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3 years ago

A1=-3;an=an-1+7 what is the explicit rule of this sequence? an=

Mathematics

2 answers:

AlladinOne [14]3 years ago

8 0

Answer:

$a_n=7n-10$

Step-by-step explanation:

If $a_1=-3$ and $a_n=a_{n-1}+7,$ then

$a_2=a_1+7=-3+7=4,\\ \\a_3=a_2+7=4+7=11,\\ \\a_4=a_3+7=11+7=18,...$

So you get the sequence

$-3,\ 4,\ 11,\ 18,\ ...$

This is the arithmetic sequence with $a_1=-3$ and the difference $d=7.$

The explicit formula of this sequence is

$a_n=a_1+(n-1)d,\\ \\a_n=-3+(n-1)\cdot7,\\ \\a_n=-3+7n-7,\\ \\a_n=7n-10.$

miskamm [114]3 years ago

7 0

Answer:

$a_n=7n-10$

Step-by-step explanation:

Without memorizing formulas for arithmetic sequences, it is best to list a first few terms, then realize that a part of each term is proportional to 7n ( a linear function). What remains to determine is the additive term (bias) based on the first value a1:

a1=-3

a2=4

a3=11

a4=18

$a_n=7(n-1)-3=7n-10$

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3 years ago

A Department of Transportation survey showed that 60% of U.S. residents over 65 years of age oppose use of cell phones in flight

Shalnov [3]

Answer:

a) $P(X=12)=(25C12)(0.6)^{12} (1-0.6)^{25-12}=0.0760$

b) $P(X>17) = P(X=18) +....+P(X=25)$

And we can use the following excel code: "=1-BINOM.DIST(17;25,0.6,TRUE)"

And we got:

$P(X>17) = P(X=18) +....+P(X=25)= 0.154$

c) $P(X$

And using the following excel code we got: "=BINOM.DIST(7,25,0.6,TRUE)"

And we got:

$P(X$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

Solution to the problem

Part a

$P(X=12)=(25C12)(0.6)^{12} (1-0.6)^{25-12}=0.0760$

Part b

For this case we want this probability:

$P(X>17) = P(X=18) +....+P(X=25)$

And we can use the following excel code: "=1-BINOM.DIST(17,25,0.6,TRUE)"

And we got:

$P(X>17) = P(X=18) +....+P(X=25)= 0.154$

Part c

For this case we want this probability:

$P(X$

And using the following excel code we got: "=BINOM.DIST(7,25,0.6,TRUE)"

And we got:

$P(X$

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3 years ago

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Juliette [100K]

Answer:

arc axb=4.938

Step-by-step explanation:

to find the measure of arc AXB find angle P first

length of the arc=rФ

in triangle APQ sin angle APQ= opp/hyp=AQ(radius)/PQ=5/√5+√21

in traingle PQB sin angle BPQ= opp/hyp.=5/√5+√21

angle P"

2arcsin 5/√5+√21= 94.324 degrees=(π*94.324)/180=1.64626 rad.

arc AXB=Фr (Ф=94.324 , r=3)

arc axb=4.938

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3 years ago

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Answer:

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Step-by-step explanation:

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The reason for this congruency is that both are right angles and in fact, all right angles are congruent.

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3 years ago

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Let r and s represent the number of times Caleb can ride the roller coaster and watch a show, respectively. The time Caleb needs to allow for each roller coaster ride is (wait time) + (ride time) = (30 +5) min = 35 min. Then we can write the equations
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Adding 25 times the first equation to the second, we get
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4 years ago

A1=-3;an=an-1+7 what is the explicit rule of this sequence? an=​

A1=-3;an=an-1+7 what is the explicit rule of this sequence? an=