Answer:
The mean of the distribution is 4.00 and the standard deviation is 2.31
Explanation:
Given
Range = 2 to 10
Type of distribution = uniform distribution
Required
1. Mean
2. Standard Deviation
The mean of uniform distribution is calculated as thus;
[tex]Mean = \frac{1}{2}(a + b)[/tex]
Where b and a are the intervals of the distribution
b = upper bound = 10
a = lower bound = 2
So,
[tex]Mean = \frac{1}{2}(a + b)[/tex]
Substitute 10 for b and 2 for a
[tex]Mean = \frac{1}{2}(2 + 10)[/tex]
[tex]Mean = \frac{1}{2}(12)[/tex]
[tex]Mean = \frac{1}{2} * 12[/tex]
[tex]Mean = 6[/tex]
[tex]Mean = 6.00[/tex] (Approximated to 2 decimal places)
The standard deviation of uniform distribution is calculated as thus;
σ = √σ²
Where σ represents the standard deviation and σ² represents the variance.
Calculate variance
σ² = Var
[tex]Var = \frac{(b-a)^2}{12}[/tex]
Substitute 10 for b and 2 for a
[tex]Var = \frac{(10 - 2)^2}{12}[/tex]
[tex]Var = \frac{8^2}{12}[/tex]
[tex]Var = \frac{64}{12}[/tex]
[tex]Var = 5.33[/tex]
Recall that
σ = √σ² = √Var
Substitute 5.33 for Var
σ = √5.33
σ = 2.309401076758503
σ = 2.31 (Approximated)
Hence, the mean of the distribution is 4.00 and the standard deviation is 2.31
Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function.
The vertical distance from the dock to the boat's mast reaches its highest value of -27cm every 3 seconds. The first time it reaches its highest point is after 1.3 seconds. Its lowest value is -44cm.
Find the formula of the trigonometric function that models the vertical height H between the dock and the boat's mast t seconds after Antonio starts his stopwatch. Define the function using radians.
What is the vertical distance 2.5 seconds after Antonio starts his stopwatch? Round your answer, if necessary, to two decimal places.
Answer:
Formula of the function is found:
[tex]H(t) = 8.5cos(\frac{2\pi}{3}(t-1.3))-35.5[/tex]
For t= 2.5s , vertical distance is:
H(2.5) = +42.38cm , H(2.5) = -42.38cm
Explanation:
General form of trigonometric function H(t) is given by:
[tex]H(t)=Acos(B(t-C))+D[/tex]
Where
A = Amplitude
Period = 3s = 2π/B
B = 2π/3
C = Phase shift = 1.3s
D = Vertical Shift
Find A (Amplitude):
Amplitude = (highest value - lowest value)/2
Amplitude = (-27-(-44))/2
Amplitude = (-27+44)/2
Amplitude = 8.5
Find D (Vertical Shift)
Vertical shift can be found by finding midpoint
Midpoint = (highest value + lowest value)/2
Midpoint = (-27-44)/2
Midpoint = -35.5
Substitute the values of A,B,C,D in the general form of trigonometric function.[tex]H(t)=Acos(B(t-C)) +D[/tex][tex]H(t) = 8.5cos(\frac{2\pi}{3}(t-1.3))-35.5[/tex]
which is the formula of the function
For t = 2.5s[tex]H(2.5)=8.5cos(\frac{2\pi}{3}(2.5-1.3))-35.5 \\H(2.5)= +42.38 {cm} ,H(2.5)=-42.38cm[/tex]
Which is a disaccharide
Answer:
Sucrose
Explanation:
Sucrose is a dissaccharide that is made up of glucose and fructose
The square below has an area of 16+8x+x216+8x+x^2 16+8x+x 2 16, plus, 8, x, plus, x, squared square meters.
