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2 years ago

For the sequence -27, -12, 3, 18, ..., the expression that defines the nth term where a1 = -27 is

Mathematics

2 answers:

skelet666 [1.2K]2 years ago

8 0

Answer:

D. -27+15 (N-1)

Step-by-step explanation:

-27, -12, 3, 18

Take the second term and subtract the first term to find the common difference

-12 - (-27)

-12+27 = 15

The common difference is +15

We are adding 15 each time

The formula for an arithmetic sequence is

an = a1+d(n-1)

an = -27 +15(n-1)

DiKsa [7]2 years ago

3 0

So the formula for an arithmetic sequence (where you're adding or subtracting by the same number each time) is $a_{n}$ = $a_{1}$ + d(n - 1)

In this equation:

$a_{n}$ is the nth term

$a_{1}$ is the first term

d is the common difference (the number you're adding or subtracting each time)

n is the number of the term (e.g. 1st term, 2nd term, 3rd term etc)

So we're given that $a_{1}$ = -27, and we can find that d = 15 (because we add 15 each term). We just plug these values into the equation to get...

$a_{n}$ = -27 + 15 (n - 1)

It looks like that's your answer, D. But if you needed to solve it out further, you could:

We can use the distributive property...

$a_{n}$ = -27 + 15n - 15

Then combine like terms...

$a_{n}$ = 15n - 42

Hope that helps! Feel free to message me if you need clarification

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2 years ago

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2 years ago

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2 years ago

A quadratic relation has zeros at 3 and –5. The parabola goes through the point (2, –14). What is the equation of the parabola i

olasank [31]

Answer:

$\displaystyle 2 {x}^{2} + 4x - 30 = 0$

Step-by-step explanation:

we are given the zeros and a point where it goes through of a quadratic equation

remember that when the roots are given then the function should be

$\displaystyle \: y = a(x - x_{1})(x - x_{2})$

where a is the leading coefficient and x1 and x2 are the roots

substitute:

$\displaystyle y = a(x - (3))(x - ( - 5))$

simplify:

$\displaystyle y = a(x - 3)(x + 5)$

now the given point tells us that when x is 2 y is -14 therefore by using the point we can figure out a

substitute:

$\displaystyle a(2 - 3)(2 + 5) = - 14$

simplify parentheses:

$\displaystyle a( - 1)(7) = - 14$

simplify multiplication:

$\displaystyle - 7a = - 14$

divide both sides by -7:

$\displaystyle a = 2$

altogether substitute:

$\displaystyle y = 2(x - 3)(x + 5)$

since it want the equation y should be

$\displaystyle 2(x - 3)(x + 5) = 0$

recall quadratic equation standard form:

$\displaystyle {ax}^{2} + bx + c = 0$

so simplify parentheses:

$\displaystyle 2( {x}^{2} + 2x - 15 ) = 0$

distribute:

$\displaystyle 2 {x}^{2} + 4x - 30 = 0$

hence,

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8 0

2 years ago

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standar

zysi [14]

Answer:

A sample of at least 68 bulbs is needed to be 96% conﬁdent that our sample mean will be within 10 hours of the true mean.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

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So it is z with a pvalue of $1-0.02 = 0.98$ , so $z = 2.055$

Now, find the margin M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

$\sigma = 40, M = 10$

$M = z*\frac{\sigma}{\sqrt{n}}$

$10 = 2.055*\frac{40}{\sqrt{n}}$

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$\sqrt{n} = 8.22$

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A sample of at least 68 bulbs is needed to be 96% conﬁdent that our sample mean will be within 10 hours of the true mean.

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2 years ago