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4 years ago

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There are ten kids in a class. When any two meet, each says “hi” to the other and the answer “hi” follows. Before the class star

ts, how many times would one hear the word “hi”?

1 answer:

kogti [31]4 years ago

7 0

Answer: 20

Step-by-step explanation:

From the question, there are ten kids in a class and when any two meet, each kid says “hi” to the other kid and the answer “hi” follows.

The number hi one would hear before the class starts would be 10 multiplied by 2 because there are 10kids and 2 hi whenever the kids greet.

= 10 × 2

= 20hi

There will be 20 times the word hi would be heard

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write an equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

dimaraw [331]

The equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is $y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

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

Given that we have to write equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

Let us first find the slope of given line AB

<em><u>The slope "m" of the line is given as:</u></em>

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here the given points are A(-2,2) and B(5,4)

$\text {Here } x_{1}=-2 ; y_{1}=2 ; x_{2}=5 ; y_{2}=4$

$m=\frac{4-2}{5-(-2)}=\frac{2}{7}$

Thus the slope of line with given points is $\frac{2}{7}$

We know that product of slopes of given line and slope of line perpendicular to given line is always -1

$\begin{array}{l}{\text {slope of given line } \times \text { slope of perpendicular bisector }=-1} \\\\ {\frac{2}{7} \times \text { slope of perpendicular bisector }=-1} \\ \\{\text {slope of perpendicular bisector }=\frac{-7}{2}}\end{array}$

The perpendicular bisector will run through the midpoint of the given points

So let us find the midpoint of A(-2,2) and B(5,4)

<em><u>The midpoint formula for given two points is given as:</u></em>

$\text {For two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right), \text { midpoint } \mathrm{m}(x, y) \text { is given as }$

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Substituting the given points A(-2,2) and B(5,4)

$m(x, y)=\left(\frac{-2+5}{2}, \frac{2+4}{2}\right)=\left(\frac{3}{2}, 3\right)$

Now let us find the equation of perpendicular bisector in point slope form

The perpendicular bisector passes through points (3/2, 3) and slope -7/2

<em><u>The point slope form is given as:</u></em>

$y - y_1 = m(x - x_1)$

$\text { Substitute } \mathrm{m}=\frac{-7}{2} \text { and }\left(x_{1}, y_{1}\right)=\left(\frac{3}{2}, 3\right)$

$y - 3 = \frac{-7}{2}(x - \frac{3}{2})\\\\y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

Thus the equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is found out

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4 years ago

Find the distance, to the nearest tenth, from T(4-2) to U(-2,3)

kiruha [24]

Distance = SQRT(x^2+y^2)
x = 4 - (-2) = 6
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3 years ago

Example 1: Calculation of Normal Probabilities Using ????????-Scores and Tables of Standard Normal Areas The U.S. Department of

Molodets [167]

Answer:

i) 0.872

ii) 0.300

iii) 0.76

iv) 0.704

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $261.50 per month

Standard Deviation, σ = $16.25

We are given that the distribution of monthly food cost for a 14- to 18-year-old male is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(Less than $280)

$P( x < 280) = P( z < \displaystyle\frac{280 - 261.50}{16.25}) = P(z< 1.138)$

Calculation the value from standard normal z table, we have,

$P(x < 280) = 0.872 = 87.2\%$

b) P(More than $270)

P(x > 270)

$P( x > 270) = P( z > \displaystyle\frac{270 - 261.50}{16.25}) = P(z > 0.523)$

$= 1 - P(z \leq 0.523)$

Calculation the value from standard normal z table, we have,

$P(x > 270) = 1 - 0.700 = 0.300 = 30.0\%$

c) P(More than $250)

P(x > 250)

$P( x > 250) = P( z > \displaystyle\frac{250 - 261.50}{16.25}) = P(z > -0.707)$

$= 1 - P(z \leq -0.707)$

Calculation the value from standard normal z table, we have,

$P(x > 250) = 1 - 0.240 = 0.76 = 76.0\%$

d) P(Between $240 and $275)

$P(240 \leq x \leq 275) = P(\displaystyle\frac{240 - 261.50}{16.25} \leq z \leq \displaystyle\frac{275-261.50}{16.25}) = P(-1.323 \leq z \leq 0.8307)\\\\= P(z \leq 0.8307) - P(z < -1.323)\\= 0.797 - 0.093 = 0.704 = 70.4\%$

$P(240 \leq x \leq 275) = 70.4\%$

e) Thus, 0.704 is the probability that the monthly food cost for a randomly selected 14- to 18-year-old male is between $240 and $275.

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3 years ago

What percentage of births occur after day 12?

rjkz [21]

Answer:

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3 years ago

If sin(a) = cos(2a), then what is the value of a?

Mariulka [41]

Answer:

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Step-by-step explanation:

sina = cos(2a)

= 1 - 2(sina)^2

2(sina)^2 + sina -- 1 = 0

( sina + 1 )( 2sina - 1 ) = 0

sina = -1 or sina = 1/2

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3 years ago