Answer:
![P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D%201-%20P%28X%3E8%29%20%3D%201-P%28X%5Cgeq%209%29%3D%201-%5BP%28X%3D9%29%2BP%28X%3D10%29%5D)
And we can find the individual probabilities like this:
And replacing we got:
![P(X\leq 8)=1-[10(0.8)^1 (1-0.8)^{1} + (0.8)^{10}]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D1-%5B10%280.8%29%5E1%20%281-0.8%29%5E%7B1%7D%20%2B%20%280.8%29%5E%7B10%7D%5D)
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by:
Solution to the problem
For this case we want this probability:

And for this case we can use the comlement rule and we got:
![P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D%201-%20P%28X%3E8%29%20%3D%201-P%28X%5Cgeq%209%29%3D%201-%5BP%28X%3D9%29%2BP%28X%3D10%29%5D)
And we can find the individual probabilities like this:
And replacing we got:
![P(X\leq 8)=1-[10(0.8)^9 (1-0.8)^{1} + (0.8)^{10}]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D1-%5B10%280.8%29%5E9%20%281-0.8%29%5E%7B1%7D%20%2B%20%280.8%29%5E%7B10%7D%5D)
Answer:
The 5 in 8523 is 10x greater than the 5 in 9852.
Step-by-step explanation:
Note the place value of the two number's digit 5:
8<u>5</u>23: Hundreds place value.
98<u>5</u>2: Tens place value.
10 x 10 = 100 ∴ The 5 in 8523 (hundreds place value) is 10x greater than the 5 in 9852 (tens place value).
~
Answer:
-8m + 3 - 32n
Step-by-step explanation:
Distributive Property
-8m + 3 - 32n
Solution:
<u>It should be noted:</u>
- Opposite sides of a rhombus are always equal.
- Opposite angles of a rhombus are always equal.
<u>Thus:</u>
- (-y - 10) = 90°
- 3z - 3 = 90°
- 4x - 2 = 90°
<u>Finding x:</u>
- 4x - 2 = 90°
- => 4x = 90 + 2
- => 4x = 92
- => x = 23
<u>Finding y:</u>
- (-y - 10) = 90°
- => -y - 10 = 90°
- => -y = 100
- => y = -100
<u>Finding z:</u>
- 3z - 3 = 90°
- => 3z = 90 + 3
- => 3z = 93
- => z = 31
Isocoleese means that 2 sides and hence 2 angles are same measure
acute means that all 3 angles are less than 90 degrees
We can rule out choice I since acut means less than 90
II is a possibility, but it doesn't best describe it
III. that is true, but it doesn't include the isocileese part
IV. that is true, but doesn't include the acute part
not sure, either III or IV