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3 years ago

The spinner above is used in a game. What is the theoretical probability of the given event with one spin? P (5)

Mathematics

1 answer:

Sloan [31]3 years ago

5 0

Answer:

1 /8

Step-by-step explanation:

Given that :

Number of sections on spinner = (1,2,3,4,5,6,7,8) = 8

Number of 5's = 1

Recall :

Probability of event A = number required outcome / Total possible outcomes

P(5) = 1/8

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3 years ago

Find the value of c so that (x-5) is a factor of the polynomial p(x)

liubo4ka [24]

I think the question is

Find the value of c so that (x-5) is a factor of the polynomial

$p(x) = x^3 + 2x^2 + cx + 10$

The other factor is going to be some quadratic. We can say a few things about its coefficients but let's start by saying in general it's

$q(x)= ax^2 + bx + k$

$p(x) = (x-5)q(x)$

$x^3 + 2x^2 + cx + 10 = (x-5)(ax^2 + bx+k) = ax^3 + (b-5a)x^2 + (k-5b)x - 5k$

Equating respective coefficients,

$a=1$

$b-5a = 2$

$k - 5b = c$

$-5k = 10$

so we get

$b = 2 + 5 = 7$

$k = 10/-5 = -2$

$c = k - 5b = 2 - 5(7)= -37$

Answer: -37

Check:

$(x^2 + 7x - 2)(x - 5) = x^3 + 2 x^2 - 37 x + 10\quad\checkmark$

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