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3 years ago

Which formula can be used to describe the sequence? –81, 108, –144, 192, ...

Mathematics

1 answer:

ale4655 [162]3 years ago

8 0

Answer:

a(n) = -81(-4/3)^(n - 1)

Step-by-step explanation:

The first term is -81. From -81 we obtain the next term, 108, by multiplying -81 by -4/3. Note how (-4/3)(108) = -144 as anticipated.

Thus, the common ratio is -4/3.

The explicit function for this geometric series is

a(n) = -81(-4/3)^(n - 1)

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What is the conjugate? √x + 2√b

Llana [10]

The correct answer is: " √x − 2√b " .
_________________________________________________________

The "conjugate" of " √x + 2√b " is: " √x − 2√b " .
_________________________________________________________

Explanation:
_________________________________________________________
In an expression with 2 (TWO) terms; that is, in a "binomial expression",
the "conjugate" of that expression refers to that very expression — with the "sign" in between those two terms—"reverse" (e.g. "minus" becomes "plus" ; or, "plus" becomes "minus" .) .
_________________________________________________________

→ So: We are given: " √x + 2√b " .

 → Note that this is a "binomial expression" ;

→ that is, there are 2 (TWO) terms: " √x " ; and: " 2√b " .
_________________________________________________________

To find the "conjugate" of the given binomial expression:

→ " √x + 2√b " ;

→ We simply change the "+" {plus sign} to a "−" {minus sign} ; and rewrite:
___________________________________________________________

→ " √x − 2√b " ;

→ which is the "conjugate" ; and is the correct answer:
___________________________________________________________
→ " √x − 2√b " ; is the "conjugate" of the expression: " √x + 2√b " .
___________________________________________________________
→ {that is: " √x − 2√b " ; is the conjugate.}.
___________________________________________________________

7 0

3 years ago

What is the next term of the arithmetic sequence? -7,-3,1,5,9,

inessss [21]

Answer:

The next term is 13.

Step-by-step explanation:

Looking at the previous numbers...

for -7 to get to -3, you have to add 4, and for -3 to get to 1 you have to add 4.... and so on. So in order to find the next number, add 4 to 9, and which you get 13.

3 0

3 years ago

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Plot the vertices (–2, –8), (–2, 2), and (8, 2). What is the last vertex of the rectangle? What is the area of the rectangle? sq

Wewaii [24]

Answer:

the last vertex is (8,-8)

the area of the rectangle is 100 square units

Step-by-step explanation:

5 0

3 years ago

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A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A ran

mart [117]

Answer:

a) The 95% confidence interval would be given (0.070;0.121).

b) "increase the sample size n"

"decrease za/2 by decreasing the confidence"

Step-by-step explanation:

Notation and definitions

$X=48$ number of vehicles classified as sports utility.

$n=500$ random sample taken

$\hat p=\frac{48}{500}=0.096$ estimated proportion of vehicles classified as sports utility vehicles.

$p$ true population proportion of vehicles classified as sports utility vehicles.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

The confidence interval would be given by this formula :

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.096 - 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.070$

$0.096 + 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.121$

And the 95% confidence interval would be given (0.070;0.121).

We are confident (95%) that about 7.0% to 12.1% of vehicles in California are classified as sports utility .

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

For this case we just have two ways to increase the accuracy one is "increase the sample size n" since if we have a larger sample size the estimation would be more accurate. And the other possibility is "decrease za/2 by decreasing the confidence" because if we decrease the confidence level the interval would be narrower and accurate

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3 years ago

How do you write 19,830 in scientific notation? _____× 10^_____

pshichka [43]

Answer:

1.983(10⁴)

Step-by-step explanation:

Since we need to have ones and decimals as proper scientific notation, we have 1.983. Since we need the value of 19830, we need to move the decimal place 4 places to the right, so our exponent is 4.

*I double checked my work this time.

8 0

3 years ago

Read 2 more answers