Nathan has 80 stamps in his collection. He adds 1 stamp to it today. Each day he plans to add twice the number of stamps as the previous day. If he keeps adding stamps at this rate for n days, which recursive function represents the number of stamps he has on any day in the future?
Answers
The recursive function which represents the number of stamps he has on any day in the future is F(n) = 80 + 2ⁿ.
Given that:
Number of stamps that Nathan has in the beginning = 80
He adds 1 stamp to it today.
Each day he plans to add twice the number of stamps as the previous day.
So, the number of stamps will be in the order:
80 + 1, 80 + 2(1), 80 + 2(2(1)), 80 + 2(2(2(1))), ...
That is each day, the added stamps become twice.
On the first day, he added 1, on the second day, he added 2, on the third day, he added 4, ...
So, the recursive function can be written as:
F(n) = 80 + 2ⁿ, where n starts from 0.
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We start with 80 and we add 1 on the first day, 2 on the 2nd, 4 on the 3rd, etc.. Looking at the numbers being added 1 = 202 = 214 = 228 = 2316 = 24...We start with 80 and we add 2n to it where n represents the number of days into the iterationwith n starting at 0 The function that shows how many stamps we have on any given day is DS = 80 + ∑ 2n Where D is the number of days we are into the iteration n=0NOTE: This starts at day 0 which would be S = 80 + 20 = 80 + 1 = 81 stamps Example: To find how many stamps we have on D = 4 we would haveS = 80+20+21+22+23+24 = 80+1+2+4+ 8+16 = 111 stamps
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Answer:
common ratio for the given sequence is 0.1
Step-by-step explanation:
Common ratio(r) defined as the ratio of term to the previous term.
Given the sequence:
0.1, 0.01, 0.001, ...
......
by definition of common difference;
Substitute the given values we have;
Simplify:
Therefore, the common ratio for the given sequence is 0.1
0.1 x 0.1 = 0.01
0.01 x 0.1 = 0.001
common ratio is the ratio of a term to the previous term.
0.1 is the previous term of 0.01
common ratio = 0.01/0.1 = 0.10
common ratio = 0.001/0.01 = 0.10
b. The gardens are similar and congruent.
c. The gardens are congruent, but not similar.
d. The gardens are similar, but not congruent.
Answers
The garden are similar, but not congruent option (D) is correct after applying the concept of similarity.
What is the congruent triangle?
Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
It is given that:
Andy has two rectangular gardens. His smaller garden is 8 feet long and 4 feet wide.
The larger garden is 12 feet long and six feet wide.
As the corresponding dimensions are not same but have in equal ratio or proportions.
Thus, the garden are similar, but not congruent option (D) is correct after applying the concept of the similarity.
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The garden are similar, but not congruent.
Answers
lemon juice = 60% in the bottle
water = 1 liter.
Since lemon juice is 60% and the rest is water. Water is 40% of the bottle.
1 liter of water is equivalent to 40% of the bottle.
1/40% = 2.50 liters amount of total liquid in the water.
2.50 x 60% = 1.5 liters of lemon juice.
0.6x + 0.4x = 2.5
Answers
You start out with (6 + 5 + 2) = 13 marbles in the hat.
You accidentally knock the hat off the table, they all roll out
onto the floor, and you have lost all of your marbles.
You pick them up, put them back in the hat, put the hat back
on the table, and you still have 13 marbles in the hat.
The probability of pulling an orange marble without looking is
(number of orange ones) / (total number of marbles) = 2/13 .
Now there are only 12 marbles left in the hat. If the first draw
was successful, then there's only 1 orange marble left in there.
The probability of pulling that one without looking is
(number of orange ones) / (total number of marbles) = 1/12 .
So the probability of BOTH events happening is
( 2/13 ) x ( 1/12 ) = 2/156 = 1/78 .
That's the answer in fraction form, like the question wants it.
That fraction is roughly equal to 1.28 % .
6 brown marbles
5 blue marbles
2 orange marbles.
Question:-
What is the probability of picking two orange marbles in a row without returning the marbles back to the hat?
Solve:-
First add all the marbles:-
6 + 5 + 2 = 13
13 marbles in total.
Now lets write the 1st probability:-
2 orange
13 together
2nd probability:-
13 - 1 = 12
1 orange (left)
12 total (without putting back)
Hope i helped ya!! xD
B. 6, 6
C. 6, -6
D. -6, -6
Answers
(Z^2 -6z) (-6z+36)
GCF 1st binomial is z
GCF of 2nd binomial is -6
(z-6)(z-6)
Solutions
6,6