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2 years ago

11

At the school carnival, Jade has a game booth with a spinner. The banner at her booth reads "70% chance of winning!" What is the

chance that a player may not win?
15%?
30%?
35%?
50%?

2 answers:

Ronch [10]2 years ago

8 0

The answer is 30% because if there is a 70% chance then minus 70% from 100% you get 30%

galina1969 [7]2 years ago

5 0

30% because 100-70=30 just add a percent sign after the number.

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Step-by-step explanation:

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2 years ago

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

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-b = -29 <=> b = 29

So

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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3 years ago

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2 years ago

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Answer:

$(x-5)^2+(y-2)^2=9\\$

Step-by-step explanation:

So, you basically want the equation of the circle.

Given:

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$(x-h)^2+(y-k)^2=r^2\\$

Where, $(h, k)$ represents the center point and $r$ is the radius of the circle.

Plotting the values in the equation:

$(x-5)^2+(y-2)^2=3^2\\$

$(x-5)^2+(y-2)^2=9\\$

This is the equation of the circle of center (5, 2) and radius 3.

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