Type the correct answer in the box. Round your answer to the nearest hundredth.

Consider Akelia’s sequence 5, 8, 11, 14, 17, ….

bonufazy [111]

Answer:

It would be 20

Step-by-step explanation:

As we can see, the sequence starts from 5 and increases by three each time. In fact, one possible formula for that sequence could be:

$a_n=3n+2\hspace{10}n\in N$

Let's confirm the formula by evaluating the first 6 terms:

$a_1=3(1)+2=3+2=5\\a_2=3(2)+2=6+2=8\\a_3=3(3)+2=9+2=11\\a_4=3(4)+2=12+2=14\\a_5=3(5)+2=15+2=17\\a_6=3(6)+2=18+2=20$

5 0

3 years ago

Which of the rectangles below have an area of 18 cm²?

Elenna [48]

$\textsf{Rectangle A}$

$\implies \mathsf {Area = 3 \times 6 = 18cm^{2}}$

$\implies \bf {Yes}$

$\textsf {Rectangle B}$

$\implies \mathsf {Area = 2 \times 9 = 18cm^{2}}$

$\implies \bf {Yes}$

$\textsf {Rectangle C}$

$\implies \mathsf {Area = 5 \times 4 = 20cm^{2}}$

$\textsf {Rectangle D}$

$\implies \mathsf {Area = 9 \times 2 = 18cm^{2}}$

$\implies \bf {Yes}$

5 0

2 years ago

Read 2 more answers

Determine whether the triangles are similar, if so what is a similarity statement in the postulate or theorem used?

alexandr1967 [171]

Answer:

It is the secon option ∆TRS ≈ ∆TPQ ; SAS

Step-by-step explanation: angle t is equal to angle t because it is the same angle

line TR divided by line TP is equal to line TS divided by TQ

3 0

3 years ago

Read 2 more answers

What is the distance, in units, between the points <img src="https://tex.z-dn.net/?f=%282%2C%20-6%29" id="TexFormula1" title="(2

Anna71 [15]

Answer: $3\sqrt{13}$

Step-by-step explanation:

$\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$\sqrt{\left(-4-2\right)^2+\left(3-\left(-6\right)\right)^2}$

$=3\sqrt{13}$

6 0

3 years ago

A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the

hichkok12 [17]

Answer:

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

A statistician calculates that 8% of Americans own a Rolls Royce.

This means that $p = 0.08$

Sample of 595:

This means that $n = 595$

Mean and standard deviation:

$\mu = p = 0.08$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111$

What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?

Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.

Probability the proportion is less than 5%:

P-value of Z when X = 0.05. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.05 - 0.08}{0.0111}$

$Z = -2.7$

$Z = -2.7$ has a p-value of 0.0035

2*0.0035 = 0.0070

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

8 0

3 years ago