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3 years ago

Identify the explicit function for the sequence in the table

1 answer:

6 0

The common difference is 19-7 = 31-19 = 12, so this is an arithmetic sequence. The initial term (when n=1) is 7.

The explicit formula for the terms of an arithmetic sequence is
an = a1 + d(n-1)
where "a1" is the first term and "d" is the common difference. The formula that matches a1=7 and d=12 is
B. a(n) = 7+(n-1)·12

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13. The radius of Earth is approximately 6.4 x 100 m. Use the formula V = 4/3pr^3

romanna [79]

<u>We are given</u>

Radius of Earth; 6.4 x 100 meters = 640 meters

Clearly, the shape of the earth is a sphere. Thus, to determine the volume of the earth, we will use a formula that determines the volume of a sphere.

$\implies \text{Volume of sphere =} \ \dfrac{4\pi r^{3}}{3}$

When we substitute the radius in the formula, we get;

$\implies\text{Volume of sphere} = \dfrac{4\pi (640)^{3}}{3}$

$\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}$

Take π as 3.14

$\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}$

$\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}$

Simplify the numerator;

$\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}$

$\implies \text{Volume of sphere} = \dfrac{3292528640}{3}$

Divide the numerator by 3;

$\implies \text{Volume of sphere} = \dfrac{3292528640}{3}$

$\implies \text{Volume of sphere} = \boxed{1097509546.67 \ \text{m}^{3} } \ \ \ (\text{Estimated})$

4 0

1 year ago

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. after 3 hours

jeka57 [31]

Ten thousand I believe let me know if wrong that’s what my math got

3 0

2 years ago

Random sample size of 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. T

Ugo [173]

Answer:

the mean and standard error of the mean are 200 and 2 respectively.

Step-by-step explanation:

Given that ;

the sample size n = 81

population mean μ = 200

standard deviation of the infinite population σ = 18

A population is the whole set of values, or individuals you are interested in, from an experimental study.

The value of population characteristics such as the Population mean (μ), standard deviation (σ) are said to be known as the population distribution.

From the given information above;

The sample size is large and hence based on the central limit theorem the mean of all the means is same as the population mean 200.

i.e

$\mu = \bar \mu_x$ = 200

∴ The mean = 200

and the standard error of the mean can be determined via the relation:

$\mathbf{standard \ error \ of \ mean = \dfrac{\sigma}{\sqrt {n}}}$

$\mathbf{standard \ error \ of \ mean = \dfrac{18}{\sqrt {81}}}$

$\mathbf{standard \ error \ of \ mean = \dfrac{18}{9}}$

$\mathbf{standard \ error \ of \ mean =2}$

Therefore ; the mean and standard error of the mean are 200 and 2 respectively.

6 0

2 years ago

4. The distribution of blood cholesterol level in the population of young men aged 20 to 34 years is close to Normal, with mean

Pie

Answer:

a) 38.59% probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.

b) By the Central Limit Theorem, the mean of the distribution of the sample mean would be 188 milligrams per deciliter

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 188, \sigma = 41$

a. Find the probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.

This is 1 subtracted by the pvalue of Z when X = 200. So

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

$Z = \frac{200 - 188}{41}$

$Z = 0.29$

$Z = 0.29$ has a pvalue of 0.6141

1 - 0.6141 = 0.3859

38.59% probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.

b. Suppose you measure the cholesterol level of 100 young men chosen at random and calculate the sample mean. If you did this many times, i. what would be the mean of the distribution of the sample mean

By the Central Limit Theorem, the mean of the distribution of the sample mean would be 188 milligrams per deciliter

5 0

2 years ago

Is the following number rational or irrational? (this is a Khan Academy question)

diamong [38]

Answer:

Irrational

Step-by-step explanation:

5 0

3 years ago