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3 years ago

P)

Mathematics

1 answer:

mars1129 [50]3 years ago

8 0

$375 - $150 is $225.

$225 divided by $25 is 9.

$25 x 9 = $225.

So it will take her 9 weeks to have enough to buy the iPad.

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If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

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2 years ago

A box contains 300 raffle tickets. Only 15 tickets are winning tickets. What is the

Roman55 [17]

Answer:

Step-by-step explanation:

15/300 = 0.05

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2 years ago

Decide if each question is statistical or nonstatistical.

lidiya [134]

Answer:

Stat, non, non, stat

Step-by-step explanation:

Only answers with numbers as answers are statistical.

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1 year ago

I need help with multiplying and dividing powers

Tamiku [17]

You need to know these two formulas:

$\huge a^b \times a^c = a^{b+c}\\\\\huge \frac{a^b}{a^c}=a^{b-c}$

For example,

$5^2 \times 5^3 = 5^{2+3} = 5^5$

$\frac{2^6}{2^4} = 2^{6-4} = 2^2$

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2 years ago

PLZ HELP ILL MARK U BRAINLIEST!!

pychu [463]

Answer:

Step-by-step explanation:

The two horizontal line segments are the parallel sides of the trapezoid.

∠1 and ∠2 are corresponding angles of a transversal across parallel lines, so

∠1 is congruent with ∠2

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2 years ago