How many triangles can be made if two sides are 4 inches and the angle between them is 90°?

denis-greek [22]

It is the one second from the top. the line is straight (y=-3) until it hits x=-1 then it starts increasing significantly

8 0

3 years ago

g What is the probability of being dealt exactly three of a kind (like three kings or three 7’s, etc.) in a five card hand from

Elena L [17]

Answer: 0.02257

Step-by-step explanation:

Given : Total cards in a deck = 52

Number of ways to select any 5 cards : $^{52}C_5$

Since , there are total 13 kinds of card (includes Numbers from 2 to 9 and Ace , king, queen and jack).

Of each kind , there are 4 cards.

Number of ways to select three cards in a five card hand of a single kind : $^{4}C_3\times^{48}C_2$

Number of ways to select three cards in a five card hand of a exactly three of a kind : $13\times^{4}C_3\times^{48}C_2$

Now , the required probability = $\dfrac{13\times^{4}C_3\times^{48}C_2}{^{52}C_5}$

$=\dfrac{13\times4\times\dfrac{48!}{2!46!}}{\dfrac{52!}{5!47!}}\\\\\\=\dfrac{58656}{2598960}$

$=0.022569027611\approx0.02257$

∴ The probability of being dealt exactly three of a kind (like three kings or three 7’s, etc.) in a five card hand from a deck of 52 cards= 0.02257

8 0

3 years ago

Sharon is painting her house. she needs 5 gallons of brown paint for every 7 gallons of white paint. How many gallons of white

Igoryamba

Answer:

19.6

Step-by-step explanation:

The ratio of brown paint to white paint is, 5:7 or $\frac{5}{7}$ so if he bought 14 gallons of white paint we need to figure out:

$\frac{5}{7} =\frac{14}{x}$

which we can as it only has one unknown:

5x=14×7

5x=98

x=19.6

So the answer is 19.6

3 0

2 years ago

Read 2 more answers

54 ÷ (−6) A. 9 B. -9 C. -8

sp2606 [1]

Answer:

Option B, -9

Hope this helps!

6 0

3 years ago

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

Firstly we will calculate the general probability that of P(a < X < b)

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

3 years ago