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tigry1 [53]
3 years ago
12

Mark each situation as an example of experimental or theoretical probability.

Mathematics
1 answer:
Delicious77 [7]3 years ago
3 0

Answer:

You chose correctly

Step-by-step explanation:

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ASAP NEED HELP!!!! ∩ω∩ Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. A san
Nikitich [7]

Answer:

Step-by-step explanation:

A. The first inequality is graphed as a shaded area below the solid line with x-and y-intercepts of 7.5 and 5, respectively. The second inequality is graphed as a shaded area above the solid line with x- and y-intercepts of 3.

The solution set is the set of integer-valued grid points one or between the lines.

__

B. The point (5, 1) is included in the solution area. Mathematically, it can be shown to satisfy the two inequalities:

  2(5) +3(1) ≤ 15   ⇒   13 ≤ 15   True

  (5) +(1) ≥ 3   ⇒   6 ≥ 3   True

__

C. The point (5, 1) is in the solution set. It means Michael can purchase 5 sandwiches and 1 hot lunch within his budget constraints. That will provide 6 meals, which is more than the minimum of 3 that he wants to provide.

8 0
3 years ago
The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) for Determine
salantis [7]

The question is incomplete. Here is the complete question.

The probability density function of the time to failure of an electronic component in a copier (in hours) is

                                              f(x)=\frac{e^{\frac{-x}{1000} }}{1000}

for x > 0. Determine the probability that

a. A component lasts more than 3000 hours before failure.

b. A componenet fails in the interval from 1000 to 2000 hours.

c. A component fails before 1000 hours.

d. Determine the number of hours at which 10% of all components have failed.

Answer: a. P(x>3000) = 0.5

              b. P(1000<x<2000) = 0.2325

              c. P(x<1000) = 0.6321

              d. 105.4 hours

Step-by-step explanation: <em>Probability Density Function</em> is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

So, probability function is given by:

P(a<x<b) = \int\limits^b_a {P(x)} \, dx

Then, for the electronic component, probability will be:

P(a<x<b) = \int\limits^b_a {\frac{e^{\frac{-x}{1000} }}{1000} } \, dx

P(a<x<b) = \frac{1000}{1000}.e^{\frac{-x}{1000} }

P(a<x<b) = e^{\frac{-b}{1000} }-e^\frac{-a}{1000}

a. For a component to last more than 3000 hours:

P(3000<x<∞) = e^{\frac{-3000}{1000} }-e^\frac{-a}{1000}

Exponential equation to the infinity tends to zero, so:

P(3000<x<∞) = e^{-3}

P(3000<x<∞) = 0.05

There is a probability of 5% of a component to last more than 3000 hours.

b. Probability between 1000 and 2000 hours:

P(1000<x<2000) = e^{\frac{-2000}{1000} }-e^\frac{-1000}{1000}

P(1000<x<2000) = e^{-2}-e^{-1}

P(1000<x<2000) = 0.2325

There is a probability of 23.25% of failure in that interval.

c. Probability of failing between 0 and 1000 hours:

P(0<x<1000) = e^{\frac{-1000}{1000} }-e^\frac{-0}{1000}

P(0<x<1000) = e^{-1}-1

P(0<x<1000) = 0.6321

There is a probability of 63.21% of failing before 1000 hours.

d. P(x) = e^{\frac{-b}{1000} }-e^\frac{-a}{1000}

0.1 = 1-e^\frac{-x}{1000}

-e^{\frac{-x}{1000} }=-0.9

{\frac{-x}{1000} }=ln0.9

-x = -1000.ln(0.9)

x = 105.4

10% of the components will have failed at 105.4 hours.

5 0
3 years ago
Who built Cape Coast Castle ​
lana [24]

Answer:

Swedish Africa Company

4 0
3 years ago
Determine the equation of the circle graphed below.
sergij07 [2.7K]

Answer:

Equation = (x - 6 )² + ( y + 3 )² = 9

Step-by-step explanation:

The circle passes through ( 6, 0) and  ( 6 , -6)

They are the coordinates of the diameter.

Using this we can find the centre of the circle.

<u>Find the centre of the circle.</u>

Centre of the circle is the mid- point of (6, 0) and ( 6, -6)

      Centre = (\frac{x_1+x_2}{2} , \frac{y_1 + y_2}{2})

                 =(\frac{6 + 6}{2}, \frac{0 + (-6)}{2})\\\\=(6, -3)

<u>Find the radius of the circle.</u>

Radius = \frac{Diameter }{2}

Diameter is the distance between the points (6 , 0) and ( 6, - 6)

Diameter = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2\\}

               =\sqrt{(6-6)^2 + (-6 -0)^2}\\\\=\sqrt{0 + 36} \\\\= 6

Therefore,

    Radius ,r = \frac{6}{2} = 3

<u>Standard equation of a circle:</u>

<u></u>(x - a)^2 + (y - b)^2 = r^2 \ where \ (a , b) \ is \ the\ centre \ coordinates.<u></u>

Therefore , equation of the circle ;

                    (x - 6)^2 + (y + 3)^2 = 3^2\\\\(x -6)^2 + (y + 3)^2 = 9

6 0
3 years ago
What is the range of possible sizes for side x?
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