MATHEMATICS HIGH SCHOOL

3 cards are drawn at random from a standard deck. Find the probability that all the cards are hearts.


Find the probability that all the cards are face cards.

Note: Face cards are kings, queens, and jacks.

Find the probability that all the cards are even.

(Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13)

Answers

Answer 1
Answer:

Answer:

i dont really understand what you mean it says 3 cards are drawn and it says to find the probability that the cards are all hearts but what is the question asking how do we find the probability

Step-by-step explanation:
Answer 2
Answer:

Final answer:

The probabilities of drawing all hearts, face cards, or even cards are calculated with the formula: (n/52) * ((n-1)/51) * ((n-2)/50) where n is the total number of cards that match the desired outcome.

Explanation:

The subject here is probability, specifically, how to determine the likelihood of a particular outcome when drawing cards from a standard deck. Let's deal with each probability one at a time.

  1. The probability that all the cards are hearts: There are 13 hearts in a deck of 52 cards. So the probability that the first card is a heart is 13/52, the second is 12/51 (because one heart is already drawn), and the third is 11/50. So, the overall probability is (13/52) * (12/51) * (11/50).
  2. The probability that all the cards are face cards: There are 12 face cards (kings, queens, and jacks) in a deck. Using the same principle, the probability is (12/52) * (11/51) * (10/50).
  3. The probability that all the cards are even: The 'even' cards are 2, 4, 6, 8, 10, which have 4 of each (hearts, diamonds, spades, clubs) totaling 20 cards. So, the probability is (20/52) * (19/51) * (18/50).

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To whitch subsets does the number - the square root of 25 belong select all that apply A)irrational numbers
B)rational numbers
C)integers
D)whole numbers
E)natural numbers

Answers

The square root of 25 belongs to the subsets of B. Rational numbers

What is a rational number in math?

Reasonable Numbers: Any number that can be written as the ratio (or fraction) of two integers is a logical number.

How do you recognize a rational number?

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, where both the number (number above) and denominator (bottom number) are whole numbers. The number 8 is a rational number because it can be written as a fraction of 8/1.

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sqrt 25 = 5....rational, integer, whole number, and natural

What are the coordinates of the point on the directed line segment from (−7,−5) to (8,−10) that partitions the segment into a ratio of 3 to 2?

Answers

let's say P(−7,−5) and  Q(8,−10) gets partitioned on a 3 : 2 ratio from P to Q by point R, so

\textit{internal division of a line segment using ratios} \n\n\n P(-7,-5)\qquad Q(8,-10)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{3:2} \n\n\n \cfrac{P\underline{R}}{\underline{R} Q} = \cfrac{3}{2}\implies \cfrac{P}{Q} = \cfrac{3}{2}\implies 2P=3Q\implies 2(-7,-5)=3(8,-10)

(\stackrel{x}{-14}~~,~~ \stackrel{y}{-10})=(\stackrel{x}{24}~~,~~ \stackrel{y}{-30}) \implies R=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-14 +24}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-10 -30}}{3+2} \right)} \n\n\n R=\left( \cfrac{ 10 }{ 5 }~~,~~\cfrac{ -40}{ 5 } \right)\implies R=(2~~,~-8)

The tangent, cotangent, and cosecant functions are odd , so the graphs of these functions have symmetry with respect to the:

Answers

Answer:

The tangent, cotangent, and cosecant functions are odd , so the graphs of these functions have symmetry with respect to the:

                                 Origin.

Step-by-step explanation:

A function f(x) is said to be a odd function if:

                    f(-x)=-f(x)

Also, an odd function always has a symmetry with respect to the origin.

whereas a function f(x) is said to be a even function if:

                      f(-x)=f(x)

Also, an even function has a symmetry with respect to the y-axis.

We know that:

Tangent function, cotangent function and cosecant function are odd functions.

Since,

\tan(-x)=-\tan x\n\n\cos (-x)=-\cot x\n\n\csc (-x)=-\csc x

( similarly sine function is also an odd function.

whereas cosine and secant function are even functions )

Hence, the graph of tangent function, cotangent function and cosecant function  is symmetric about the origin.

Final answer:

The tangent, cotangent, and cosecant functions are odd and exhibit symmetry with respect to the origin. This is because an odd function satisfies the condition y(x) = -y(-x), meaning for every point (x, y) on the graph, the point (-x, -y) is also on the graph.

Explanation:

The tangent, cotangent, and cosecant functions are indeed odd functions, meaning they exhibit symmetry with respect to the origin. An odd function satisfies the condition y(x) = -y(-x), and when graphed, this produces a symmetry with respect to the origin of the coordinate plane. Essentially, this means that if a point (x, y) is on the graph of an odd function, the point (-x, -y) is also on the graph.

For an example, let's consider the tangent function, which is an odd function: For any angle A, the tangent of -A is the opposite of the tangent of A, or tan(-A) = -tan(A). Graphically, this implies that if we reflect the graph of the tangent function over the x-axis, and then over the y-axis, we will get the original function back, thus verifying the symmetry in odd functions.

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Mars takes 686 days to orbit the Sun. What percent is this of the time it takes the Earth to orbit the Sun?

Answers

All you want to do is find what 686-365 is because that's the percent increase. Next you divide the number that you got by 365 and that's your percentage increase.

On average Exante Express trains are 50km/hr faster than Paral passenger trains. A Paral passenger train requires 60% more time then Exante train to travel 1800 km from Matsay to Rawindi. Calculate average speed of each train. Calculate time it takes for each train for the journey.

Answers

V- average\ speed\ of\ Exante\ Express\ train\nt-travel\ time\ of\ Exante\ Express\ train \n \nV= (S)/(t) \ \ \ \ and\ \ \ V-50= (S)/(t+60\%t) = (S)/(1.6t)\ \ \ \ and\ \ \ S=1800\n \nV= (1800)/(t) \ \ \ and\ \ \ V-50=(1800)/(1.6t)\ \ \ \Rightarrow\ \ \ (1800)/(t)-50= (1125)/(t) \ /\cdot t\n \n1800-50 t=1125\ \ \ \Rightarrow\ \ \ 50t=1800-1125\ \ \ \Rightarrow\ \ \ 50t=675\ /:50\n \nt=13.5\ [h]=13\ [h]\ 30\ [min]\n\n1.6t=21.6\ [h]=21\ [h]+ 0.6\cdot60\ [min]=21\ [h]\ 36\ [min]

V= (1800)/(t) =(1800)/(13,5) =133 (1)/(3) \ [km/h]\approx133.3\ [km/h]\n\nV-50\approx83.3\ [km/h]

Ans.\n average\ speed\ of\ Exante\ Express\ train\ is\ 133.3\ km/h,\ntravel\ time\ of\ Exante\ Express\ train\ is\ 13\ h\ 30\ min;\naverage\ speed\ of\ Paral \ passenger \ train\ is\ 83.3\ km/h,\ntravel\ time\ of\ Paral \ passenger\ train\ is\ 21\ h\ 36\ min

PLS HELPPPPP SOS HELP !!!!!Shandra is on vacation and wants to
buy souvenirs for at least 8 friends.
A postcard book costs $2.50 and a magnet costs $4.00. She can spend up to $30 altogether. Let x represent the number of postcard books and y represent the number of magnets.
Part A

A. x + y <8
B. 2.5x +4y <30
C. x+y > 8
D. 2.5x + 4y >8
E. x>0
F. y>0
G. x + y>0

Plsss help the one in the picture is part 2

Answers