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Korvikt [17]
3 years ago
15

Consider two events such that P(A)=1/4, P(B)=2/5, and P(A∩B)=1/10. Are events A and B independent events?

Mathematics
1 answer:
Ray Of Light [21]3 years ago
3 0
Yes, they are independent. First of all, we know that P(A) = 1/4, P(B) = 2/5, and P(A and B) = 1/10. To know if two events are independent, the following questions must be true: P(A)*P(B) = P(A and B). So since (1/4)*(2/5) = 2/20 which equals 1/10, these events are independent
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Simplify the expression:-5-(-26)​
cluponka [151]

Answer:

21

Step-by-step explanation:

-(-26) would be positive 26 because one negative multiplied by another negative equals a positive. We are left with -5+26 which would equal 21.

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3 years ago
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A person can pay $27 for a membership to the science Museum and then go to the museum for just a $1.00 per visit. What is the ma
HACTEHA [7]

Answer:

10

Step-by-step explanation:

27 + 1(10) = 37

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Let f(x)=x^3-x-1
alexira [117]
f(x) = x^3 - x - 1

To find the gradient of the tangent, we must first differentiate the function.

f'(x) = \frac{d}{dx}(x^3 - x - 1) = 3x^2 - 1

The gradient at x = 0 is given by evaluating f'(0).

f'(0) = 3(0)^2 - 1 = -1

The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.

The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

y = -x + c

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

f(0) = (0)^3 - (0) - 1 = -1

So the point (0, -1) lies on the tangent. Substituting into the tangent equation:

y = -x + c \\\\ -1 = -(0) + c \\\\ -1 = c \\\\ \text{Equation of tangent is } \boxed{y = -x - 1}
6 0
3 years ago
Which is the function represented by the table?
gregori [183]
I’m pretty sure it’s B
7 0
3 years ago
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A waitress sold 12 ribeye steak dinners and 39 grilled salmon totaling $575.53 on a particular day. Another day she sold 25 ribe
Talja [164]

Answer:

cost of ribeye steak dinners = $10.36

cost of grilled salmon= $11.581

Step-by-step explanation:

Let the cost of one steak dinners be x

Let the cost of one  grilled salmon be y

One a particular day the waitress sells  12 ribeye steak dinners and 39 grilled salmon for a total is $575.53 which can be written in equation as

12(x)+39(y)= $575.53-------------------------------------(1)

On another day she sells  25 ribeye steak dinners and 13 grilled salmon dinners  totals to $582.43.This can be represented  as

25(x)+ 13(y)= $582.43-------------------------------------(2)

solving the equation (1) and (2)

eq(1) x 112x+39y= 575.53

eq(2) x 3125x+ 39y= 1747.29-------------------------(3)

Subtracting these equation we get,

113x=1171.76

x=\frac{1171.76}{113}

x= 10.36

Now  substituting this in equation (1)

12(10.36)+39(y)= $575.53

123.84+39y=575.53

39y=575.53 - 123.84

y=\frac{451.69}{39}

y=11.581

7 0
3 years ago
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