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2 years ago

13

there are ten names in a hat. how many ways are there to draw three names for first, second and third prizes from the hat, assum

ing each person can win only one prize

1 answer:

DIA [1.3K]2 years ago

8 0

Answer:

720 ways

Step-by-step explanation:

10 P 3

or 10 * 9 * 8 = 720 ways

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Rewrite the function by completing the square. 4x^2-4x+1=0

andrey2020 [161]

Do in <u>completing the square method.</u>

${4x}^{2} - 4x + 1 = 0 \\ 4x^{2}-4x=-1 \\ \frac{4x^{2}-4x}{4}=\frac{-1}{4} \\ x^{2}+\frac{-4}{4}x=\frac{-1}{4} \\ x^{2}-x=\frac{-1}{4} \\ x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-\frac{1}{4}+\left(-\frac{1}{2}\right)^{2} \\ x^{2}-x+\frac{1}{4}=\frac{-1+1}{4} \\ x^{2}-x+\frac{1}{4}=0 \\ \left(x-\frac{1}{2}\right)^{2}=0 \\ \sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{0}$

Now simplify.

$x-\frac{1}{2}=0 \\ x-\frac{1}{2}=0 \\ \\ \rightarrow \: x=\frac{1}{2} \\ \rightarrow \: x=\frac{1}{2}$

So, answer is..

$\boxed{x=\frac{1}{2} }$

Now <u>rewrite</u> the equation.

$4 x ^ { 2 } - 4 x + 1 = 0 \\ \boxed{4\times \left(\frac{1}{4}\right)-4\times \left(\frac{1}{2}\right)+1=0 }$

<u>Verification :-</u>

$4 x ^ { 2 } - 4 x + 1 = 0 \\ 4\times \left(\frac{1}{4}\right)-4\times \left(\frac{1}{2}\right)+1=0 \\ 1-4\times \left(\frac{1}{2}\right)+1=0 \\ 1-\frac{4}{2}+1=0 \\ 1-2+1=0 \\ -1+1=0 \\ \underline{ 0 = 0} \: \\ \dashrightarrow \text{true}$

3 0

3 years ago

Use simpson's rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. compare y

Lubov Fominskaja [6]

y = ln x , 1 <= x <= 3, about x axis and n = 10, dy/dx = 1/ x

S = (b a) ∫ 2π y √( 1 + (dy/dx) ^2) dx

so our f(x) is 2π y √( 1 + (dy/dx) ^2)

(b - a) / n = / 3 = (3-1) / 30 = 1/15

x0 = 1 , x1 = 1.2, x2 = 1.4, x3 = 1.6 ....... x(10) = 3

So we have , using Simpsons rule:-

S10 = (1/15) ( f(x0) + 4 f(x1) + 2 f)x2) +.... + f(x10) )

= (1/15) f(1) + f(3) + 4(f(1.2) + f(1.6) + f(2) + f(2.4) + f(2.8)) + 2(f(1.4) + f(1.8) + f(2.2) + f(2.6) )

( Note f(1) = 2 * π * ln 1 * √(1 + (1/1)^2) = 0 and f(3) = 2π ln3√(1+(1/3^2) = 7,276)

so we have S(10)

= 1/15 ( 0 + 7.2761738 + 4(1.4911851 +

5 0

4 years ago

Whats the solution X3=9

Naya [18.7K]

Answer:

x=2.080084

Step-by-step explanation: take cube root

8 0

3 years ago

Read 2 more answers

Tickets for the school football game cost $10 for students and $12 for non-students. A total of 150 ticketswere sold and $1440 w

lyudmila [28]

x = students = $10

y = non students = $12

total tickets = 150

Equations

x + y = 150

10x + 12y = 1440

x = 150 - y

10(150 - y) + 12y = 1440

1500 - 10y + 12y = 1440

2y = 1440 - 1500

2y = -60

y = -60/2

y = 30

x = 150 -

4 0

1 year ago

{(-1, 4), (-1, 9), (-1, 15), (-1, 0)}

marishachu [46]

Answer:

domain is -1

range is {4, 9, 15, 0}

function: not a function

6 0

3 years ago