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Rashid [163]
3 years ago
5

One angle of a rhombus measures 102°, and the shorter diagonal is 4 inches long. Approximately how long is the side of the rhomb

us? (Hint: Diagonals of a rhombus bisect the angles.)
2 in.
3 in.
4 in.
5 in.
Mathematics
1 answer:
liq [111]3 years ago
7 0

Answer:

Approximately 3 inches.

Step-by-step explanation:

The shorter diagonal will bisect the 102 degree angle. so we have a triangle  with base angles of 51, vertex 180 - 102 = 78 degrees and base length 4 inches.

Applying the Sine Rule:

4 / sin 78 = x / sin 51  where x = the length of the  side of the rhombus.

x = 4 * sin 51 / sin 78

= 3.17 inches.

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Suppose that you were not given the sample mean and sample standard deviation and instead you were given a list of data for the
Troyanec [42]

Answer:

So, the sample mean is 31.3.

So, the sample standard deviation is 6.98.

Step-by-step explanation:

We have a list of data for the speeds (in miles per hour) of the 20 vehicles. So, N=20.

We calculate the sample mean :

\mu=\frac{19 +19 +22 +24 +25 +27 +28+ 37 +35 +30+ 37+ 36+ 39+ 40+ 43+ 30+ 31+ 36+ 33+ 35}{20}\\\\\mu=\frac{626}{20}\\\\\mu=31.3

So, the sample mean is 31.3.

We use the formula for a sample standard deviation:

\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\mu)^2}

Now, we calculate the sum

\sum_{i=1}^{20}(x_i-31.3)^2=(19-31.3)^2+(19-31.3)^2+(22-31.3)^2+(24-31.3)^2+(25-31.3)^2+(27-31.3)^2+(28-31.3)^2+(37-31.3)^2+(35-31.3)^2+(30-31.3)^2+(37-31.3)^2+(36-31.3)^2+(39-31.3)^2+(40-31.3)^2+(43-31.3)^2+(30-31.3)^2+(31-31.3)^2+(36-31.3)^2+(33-31.3)^2+(35-31.3)^2\\\\\sum_{i=1}^{20}(x_i-31.3})^2=926.2\\

Therefore, we get

\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\mu)^2}\\\\\sigma=\sqrt{\frac{1}{19}\cdot926.2}\\\\\sigma=6.98

So, the sample standard deviation is 6.98.

3 0
2 years ago
In Erin's career on the basketball team, she made 7 out of every 10 free throws Last season, she
Crazy boy [7]

Answer: 42

For this situation we will use a ratio to show how many free throws Erin will make. Using the ratio 7:10 represents that Erin will make 7 out of every 10 free throws. You want to know how many free throws  she will make if she attempts 60 free throws.

Using ratios we will be able to find how many free throws she will make if she attempts 60.

7:10

14:20

21:30

28:40

35:50

42:60

Basically we kept multiply the right side of the ratio which is 10 by 2 until we were at 60 free throws.

Erin will make 42 free throws if she attempts 60 free throws.

6 0
3 years ago
I HAVE ANOTHER CLASS TODAY AND NEED TO FINISH IT RIGHT NOW (MAYBE 20 MIN MAX) SOMEBODY PLEASE HELP, ME! ANY ANNOYING OR FAKE ANS
lys-0071 [83]

Answer:

|x - 5| = 2

Step-by-step explanation:

Since we are not given a zero on the number line, we do the following:

Average = midpoint between two numbers on the number line

For this number line,

Average = 3 + 7 ÷ 2

Average = 5

Next we find how many units away are each number from the middle:

3 is 2 units away from 5

7 is 2 units away from 5

Units away = 2

Let's use the formula:

|x - average| = Units away

Substitute values into equation

|x - 5| = 2

Now we solve

Solve for x over the integers:

|x - 5| = 2

Split the equation into two possible equations:

x - 5 = 2 or x - 5 = -2

Add 5 to both sides:

x = -5 + 5 = 2 + 5 or x - 5 + 5 = -2 + 5

Answer:

x = 7 or x = 3

LOOK AT THE GRAPH AND NUMBER LINE

5 0
2 years ago
Triangles are similar. Round answer to nearest tenth (step by step)
ozzi

Answer:

13.5

Step-by-step explanation:

Similar = alike but not the same

A lot of times in geometry it would mean that they have the same shape, just different size, so first find the ratio:

6/12 = 1/2

27 * 1/2 = 27/2 = 13.5

7 0
2 years ago
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When sound is created it travels to the ear through a
dusya [7]

Answer:

medium

Step-by-step explanation:

The right answer is Medium, because to travel through the ear the sound wave must go through the ear drum.

3 0
3 years ago
Read 2 more answers
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