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2 years ago

The segment shown below could form a triangle. True or False

Mathematics

2 answers:

Hatshy [7]2 years ago

8 0

Answer:

Yes, this can form a triangle.

Step-by-step explanation:

As long as the two shorter legs' sum IS NOT GREATER THAN the length of the larger segment, then a triangle can be formed! As we can see, 6 + 5 = 11, which is less than 12.

Tanzania [10]2 years ago

4 0

True! If you have any 3 segments, it could form a triangle, just not a right triangle.

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A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a g

cricket20 [7]

Answer:

a) $r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

b) $m=\frac{90}{15}=6$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

c) For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

Step-by-step explanation:

We have the following data:

Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game (y) 5 8 11 14 17 20 23 26 29

Part a

The correlation coefficient is given:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=9 $\sum x = 18, \sum y = 153, \sum xy = 396, \sum x^2 =51, \sum y^2 =3141$

$r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

Part b

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=51-\frac{18^2}{9}=15$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=396-\frac{18*153}{9}=90$

And the slope would be:

$m=\frac{90}{15}=6$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

Part c

For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

5 0

2 years ago

Identify a pattern in the given list of numbers. Then use this pattern to find the next number.

Rom4ik [11]

Answer:

The given sequence is geometric sequence

In the given pattern we have next number is $a_5=\frac{1}{4}$

Step-by-step explanation:

Given numbers are 64,-16,4,-1

To identify the pattern of the given numbers :

Let $a_1=64$ , $a_2=-16$ , $a_3=4$ and $a_4=-1$

To find the next number that is $a_5$

common ratio $r=\frac{a_2}{a_1}$

$=\frac{-16}{64}$

$r=-\frac{1}{4}$

$r=\frac{a_3}{a_2}$

$=\frac{4}{-16}$

$r=-\frac{1}{4}$

Therefore the common ration is $r=-\frac{1}{4}$

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is $a_n=a_1r^{n-1}$

Now find the 5th term so put n=5 , $a_1=64andr=\frac{-1}{4}$ we have

$a_5=64(\frac{-1}{4})^{5-1}$

$=64(\frac{-1}{4})^{4}$

$=64(\frac{1}{4})^{4}$

$=64(\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4})$

$=\frac{1}{4}$

Therefore $a_5=\frac{1}{4}$

8 0

2 years ago

HURRY PLEASE!! find the lcm of 3x^2-6x-24 and 9x^2-36

Mrac [35]

Answer:

yeeeeeeeeeeee

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Best Buy is displaying 15 laptops for a big store sale. The laptops include 6 identical Dells, 4 identical Chromebooks, and 5

Alchen [17]

Answer:

630,630 different arrangements are possible for the given laptops.

Step-by-step explanation:

Total number of laptops = n = 15

Number of identical Dell laptops = 6

Number of identical Chromebooks = 4

Number of identical Mackbooks = 5

We have to find in how many ways can the laptops be arranged. Number of arrangement of objects is calculated using Permutations as the order of objects matter during the arrangement. The formula to calculate the number of possible arrangements when there are similar objects is given as:

$\frac{n!}{a!b!c!...}$