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3 years ago

Evaluate each expression

Mathematics

1 answer:

aliina [53]3 years ago

5 0

I’m only in 7 grade I don’t know how to do it

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A curious patterns occurs in a group of people who all shake hands with one another. It turns out that you can predict the numbe

ycow [4]

Missing part of the question

Determine the number of handshakes, i, that will occur for each number of people, n, in a particular room. (people)

Answer:

$S_n = \frac{n}{2}(n - 1)$

Step-by-step explanation:

Given

For 5 people

$\begin{array}{cc}{People} & {Handshakes} & {5} & {4} & {4} & {3} & {3} & {2} & {2} & {1} & {1} & {0} &{Total} & {10} \ \end{array}$

Using the given instance of 5 people, the number of handshakes can be represented as:

$(n - 1) + (n - 2) + (n - 3) + ........ + 3 + 2 + 1 + 0$

The above sequence is an arithmetic sequence and the total number of handshakes is the sum of n terms of the sequence.

$S_n = \frac{n}{2}{(T_1 + T_n})$

Where

$T_1 = n - 1$ --- The first term

$T_n = 0$ --- The last term

So:

$S_n = \frac{n}{2}(n - 1 + 0)$

$S_n = \frac{n}{2}(n - 1)$

7 0

2 years ago

Give one pair of vertical angles and one pair of supplementary angles shown in the figure below.

vichka [17]

Answer:

Vertical : Angles 1 & 4 Supplementary: 5 & 6

Step-by-step explanation:

Vertical angels are angles that have the same measure that are opposites of each other (1 & 4) and supplementary angles are 2 angles that equal 180 degrees that are right next to each other or right above each other (5 & 6) (3 & 5)

7 0

3 years ago

a previous analysis of paper boxes showed that the standard deviation of their lengths is 15 millimeters. A packers wishes to fi

vladimir1956 [14]

Answer:

864.36 boxes

Step-by-step explanation:

In the question above, we are given the following values,

Confidence interval 95%

Since we know the confidence interval, we can find the score.

Z score = 1.96

σ , Standards deviation = 15mm

Margin of error = 1 mm

The formula to use to solve the above question is given as:

No of boxes =[ (z score × standard deviation)/ margin of error]²

No of boxes = [(1.96 × 15)/1]²

= 864.36 boxes

Based on the options above, we can round it up to 97 boxes.

8 0

3 years ago

What is the answer to 16a5 b3/8ab ?

marishachu [46]

Answer:

When we are dividing exponents, there is this rule:

$\frac{a^n}{a^m}=a^{(n-m)}$

So, in our case we have this:

$\frac{16a^5b^3}{8ab} = \frac{16}{8}a^{(5-1)}b^{(3-1)}$ $=2a^4b^2$

5 0

3 years ago

The population is a Midwest industrial town decreased from 224,000 to 221,000 in just 4 years. Assuming that this trend continue

valina [46]

Answer:

227750

Step-by-step explanation:

If we assume that the rate of increase in population is linear, then in 4 years the increase in population is (224000 - 221000) = 3000.

So, the rate of increase in population is $\frac{3000}{4} = 750$ persons per year.

Now, we have to calculate the population of the town after an additional 5 years.

So, the population in 5 years will increase by (750 × 5) = 3750

Therefore, the population after an additional 5 years will be (224000 + 3750) = 227750. (Answer)

7 0

4 years ago