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omeli [17]
3 years ago
8

Which pair of undefined terms is used to define the term parallel lines?

Mathematics
1 answer:
nikdorinn [45]3 years ago
3 0

Answer:

The undefined terms needed to define parallel lines are 'lines' and 'points. ' In geometry, there are three undefined terms: points, lines

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
What are the next three terms of the following sequence?
kaheart [24]

we know that given terms were i geometric progression.

which means common ratio is same between two consecutive terms .

here we have 8,40,200,1000.

we know that common ratio =second term/first term =40/8=5.

so each and every terms is multiplied by 5 to get next term for this series the term after 1000 is 5000 =1000*5.

in part b we have another series which is having common ratio of -2.

so we need to multiply with -2 to find next term.

80*(-2)=-160.

for part c the common ratio is -2 .

so we need to multiply with -2 *previous term =-2*16 =-32.

5 0
3 years ago
Read 2 more answers
Please solve quickly
Lilit [14]
6/9 .. z. Z. Z. Z. Z. Z.
3 0
3 years ago
Aaron, Bonny and Connor are playing a game with cards.
professor190 [17]

Let the number of cards Aaron has : A

Given :

⊕   Bonny has twice as many cards as Aaron

⊕   Connor has 6 cards more than Bonny

⊕   Total cards : 101

⇒  Number of cards Bonny has : 2A

⇒  Number of cards Connor has : 2A + 6

⇒   Aaron cards + Bonny cards + Connor cards = 101

⇒   A + 2A + 2A + 6 = 101

⇒   5A = 101 - 6

⇒   5A = 95

⇒   A = 19

<u>Answer</u> : Aaron has 19 Cards

6 0
3 years ago
A recipe for lemon bars called for 9" X 13" pan. How many 1" X 1" bars can be cut? How many 2" X 2" bars can be cut? How much is
gregori [183]

The number of bars which can be cut for the 1" X 1" and 2" X 2" square bars are; 117 and 29 units respectively.

<h3>How many bars can be cut from the pan in each case?</h3>

The total area of the given pan can be evaluated as follows;

Area = length × width

= 9 × 13

= 117 square units.

Hence, the number of 1" X 1" bars can be cut which can be cut from the pan;

= 117/(1×1)

= 117 1" X 1" bars.

For the 2" X 2" square bars, we have;

= 117/(2×2);

29 remainder 1 square unit.

Ultimately, one square unit of the pan is wasted for the 2" X 2" square bars.

Read more on area;

brainly.com/question/8294080

#SPJ1

8 0
2 years ago
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