I suppose the integral is

The integration region corresponds to a sector of a cirlce with radius 5 subtended by a central angle of π/4 rad. We can capture this region in polar coordinates by the set

Then
,
, and
. So the integral becomes

The equation for the line would be Y=1/2x -2
Answer:
You would use a^2 + b^2 = c^2
Step-by-step explanation:
a and b are the shorter side of the triangle whereas c is the hypotenuse or longest side of the triangle
Answer:
<em> Anna's wand can cast 70 spells</em>
<em></em>
Step-by-step explanation:
Elsa's wand can cast 53 spells
her wand casts 17 fewer cells than her sister Anna's
Amount of spells cast by Anna's wand = ?
We write the question down in the form of an equation

where
is the amount of spells Anna's wand can cast.
we then proceed to solve by collecting like terms to different sides of the equation. We'll have

which leaves us with

This means that<em> Anna's wand can cast 70 spells.</em>
Answer:
A) 68.33%
B) (234, 298)
Step-by-step explanation:
We have that the mean is 266 days (m) and the standard deviation is 16 days (sd), so we are asked:
A. P (250 x < 282)
P ((x1 - m) / sd < x < (x2 - m) / sd)
P ((250 - 266) / 16 < x < (282 - 266) / 16)
P (- 1 < z < 1)
P (z < 1) - P (-1 < z)
If we look in the normal distribution table we have to:
P (-1 < z) = 0.1587
P (z < 1) = 0.8413
replacing
0.8413 - 0.1587 = 0.6833
The percentage of pregnancies last between 250 and 282 days is 68.33%
B. We apply the experimental formula of 68-95-99.7
For middle 95% it is:
(m - 2 * sd, m + 2 * sd)
Thus,
m - 2 * sd <x <m + 2 * sd
we replace
266 - 2 * 16 <x <266 + 2 * 16
234 <x <298
That is, the interval would be (234, 298)