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3 years ago

Which of the following best describe(s) the diagonals of a rectangle. Select all that apply.

Mathematics

2 answers:

marin [14]3 years ago

7 0

The answers are congruent and intersecting

Mumz [18]3 years ago

6 0

Answer: The correct options are (a) congruent and (d) intersecting.

Step-by-step explanation: We are to select the correct options that best describes the diagonals of a rectangle.

<u>RECTANGLE:</u> A rectangle is a quadrilateral in which

(i) the adjacent sides are perpendicular,

(ii) opposite sides are parallel and congruent,

(iii) Each angle is a right angle,

(iv) The diagonals are congruent and bisect each other.

For example, in the attached figure, ABCD is a rectangle.

The diagonals AC and BD are congruent and they intersect at the point 'O' such that AO = OC, BO = OD.

Therefore, the diagonals of a rectangle are congruent and intersecting.

Thus, the correct options are (a) and (d).

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3 years ago

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3 years ago

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

Troyanec [42]

Answer:

a) P (x <= 3 ) = 0.36

b) P ( 2.5 <= x <= 3 ) = 0.11

c) P (x > 3.5 ) = 1 - 0.49 = 0.51

d) x = 3.5355

e) f(x) = x / 12.5

f) E(X) = 3.3333

g) Var (X) = 13.8891 , s.d (X) = 3.7268

h) E[h(X)] = 2500

Step-by-step explanation:

Given:

The cdf is as follows:

F(x) = 0 x < 0

F(x) = (x^2 / 25) 0 < x < 5

F(x) = 1 x > 5

Find:

(a) Calculate P(X ≤ 3).

(b) Calculate P(2.5 ≤ X ≤ 3).

(d) What is the median checkout duration ? [solve 0.5 = F()].

(e) Obtain the density function f(x). f(x) = F '(x) =

(f) Calculate E(X).

(g) Calculate V(X) and σx. V(X) = σx =

(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Solution:

a) Evaluate the cdf given with the limits 0 < x < 3.

So, P (x <= 3 ) = (x^2 / 25) | 0 to 3

P (x <= 3 ) = (3^2 / 25) - 0

P (x <= 3 ) = 0.36

b) Evaluate the cdf given with the limits 2.5 < x < 3.

So, P ( 2.5 <= x <= 3 ) = (x^2 / 25) | 2.5 to 3

P ( 2.5 <= x <= 3 ) = (3^2 / 25) - (2.5^2 / 25)

P ( 2.5 <= x <= 3 ) = 0.36 - 0.25 = 0.11

c) Evaluate the cdf given with the limits x > 3.5

So, P (x > 3.5 ) = 1 - P (x <= 3.5 )

P (x > 3.5 ) = 1 - (3.5^2 / 25) - 0

P (x > 3.5 ) = 1 - 0.49 = 0.51

d) The median checkout for the duration that is 50% of the probability:

So, P( x < a ) = 0.5

(x^2 / 25) = 0.5

x^2 = 12.5

x = 3.5355

e) The probability density function can be evaluated by taking the derivative of the cdf as follows:

pdf f(x) = d(F(x)) / dx = x / 12.5

f) The expected value of X can be evaluated by the following formula from limits - ∞ to +∞:

E(X) = integral ( x . f(x)).dx limits: - ∞ to +∞

E(X) = integral ( x^2 / 12.5)

E(X) = x^3 / 37.5 limits: 0 to 5

E(X) = 5^3 / 37.5 = 3.3333

g) The variance of X can be evaluated by the following formula from limits - ∞ to +∞:

Var(X) = integral ( x^2 . f(x)).dx - (E(X))^2 limits: - ∞ to +∞

Var(X) = integral ( x^3 / 12.5).dx - (E(X))^2

Var(X) = x^4 / 50 | - (3.3333)^2 limits: 0 to 5

Var(X) = 5^4 / 50 - (3.3333)^2 = 13.8891

s.d(X) = sqrt (Var(X)) = sqrt (13.8891) = 3.7268

h) Find the expected charge E[h(X)] , where h(X) is given by:

h(x) = (f(x))^2 = x^2 / 156.25

The expected value of h(X) can be evaluated by the following formula from limits - ∞ to +∞:

E(h(X))) = integral ( x . h(x) ).dx limits: - ∞ to +∞

E(h(X))) = integral ( x^3 / 156.25)

E(h(X))) = x^4 / 156.25 limits: 0 to 25

E(h(X))) = 25^4 / 156.25 = 2500

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3 years ago

Ashley makes 6 gallons of broth for the restaurant, she serves 30 cups of broth to guests. how many cups of soup are left over?

CaHeK987 [17]

Answer:

66 cups

Step-by-step explanation:

16 cups in 1 gallon

16*6 = 96 cups in 6 gallons

96 - 30 = 66

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2 years ago

A certain group of women has a 0.86% rate of red/green color blindness. If a woman is randomly selected, what is the probabil

Mariana [72]

Answer:

The probability that a randomly selected woman has red/green color blindness is 0.9914

Step-by-step explanation:

Given that the proportion of women having red/green color blindness is 0.86%

Represent that with p

$p= 0.86\%$

Convert proportion from percentage to decimal;

$p= \frac{0.86}{100}$

$p= 0.0086$

In probability; opposite probabilities add up to 1;

Let the probability that a woman selected have red/green color blindness be represented with q;

$p + q = 1$

Subtract p from both sides

$p - p + q = 1 - p$

$q = 1 - p$

Substitute 0.0086 for p

$q = 1 - 0.0086$

$q = 0.9914$

<em>Hence, the probability that a randomly selected woman has red/green color blindness is 0.9914</em>

3 0

3 years ago