Given the sequence: {2, 8, 32, 128, 512…}, S12 = ???
In the game of blackjack, determine the odds of dealing yourself a blackjack (ace plus face-card or 10) from a single deck. show how you arrived at your answer.
Final answer:
The odds of dealing yourself a blackjack in a single deck game of blackjack, by drawing an ace and a face card or 10 in either order, is 128 out of 2652, which simplifies to approximately 1 in 20.7.
Explanation:
In the game of blackjack, to determine the odds of dealing yourself a blackjack (ace plus a face card or 10), we need to calculate the probability of drawing an ace and then a ten-value card, or vice versa, from a single deck. A standard deck of cards has 52 cards, with 4 aces and 16 ten-valued cards (10, J, Q, K across four suits). The probability of drawing an ace first is 4 out of 52, and then a ten-value card is 16 out of 51. Alternatively, the probability of drawing a ten-value card first is 16 out of 52, and then an ace is 4 out of 51.
The total probability is the sum of both probabilities:
Probability of Ace first, then ten-value card: (4/52) * (16/51)Probability of ten-value card first, then Ace: (16/52) * (4/51)We then add these two probabilities together to find the total probability of dealing a blackjack from a single deck.
The total probability is (4/52) * (16/51) + (16/52) * (4/51) which simplifies to (64/2652) + (64/2652), or 2 * (64/2652), which simplifies further to (128/2652). Therefore, the odds of dealing a blackjack are 128 out of 2652, or approximately 1 in 20.7 when simplified.
,[PICTURE INCLUDED] Kite CDEF is rotated 180° about the origin and translated 3 units up to form kite WXYZ. If CD is x units long, what is the length of WX?
he 2 kites are identical
CD is the same as WX
so it would be x +0
answer is A
Find the volume of this oblique pyramid.
The fraction 10/19 is in lowest terms
Answer:
True
Step-by-step explanation:
A quadrilateral has three angles that measure 90o , 100o, and 120o. which is the measure of the fourth angle?
Answer: The measure of the fourth angle of the given quadrilateral is 50°.
Step-by-step explanation: Given that a quadrilateral has three angles that measure 90° , 100° and 120°.
We are to find the measure of the fourth angle of the quadrilateral.
Let x° be the measure of the fourth angle of the quadrilateral.
We know that
The sum of the measures of the four angles of a quadrilateral is 360°.
So, for the given quadrilateral, we have
[tex]90^\circ+100^\circ+120^\circ+x^\circ=360^\circ\\\\\Rightarrow 310^\circ+x^\circ=360^\circ\\\\\Rightarrow x^\circ=360^\circ-310^\circ\\\\\Rightarrow x^\circ=50^\circ.[/tex]
Thus, the measure of the fourth angle of the given quadrilateral is 50°.
(03.05 LC)
What is the volume of a cone (in cubic inches) with a radius of 3 inches and a height of 6 inches?
Use 3.14 for π. Round your answer to the nearest hundredth.
18.84 cubic inches
28.26 cubic inches
56.52 cubic inches
169.56 cubic inches
The volume of the cone is 56.52 cubic inches.
What is a cone?Having a flat base and a smooth tapering tip or vertex, a cone is a three-dimensional geometric object.
Given, the radius of the cone is 3 inches and the height of the cone is 6 inches.
The volume of a cone is given by,
V=(1/3)πr²h
V = (1/3) × 3.14 × 3² ×6
V = 56.52 cubic inches
Hence, the volume of the cone is 56.52 cubic inches.
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A game is biased such that the choices A-J have the following probabilities of winning: A 5% B 10% C 15% D 5% E 5% F 25% G 10% H 10% I 10% J 5% If you chose the letters D and H for 20 turns, how many times are you most likely to win? 1 2 3 4 5
Since we have chosen 2 letters, then the total probability of winning the game is the sum of the probabilities of each letter. Therefore:
Total probability of winning = Probability of D + Probability of H
Total probability of winning = 5% + 10%
Total probability of winning = 15%
Since we are playing the game for 20 turns, therefore out of those 20 games, we will win 15% of the time. So:
15% = 0.15
Winning times = 0.15 * 20
Winning times = 3
Therefore we have a chance or probability to win at least 3 games out of 20 turns.
