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4 years ago

The mean of four consecutive even numbers is 15

1 answer:

4 0

I suppose you have to find the four numbers. If $x$ is the smallest of the four, then the next three numbers are $x+2$ , $x+4$ , and $x+6$ . The mean is 15, so

$\dfrac{x+(x+2)+(x+4)+(x+6)}4=\dfrac{4x+12}4=15$
$\implies x+3=15$
$\implies x=12$

So the four numbers are 12, 14, 16, and 18.

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What are the values of a and b?

Helen [10]

A is 6 because so is the side across from it

And B is 8 because it the same size just flip it

Brainliest would be appreciated

4 0

3 years ago

find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B

SashulF [63]

Answer:

$\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190$

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately $\theta \approx 48$

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

$a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

$|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3$

$|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5$

And finally we can calculate the angle between the vectors like this:

$cos \theta = \frac{ab}{|a| |b|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{ab}{|a| |b|})$

If we replace we got:

$\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190$

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately $\theta \approx 48$

3 0

3 years ago

You can trim the grass using a lawnmower at a rate of 80 square feet per minute. You can use a string trimmer at a rate of 20 sq

docker41 [41]

So first its 20 x 20 which is 400 so then the lawnmower does 80 per min so 80 x 5 and u get 400

5 0

3 years ago

Tell whether the two quantities vary directly. Explain your reasoning. The cafeteria provides three meals per day.

Dafna11 [192]

Answer:

The cafeteria provides three meals per day.

<u>Reason 1</u>

Yes, they vary directly

As number of days increases ,Total number of meals i.e

1st day ⇒ 3

2nd day⇒6

3 rd day⇒9

4th day⇒12

......................

.........................

increases.

Total number of Meals = k×Number of days

But there is another possibility also

<u>Reason 2</u>

1 st day ⇒ 3

2nd day ⇒3

3rd day⇒ 3

.....................

As you can see from the above expression On each day number of meals is

constant.

So we can say that ,

On each Day=Constant amount of meal=3

So, there is no Proportionality between Days and Meal.

3 0

3 years ago

At the party, 6/16 of the guest were playing games and 3/8 of the guest were singing.Pat said that the number of guest were play

ziro4ka [17]

Yes. 6/16 simplifies to 3/8, which is the same amount of people singing.

8 0

3 years ago

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