Imagine that you are taking a multiple-choice quiz written in Icelandic and must guess randomly. Each question has 4 choices and 1 correct answer. Calculate the probability that you... answer the first question incorrectly. answer the first 2 questions incorrectly. answer the first 5 questions incorrectly. answer at least 1 of the first 5 questions correctly. (Note: Enter each answer as a fraction or as a decimal rounded to the nearest thousandth.)
The probabilities are:
- Answer the first question incorrectly: 0.750
- Answer the first 2 questions incorrectly: 0.5625
- Answer the first 5 questions incorrectly: 0.237
- Answer at least 1 of the first 5 questions correctly: 0.763
1. The probability of answering the first question incorrectly: Since there are 4 choices and only 1 is correct, the probability of choosing an incorrect answer is 3 incorrect choices out of 4 total choices. So, the probability is 3/4 or 0.750.
2. The probability of answering the first 2 questions incorrectly: For each question, the probability of answering incorrectly is 3/4. To find the combined probability, multiply the individual probabilities: (3/4) * (3/4) = 9/16 or 0.5625.
3. The probability of answering the first 5 questions incorrectly: Similarly, the combined probability is (3/4) * (3/4) * (3/4) * (3/4) * (3/4) = 243/1024 or approximately 0.237.
4. The probability of answering at least 1 of the first 5 questions correctly: Instead of calculating the probability of each possible correct scenario, it's easier to calculate the probability of answering all 5 questions incorrectly (which we've already done in step 3) and subtract that from 1. So, the probability is 1 - 0.237 = 0.763 or 763/1000.
So, the probabilities are:
- Answer the first question incorrectly: 0.750
- Answer the first 2 questions incorrectly: 0.5625
- Answer the first 5 questions incorrectly: 0.237
- Answer at least 1 of the first 5 questions correctly: 0.763
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Ava has a collection of 48 fiction books and 22 nonfiction books. She has 18 total books that are signed by their author. There are 40 fiction books
that are unsigned.
Complete the two-way frequency table to show the number of each type of book in Ava's collection.
The required two-way frequency table is given below:
How to solveGiven, the number of fiction books
, number of non-fiction books
, number of signed books
, and number of unsigned fiction books
.
We need to construct the two-way frequency table based on the above information.
The required two-way frequency table is obtained as follows:
Fiction
Non-fiction
Total
Signed
(48-40)=8
(22-12)=10
18
Unsigned
40
(52-40)=12
(70-18)=52
Total
48
22
70
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In a certain county in 2013, it was thought that 50% of men 50 years old or older had never been screened for prostate cancer. Suppose a random sample of 200 of these men shows that 160 of them had never been screened. What is the observed proportion of men who said they had not been screened?
The observed proportion of men who said they had not been screened is 0.8 or 80%.
Proportion calculationThe observed proportion of men who had not been screened can be calculated by dividing the number of men who had not been screened (160) by the total sample size (200):
Observed proportion of yet-to-be-screened men = number of unscreened men/ total sample size.
Observed proportion = 160/200 = 0.8
Therefore, the observed proportion of men who said they had not been screened is 0.8 or 80%.
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The area of a square is defined by, A(x) = x2 - 6x + 9. What is the length of a side of the square?
The length of one side of the square is 3, as solving for "x" in the equation A(x) = x² - 6x + 9 yields (x - 3)² = 0, which has a solution of x = 3.
The area of a square is typically calculated using the formula A = s², where "s" represents the length of one side of the square.
In this problem, we are given the area of the square as A(x) = x² - 6x + 9.
To find the length of one side of the square, we need to solve for "x" in the equation A(x) = x² - 6x + 9.
Setting A(x) equal to zero
x² - 6x + 9 = 0
Factoring the quadratic
(x - 3)² = 0
Expanding the squared term
x - 3 = 0
Solving for "x"
x = 3
Therefore, the length of one side of the square is 3.
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shat is % of 80 = 4 ?
Answer:
5% is the answer I think
Step-by-step explanation:
I hope this helps
Answer:
5
Step-by-step explanation:
Y= 4/80
4/80 * 100/100 = 5/100
Y= 5
Garret had 1/2 of pizza. He split the pizza into 5 equal pieces. What fraction of pizza was left?
Answer:Garret had 1/10 of the pizza left.
Step-by-step explanation:thats good
(1 point) Let T be the linear transformation defined by T(x, y) = (62 - 8y, 2x – 7y,5y, Iz 9x – 3y) . Find its associated matrix A. A=
The associated matrix A of the linear transformation T is:
A =
[ 0 -8 0 62 ]
[ 2 -7 0 0 ]
[ 0 5 0 0 ]
[ 9 -3 1 0 ]
To find the associated matrix A, we need to apply T to the standard basis vectors e1 = (1,0,0,0), e2 = (0,1,0,0), e3 = (0,0,1,0), and e4 = (0,0,0,1), and write the resulting vectors in terms of the standard basis.
T(e1) = (62, 0, 0, 9)
T(e2) = (-8, 2, 5, -3)
T(e3) = (0, 0, 0, 0)
T(e4) = (0, 0, 0, 0)
Thus, the first column of A is T(e1) written in terms of the standard basis, which is (62, 0, 0, 9), the second column is T(e2) written in terms of the standard basis, which is (-8, 2, 5, -3), the third and fourth columns are T(e3) and T(e4) written in terms of the standard basis, which are (0, 0, 0, 0) and (0, 0, 0, 0) respectively.
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