Please help guys its due soon 24 points

A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature

Westkost [7]

Answer:

(a) The value of k is $\frac{1}{15}$ .

(b) The probability that at most three forms are required is 0.40.

(c) The probability that between two and four forms (inclusive) are required is 0.60.

(d) $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ is not the pmf of y.

Step-by-step explanation:

The random variable Y is defined as the number of forms required of the next applicant.

The probability mass function is defined as:

$P(y) = \left \{ {{ky};\ for \ y=1,2,...5 \atop {0};\ otherwise} \right$

(a)

The sum of all probabilities of an event is 1.

Use this law to compute the value of k.

$\sum P(y) = 1\\k+2k+3k+4k+5k=1\\15k=1\\k=\frac{1}{15}$

Thus, the value of k is $\frac{1}{15}$ .

(b)

Compute the value of P (Y ≤ 3) as follows:

$P(Y\leq 3)=P(Y=1)+P(Y=2)+P(Y=3)\\=\frac{1}{15}+\frac{2}{15}+ \frac{3}{15}\\=\frac{1+2+3}{15}\\ =\frac{6}{15} \\=0.40$

Thus, the probability that at most three forms are required is 0.40.

(c)

Compute the value of P (2 ≤ Y ≤ 4) as follows:

$P(2\leq Y\leq 4)=P(Y=2)+P(Y=3)+P(Y=4)\\=\frac{2}{15}+\frac{3}{15}+\frac{4}{15}\\ =\frac{2+3+4}{15}\\ =\frac{9}{15} \\=0.60$

Thus, the probability that between two and four forms (inclusive) are required is 0.60.

(d)

Now, for $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ to be the pmf of Y it has to satisfy the conditions:

$P(y)=\frac{y^{2}}{50}>0;\ for\ all\ values\ of\ y \\$
$\sum P(y)=1$

Check condition 1:

$y=1:\ P(y)=\frac{y^{2}}{50}=\frac{1}{50}=0.02>0\\y=2:\ P(y)=\frac{y^{2}}{50}=\frac{4}{50}=0.08>0 \\y=3:\ P(y)=\frac{y^{2}}{50}=\frac{9}{50}=0.18>0\\y=4:\ P(y)=\frac{y^{2}}{50}=\frac{16}{50}=0.32>0 \\y=5:\ P(y)=\frac{y^{2}}{50}=\frac{25}{50}=0.50>0$

Condition 1 is fulfilled.

Check condition 2:

$\sum P(y)=0.02+0.08+0.18+0.32+0.50=1.1>1$

Condition 2 is not satisfied.

Thus, $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ is not the pmf of y.

7 0

3 years ago

The hypotenuse of a 45 -45 -90 triangle measures 128 cm what is the length of one leg of the triangle

erma4kov [3.2K]

This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.

4 0

3 years ago

Read 2 more answers

Calculate the shaded areas for c and d

KiRa [710]

C)
Area of full triangle
1/2(8)(6)=24cm^2
Area of non shaded triangle
1/2(4)(3)=6cm^2
Area of full minus area of small triangle
24-6=18cm^2

D)
Area of Big rectangle
(4)(12)=48
Area of non shaded triangle
1/2(9)(4)=18
Area of Big rectangle minus non shaded triangle
48-18=30cm^2

5 0

3 years ago

If f(x) = 6x2 - 4 and g(x) = 2x + 2, find (f - g)(x).

Dafna11 [192]

Answer:

6x² - 2x - 6

Step-by-step explanation:

note (f - g)(x) = f(x) - g(x), thus

f(x) - g(x)

= 6x² - 4 - (2x + 2) ← distribute

= 6x² - 4 - 2x - 2 ← collect like terms

= 6x² - 2x - 6

7 0

3 years ago

Read 2 more answers

Jennifer edwards can subscribe to a newspaper for $99 for a year, $67 for eight months, $38 for four months, or $0.30 per day. w

mylen [45]

There are some kinds of subscription to a newspaper given. We have to find which is the best buy for it. We will find each subscription for a year and check which one is the lowest.

$99 for a year.

$67 for 8 months.

So for 1 month we will get by dividing it by 8.

We know that there are 12 months in a year.

So for 1 month = $67/8 = $8.375.

For 12 months = $(8.375)×12 = $100.5

So when the subscription is $67 for 8 months, it will take $100.5 for a year.

$38 for 4 months.

For 1 month = $38/4 = $9.5

For 12 months = $(9.5)×12 = $114

So when the subscription is $38 for 4 months, it is $114 for a year.

$0.30 per day.

We know that there are 365 days in a year.

So for 1 day = $0.30

For 365 days = $(0.30) × 365 = $109.5

So when the subscription is $0.30 per day, it is $109.5 for a year.

So the lowest is $99 for a year.

So we can say $99 for a year is the best buy.

6 0

3 years ago