Answer:
∠ OMN = 90°
Step-by-step explanation:
The angle between the tangent and the radius of a circle at the point of contact is right, thus
∠ OMN = 90° ( angle between tangent and radius )
Remember that a function composed with its inverse results in the placeholder
aka
(f o f⁻¹)(x)=x
so
(f o f⁻¹)(4)=4
The value of P(R = 3) is 0.2854
<h3>Probability</h3>
Probabilities are used to determine the chances of events.
The given parameters are:
--- the number of slots
. --- the number of red slot
. --- the number of black slot
. --- the number of green slot
<h3>Individual probabilities</h3>
The probability that the ball lands on a red slot is calculated as:
![p = \frac{18}{38}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B18%7D%7B38%7D)
Simplify
![p= \frac{9}{19}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7B9%7D%7B19%7D)
The probability that the ball does not land on a red slot is calculated as:
![q = \frac{18+2}{38}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B18%2B2%7D%7B38%7D)
![q = \frac{20}{38}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B20%7D%7B38%7D)
Simplify
![q = \frac{10}{19}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B10%7D%7B19%7D)
<h3>
Binomial probability</h3>
The value of P(R = 3) is then calculated using the following binomial probability formula
![P(R = r) = ^nC_rp^rq^{n-r}](https://tex.z-dn.net/?f=P%28R%20%3D%20r%29%20%3D%20%5EnC_rp%5Erq%5E%7Bn-r%7D)
Where:
![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
![r = 3](https://tex.z-dn.net/?f=r%20%3D%203)
So, we have:
![P(R = 3) = ^7C_3 \times (9/19)^3 \times (10/19)^{7-3}](https://tex.z-dn.net/?f=P%28R%20%3D%203%29%20%3D%20%5E7C_3%20%5Ctimes%20%289%2F19%29%5E3%20%5Ctimes%20%2810%2F19%29%5E%7B7-3%7D)
![P(R = 3) = 35 \times (9/19)^3 \times (10/19)^4](https://tex.z-dn.net/?f=P%28R%20%3D%203%29%20%3D%2035%20%5Ctimes%20%289%2F19%29%5E3%20%5Ctimes%20%2810%2F19%29%5E4)
![P(R = 3) = 0.2854](https://tex.z-dn.net/?f=P%28R%20%3D%203%29%20%3D%200.2854)
Hence, the value of P(R = 3) is 0.2854
Read more about probabilities at:
brainly.com/question/15246027
Answer: 22 millimeters
Step-by-step explanation:
The radius is the line that connects any part of the circle to its center, while a diameter is the line that cut into two equal halves the circle while passing through the centre.
Thus, Diameter is twice a radius
So, if radius of the circle is 11 millimeters.
Diameter = 2 x radius
= 2 x 11 millimeters
= 22 millimeters
<u>Answer plus step-to-step explanation:</u>
1. Slope formula = Change in y ÷ change in x.
i.e slope(m) =
(Δ means change in)
2. Slope-intercept form is representing equation of a straight line on cartesian plane in the form y = mx + c. <em>Where (m) is the slope of that line and c is the y-intercept.</em>
3. Standard form - is writing numbers in the form of number times ten to power of an exponent. This is also referred to as scientific notation form.
<u>Example:</u>
To write 512 in standard form would be 5.12 × 10²