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3 years ago

7

If A and B are two independent events with P(A)=2÷3 and P(B) =1÷5, find P(AUB).

1 answer:

iren [92.7K]3 years ago

3 0

Answer:

$for \: independent \: events : \\ P(AUB) = P(A) + P(B) \\ P(AUB) = \frac{2}{3} + \frac{1}{5} \\ = \frac{13}{15}$

Step-by-step explanation:

P(AUB) is P(A) + P(B) because P(AnB) is zero.

$P(AUB) = P(A) + P(B) - P(A{ \huge{n} }B) \\ P(AUB) = P(A) + P(B) + 0$

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60 POINTS!!!!!!!!!! If each square of the grid below is 0.5 cm by 0.5 cm, how many centimeters (cm) are in the perimeter of the

Aleks04 [339]

Answer:

21 cm

Step-by-step explanation:

The perimeter is the length of the outside of a shape. In this case, we can simply add up all the edges and multiply by .5(the length of one edge).

Horizontal Edges: 22

Vertical Edges: 20

Total: 42

Perimeter = $42 * 0.5 = 21 cm$

8 0

3 years ago

Find the derivative of f(x) = 12x^2 + 8x at x = 9.

zvonat [6]

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

$(f+g)'=f'+g'$ Sum rule.

$(cf)'=cf'$ Constant multiple rule.

$(x^n)'=nx^{n-1}$ Power rule.

$(x)'=1$ Slope of y=x is 1.

$f(x)=12x^2+8x$

$f'(x)=(12x^2+8x)'$

$f'(x)=(12x^2)'+(8x)'$ by sum rule.

$f'(x)=12(x^2)+8(x)'$ by constant multiple rule.

$f'(x)=12(2x)+8(1)$ by power rule.

$f'(x)=24x+8$

Now we need to find the derivative function evaluated at x=9.

$f'(9)=24(9)+8$

$f'(9)=216+8$

$f'(9)=224$

In case you wanted to use the formal definition of derivative:

$f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

Or the formal definition evaluated at x=a:

$f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$

Let's use that a=9.

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

We need to find f(9+h) and f(9):

$f(9+h)=12(9+h)^2+8(9+h)$

$f(9+h)=12(9+h)(9+h)+72+8h$

$f(9+h)=12(81+18h+h^2)+72+8h$

(used foil or the formula (x+a)(x+a)=x^2+2ax+a^2)

$f(9+h)=972+216h+12h^2+72+8h$

Combine like terms:

$f(9+h)=1044+224h+12h^2$

$f(9)=12(9)^2+8(9)$

$f(9)=12(81)+72$

$f(9)=972+72$

$f(9)=1044$

Ok now back to our definition:

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

$f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}$

Simplify by doing 1044-1044:

$f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}$

Each term has a factor of h so divide top and bottom by h:

$f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}$

$f'(9)=\lim_{h \rightarrow 0}(224+12h)$

$f'(9)=224+12(0)$

$f'(9)=224+0$

$f'(9)=224$

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3 years ago

What is the answer and if you answer it thank you

stiv31 [10]

Answer:

you didn't put a question.

Step-by-step explanation:

8 0

3 years ago

HELP ASSAP WILL MARK BRAINIEST!!!!!!

hram777 [196]

Answer:

m= -5/4

Step-by-step explanation:

Slope can be translated to "rise over run". You go down 5 spaces and then move over 4 spaces.

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4 years ago

According to the Rational Root Theorem, what are all the potential rational roots of fx) = 5x - 7x + 11?

Ahat [919]

Answer:

±1/5, ±1, ±11/5, ±11

Step-by-step explanation:

Potential rational roots of 5x² -7x +11 will be of the form ...

(divisor of 11)/(divisor of 5)

so will include ...

±1/5, ±1, ±11/5, ±11

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3 years ago