Answer and Step-by-step explanation: P(X) calculated by the binomial probability formula is:
P(X) = ![\left[\begin{array}{ccc}n\\X\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dn%5C%5CX%5Cend%7Barray%7D%5Cright%5D)
.
P(20) = ![\left[\begin{array}{ccc}53\\20\end{array}\right] .(0.3)^{20}.(1-0.3)^{33}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D53%5C%5C20%5Cend%7Barray%7D%5Cright%5D%20.%280.3%29%5E%7B20%7D.%281-0.3%29%5E%7B33%7D)
P(20) = 
P(20) = 0.0552
To determine whether the normal distribution can be used to estimate this probability, both n.p and n.(1-p) must be greater than 5:
n . p = 53*0.3 = 15.9
n.(1-p) = 53(1-0.3) = 37.1
Since both ARE greater than 5, normal distribution can be used.
To approximate:
mean = n . p = 15.9
standard deviation = 
= 3.34
Find the z-score:
z = 
= 
z-score = 0.8907
Comparing values:
0.8907 - 0.0552 = 0.8355
<u>Step-by-step explanation:</u>
Use the formula y = A cos (Bx - C) + D where
- A = amplitude
- Period = 2π/B
- Phase Shift = C/B
- D = vertical shift (aka midline)
Given: Max = 8, Min = 2, (1/2)Period = 20 → Period = 40
Amplitude (A) = (Max - Min)/2
= (8 - 2)/2
= 6/2
= 3
Midline (D) = (Max + Min)/2
= (8 + 2)/2
= 10/2
= 5
Period = 2π/B
→ B = 2π/Period
= 2π/40
= π/20
Notice that the Minimum touches the y-axis (not the Max) so there is no phase shift but there is a reflection → C-value = 0 & A-value is negative
Now, let's put it all together:
A = -3, B = π/20, C = 0, D = 5
Answer:
1.8 meters
Step-by-step explanation:
It was easy for me
Answer:
A is the answerbut im just guesting
Answer:
b=7
Step-by-step explanation:
Plug 3 into a since a=3.
2(3)+b=13
Then solve for 2(3)
6+b=13
Now isolate the b, so move the 6 to the other side. (Basically subtract 6 from both sides)
b=13-6
b=7
