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Natali5045456 [20]
3 years ago
15

Can someone help me with this question?

Mathematics
1 answer:
Likurg_2 [28]3 years ago
6 0
I’d say the answer is 72
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It takes 18 hours to fill a pool using 8 garden hoses. How long would it take to fill the same pool using 9 garden hoses?
levacccp [35]
Use rates, so 8 garden hoses over 18 hours
then find the how many hours one garden house can fill up by doing this = 18/8 you divide the 8 for both sides which is about 2.25/1
so then you times 9 which is about 20/9 hoses
your answer is 20
3 0
3 years ago
Read 2 more answers
Find two vectors in R2 with Euclidian Norm 1<br> whoseEuclidian inner product with (3,1) is zero.
alina1380 [7]

Answer:

v_1=(\frac{1}{10},-\frac{3}{10})

v_2=(-\frac{1}{10},\frac{3}{10})

Step-by-step explanation:

First we define two generic vectors in our \mathbb{R}^2 space:

  1. v_1 = (x_1,y_1)
  2. v_2 = (x_2,y_2)

By definition we know that Euclidean norm on an 2-dimensional Euclidean space \mathbb{R}^2 is:

\left \| v \right \|= \sqrt{x^2+y^2}

Also we know that the inner product in \mathbb{R}^2 space is defined as:

v_1 \bullet v_2 = (x_1,y_1) \bullet(x_2,y_2)= x_1x_2+y_1y_2

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

\left \| v_1 \right \|= \sqrt{x^2+y^2}=1

and

\left \| v_2 \right \|= \sqrt{x^2+y^2}=1

As second condition we have that:

v_1 \bullet (3,1) = (x_1,y_1) \bullet(3,1)= 3x_1+y_1=0

v_2 \bullet (3,1) = (x_2,y_2) \bullet(3,1)= 3x_2+y_2=0

Which is the same:

y_1=-3x_1\\y_2=-3x_2

Replacing the second condition on the first condition we have:

\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}

Since x_1^2= \frac{1}{10} we have two posible solutions, x_1=\frac{1}{10} or x_1=-\frac{1}{10}. If we choose x_1=\frac{1}{10}, we can choose next the other solution for x_2.

Remembering,

y_1=-3x_1\\y_2=-3x_2

The two vectors we are looking for are:

v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})

5 0
3 years ago
There are 15 students in the 8th grade. The students are randomly placed into three different algebra classes of 5 students each
xeze [42]

Answer:

The probability is   \frac{6}{91} ≅ 0.0659

Step-by-step explanation:

Let's analyze the question.

There are 15 students in the 8th grade.

The students are randomly placed into three different algebra classes of 5 students each.

We are looking for the probability that Trevor, Terry and Evan will be in the same algebra class.

One possible way to solve this question is to think about the product probability rule.

We can use it because we are in an equiprobable space. (And  also the events are independent).

Let's set for example a class for Evan.

The probability that Evan will be in a class is 1

Then for Terry there are 4 places out of 14 that puts Terry in the Evan's class.

We write 1.\frac{4}{14}

Finally for Trevor there are 3 places out of the remaining 13 that puts Trevor in the same class with Evan and Terry.

Using the product rule we write :

1.\frac{4}{14}.\frac{3}{13}=\frac{6}{91}

The probability of the event is \frac{6}{91} ≅ 0.0659

5 0
3 years ago
GIVING BRAINIEST!!!!
lesya692 [45]

Answer:

is will cost 200 dollars by memorial dsy

7 0
3 years ago
A pack of 8 batteries cost 4.72!What is cost per battery?
Mrrafil [7]
4.72 x 1 = 4.72
8 x X =8x
We need to let the X alone so
4.72 divided 8 = 0.59
1 battery = 0.59
8 0
2 years ago
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