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aivan3 [116]
3 years ago
13

What is the probability of drawing a heart or a club? A)0% B)50% C)100%

Mathematics
1 answer:
zlopas [31]3 years ago
5 0

Answer:

b = 50%

Step-by-step explanation:

P(Heart or Club)

= P(Heart) + P(Club)

= 13/52 + 13/52

= .25 + .25

= .5 --> 50%

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
nataly862011 [7]

Let (<em>x</em>, <em>y</em>, <em>z</em>) be a point on the plane in the first octant. The box formed by this point has volume <em>xyz</em>, and you want to maximize this subject to the equation of the plane.

Use the method of Lagrange multipliers: the Lagrangian is

<em>L</em>(<em>x</em>, <em>y</em>, <em>z</em>) = <em>xyz</em> - <em>λ</em> (<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6)

Find its critical points:

∂<em>L</em>/∂<em>x</em> = <em>yz</em> - <em>λ</em> = 0

∂<em>L</em>/∂<em>y</em> = <em>xz</em> - 2<em>λ</em> = 0

∂<em>L</em>/∂<em>z</em> = <em>xy</em> - 3<em>λ</em> = 0

∂<em>L</em>/∂<em>λ</em> = -(<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6) = 0

Solving the first three equations for <em>λ</em> gives

<em>λ</em> = <em>yz</em> = <em>xz</em>/2 = <em>xy</em>/3

Solve these equations for <em>y</em> and <em>z</em> :

• <em>yz</em> = <em>xz</em>/2   =>   <em>y</em> = <em>x</em>/2   =>   2<em>y</em> = <em>x</em>

• <em>yz</em> = <em>xy</em>/3   =>   <em>z</em> = <em>x</em>/3   =>   3<em>z</em> = <em>x</em>

Substitute these solutions into the last equation and solve for <em>x</em>, then again for <em>y</em> and <em>z</em> :

<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6 = 3<em>x</em> - 6 = 0   =>   3<em>x</em> = 6   =>   <em>x</em> = 2, <em>y</em> = 1, <em>z</em> = 2/3

At this critical point, the maximum volume is

<em>xyz</em> = 2*1*2/3 = 4/3

4 0
3 years ago
Find the average rate of change of the function from <img src="https://tex.z-dn.net/?f=x_%7B1%7D" id="TexFormula1" title="x_{1}"
meriva

Hi there!

\large\boxed{\text{Average rate} = 2}

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\text{Average rate} = \frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}

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f(1) = 1² - 4(1) + 10 = 7

f(5) = 5² - 4(5) + 10 = 15

Plug  the solved values into the equation:

\text{Average rate} = \frac{15 - 7}{5-1}

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2 years ago
(y 3 - y 2 + y + 3) ÷ (y + 1)
Rufina [12.5K]

Answer:

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Step-by-step explanation:

use synthetic division

-1| 1  -1  1  3

      -1  2 -3

   1  -2  3 (0)

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ladessa [460]

Answer:

because this figure does not have two parallel sides

I'm Sorry for by bad English but I am italian

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Estimate a 15% tip on a dinner bill of 71.85
Step2247 [10]
15% = 0.15
15% of 71.85 is equal 0.15*71.85 ≈ 10.78
4 0
3 years ago
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