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4 years ago

HELP PLEASE!!! 10 PTS BRAINLIEST!!!

Mathematics

1 answer:

madam [21]4 years ago

8 0

Answer:

Perimeter of the triangle formed by connecting the midpoint of the triangle $=18\ inches$

Step-by-step explanation:

Here is an image of the triangles.

The Midpoint Theorem: It states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

So we have $\triangle ABC\ and\ \triangle XYZ$ .

We see that by applying midpoint theorem.

$XY=\frac{1}{2}\ AC$

$XZ=\frac{1}{2}\ BC$

$YZ=\frac{1}{2}\ AB$

Lets say that $AB+BC+CA =36\inches$

As perimeter is the summation of the side lengths.

Dividing both sides with $2$

$\frac{AB+BC+CA}{2} =\frac{36}{2}$

$\frac{AB}{2} +\frac{BC}{2} +\frac{CA}{2} =18$

Now replacing $\frac{AB}{2}$ with $YZ$ and following the same for the rest.

We will have: $XY+XZ+YZ=18\inches$ .

So the perimeter of the triangles formed by the midpoints of the triangle $18\ inches$

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4 years ago

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3 years ago

You roll 2 dice. If the sum of the dice is: 2, 3, 4 you win $20. If the sum is 5, 6, 7, 8 you win $10. If the sum is 9, 10, 11 y

Elis [28]

Answer:

1) The expected value of the "winnings" is $(-0.97 $\overline 2$ )

2) The variance for the "winnings" is $0.57966

3) The standard deviation for the "winnings" is$0.761354

4) The game is not a fair game because one is expected to lose $0.97 $\overline 2$

Step-by-step explanation:

1) The probability of having a sum of 2 = 1/6×1/6 = 1/36

The probability of having a sum of 3 = 1/6×1/6 = 1/36

The probability of having a sum of 4 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 5 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 6 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 7 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 8 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 9 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 10 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 11 = 1/6×1/6 = 1/36

The probability of having a sum of 12 = 1/6×1/6 = 1/36

The values are;

For 2, we have 1/36 × (20 - 5) = 0.41 $\overline 6$

For 3, we have 1/36 × (20 - 5) = 0.41 $\overline 6$

For 4, we have 1/18 × (20 - 5) = 0.8 $\overline 3$

For 5, we have 1/18 × (10 - 5) = 0.2 $\overline 7$

For 6, we have 1/12 × (10 - 5) = 0.41 $\overline 6$

For 7, we have 1/12 × (10 - 5) = 0.41 $\overline 6$

For 8, we have 1/12 × (10 - 5) = 0.41 $\overline 6$

For 9, we have 1/18 × (-20 - 5) = -1.3 $\overline 8$

For 10, we have 1/18 × (-20 - 5) = -1.3 $\overline 8$

For 11, we have 1/36 × (-20 - 5) = -0.69 $\overline 4$

For 12, we have 1/36 × (-25 - 5) = -0.69 $\overline 4$

The expected value of the winnings is given as follows;

0.41 $\overline 6$ + 0.41 $\overline 6$ + 0.8 $\overline 3$ + 0.8 $\overline 3$ + 0.8 $\overline 3$ + 0.41 $\overline 6$ + 0.41 $\overline 6$ + -1.3 $\overline 8$ -1.3 - 0.69 $\overline 4$ - 0.69 $\overline 4$ = -0.97 $\overline 2$

Therefore, the expected value = $-0.97 $\overline 2$ , which is one is expected to lose $0.97 $\overline 2$

2) Using Microsoft Excel, we have;

The variance for the "winnings", σ² = $0.57966

3) The standard deviation for the "winnings" = √σ² = √(0.57966) ≈ $0.761354

4) The game is not a fair game because one is expected to lose $0.97 $\overline 2$

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3 years ago

The graph below represents which system of inequalities? graph of two infinite lines that intersect at a point. One line is soli

stiks02 [169]

The first line through points (-3, 0) and (-4, -1) is the orange line.

The second line, through (1, 1) and (2, -1) is the purple line.

Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.

Both lines are included, since they are solid lines.

The equation of the first line can be found as follows:

the slope is $\frac{0-(-1)}{-3-(-4)}=\frac{1}{1}=1$ , thus, the equation is:
$y-0=1(x-(-4))\\\\y=x+4$

The equation of the second line can be found as follows:

the slope is $\frac{1-(-1)}{1-2}= \frac{2}{-1}=-2$ ,

thus the equation of the second line is :

$y-1=-2(x-1)\\\\y-1=-2x+2\\\\y=-2x+3$

We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,

so we write the inequalities so that they do not hold for (0, 4)

line 1:

y≥x+4

4≥0+4=4 is true, so we change the sign and write : y≤x+4

similarly, line 2:

y≤-2x+3

4≤-2*0+3=3, which is not true, so we have the correct direction.

Note that since the lines were solid, we include the equality case:

Answer:

the shaded region is the solution to the system of inequalities:

i) y≤x+4
ii) y≤-2x+3

3 0

3 years ago

Read 2 more answers