Answer:
C: 3
Step-by-step explanation:
c. When the center of Earth is 2 × 1011 meters from the center of Mars, the force of gravity between the two planets is about 64.32 × 1014 newtons. The mass of Earth is about 6 × 1024 kilograms, and the mass of Mars is about 6.4 × 1023 kilograms. Using these values, estimate the gravitational constant.
To estimate the gravitational constant (G), we apply Newton's law of universal gravitation, using the provided values of the force of gravity between Earth and Mars, the masses of both planets and their distance apart. The calculation yields an estimated G value of approximately 6.67 × 10⁻¹¹ N·m²/kg², which aligns with the known gravitational constant.
Explanation:To estimate the gravitational constant (G), we can use Newton's law of universal gravitation, which states that the force of gravity (F) between two masses (m₁ and m₂) is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers:
F = G * (m₁*m₂) / r²
Given that:
The force of gravity (F) between Earth and Mars is approximately 64.32 × 10¹⁴ newtons.The mass of Earth (m₁) is about 6 × 10²⁴ kilograms.The mass of Mars (m₂) is about 6.4 × 10²³ kilograms.The distance between the centers of Earth and Mars (r) is 2 × 10¹¹ meters.We can rearrange the formula to solve for G:
G = F * r² / (m₁ * m₂)
Plugging in the values:
G = (64.32 × 10¹⁴ N) * (2 × 1011 m)² / (6 × 10²⁴ kg * 6.4 × 10²³ kg)
G ≈ 6.67 × 10⁻¹¹ N·m²/kg²
This value is approximately equal to the known gravitational constant, solidifying our understanding of gravitational forces and confirming the validity of our calculations.
Factor the GCF from 96x2 + 88x. Use the drop-down menus to complete the statements. The GCF of 96x2 and 88x is . Each term written as a product, where one factor is the GCF, is . The factored form of the expression is
Answer:
1: The GCF of 96x2 and 88x is: Answer: 8x
2: Each term written as a product, where one factor is the GCF, is: Answer: 8x(12x)+8x(11)
3: The factored form of the expression is: Answer: 8x(12x+11)
Step-by-step explanation:
You're explanation is the answers hope I helped !!!! Good luck!!!!!
A rectangle with vertices located at (1, 2), (1, 5), (3, 5), and (3, 2) is stretched horizontally by a factor of 3 with respect to the y-axis. What is the area of the image that is produced?
Solve for x: 5 over quantity x squared minus 4 plus 2 over x equals 2 over quantity x minus 2
Select all that apply. Which of the following ratios are equivalent?
A. 3 to 4
B. 3/4
C. 6/7
D. 15/20
Answer:
A,B,D
Step-by-step explanation:
A 20 sided die is rolled. What is the probability that a 1 is rolled?
Someone help me fast please
6 * (4+2)^2 -3^2 =
6 * 6^2 -3^2 =
6* 36-9 =
216-9=
207
Answer is C. 207
Find the value of x in the figure below. Round to the nearest tenth.
6.7
20
4
15
on a particular day, the Dow Jones had a rate of change of 2.8%. Which of the following statements must also be true?
-The average of the 30 stocks in the Dow Jones increased.
-The NASDAQ decreased.
-The S&P 500 increased.
-Every stock in the Dow Jones increased.
Answer
THE AVERAGE OF THE 30 STOCKS IN THE DOW JONES INCREASED
Step-by-step explanation:
if the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 years, what is the present value of that sum? a. 3,900.00 b. 3,947.00 c. 3,977.40 d. 4,000.00
%) points. Brainliest.
The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:
C = 5/9 (F − 32)
Which of the following formulas correctly solves for F?
F = 9/5C + 32
F = 9/5C − 32
F = 9C + 32/5
F = 9C − 32/5
Hugh has to earn at least $400 to meet his fundraising goal. He has only 100 books that he plans to sell at $8 each. Which inequality shows the number of books, x, Hugh can sell to meet his goal?
