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alexira [117]
3 years ago
10

Circle b with center b(0, -2) that passes through (-6, 0)

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
5 0

Answer:

h

Step-by-step explanation:

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11. Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x) 5 5 0 x , 0
NISA [10]

Question not properly presented

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x)

0 ------ x<0

x²/25 ---- 0 ≤ x ≤ 5

1 ----- 5 ≤ x

Use the cdf to obtain the following.

(a) Calculate P(X ≤ 4).

(b) Calculate P(3.5 ≤ X ≤ 4).

(c) Calculate P(X > 4.5)

(d) What is the median checkout duration, μ?

e. Obtain the density function f (x).

f. Calculate E(X).

Answer:

a. P(X ≤ 4) = 16/25

b. P(3.5 ≤ X ≤ 4) = 3.75/25

c. P(4.5 ≤ X ≤ 5) = 4.75/25

d. μ = 3.5

e. f(x) = 2x/25 for 0≤x≤2/5

f. E(x) = 16/9375

Step-by-step explanation:

a. Calculate P(X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(X ≤ 4) = F(x) {0,4}

P(X ≤ 4) = x²/25 {0,4}

P(X ≤ 4) = 4²/25

P(X ≤ 4) = 16/25

b. Calculate P(3.5 ≤ X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(3.5 ≤ X ≤ 4) = F(x) {3.5,4}

P(3.5 ≤ X ≤ 4) = x²/25 {3.5,4}

P(3.5 ≤ X ≤ 4) = 4²/25 - 3.5²/25

P(3.5 ≤ X ≤ 4) = 16/25 - 12.25/25

P(3.5 ≤ X ≤ 4) = 3.75/25

(c) Calculate P(X > 4.5).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(4.5 ≤ X ≤ 5) = F(x) {4.5,5}

P(4.5 ≤ X ≤ 5) = x²/25 {4.5,5}

P(4.5 ≤ X ≤ 5)) = 5²/25 - 4.5²/25

P(4.5 ≤ X ≤ 5) = 25/25 - 20.25/25

P(4.5 ≤ X ≤ 5) = 4.75/25

(d) What is the median checkout duration, μ?

Median is calculated as follows;

∫f(x) dx {-∝,μ} = ½

This implies

F(x) {-∝,μ} = ½

where F(x) = x²/25 for 0 ≤ x ≤ 5

F(x) {-∝,μ} = ½ becomes

x²/25 {0,μ} = ½

μ² = ½ * 25

μ² = 12.5

μ = √12.5

μ = 3.5

e. Calculating density function f (x).

If F(x) = ∫f(x) dx

Then f(x) = d/dx (F(x))

where F(x) = x²/25 for 0 ≤ x ≤ 5

f(x) = d/dx(x²/25)

f(x) = 2x/25

When

F(x) = 0, f(x) = 2(0)/25 = 0

When

F(x) = 5, f(x) = 2(5)/25 = 2/5

f(x) = 2x/25 for 0≤x≤2/5

f. Calculating E(X).

E(x) = ∫xf(x) dx, 0,2/5

E(x) = ∫x * 2x/25 dx, 0,2/5

E(x) = 2∫x ²/25 dx, 0,2/5

E(x) = 2x³/75 , 0,2/5

E(x) = 2(2/5)³/75

E(x) = 16/9375

4 0
3 years ago
A football field is 160 feet wide and 360 feet in length. What is the distance around the field?
charle [14.2K]

Answer: 160 + 160 = 320

360 + 360 = 720

720 + 320 = 1040

6 0
3 years ago
Determined to find the slope<br>(1,7K) and (-3,5k)​
Nadusha1986 [10]

9514 1404 393

Answer:

  slope = k/2

Step-by-step explanation:

The slope formula is useful for finding slope.

  m = (y2 -y1)/(x2 -x1)

  m = (5k -7k)/(-3 -1)

  m = -2k/-4

  m = k/2

The slope is k/2.

4 0
3 years ago
Simplify.
NikAS [45]

= (16x3 - 8x2 + 4x4) / 2x

= 4x * (4x2 - 2x + x3) / 2x

= 2 * (4x2 - 2x + x3)

= 8x2 - 4x + 2x3

Answer A

4 0
3 years ago
Read 2 more answers
Which values for h and k are used to write the function f of x = x squared 12 x 6 in vertex form?
Nesterboy [21]

The values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

<h3>How to rewrite in vertex form?</h3>

The equation is given as:

f(x) = x^2 + 12x + 6

Rewrite as:

x^2 + 12x + 6 = 0

Subtract 6 from both sides

x^2 + 12x = -6

Take the coefficient of x

k = 12

Divide by 2

k/2 = 6

Square both sides

(k/2)^2 = 36

Add 36 to both sides of x^2 + 12x = -6

x^2 + 12x + 36= -6 + 36

Evaluate the sum

x^2 + 12x + 36= 30

Express as perfect square

(x + 6)^2 = 30

Subtract 30 from both sides

(x + 6)^2 -30 = 0

So, the equation f(x) = x^2 + 12x + 6 becomes

f(x) = (x + 6)^2 -30

A quadratic equation in vertex form is represented as:

f(x) = a(x - h)^2 + k

Where:

Vertex = (h,k)

By comparison, we have:

(h,k) = (-6,-30)

Hence, the values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

Read more about quadratic functions at:

brainly.com/question/1214333

#SPJ1

3 0
2 years ago
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