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3 years ago

Drag the expressions into the boxes to correctly complete the table.

Mathematics

1 answer:

mel-nik [20]3 years ago

7 0

Answer:

see below

Step-by-step explanation:

A polynomial is a sum of terms, each of which is the product of a constant and some constellation of variables to integer non-negative powers. Anything with a variable in a denominator, a non-linear function such as absolute value, or square root (a fractional power) will <em>not</em> be a polynomial.

The constants in a polynomial may be rational or irrational. The polynomials we generally study are ones with real coefficients, but there is no reason why the coefficients could not be complex numbers.

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Which expression is equivalent to *picture attached*

Sedbober [7]

Answer:

$\sum_{n=3}^{20}(n(n+1))=\sum _{n=3}^{20} n^2+ \sum _{n=3}^{20} n$

Step-by-step explanation:

Given expression : $\sum_{n=3}^{20}(n(n+1))$

Solving further :

$\Rightarrow \sum_{n=3}^{20}(n^2+n)$

$\Rightarrow \sum _{n=3}^{20} n^2+ \sum _{n=3}^{20} n$

So, $\sum_{n=3}^{20}(n(n+1))=\sum _{n=3}^{20} n^2+ \sum _{n=3}^{20} n$

So, The given expression is equivalent to Option A

So, Option A is the answer

7 0

3 years ago

A study of long-distance phone calls made from General Electric's corporate headquarters in Fairfield, Connecticut, revealed the

Jet001 [13]

Answer:

a) 0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

b) 0.0668 = 6.68% of the calls last more than 4.2 minutes

c) 0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

d) 0.9330 = 93.30% of the calls last between 3 and 5 minutes

e) They last at least 4.3 minutes

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:

$\mu = 3.6, \sigma = 0.4$

(a) What fraction of the calls last between 3.6 and 4.2 minutes?

This is the pvalue of Z when X = 4.2 subtracted by the pvalue of Z when X = 3.6.

X = 4.2

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

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 3.6

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

$Z = \frac{3.6 - 3.6}{0.4}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

0.9332 - 0.5 = 0.4332

0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

(b) What fraction of the calls last more than 4.2 minutes?

This is 1 subtracted by the pvalue of Z when X = 4.2. So

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

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% of the calls last more than 4.2 minutes

(c) What fraction of the calls last between 4.2 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 4.2. So

X = 5

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

$Z = \frac{5 - 3.6}{0.4}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998

X = 4.2

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

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

0.9998 - 0.9332 = 0.0666

0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

(d) What fraction of the calls last between 3 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 3.

X = 5

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

$Z = \frac{5 - 3.6}{0.4}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998

X = 3

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

$Z = \frac{3 - 3.6}{0.4}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.9998 - 0.0668 = 0.9330

0.9330 = 93.30% of the calls last between 3 and 5 minutes

(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4% of the calls. What is this time?

At least X minutes

X is the 100-4 = 96th percentile, which is found when Z has a pvalue of 0.96. So X when Z = 1.75.

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

$1.75 = \frac{X - 3.6}{0.4}$

$X - 3.6 = 0.4*1.75$

$X = 4.3$

They last at least 4.3 minutes

7 0

3 years ago

Find the values of which satisfy the equation. 2 cos (2B+30°) = -√3 in the domain OP ≤B≤360°

PSYCHO15rus [73]

Answer:

60 and 90

Step-by-step explanation:

$2 \cos(2 \beta + 30) = - \sqrt{3}$

$\cos(2 \beta + 30) = - \frac{ \sqrt{3} }{2}$

$2 \beta + 30 = \cos {}^{ - 1} ( \frac{ - \sqrt{3} }{2} )$

First solution.

$2 \beta + 30 = 150$

$2 \beta = 120$

$\beta = 60$

Second solution

$2 \beta + 30 = 210$

$2 \beta = 180$

$\beta = 90$

5 0

2 years ago

Separate 53 people into two groups so that the first group has 7 fewer than 4 times the number of people in the second group.

N76 [4]

There would be a group of 12 and a group of 41

3 0

3 years ago

Choose the equation that represents the line passing through the point (2,-4) with a slope of 1/2? y=1/2x+5, y=1/2x-3, y=1/2x-5,

LUCKY_DIMON [66]

Correct answer: <span>y=1/2x-5
</span>
given: point = (2,-4)
slope = 1/2

Explanation: equation of line is: y = mx + c
where, m is the slope
c is the y-intercept

Now,
here, y = 1/2x + c
put, x = 2, y = -4
we get, -4 = (1/2).2 + c
or c = -4 - 1
or c = -5

Hence, equation of line is : y = 1/2x-5

3 0

3 years ago