Original position: P1=(0,0)
<span>You drive 30 miles due east in a half hour: x=+30 miles, t1=1/2 hour=0.5 hours
</span><span>Then, you turn left and drive 30 miles north in 1 hour: y=+30 miles, t2=1 hour
Rectangular coordinates of final position: P2=(x,y)→P2=(30,30)
Total time: t=t1+t2=0.5 hours+1 hour→t=1.5 hours
Average speed: S ave=d/t
Total distance: d=x+y=30 miles+30 miles→d=60 miles
S ave = 60 miles / (1.5 hours)
S ave = 40 miles/hour
Velocity is a vector, the magnitude of this vector is the magnitude of the vector of change of position dividing by the total time t
The vector of change of position: s=P1-P2=(30,30)-(0,0)=(30-0,30-0)→
s=(30,30)
Magnitude of vector s=sqrt[30^2+30^2]=sqrt[30^2*2]=sqrt[30^2]*sqrt(2)
Magnitude of vector s=30*sqrt(2) miles
Magnitude of velocity vector = Magnitud of vector s / t
Magnitude of velocity vector = [30*sqrt(2) miles] / (1.5 hours)
Magnitude of velocity vector = 20*sqrt(2) miles / hour
Magnitude of velocity vector=20*1.4142 miles / hour
Magnitude of velocity vector=28.284 miles/hour
Polar coordinates of your position=(r, theta)
r=Magnitude of vector s=30*sqrt(2) miles
theta=tan^(-1) (y/x) = tan^(-1) [(30 miles) / (30 miles)]
theta=tan^(-1) (1)→theta=45°=Pi/4 (Pi=3.1416)
Polar coordinates of your position: ( 30*sqrt(2) miles, 45°)
Polar coordinate of your position: ( 30*sqrt(2) miles, Pi/4 )
Answers:
Average speed: 40 miles / hour
Velocity: 20*sqrt(2) miles / hour = 28.284 miles / hour
Rectangular coordinates of your position = (30,30)
Polar coordinates of your position=(30*sqrt(2) miles,45°)
Polar coordinates of your position=(30*sqrt(2) miles,Pi/4)</span>
Answer: For California: μ = 33.1; σ² = 1120.50; Range = 32;
For Iowa: μ = 24.5; σ² = 32.73; Range = 19
Step-by-step explanation:
Mean is the average of a population or a sample. It is defined as
μ = ∑x / n, where
x is each number of the set;
n is the total individuals in the sample.
Calculating the <u>Mean</u> for sample of taste of pizza in <u>California</u>:
μ₁ = 
= 33.1
Calculating the <u>Mean</u> for the sample in Iowa:
μ₂ = 
= 24.5
Variance measures how far the number in the set is from the mean. Its formula is
σ² = (∑x-μ)² / n -1
which means to find the variance, you have to get the difference between the number and the mean, square the result, add all of them and then divide by (n-1) individuals.
The <u>Variance</u> for the sample in <u>California</u> is
σ² = 
σ² = 120.50
The <u>Variance</u> for the sample in <u>Iowa</u> is
σ² = 32.73
Range is the difference between the highest and the lowest number of the set: range = highest - lowest
For the sample in <u>California</u>, the <u>Range</u> is
range = 46 - 14 = 32
For the sample in Iowa:
range = 35 - 16 = 19
For California:
- Mean = 33.1;
- Variance = 120.50;
- Range = 32;
For Iowa:
- Mean = 24.5;
- Variance = 32.73;
- Range = 19;
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Answer:
and they are actual solutions
Step-by-step explanation:
we have
Factor the denominators both sides
Simplify
<u><em>Verify</em></u>
1) For 
---> is true
therefore
----> is an actual solution
2) For 
---> is true
therefore
----> is an actual solution
therefore
Answer:
This problem is incomplete, we do not know the fraction of the students that have a dog and also have a cat. Suppose we write the problem as:
"In Mrs.Hu's classroom, 4/5 of the students have a dog as a pet. X of the students who have a dog as a pet also have cat as a pet. If there are 45 students in her class, how many have both a dog and a cat as pets?"
Where X must be a positive number smaller than one, now we can solve it:
we know that in the class we have 45 students, and 4/5 of those students have dogs, so the number of students that have a dog as a pet is:
N = 45*(4/5) = 36
And we know that X of those 36 students also have a cat, so the number of students that have a dog and a cat is:
M = 36*X
now, we do not have, suppose that the value of X is 1/2 ("1/2 of the students who have a dog also have a cat")
M = 36*(1/2) = 18
So you can replace the value of X in the equation and find the number of students that have a dog and a cat as pets.
Answer:
a
Step-by-step explanation:
