I don't know any <em><u>slick</u></em> way to do this. I would just list the prime numbers
between 40 and 50 and test them one at a time.
The prime numbers between 40 and 50 are: 41, 43, 47
<u>Test 41:</u>
-- add 1 . . . 42
-- prime factors of 42 . . . 2, 3, 7
-- sum of the factors . . . 12
<u>Test 43:</u>
-- add 1 . . . 44
-- prime factors of 44 . . . 2, 11
-- sum of the factors . . . 13
<u>Test 47:</u>
-- add 1 . . . 48
-- prime factors of 48 . . . 2, 3,
-- sum of the factors . . . 5
Maybe I'm not understanding how to list prime factors, but so far,
I haven't found any number that answers the question.
Maybe if I write the prime factorization of 44 like this:
44 = 2 * 2 * 11
Now the items in the prime factorization do add up to 15.
So the answer would seem to be <em>43.</em>
Answer:
P(S=k) = (1/35)k
8/21
Step-by-step explanation:
P(S=k) is proportional to k
P(S=k) = ck
Total probability is 1
k = 2,3.... 8
Sum of all probabilities =
2c + 3c + 4c + 5c + 6c + 7c + 8c = 1
35c = 1
c = 1/35
P(S=k) = (1/35)k, where k = 2,3,...8
P(1&1):
P(S=2) = 2/35
P(2&2):
P(S=4)/3 = (1/3)(4/35) = 4/105
Because for S=4: (1,3) (2,2) (3,1) and all are equally likely
P(3&3):
P(S=6)/3 = (1/3)(6/35) = 2/35
Because for S=6: (2,4) (3,3) (4,2)
P(4&4):
P(S=8) = 8/35
P(getting doubles = 2/35 + 4/105 + 2/35 + 8/35 = 40/105 = 8/21
The student would have 18 dimes in the bank.. 54 coins. x+2x+3x=54
6x=54
18 dimes,
9 quarters
27 nickles.
we have
<u>Statements</u>
<u>case A)</u> The graph is a straight line.
The statement is True
Because, this is a linear equation (see the attached figure)
<u>case B)</u> The line passes through the origin.
The statement is False
Because the point 
is not a solution of the equation
Verify
Substitute the value of x and y in the equation
------> is not true
the point is not a solution
therefore
The line does not pass through the origin
<u>case C)</u> The line passes through the point 
The statement is True
Because the point is a solution of the equation
Verify
Substitute the value of x and y in the equation
------> is true
the point is a solution
therefore
The line passes through the point
<u>case D) </u>The slope of the line is 
The statement is False
Because, the slope of the line is 
<u>case E)</u> The y-intercept of the line is 
The statement is False
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For 
find the value of y
the y-intercept is equal to 
Answer:
The correct answer is certain with probability equal to 1.
Step-by-step explanation:
Probability is a mathematical framework which helps us to analyze chance of the outcome in a particular experiment. The value of probability is given by the ratio of the possible outcomes favorable to a certain experiment to the total outcomes.
We say an event is certain when the probability is 1 and the probability is zero when the event is uncertain.
Here the experiment is picking a blue card from a bag containing all blue cards.
Possible outcomes are all the cards colored blue in the bag.
Total outcomes are also all the blue cards in the bag.
∴ The value of probability is 1 as the event is certain because if we pick a card from the bag containing only blue cards, it would certainly give us a blue card.
