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3 years ago

If you and a friend each toss two pennies at the same time, what is the probability that all four pennies will be tails?

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

4 0

Answer:

1/16

Step-by-step explanation:

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2) I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

Given function:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find a, compare the coefficients of x³:

$\implies a=3$

To find b, substitute the found value of a into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find c, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

Zero Product Property

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

1 year ago

Find the least common denominator x^4/x^2+2x+1 and -8/x^2+5x+4

Harman [31]

Answer:

(x + 4)(x + 1)(x + 1) or (x + 4)(x + 1)²

Step-by-step explanation:

Factor both denominators and see what you are missing between them

(x^4)/[(x + 1)(x + 1) -8/[x + 4)(x + 1)]

So in order to get a common denominator, we need

(x + 4)(x + 1)(x + 1) as a denominator, or (x +4)(x + 1)²

6 0

3 years ago

PLZZZ HELP ME!!!!! Complete the table for the function f(x) = 2x - 3

Lana71 [14]

Answer:

Step-by-step explanation:

f(x) = 2x - 3

f(-2) = 2(-2) -3 = -4 - 3 = -7

f(-1) = 2(-1) -3 = -2 - 3 = - 5

f(0) = 2(0) -3 = 0 - 3 = -3

f(1) = 2(1) -3 = 2 - 3 = -1

f(2) = 2(2) -3 = 4 - 3 = 1

f(3) = 2(3) -3 = 6 - 3 = 3

4 0

3 years ago

Convert each degrees minutes seconds into decimal degrees 351°41’142”

pav-90 [236]

Answer:

351.7227778°

Step-by-step explanation:

3 0

2 years ago

Select the correct answer.

Katena32 [7]

Answer:C consumer price index

Step-by-step explanation:

7 0

2 years ago