MATHEMATICS COLLEGE

Find the surface area of the triangular prism.5 ft
5 ft
13 ft
4 ft
6 ft

Answers

Answer 1

Answer:

Answer:

234ft²

Step-by-step explanation:

Surface of the triangular prism

= ab+3bh

= (6ft×13ft)+(3×13ft×4ft)

= 78ft²+156ft²

= 234ft²

Hence, the surface area of the given triangular prism is 234ft².

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The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes; mean = 114.15): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the range?

Answers

Answer:

The range will be 103 because 148-45 = 103

Assume that a lost treasure will be in a certain area of the ocean with probability 0.4, and that a search of that area will find the treasure with probability 0.9 if it is there. What is the conditional probability of the treasure being in the area if the area is searched and no treasure is found?

Answers

Answer:

the probability of the treasure being in the area given that no treasure is found is 0.0625 (6.25%)

Step-by-step explanation:

denoting the event N= no treasure is found , then

P(N) = probability that the lost treasure is in the area* probability that the lost treasure is not found in the treasure's area + probability that the lost treasure is not in the area* probability that the lost treasure is not found in other areas = 0.4*0.1 + 0.6*1 = 0.64

P(N) = 0.64

then we can get the conditional probability using the theorem of Bayes . Denoting the event A= the treasure being in the area

P(A/N) = P(A∩N)/P(N) = 0.4*0.1/0.64 = 0.0625 (6.25%)

where

P(A∩N) = probability of the treasure being in the area and no treasure is found

P(A/N) = probability of the treasure being in the area given that no treasure is found

A restaurant in a fast food franchise has determined that the chance a customer will order a soft drink is 0.88. The probability that a customer will order a hamburger is 0.53.
The probability that a customer will order french fries is 0.49.
Complete parts a and b below.
a. If a customer places an order, what is the probability that the order will include a soft drink and no fries, if these two events are independent? (Round to four decimal places as needed.)
The probability is____________.
b. The restaurant has also determined that, if a customer orders a hamburger, the probability the customer will order fries is 0.71.
Determine the probability that the order will include a hamburger and fries. (Round to four decimal places as needed.)
The probability is________

Answers

Answer:

A) P(soft drink, hamburger, no fries) = 0.1912

B) P(fries and hamburger) = 0.3763

Step-by-step explanation:

A) Probability that the order will include a soft drink, a hamburger and no fries is;

P(soft drink, hamburger, no fries) = P(soft drink) x P(hamburger) x P(no French fries)

P(soft drink, hamburger, no fries) = 0.88 x 0.53 x (1 - 0.49) = 0.88 × 0.53 × 0.41 ≈ 0.1912

B) we are told that;

P(fries|hamburger)=0.71

Since P(fries|hamburger) = P(fries and hamburger)/P(hamburger)

Thus;

0.71 = P(fries and hamburger)/0.53

P(fries and hamburger)= 0.71 *0.53

P(fries and hamburger) = 0.3763

Final answer:

Question a's answer is 0.4488 meaning there's a 44.88% chance a customer will order a soft drink and no fries. For question b, the answer is 0.3763 meaning there's a 37.63% chance that an order will include a hamburger and fries.

Explanation:

To calculate probabilities of independent events, you simply multiply the probability of each event happening.

For question a. the probability of ordering a soft drink is given as 0.88, and the probability of ordering fries is given as 0.49. However, we want the probability of ordering a soft drink and not ordering fries, which means we need to take the complement of the fries event (1-0.49) which is 0.51. Multiply the probability of ordering a soft drink (0.88) with the probability of not ordering fries (0.51):

0.88 x 0.51 = 0.4488

Therefore the probability of a customer ordering a soft drink and no fries is 0.4488.

For question b. we are given the conditional probability that a customer will order fries given they have already ordered a hamburger, which is 0.71. To calculate the joint probability of both events (hamburger and fries), we must multiply the conditional probability by the probability of the hamburger event:

0.71 x 0.53 = 0.3763

Therefore the probability of an order including a hamburger and fries is 0.3763.

Learn more about Probability here:

brainly.com/question/22962752

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One cup of popcorn kernels makes four cups of popped corn. There are eight cups of kernels in a bag. How many cups of popped corn will one bag of kernels make?