Answer:
(a) The population parameter is students who ran the mile in less than 10 minutes.
(b) The hypothesis being tested is:
H0: p = 0.70
Ha: p < 0.70
(c) The significance level is 0.05.
(d) In order to conduct a one-sample proportion z-test, the following conditions should be met:
The data are a simple random sample from the population of interest.
The population is at least 10 times as large as the sample.
n⋅p ≥ 10 and n⋅(1−p) ≥ 10, where n is the sample size and p is the true population proportion.
n⋅p = 756 * 0.70 ≥ 10
n⋅(1−p) = 756 * (1 - 0.70) ≥ 10
All the conditions are met.
(e) p = 504/756 = 0.67
The test statistic, z = (p - p)/√p(1-p)/n = (0.67 - 0.70)/√0.70(1-0.70)/756 = -2.00
(f) The p-value is 0.0228.
(g) Since the p-value (0.0228) is less than the significance level (0.05), we can reject the null hypothesis.
(h) Therefore, we can conclude that less than 70% of students run one mile in less than 10 minutes.
Step-by-step explanation:
Answer:
160 metres per minute
Step-by-step explanation:
800 / 5 = 160
The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
- If the equation of a line is ax + by = k is dilated, with center origin and scale factor k, then the equation of the image of the line is kax + kby = kc
- The line and its image are parallel
- The coordinates of a general point on the image is (kx , ky)
Line L is mapped onto the line T by a dilation centered at the origin and a scale factor of 3.
That means lint T is the image of line L after dilation
∵ The equation of line L is 2x - y = 7
∵ Line L is dilated by scale factor 3 and centered at origin
- That means multiply the equation of line L by 3 to find the
equation of line t
∵ Line T is the image of line L after dilation
∴ The equation of line T is (3)(2x) - (3)(y) = (3)(7)
∴ The equation of line T is 6x - 3y = 21
<em>Very important note:</em>
The equation of line T is the same with equation of line L but multiplied by the scale factor 3 ⇒ L and T are coincide lines (same line)
That means the equation of lines T and L is 2x - y = 7
The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)
Learn more:
You can learn more about dilation in brainly.com/question/2480897
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A= 3.14* 12^2
= 3.14* 144
= 452.16cm^2
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