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2 years ago

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of AC.

Mathematics

1 answer:

WARRIOR [948]2 years ago

6 0

Answer: 8 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, so you can set AE and CE equal to each other, as well as BE and ED

2x=x+2

x=2

AC=2x+x+2

AC=3x+2

SUbstitute x

AC=3(2)+2

AC=6+2

AC=8

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Suppose that two cards are randomly selected from a standard 52-card deck. (a) What is the probability that the first card is

ser-zykov [4K]

Answer:

(a) $\frac{1}{17}$ (b) $\frac{1}{16}$

Step-by-step explanation:

GIVEN: Suppose that two cards are randomly selected from a standard $52$ card deck.

TO FIND: (a) What is the probability that the first card is a club and the second card is a club if the sampling is done without replacement? (b) What is the probability that the first card is a club and the second card is a club if the sampling is done with replacement.

SOLUTION:

(a)

Probability that first card is club $P(A)=\frac{\text{total club cards}}{\text{total cards}}$

$=\frac{13}{52}$

$=\frac{1}{4}$

As sampling is done without replacement.

probability that second card is club $P(B)=\frac{\text{total club cards}}{\text{total cards}}$

$=\frac{12}{51}$

$=\frac{4}{17}$

Probability that first card is club and second card is club $=P(A)\times P(B)$

$=\frac{1}{4}\times\frac{4}{17}=\frac{1}{17}$

(b)

Probability that first card is club $P(A)=\frac{\text{total club cards}}{\text{total cards}}$

$=\frac{13}{52}$

$=\frac{1}{4}$

As sampling is done with replacement.

probability that second card is club $P(B)=\frac{\text{total club cards}}{\text{total cards}}$

$=\frac{13}{52}$

$=\frac{1}{4}$

Probability that first card is club and second card is club $=P(A)\times P(B)$

$=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}$

3 0

3 years ago

A traffic engineer monitors the rate at which cars enter the main highway during the afternoon rush hour. From her data she esti

sertanlavr [38]

Answer:

On average, cars enter the highway during the first half hour of rush hour at a rate 97 per minute.

Step-by-step explanation:

Given that, the rate R(t) at which cars enter the highway is given the formula

$R(t)= 100(1-0.0001t^2)$

The average rate of car enter the highway during first half hour of rush hour is the average value of R(t) from t=0 to t=30.

$\therefore \int_0^{30} 100(1-0.0001t^2)\ dt$

$=[100(t-0.0001\frac{t^3}{3})]_0^{30}$

$=100[(30-0.0001\frac{30^3}{3})-(0-0.0001\frac{0^3}{3})]$

=2901

The average rate of car is $=\frac{\textrm{The number of car}}{Time}$

$=\frac{2910}{30}$

=97

On average, cars enter the highway during the first half hour of rush hour at a rate 97 per minute.

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3 years ago

How many integers from 1 through a

AysviL [449]

Answer:

sorry but I don't understand

Step-by-step explanation:

please forgive me

comment if I am forgiven

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3 years ago

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.

lakkis [162]

The smallest perimeter is 72.44 inches. The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. As much as possible, the sum of the length of the two remaining side must be greater than the other side. Given the side is 30, then the sum of the two remaining sides should be greater than 30 inches.

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3 years ago

Dicriminant of x² – 49 = 0

Mama L [17]

Answer:

196

Step-by-step explanation:

The discriminant (Δ) is given by:

$\Delta = b^2-4ac$