Find the area:
A.16
B.64
C.256
D.none of these
Answers
Answer:
64π in²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr²
where r is the radius.
The radius of a circle is half the diameter. For the circle shown, the radius is ...
r = d/2 = (16 in)/2 = 8 in
Then the area is ...
A = π(8 in)² = 64π in²
_____
Often, units are left off, so the appropriate choice might be 64π.
_____
If you want to be technically correct (at the expense of getting your answer marked wrong), you can select "None of the above." That is because none of the offered choices have the correct units: square inches. You may want to discuss this with your teacher.
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Lots of points if answer is serious Point Z on a coordinate grid is at (-1, 3). What are the coordinates of R y=-x (Z)
Answers
Answer:
The probability that a baby born with Down's syndrome is a boy is .
Step-by-step explanation:
The probability of a baby born being a boy (B) or a girl (G) is same, i.e.
P (B) = P (G) = 0.50.
The probability of a boy is born with Down's syndrome is, P (D|B) = p.
The probability of a girl is born with Down's syndrome is, P (D|G) = q.
The law of total probability states that:
Use this law to compute the probability of a baby born with Down's syndrome as follows:
The conditional probability of an event X given that another event Y has already occurred is:
Compute the probability that a baby born with Down's syndrome is a boy as follows:
Thus, the probability that a baby born with Down's syndrome is a boy is .
f(x)= 11x + 10 ; shifts 3 units up.
Answers
The 3 units vertical shift graph of f(x) = 11x + 10 is g(x) = 11x + 13.
What is vertical shift?
A vertical shift is just a change in the y-value of each function. It is literally picking up the entire function or graph and moving the entire thing up or down. If it is moved up, we add to the y-value, if it is moved down, we subtract from the y-value.
A shift of 3 units up, implies adding 3 to the y value.
New function becomes,
Learn more about vertical shift here
#SPJ3
Answer:
f(x)= 11x +10 +3 or 11x +13
Step-by-step explanation:
represents the volume of a solid obtained by rotating a region around y=-1. Evaluate.
Answers
Answer:
V = π (-2 (ln 2)² + 4 ln 2 − 1)
V ≈ 2.55
Step-by-step explanation:
V = π ∫₁² (1 − (ln x)²) dx
V/π = ∫₁² (1 − (ln x)²) dx
V/π = ∫₁² dx − ∫₁² (ln x)² dx
V/π = x |₁² − ∫₁² (ln x)² dx
V/π = 1 − ∫₁² (ln x)² dx
To evaluate the second integral, integrate by parts.
If u = (ln x)², then du = 2 (ln x) / x dx.
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= (ln x)² x − ∫ x (2 (ln x) / x) dx
= x (ln x)² − 2 ∫ ln x dx
Integrate by parts again.
If u = ln x, then du = 1/x dx.
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= x ln x − ∫ x (1/x dx)
= x ln x − ∫ dx
= x ln x − x
Substitute:
∫ (ln x)² dx = x (ln x)² − 2 ∫ ln x dx
∫ (ln x)² dx = x (ln x)² − 2 (x ln x − x)
∫ (ln x)² dx = x (ln x)² − 2x ln x + 2x
Substitute again:
V/π = 1 − ∫₁² (ln x)² dx
V/π = 1 − (x (ln x)² − 2x ln x + 2x) |₁²
V/π = 1 + (-x (ln x)² + 2x ln x − 2x) |₁²
V/π = 1 + (-2 (ln 2)² + 4 ln 2 − 4) − (-1 (ln 1)² + 2 ln 1 − 2)
V/π = 1 − 2 (ln 2)² + 4 ln 2 − 4 + 2
V/π = -2 (ln 2)² + 4 ln 2 − 1
V = π (-2 (ln 2)² + 4 ln 2 − 1)
V ≈ 2.55
Answers
Answer:
(a) The value of P (None) is 0.062.
(b) The value of P(at least one) is 0.938.
(c) The value of P(at most one) is 0.253.
(d) The event is not unusual.
Step-by-step explanation:
Let X = number of households watching the show.
The probability of the random variable x is, P (X) = p = 0.18.
The sample selected for the survey is of size, n = 14
The random variable X follows a Binomial distribution with parameter n = 14 and p = 0.18.
The probability of a Binomial distribution is computed using the formula:
(a)
Compute the probability that none of the households are tuned to CSI: Shoboygan as follows:
Thus, the value of P (None) is 0.062.
(b)
Compute the probability that at least one household is tuned to CSI: Shoboygan as follows:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
Thus, the value of P(at least one) is 0.938.
(c)
Compute the probability that at most one household is tuned to CSI: Shoboygan as follows:
P (X ≤ 1) = P (X = 0) + P (X = 1)
Thus, the value of P(at most one) is 0.253.
(d)
An event that has a very low probability of occurrence is known as an unusual event.
The probability of the event "at most one household is tuned to CSI: Shoboygan" is 0.253.
This probability value is not low.
Hence, the event is not unusual.
50°
60°
709
Х
50°
The value of xis
o, and the value of yis
Answers
Answer:
x = 60°
y = 50°
Step-by-step explanation:
✅x = 180° - (50° + 70°) (sum of interior angles of a triangle theorem)
x = 180° - 120°
x = 60°
✅Based on the exterior angle theorem, the sum of the opposite interior angles of a triangle = the exterior angle.
Therefore,
50° + 60° = x + y
Plug in the value of x
50° + 60° = 60° + y
110° = 60° + y
y = 110° - 60°
y = 50°