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gizmo_the_mogwai [7]
2 years ago
15

Which of the following is a geometric series?

Mathematics
1 answer:
Alenkasestr [34]2 years ago
7 0
<h2>Answer:</h2>

The geometric series is:

               2+14+98+686

<h2>Step-by-step explanation:</h2>

The geometric series is a series in which each term of the series is a constant multiple of the preceding term of the series.

a)

6+13+20+27

This is not a geometric series but is a arithmetic series.

Since, each term is increased from the preceding term by 7.

Since, 6+7=13

13+7=20

20+7=27

b)

7+21+35+45

This is not a geometric  series.

Since 7×3=21

But 21×3=63

But the next term that is given is: 28 and not 63

c)

14+21+28+35

This is a arithmetic sequence.

Since

14+7=21

21+7=28

and 28+7=35

d)

2+14+98+686

This is a geometric sequence.

Since,. we get a common ratio i.e. a term which when multiplied to each term of sequence gives the next term of the series.

i.e. 2×7=14

14×7=98

98×7=686

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Estimate the perimeter of the figure to the nearest whole number.
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Answer:

The perimeter (to the nearest integer) is 9.

Step-by-step explanation:

The upper half of this figure is a triangle with height 3 and base 6.  If we divide this vertically we get two congruent triangles of height 3 and base 3.  Using the Pythagorean Theorem we find the length of the diagonal of one of these small triangles:  (diagonal)^2 = 3^2 + 3^2, or (diagonal)^2 = 2*3^2.

Therefore the diagonal length is (diagonal) = 3√2, and thus the total length of the uppermost two sides of this figure is 6√2.

The lower half of the figure has the shape of a trapezoid.  Its base is 4.  Both to the left and to the right of the vertical centerline of this trapezoid is a triangle of base 1 and height 3; we need to find the length of the diagonal of one such triangle.  Using the Pythagorean Theorem, we get

(diagonal)^2 = 1^2 + 3^2, or 1 + 9, or 10.  Thus, the length of each diagonal is √10, and so two diagonals comes to 2√10.

Then the perimeter consists of the sum 2√10 + 4 + 6√2.

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4 0
3 years ago
Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58​, what is the
aliina [53]

Answer:

0.36% probability that fewer than half in your sample will watch news​ videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 250, p = 0.58

So

\mu = E(X) = 250*0.58 = 145

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If the population proportion of adults who watch news videos is 0.58​, what is the probability that fewer than half in your sample will watch news​ videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

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

Z = \frac{124 - 145}{7.8}

Z = -2.69

Z = -2.69 has a pvalue of 0.0036

0.36% probability that fewer than half in your sample will watch news​ videos

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