A student pulls a box of mass 5 kg with a force of
1 answer:
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Answer:
Step-by-step explanation:
Hello!
You have the data on 443 rounds of golf played on the 12th hole.
The variable of interest is:
X: score of one round of golf played on the 12th hole.
To construct the empirical distribution of the discrete variable you have to organize the data from least to highest and count how many times each score was recorded, establishing the absolute frequency for each value of the variable.
a. Check attachment.
fi= absolute frequency
Fi= accumulated absolute frequencies
hi= relative frequency
Hi= accumulated relative frequency
b.
P(X≤4)
This is the probability of the player scoring "4 or less", so it includes the probability of the player scoring 3 and the player scoring 4, symbolically:
P(X≤4)= P(X=3)+P(X=4)= H(4)= 0.136
c.
The expected score of a discrete variable is:
E(X)= [∑(Xi*fi)]/n= 2343/443= 5.29
d.
To calculate the variance of the variable you have to use the following formula:
V(X)= 1/(n-1)*[∑(Xi²*fi)-(∑(Xi*fi)²]/n)] = (1/442)*[12831-(2343²/443)]
V(X)= 0.993
e.
The standard deviation is the square root of the variance:
√V(X)=√0.993= 0.994
I hope it helps!
Answer:
The distance between them after 30 minutes is 6.5 km.
Step-by-step explanation:
Speed =
Sarah's speed = 6 km/hr = 1.6667 m/s
Emily's speed = 10 km/hr = 2.7778 m/s
The measure of angle between their bearings =
After 30 minutes (1800 seconds);
distance = speed x time
Sarah would have covered a distance = 1.6667 x 1800
= 3000 m
= 3 km
Emily would have covered a distance = 2.7778 x 1800
= 5000 m
= 5 km
The distance between them, a, can be determined by applying the cosine rule;
=
+
- 2bcCos A
= +
-2(5000 x 3000) Cos 105
= +
-2(5000 x 3000) x (-0.2588)
= 2.5 x + 9 x
+ 7764000
= 41764000
a =
= 6462.5073
a = 6462.5 m
The distance between them after 30 minutes is 6.5 km.
The dimensions of the rectangle are length 156 m and a width of 65m, and a perimeter P = 442m
<h3>How to find the dimensions of the rectangle?</h3>For a rectangle of length L and width W, the diagonal is:
Here we know that the diagonal is 169m.
And the ratio of the length to the width is 12:5
This means that:
W = (5/12)*L
Replacing all that in the diagonal equation:
So the length is 156 meters, and the width is:
W = (5/12)*156 m = 65m
Finally, the perimeter is:
P = 2*(L + W) = 2*(156 m + 65m) = 442m
If you want to learn more about rectangles:
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