In triangle QNP and QNM
3.QN=QN[common side]
so triangle QNP and QNM is CONGRUENT by A.A .S axiom.
Answer:
Area = 733 m² (to the nearest meter)
Step-by-step explanation:
<u></u>
<u>Formulae</u>
- Circumference of a circle = 2
r - Area of a circle = r²
(where r is the radius of the circle)
<u>Find the radius</u>
circumference = 96 m
Using the circumference of a circle formula:
⇒ 2r = 96
⇒ r = 96 ÷ 2 = 48
⇒ r = 48 ÷ = 48/
<u>Find the area</u>
radius r = 48/
Using the area of a circle formula:
⇒ A = r²
⇒ A = (48/)²
⇒ A = 2304/
⇒ A = 733.3859778...
⇒ A = 733 m² (to the nearest meter)
Answer:
2x + 4y = 16.
Step-by-step explanation:
14x - 7y = 8
Convert to slope-intercept form:
-7y = -14x + 8
y = 2x - 8/7
The slope is 2 so the line perpendicular to it has a slope of -1/2, so we have:
y = 1/2x + c
This line passes through the point (-2, 5) so:
5 = -1/2* (-2) + c
5 = 1 + c
c = 5 - 1 = 4
So our equation is y = -1/2x + 4.
Convert to standard from
4y = -2x + 16
2x + 4y = 16.