20 ≤ x ≤ 400
40 ≤ x ≤ 100
50 ≤ x ≤ 400
50 ≤ x ≤ 100
Mike observed that 75% of the students of a school liked skating. If 35 students of the school did not like skating, the number of students who liked skating was ______. (only put numeric values, no other symbols)
9c + 32/5=f this is the answer
i think
A kite with a string 50 meters long makes an angle of elevation of 58o with the ground, assuming the string is straight, how high is the kite? Round your answer to the nearest tenth of a foot.
An angle of elevation of 58 degrees with the ground means that the angle started at the x-axis and terminates on the first quadrant region through a counter clockwise direction. Imagining a triangle, the string of the kite becomes the hypotenuse, the angle 58 degrees is the angle between the hypotenuse and the ground, and the height of the kite is the side opposite to the angle.
Therefore, we can calculate for the height of the kite using the sin function:
sin θ = opposite side / hypotenuse
sin 58 = opposite side / 50 m
opposite side = 50 m * sin 58
opposite side = 42.4 m
Therefore the kite is about 42.4 m above the ground.
Solve for x: (3x−2)(2x+3)=0
The howler monkeys at a zoo are fed a diet that contains 3.35 kcal/gram. Write a function g(x) that gives the mass of food in grams that a howler monkey must eat to obtain x kilocalories of energy.
what is the value of m in the equation 4m + 2(m + 1) = 9m + 5
What is the slope of the line determined by any two solutions to the equation $\frac{2}{x}+\frac{3}{y} = 0$? Express your answer as a common fraction.
Final answer:
To determine the slope, solve for y in terms of x, resulting in the equation y = (-3/2)x. Hence, the slope of the line described by the equation 2/x + 3/y = 0 is -3/2.
Explanation:
To find the slope of the line determined by any two solutions to the equation 2/x + 3/y = 0, let's begin by solving for y in terms of x.
First, we isolate the term 3/y:
2/x = -3/y
Then we cross-multiply and get:
2y = -3x
Now we solve for y:
y = (-3/2)x
This is now in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, there is no y-intercept since the line passes through the origin.
The slope m is -3/2. So any two solutions to the original equation will yield a line with a slope of -3/2.
The isometric dot paper shoes 2 vertices 1 edge of the cube structure . Complete the isometric drawing
How would you write 0.00568 in scientific notation?
nutrient level required to maintain energy and growth what is it called
a man divided $9000 among his wife , son and daughter. the wife received twice as much as the daughter and the son received $1000 more than the daughter how much did each receive
with working please
thank you
HELP PLEASE!!! (I will give brainliest to the first one to answer)
Your friend lives exactly 3 miles south of your house. That means the distance between your houses is negative three (-3) miles. Answer yes or no and explain your answer.
The statement that "the distance between your houses is negative three (-3) miles" is correct.
What is a cartesian coordinate?A Cartesian coordinate system on a plane is a coordinate system in which each point is uniquely specified by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicularly oriented lines measured in the same unit of length.
If we assume that your house is the origin of a graph, and each unit square on the graph is equal to 1 square mile. Therefore, if your friend's house is exactly south of your house then it will be on the y-axis that too in the negative direction.
Therefore, the statement that "the distance between your houses is negative three (-3) miles" is correct.
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Match the sets of points representing one-to-one functions with the sets of points representing their inverse functions.
Tiles
h = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
g = {(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)}
f = {(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)}
i = {(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)}
Pairs
Sets of Points Representing Inverse Functions Sets of Points Representing Functions
h-1 = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
arrowBoth
i -1 = {(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)}
arrowBoth
g-1 = {(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)}
arrowBoth
f -1 = {(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)}
arrowBoth
NextReset
Each pair has the inverse points corresponding to the points in the original set.
To match the sets of points representing one-to-one functions with the sets of points representing their inverse functions, we need to find the pairs where each point in one set corresponds to the inverse point in the other set.
Here are the matches:
1. Set of Points Representing Function: [tex]\( h = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( h^{-1} = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]
2. Set of Points Representing Function: [tex]\( g = \{(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( g^{-1} = \{(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)\} \)[/tex]
3. Set of Points Representing Function: [tex]\( f = \{(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( f^{-1} = \{(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)\} \)[/tex]
4. Set of Points Representing Function: [tex]\( i = \{(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( i^{-1} = \{(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)\} \)[/tex]
Each pair has the inverse points corresponding to the points in the original set.