Answer:
0.128rad/sec
Step-by-step explanation:
Let x represent the between the man and the point on the path
θ = the angle
dx/dt = 4 ft/s
dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight
tan θ = x/20 ft
Cross Multiply
20tan θ = x
dx/dt = 20sec² θ dθ/dt
dθ/dt = 1/20 × cos² θ dx/dt
dθ/dt= 1/20 × cos² θ × 4
dθ/dt = 1/5 × cos² θ
Note : cos θ = 4/5
dθ/dt = 1/5 × (4/5)²
dθ/dt = 16/125
dθ/dt = 0.128rad/sec
Answer:
The hypothesis can be defined as follows:
H₀: The rate of home ownership is 67.4%, i.e. p = 0.674.
Hₐ: The rate of home ownership is more than 67.4%, i.e. p > 0.674.
Step-by-step explanation:
In this case we need to determine whether the city should continue with plan of offering tax breaks to first-time home buyers in order to encourage people to become homeowners.
It is provided that, a few years ago, a census bureau reported that 67.4% of American families owned their homes.
But the Census data reveal that the ownership rate in one small city is much lower.
So, to improvise this the city council wants to offer tax breaks to first-time home buyers in order to encourage people to become homeowners.
They decide to adopt the plan on a 2-year trial basis and use the data they collect to make a decision about continuing the tax breaks.
To determine whether the city council should continue with the plan or not, the hypothesis can be defined as follows:
H₀: The rate of home ownership is 67.4%, i.e. p = 0.674.
Hₐ: The rate of home ownership is more than 67.4%, i.e. p > 0.674.
Mean is the average....so you add all the numbers and then divide by how many numbers there were.
12 + 13 + 15 + 28 + 28 +30 + 42 = 168
since there are 7 numbers, you divide 168 by 7.
168/7 = 24
Therefore, 24 is the mean.
The flag is Japan I believe.
Hope this helps!
Number of boys:
1000/2+20/2=510
Number of girls:
1000/2-20/2=490
510 boys and 490 girls competed at Special Olympics
we have
y > -2
x + y < 4
using a graph tool
see the attached figure
The shaded area is the solution of the system
<u>Part 1) </u>Name an ordered pair that is a solution to this system and explain how you know that this is a solution point
Let
A ( -40,20)
The point A is solution of the system because the point lie on the shaded area
<u>Check</u>
If the point A is solution of the system must satisfy both system inequalities
point A
x=-40
y=20
substitute
y > -2-------> 20 > -2-------> is ok
x + y < 4----> -40+20 < 4-----> -20 < 4-----> is ok
therefore
<u>the answer Part 1) is</u>
The point A is a solution of the system
Part 2) Name an ordered pair that is not a solution to the system and explain how you know that it is not a solution
Let
B(20,20)
The point B is not solution of the system because the point not lie on the shaded area
<u>Check</u>
If the point B is not solution of the system must not satisfy both system inequalities
point B
x=20
y=20
substitute
y > -2 -------> 20 > -2-------> is ok
x + y < 4---->20+20 < 4-----> 40 < 4------> is not ok
therefore
<u>the answer part 2) is</u>
The point B is not a solution to the system
