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Andrej [43]
2 years ago
11

An arithmetic sequence has this recursive formula

Mathematics
2 answers:
ycow [4]2 years ago
7 0

Answer:

\text{The explicit formula is }a_n=7+(n-1)(-4)

Option B is correct.    

Step-by-step explanation:

Given the recursive formula of arithmetic sequence

a_1=7

a_{n}=a_{n-1}-4

we have to find the explicit formula for the above sequence.

a_{n}=a_{n-1}-4

a_{n}-a_{n-1}=-4

which is the common difference, d=-4

The explicit formula for A.P is

a_n=a_1+(n-1)d

a_n=7+(n-1)(-4)

Option B is correct.

OLga [1]2 years ago
6 0
Answer: B
This is because 7 is standing in place for a1 and -4 is standing in place for d in the explicit equation: an=a1+(n-1)d
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A 20-inch diameter bicycle tire rotates 200 times.
fenix001 [56]

Answer: B)1,047 feet

Step-by-step explanation:

Hi, to answer this question, first, we have to calculate the circumference of the tire:

Circumference(C): π x diameter

C = π (20) = 62.83 inches.

Since 1 foot is equal to 12 inches.

62.83 ÷ 12 = 5.23 feet

Finally we have to multiply the result by 200:

5.23 x 200 = 1,047 feet

Feel free to ask for more if needed or if you did not understand something.

8 0
2 years ago
Anita can clean a typical pool in 8 hours. Chao can clean a typical pool in 6 hours. How long should it take Anita and Chao work
ivanzaharov [21]
Anita can clean 1/8 portion of the pool in 1 hour

Chao can clean 1/6 portion of the pool in 1 hour

Both of them working together can clean 1/8 + 1/6 = 7/24 portion of the pool in 1 hour

Therefore, it will take both of the working together 1/(7/24) = 24/7 or 3 3/7 hours to clean a typical pool.
3 0
2 years ago
7.8c + 6p - 3.4c - 10
bija089 [108]

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3 0
2 years ago
A new car is purchased for 20300 dollars. The value of the car depreciates at 9.5% per year. What will the value of the car be,
Iteru [2.4K]
The starting value is 20,300, and the value is decreasing by 9.5% each year.

Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.

A decrease by 9.5% corresponds to multiplying by 91.5% each year.

We write . We plug in 11 years for t.

A(t)=23000(0.915)^{t}\\\\A(11)=23000(0.915)^{11}\\\\A(11)=7671.18

$7,671.18
6 0
2 years ago
A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if
topjm [15]

Answer:

a) The expected value is \frac{-1}{15}

b) The variance is  \frac{49}{45}

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is \binom{10}{2}.

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is \binom{5}{2}. Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is \binom{5}{1}\cdot \binom{5}{1}. So, we define the following probabilities.

Probability of winning: \frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}

Probability of losing \frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing =1.10\cdot  \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing =1.10^2\cdot  \frac{4}{9}+\frac{5}{9}=\frac{82}{75}

We will use the following formula

Var(X) = E(X^2)-E(X)^2

Thus

Var(X) = \frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}

7 0
2 years ago
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