Find the rate in miles per hour. 5 1/3 miles in 7 1/2 minutes

The mean value of 8 numbers is 17. Three of these numbers (9, 11, and 20) are discarded.

Viktor [21]

Answer:

19.2

Step-by-step explanation:

You get the mean of a set of numbers by adding them and dividing the sum by how many numbers there are. In this case, you don't know what the individual 8 numbers are, but you can find out what they add up to.

Mean = (sum) / 8

17 = (sum) / 8

17 x 8 = sum

136 = sum

Now take out the numbers 9, 11, 20, which reduces the sum by 40. There are 5 numbers left and they add up to 136 - 40 = 96.

The new mean is 96 / 5 = 19.2

3 0

3 years ago

Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

so

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

7 0

3 years ago

creativ13 [48]

Step-by-step explanation:

since the house, the school and the grocery store all have the same x coordinate (-4), they are on the same vertical line of x = -4.

and that means their distances are simply the differences in their y coordinates.

the only one different in that regard is the community center, but it is on the same y coordinate as the school, so the distance to the school is only the difference in their x coordinates.

A

so, the distance from house to school is

|5 - 3| = |3 - 5| = 2

as it is the same distance in either direction.

B

the distance from house to school to grocery store is the distance from house to school plus the distance from school to grocery store :

2 + |3 - -9| = 2 + |-9 - 3| = 2 + 12 = 14

now we need to find the distance from home to school to community center.

that is 2 + the distance from school to community center.

as mentioned above, since the school and the community center have the same y coordinate, their distance is the difference in their x coordinates :

|-4 - 6| = |6 - -4| = 10

so, in total the way house to school to community center is 2 + 10 = 12.

and that is shorter than the way house to school to grocery store, which is 14.

so, yes, the distance house to school to grocery store (14) is greater than the distance house to school to community center (12).

8 0

2 years ago

Which is equivalent to sqrt x^10<br> A. X-5<br> B. X -1/5<br> C. X sqrt 10<br> D. X 1/5<br> E. X^5

Lesechka [4]

<h3>Answer: E) x^5</h3>

$\sqrt{x^{10}} = x^5$

=====================================================

Explanation:

We simply take half of the exponent 10 to get 5. This applies to square roots only.

So the rule is $\sqrt{a^b} = a^{b/2}$

A more general rule is

$\sqrt[n]{a^b} = a^{b/n}$

If n = 2, then we're dealing with square roots like with this problem. In this case, a = x and b = 10.

5 0

3 years ago

Read 2 more answers

I need helpp!!!!!!!!!!!!

Rasek [7]

Hey,
We can see here 2 of the angles are equal and the third one is a right angle right?
That means it is an isosceles triangle since they have 2 equel angles and a right anlgle.

Another feature of the isosceles triangle is that 2 sides are equal.
We are given one side is 5.5 right?
So the side BC has to be 5.5 or the side AB has to be 5.5
In isosceles triangles the side opposite to the 90 degree angle is the hypotenuse.This means it is the longest angle.
So it has to be AB which is equal to 5.5 since BC is the hypotenuse.

Hope this helps,Happy New Year

8 0

3 years ago