Answer:
4
Step-by-step explanation:
The general equation circle is
Where r is the radius
Plug in the equation
Take the sqr root of 16 tocfind the radius
Answer:
The confidence interval has an lower limit of 
and an upper limit of 
, in which 
is the sample proportion and 
is the size of the sample.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
90% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The confidence interval has an lower limit of and an upper limit of , in which is the sample proportion and is the size of the sample.
The width and length of this rectangle are 3 7/12cm and 4 1/12cm respectively.
Hope this helped! ^v^
If you drew the two vectors for the velocity you find a triangle rectangle since the two directions East and North form an angle of 90°. I drew first the vector towards East and second the vector towards North.
Therefore, to get the speed relative to the surface you have to sum the two vectors, which means you can apply the Pythagorean theorem to find the hypotenuse, having the two legs.
h = √(4² + 12²) = √160 = 4√10 = 12.65mph
In order to find the direction, you need to use trigonometry:
- the sine of an angle is given by the ratio between the opposite side divided the hypotenuse;
- the cosine of an angle is given by the ratio between the adjacent side divided by the hypotenuse.
You can use either one, I will show you both:
sinα = O / H
inverting the formula: α = arcsin (O / H) = sin⁻¹ <span>(O / H)
these two forms are equivalent.
Similarly:
cos</span>β = A / H
β = arccos (A / H) = cos⁻¹ <span>(A / H).
Substituting your numbers:
</span>α = sin⁻¹ (12 / 12.65) = <span>sin⁻¹ (0.9486) = 1.25rad
</span>β = cos⁻¹ (4 / 12.65) = cos⁻¹<span> (0.3162) = 1.25rad
As you can see, </span>α = β so you can use either formula.
Your answer will then be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 1.25rad from East towards North.
ATTENTION!
If you drew first the vector towards North and then the one towards East, you get an equivalent triangle, which is rotated by 180° respect to the previous one. This way, what you earlier called Opposite is now Adjacent and vice-versa, but the formulas are still valid.
You will get:
α = sin⁻¹ (4 / 12.65) = <span>sin⁻¹ (0.3162) = 0.32rad
</span>β = cos⁻¹ (12 / 12.65) = cos⁻¹<span> (0.9486) = 0.32rad
And your answer will be: </span><span>the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 0.32rad from North towards East.</span>
Answer:
<h2>Slope = 1/2</h2>
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question the equation is
- 5x + 10y = 20
To find the slope we must first write the equation in the form above
- 5x + 10y = 20
Move - 5x to the right side of the equation
10y = 5x + 20
Divide both sides by 10
We have
Comparing with the general form of equation above
Slope / m = 1/2
Hope this helps you
