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.
Any smooth curve connecting two points is called an arc. The length of the arc m∠QPR is 2.8334π m.
<h3>What is the Length of an Arc?</h3>
Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
where
θ is the angle, that which arc creates at the centre of the circle in degree.
Given the radius of the circle is 3m, while the angle made by the arc at the centre of the circle is 170°. Therefore,
The length of an arc = 2πr×(θ/360°) = 2π × 3 ×(170/360°) = 2.8334π m
Hence, the length of the arc m∠QPR is 2.8334π m.
Learn more about Length of an Arc:
brainly.com/question/1577784
#SPJ1
Answer: x = 10 y=20
Step-by-step explanation:
You can answer this question by plugging in each equation:
2x=y, x+y=30. Let us plug y as 2x in the second equation x+y=30
x+2x= 30
3x= 30
x=10
After we found x we can then find y by plugging the 10 for x.
2(10) = y
y =20
or you could plug in the other equation
10+y=30
subtract 10 from 30 and we get 20
to double check we can plug in both numbers
2(10) = 20 which is correct
and 10 + 20 = 30 which is correct
Answer:
S.A = 730mm²
Step-by-step explanation:
Since the solid is made up of two rectangles. Then the surface area (S.A) would be
S.A = area of first rectangle + area of second rectangle
Since the first rectangle has it's base to be 25mm and height to be 21mm, then it's area is
25mm x 21mm = 525mm²
Since the second rectangle has it's base to be 41mm and height to be 5mm, then it's area is
41mm x 5mm = 205mm²
Therefore
S.A = 525mm² + 205mm² = 730mm²
