Can a trapezoid have four obtuse angles? Explain.

(1 point) An insurance company offers its policyholders a number of different premium payment options. For a randomly selected p

Olegator [25]

Answer:

a)

X | 1 3 5 7

f(X) | 0.4 0.2 0.2 0.2

b) $P(4$

Step-by-step explanation:

For this case we have defined the cumulative distribution function like this:

$F(X) = 0, x$

$F(X) = 0.4, 1 \leq x$

$F(X) = 0.6, 3 \leq x$

$F(X) = 0.8, 5 \leq x$

$F(X) = 1, x \geq 7$

And we know that the general definition for the distribution function is given by:

$F(x) = P(X \leq x) = \sum_{i\leq k} f(i)$

Where f represent the density function.

Part a

For this case we need to find the density function, so we can find the values for the density for each value of X = 1,2,3,4,5,6,7,... since X is a discrete random variable.

$f(1) = P(X=1) = P(X \leq 1) - P(X=0) = F(1) -F(0) = 0.4-0=0.4$

$f(2) = P(X=2) = P(X \leq 2) - P(X=0)- P(X=1) = F(2) -F(1) = 0.4-0.4=0$

$f(3) = P(X=3) = P(X \leq 3) - P(X=0)- P(X=1) -P(X=2) = F(3) -F(2) = 0.6-0.4=0.2$

$f(4) = P(X=4) = P(X \leq 4) - P(X=0)- P(X=1) -P(X=2)-P(X=3) = F(4) -F(3) = 0.6-0.6=0$

$f(5) = P(X=5) = P(X \leq 5) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4) = F(5) -F(4) = 0.8-0.6=0.2$

$f(6) = P(X=6) = P(X \leq 6) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5) = F(6) -F(5) = 0.8-0.8=0$

$f(7) = P(X=7) = P(X \leq 7) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5)-P(X=6) = F(7) -F(6) = 1-0.8=0.2$

And for any value higher than 7 we have that:

$x_i \in [8,9,10,...]$

$f(x_i) = F(X_i) -F(X_i -1) = 1-1=0$

So then we have our density function defined like this:

X | 1 3 5 7

f(X) | 0.4 0.2 0.2 0.2

Part b

For this case we want to find this probability $P(4$

And since the random variable is discrete we can write this like that:

$P(4$

5 0

3 years ago

14. A unfair coin has the probability of heads

Hitman42 [59]

Answer :

the probability of tossing three heads in a row

$=\left( \frac{3}{8} \right)^{3} =\frac{27}{512} =0.052734375$

…………………………………………

the probability of tossing two heads followed by one tail

$=\left( \frac{3}{8} \right)^{2} \times \left( \frac{5}{8} \right) =\frac{45}{512}$

……………………………

the probability of two heads and one tail in any order

$=3\times \left( \frac{3}{8} \right)^{2} \times \left( \frac{5}{8} \right) =\frac{135}{512}$

3 0

2 years ago

What is the value of r in the equation 4r – 8 = 5r + 12? (4 points)

katrin [286]

4r - 8 = 5r + 12
4r - 5r = 12 + 8
-r = 20
r = -20 <===

7 0

3 years ago

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the relationship between the x- and y- values in each table is linear. write a function. find the amount and rate of change. (5

Doss [256]

(5)

Since, the relationship is linear

so, we can use point slope form of line and find equation of line

we can select any two points

first point is (4,10)

so, x1=4 , y1=10

second point is (7,17.5)

so, x2=7 , y2=17.5

now, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{17.5-10}{7-4}$

$m=2.5$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

now, we can plug values

$y-10=2.5(x-4)$

we get

$y=2.5x$

Initial amount:

It is the value of y when x=0

so, we can plug x=0 and find y

$y=2.5\times 0$

$y=0$

So, initial amount is 0

Rate of change:

we know that rate of change is slope

so, m=2.5

so, the rate of change is 2.5

(6)

Since, the relationship is linear

so, we can use point slope form of line and find equation of line

we can select any two points

first point is (2,29)

so, x1=2 , y1=29

second point is (5,41)

so, x2=5 , y2=41

now, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{41-29}{5-2}$

$m=4$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

now, we can plug values

$y-29=4(x-2)$

we get

$y=4x+21$

Initial amount:

It is the value of y when x=0

so, we can plug x=0 and find y

$y=4\times 0+21$

$y=21$

So, initial amount is 21

Rate of change:

we know that rate of change is slope

so, m=4

so, the rate of change is 4

6 0

3 years ago

Eileen plant a tree that is 2 meters tall in her yard which of the following is equivalent to meters following is equivalent to

Grace [21]

Answer:

D

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers