Answer:
CE = 17
Step-by-step explanation:
∵ m∠D = 90
∵ DK ⊥ CE
∴ m∠KDE = m∠KCD⇒Complement angles to angle CDK
In the two Δ KDE and KCD:
∵ m∠KDE = m∠KCD
∵ m∠DKE = m∠CKD
∵ DK is a common side
∴ Δ KDE is similar to ΔKCD
∴
∵ DE : CD = 5 : 3
∴
∴ KD = 5/3 KC
∵ KE = KC + 8
∵
∴
∴
∴
∴
∴ KC = (8 × 9) ÷ 16 = 4.5
∴ KE = 8 + 4.5 = 12.5
∴ CE = 12.5 + 4.5 = 17
Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
<h3>What is the binomial distribution formula?</h3>
The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:
n = 4, p = 1/5 = 0.2.
The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:
0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
More can be learned about the binomial distribution at brainly.com/question/24863377
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The best way to answer this would be making a graph
For 1 sign it costs 54.50 and he makes 15
For 2 signs it costs 59 and he makes 30
For 3 signs it costs 63.50 and he makes 45
For 4 signs it costs 68 and he makes 60
For 5 signs it costs 72.50 and he makes 75
This means that after 5 signs Larry will be making profit
Find the circumference of the puck using circumference = pi x diameter
Circumference = 3.14 x 3 = 9.42 inches.
For every rotation the puck would travel 9.42 inches.
Now multiply y by 24 rotations:
9.42 x 24 = 226.08 inches.
Answer: 226.08 inches
The scientific notation is 2.3 x 10^3