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2 years ago

Find the 61st term of -12, -28, -44,

Mathematics

1 answer:

Citrus2011 [14]2 years ago

6 0

Answer:

$a_{61}=-972$

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

$a_n=a_1+(n-1)r$

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

We are given the first terms of a sequence:

-12, -28, -44,...

Find the common difference by subtracting consecutive terms:

r = -28 - (-12) = -16

r = -44 - (-28) = -16

The first term is a1 = -12. Now we calculate the term n=61:

$a_{61}=-12+(61-1)(-16)$

$a_{61}=-12-60*16=-12-960$

$\mathbf{a_{61}=-972}$

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2. If x=2, y=3 find value of x²-5y+2

Damm [24]

Answer:

-9

Step-by-step explanation:

Substitute the give values into the correct place in the equation.

Since x=2, y=3,

Place "2" in the x of the equation, and "3" into the y of the equation.

x²-5y+2

= 2² - 5(3) + 2

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3 years ago

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Arada [10]

Answer: b<5

Step-by-step explanation:

B Represnts the books and 5 is the 5 dollars so then 5 is greater than b and since 5 dollars is greater than the books price then you should be b<5.

this should be right.

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2 years ago

Two trucks are driving to the same place. The first truck starts 50 miles ahead of the second truck and travels at an average sp

Dominik [7]

Well obviously the two bottom graphs don't represent the two trucks meeting. So we can cross those out. Looking at the top two graphs we can tell that the line above is truck #2. In graph 1 it shows the second truck is slowing down which is wrong since that isn't told.

So the answer would be Graph #2

I hope this helps!

-Ayden

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3 years ago

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Which of the following is equivalent to the expression below?-36A. -6B. 6ОООC. 6D. -6

Vadim26 [7]

SOLUTION;

$\sqrt[]{-36}\text{ = }\sqrt[]{(36)(-1)}\text{ = }\sqrt[]{36}\text{ x }\sqrt[]{-1\text{ }}\text{ = 6i}$

Recall that the square root of the negative one is "i" meaning that it is a complex number and not a real number.

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1 year ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection.

This means that,

Probability that at least one of them needs replacement at the first inspection =

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

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3 years ago