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Alex73 [517]
3 years ago
10

What is the 48th term of the arithmetic sequence with this explicit formula?

Mathematics
1 answer:
mariarad [96]3 years ago
4 0

Option B

48th term of arithmetic sequence is -152

<h3><u>Solution:</u></h3>

Given that a arithmetic sequence has explict formula,

a_n = -11 + (n - 1)(-3)

To find: 48th term of the arithmetic sequence

The nth term of arithmetic sequence can be found by substituting the required value of n in the explict formula

So 48th term of the arithmetic sequence can be found by substituting n = 48 in explict formula

a_n = -11 + (n - 1)(-3)

Plug in n = 48

a_{48} = -11 + (48 - 1)(-3)

On solving we get,

a_{48} = -11 + (47)(-3)\\\\a_{48} = -11 - 141\\\\a_{48} = - 152

Thus 48th term of arithmetic sequence is -152

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Step-by-step explanation:

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3 years ago
The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime
Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334

X[bar] ± Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }

174.5 ± 2.334* \frac{6.9}{\sqrt{50} }

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0
2 years ago
A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the d
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Answer:

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A function is graphed on a coordinate grid.

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       Range: y\rightarrow \infty

  • As the domain values negative infinity, the range values approach infinity.

       Domain: If x\rightarrow -\infty then

       Range: y\rightarrow \infty

We need to choose correct option which follows given domain and range.

Only quadratic function will follow the rule because it has even degree polynomial.

Quadratic function: f(x)=ax^2+bx+c

Degree = 2 and leading coefficient is positive.

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Therefore, the other side is 7 inches

6 0
1 year ago
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