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3 years ago

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Let the positive numbers a, b, c. Prove that

7B2013%7D%20%7D%7Ba%5E%7B2012%7D%2Bb%5E%7B2012%7D%2Bc%5E%7B2012%7D%7D%20%5Cgeq%20%5Cfrac%7Ba%2Bb%2Bc%7D%7B3%5C%5C%7D" id="TexFormula1" title="\frac{a^{2013}+b^{2013}+c^{2013} }{a^{2012}+b^{2012}+c^{2012}} \geq \frac{a+b+c}{3\\}" alt="\frac{a^{2013}+b^{2013}+c^{2013} }{a^{2012}+b^{2012}+c^{2012}} \geq \frac{a+b+c}{3\\}" align="absmiddle" class="latex-formula">

1 answer:

Serggg [28]3 years ago

7 0

Answer:

I don't need to prove it, I already believe you

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The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz

9966 [12]

Answer:

$(a)\ Area = 3765.32$

$(b)\ Area = 4773$

Step-by-step explanation:

Given

$A_1 = 169in^2$ --- area of each square

$Shade = 4in$

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

$L^2 = A_1$

$L^2 = 169$

$L = \sqrt{169$

$L=13$

The length of two squares make up the radius of the semicircle.

So:

$r = 2 * L$

$r = 2*13$

$r = 26$

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

$A_2 = 16 * 169$

$A_2 = 2704$

The area of the semicircle is:

$A_3 = \frac{\pi r^2}{2}$

$A_3 = \frac{3.14 * 26^2}{2}$

$A_3 = 1061.32$

So, the area of the window is:

$Area = A_2 + A_3$

$Area = 2704 + 1061.32$

$Area = 3765.32$

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

$Length = 4 * 13 + 8$

$Length = 60$

$Height = 4*13 + 4$

$Height = 56$

The area is:

$A_1 = 60 * 56 = 3360$

The radius of the semicircle becomes initial radius + 4

$r = 26 + 4 = 30$

The area is:

$A_2 = \frac{3.14 * 30^2}{2} = 1413$

The area of the shade is:

$Area = A_1 + A_2$

$Area = 3360 + 1413$

$Area = 4773$

7 0

3 years ago

Ann has bought 10 pounds of dog food. She feeds her dog

Yanka [14]

Answer:

25 meals

Step-by-step explanation:

She has 10 pounds total and she feeds 2/5 per meal, so we do 10/(2/5)) to get 25

Hope this helps

5 0

3 years ago

PLZZZZ HELPPPPPPPPP!!!! a survey asks teachers and students whether they would like the new school mascot to be a Viking or a Pa

VARVARA [1.3K]

Answer:

B

Step-by-step explanation:

Two events A and B are called independent, when

$P(B|A)=P(B),$

where $P(B|A)$ is the probability that B occurs given that A has already occurred.

A = randomly selected person is a student

B = randomly selected person prefer "Vikings"

B|A = randomly selected student prefer "Vikings"

Probabilities:

$P(A)=\dfrac{100}{125}=\dfrac{4}{5}=0.8\\ \\P(B|A)=\dfrac{80}{85}=\dfrac{16}{17}\approx 0.94$

Since

$0.80\neq 0.94$

we can state that events are not independent.

8 0

3 years ago

Read 2 more answers

Suppose that P(A) = 0.25 and P(B) = 0.40 . If P(A|B)=0.20 , what is P(B|A) ?

Ket [755]

Answer:

0.32

Step-by-step explanation:

<u>Use of formula:</u>

P(A and B) = P(A)*P(B|A) and
P(A and B) = P(B)*P(A|B)

<u>According to above and based on given:</u>

P(A)P(B|A) = P(B)P(A|B)
P(B|A) = P(A|B)*P(B)/P(A)
P(B|A) = 0.20*0.40/0.25 = 0.32

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3 years ago

A surveyor wants to know how many shoppers at a mall like to read books. He surveys 100 people coming out of a bookstore at the

denpristay [2]

Its B. <span>People who shop in bookstores are likely to read more books than those who do not.</span>

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3 years ago