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iris [78.8K]
3 years ago
6

A square pool has a side length of x feet. a uniform border around the pool is 1 foot wide. the total area of the pool and the b

order is 361 square feet. what is the area of the pool?
Mathematics
1 answer:
Alex73 [517]3 years ago
5 0
----------------------------------------
Define x:
----------------------------------------
Let x be the length of the pool.

Length of the pool and its border = x + 1 + 1
Length of the pool and its border = x + 2

----------------------------------------
Given area = 361 ft², find x:
----------------------------------------
(x+2)² = 361
x+ 2 = √361
x + 2 = 19
x = 19 - 2
x = 17

----------------------------------------
Find Length of the pool:
----------------------------------------
Length of the pool = x = 17 feet

----------------------------------------
Find Area of the pool:
----------------------------------------
Area = 17 x 17 
Area = 289 ft²

------------------------------------------------------------
Answer: Area of the pool = 289 ft²
------------------------------------------------------------

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Suppose that a brand of lightbulb lasts on average 1730 hours with a standard deviation of 257 hours. Assume the life of the lig
Debora [2.8K]

Answer:

P [  1689  ≤   X  ≤  2267 ]  = 54,88 %

Step-by-step explanation:

Normal Distribution

Mean        μ₀  =  1730

Standard Deviation      σ  = 257

We need to calculate  z scores for the values   1689     and      2267

We apply formula for z scores

z =  ( X -  μ₀ ) /σ

X = 1689     then

z = (1689 - 1730)/ 257      ⇒ z = - 41 / 257

z  = -  0.1595

And from z table we get  for  z =  - 0,1595

We have to interpolate

        - 0,15          0,4364

        - 0,16          0,4325

Δ  =   0.01           0.0039

0,1595  -  0,15  =  0.0095

By rule of three

0,01                  0,0039

0,0095                 x ??      x  =  0.0037

And    0,4364  -  0.0037  = 0,4327

Then    P [ X ≤ 1689 ]  =  0.4327     or    P [ X ≤ 1689 ]  = 43,27 %

And for the upper limit  2267  z  score will be

z  =  ( X - 1730 ) / 257       ⇒  z =  537 / 257

z  =  2.0894

Now from z table   we find  for score   2.0894

We interpolate and assume  0.9815

P [ X ≤ 2267 ]  =  0,9815

Ths vale already contains th value of   P [ X ≤ 1689 ]  =  0.4327

Then we subtract  to get    0,9815  -  0,4327   = 0,5488

Finally

P [ 1689  ≤   X  ≤  2267 ]  =  0,5488  or  P [  1689  ≤   X  ≤  2267 ]  = 54,88 %

8 0
3 years ago
Is that better is just need help
yawa3891 [41]
#1 Mrs. Garcia is making 50 snacks for her 5th grade class. If she uses four 1-kilogram bags of dried fruit, how many of grams of fruit will she use for each snack? 

1 kilogram is equal to 1000 grams.
4 kilograms is equal to 4000 grams. 

You would need to divide the 4000 total grams by the 50 snack to get how many grams would be in each snack.
So you would do..

4000grams/50snacks = 80 grams each snack.

#3 Toni's recipe also calls for seasonings. She needs to stir in 215 milligrams of pepper and 437 milligrams of salt. What is the difference between the total amount of seasonings and 1 gram?

215 milligrams is equal to 0.215 grams
437 milligrams is equal to 0.437 grams 

So you would add these two together
0.215 + 0.437 = 0.652 grams
Then to find the difference you would subtract 0.652 grams from 1 gram
1 - 0.652 = 0.348 
0.348 is the difference.

5 0
3 years ago
Read 2 more answers
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Otrada [13]

Step-by-step explanation:

the answer is in picture

4 0
3 years ago
Read 2 more answers
What would it cost to carpet a rectangular floor measuring 18 feet by 24 feet if the carpet costs $17.10 per square yard
cestrela7 [59]
It would cost $7387.20 for the entire rectangular floor. Hope this answers your question. :)
5 0
3 years ago
The graph of an inverse trigonometric function passes through the point (1, pi/2). Which of the following could be the equation
rodikova [14]

Answer: C) y=sin^-1 x

Step-by-step explanation:

Since, the graph of an inverse trigonometric function will pass through the point (1,\frac{\pi}{2}),

If this point satisfies the function,

For the function y=cos^{-1} x

If x = 1

y=cos^{-1}1=0

Thus,  (1,\frac{\pi}{2}) is not satisfying function  y=cos^{-1} x,

⇒ The graph of   y=cos^{-1} x is not passing through the point  (1,\frac{\pi}{2})

For the function y=cot^{-1}x

If x = 1

y=cot^{-1}1=\frac{\pi}{4}

Thus,  (1,\frac{\pi}{2}) is not satisfying function y=cot^{-1}x,

⇒ The graph of   y=cot^{-1}x is not passing through the point  (1,\frac{\pi}{2})

For the function y=sin^{-1} x

If x = 1

y=sin^{-1}1=\frac{\pi}{2}

Thus,  (1,\frac{\pi}{2}) is satisfying function y=sin^{-1} x,

⇒ The graph of   y=sin^{-1} x is passing through the point  (1,\frac{\pi}{2}).

For the function y=tan^{-1}x

If x = 1

y=tan^{-1}1=\frac{\pi}{4}

Thus,  (1,\frac{\pi}{2}) is not satisfying function  y=cos^{-1} x,

⇒ The graph of   y=tan^{-1} x is not passing through the point (1,\frac{\pi}{2}).

Hence, Option C is correct.

3 0
3 years ago
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