In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.)
(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?
To calculate the probability of getting a blackjack from a single well-shuffled deck, you must consider the probability of drawing an Ace and then a 10-value card or vice versa, and add those probabilities together. The same process applies to two decks with adjusted numbers. You will then round the final probabilities to four decimal places.
Explanation:To answer the question of the probability of getting a blackjack in a single deck, consider that there are 4 aces in a deck and 16 cards that are either a face card or a 10 (each suit has 4 such cards - Jacks, Queens, Kings, and 10s). When one card is drawn, the remaining cards are one fewer, so we need to adjust our probability for the second card.
Calculate the probability of drawing an Ace first and then a card with a value of ten: P(Ace first, then 10) = (4/52) × (16/51).Calculate the probability of drawing a 10-value card first and then an Ace: P(10 first, then Ace) = (16/52) × (4/51).Add the two probabilities together for the final answer.For the probability of a blackjack from two decks, follow the same steps, but adjust the numbers for a 104-card deck.
P(Ace first, then 10) = (8/104) × (32/103).P(10 first, then Ace) = (32/104) × (8/103).Add the two probabilities together for the final answer.After doing the calculations, we round the probabilities to four decimal places as instructed.
2 times the sum of a number and 4 is no more than three times the sum of a number and 7 decreased by 4
what is 14 9/100 as a decimal
(04.02 LC)
Triangle ABC is similar to triangle PQR, as shown below:
Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r,
Which ratio is equal to b:q? (1 point)
b:a
c:r
r:a
q:c
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that triangle ABC is similar to triangle PQR.
In triangle ABC, AB=c, BC=a, and AC=b.
In triangle PQR, PQ=r, QR=p, PR=q.
The corresponding sides of similar triangles are proportional.
Since [tex]\triangle ABC\sim \triangle PQR[/tex], therefore their corresponding sides are proportional.
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]
[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]
It meas the ratio c:r = a:p = b:q.
Therefore the correct option is 2.
what are the x and y intecepts of the graph of the equation 6x - 5y=3
What is 0.853 to the nearest tenth?
The ratio of two numbers is 1 to 4, and the sum of the numbers is 45. What is the smaller number?
10
9
8
7
9 i think
Suppose that ln 2=a and ln3=b. Use properties of logarithms to write each logarithm in terms of a and b
ln0.5 ...?
which is bigger 40% of 210 or 1/4 of 320
To find out which is bigger, we calculate 40% of 210 and 1/4 of 320. 40% of 210 is greater than 1/4 of 320.
Explanation:To find out which is bigger, 40% of 210 or 1/4 of 320, we need to calculate both values.
First, 40% of 210 can be calculated by multiplying 210 by 0.4. This gives us 84.
Next, 1/4 of 320 can be calculated by dividing 320 by 4. This gives us 80.
Therefore, 40% of 210 is greater than 1/4 of 320.
the bryant family reuion and the jordan family reunion both include a visit to the zoo desert archers different amounts for children and adults in the following system A represents the cost of an adult ticket and C represents the cost of a child ticket. The first equation in the system represents the amount of money the Bryant family spends and the second equation represents the amount of money that the Jordan family spends
12a + 16c =176
10a + 8c =120
Which of the following statements are true?
A. the Bryants take 12 adults and 16 children to the zoo
B. There is a total of 22 children at the reuions
C.There is a total of 18 people at the Jordans reuion
D.16 represents the cost of a child ticket for the Bryant reuion
E. 10 represents the cost of an adult ticket for the Jordan family
F. The Bryant family spends $120 on tickets for the children and adults
G. Together the family spends $296
❗PLEASE HELP❗
Answer:
D. 16 represents the cost of a child ticket for the Bryant reunion.G. Together the family spends $296Step-by-step explanation:
To find the right answer we have to solve the system of equation:
[tex]\left \{ {{12a+16c=176} \atop {10a+8c=120}} \right.[/tex]
If we multiply the second equation by -2, we could eliminate the c-variable and solve for a-variable:
[tex]\left \{ {{12a+16c=176} \atop {-20a-16c=-240}} \right.\\-8a=-64\\a=\frac{-64}{-8}=8[/tex]
Now, we replace this value in one equation to obtain the other value:
[tex]10a + 8c =120\\10(8)+8c=120\\80+8c=120\\8c=120-80\\c=\frac{40}{8}=5[/tex]
So, the solution of the system is [tex](8,5)[/tex], which means that there are 8 adults and 5 children.
Also, according to the linear expressions The Bryants spend $12 per adult and $16 per child, and a total amount of $176. The Jordan family spend $10 per adult and $8 per child, and a total amount of $120. Both families together spent $296.
Therefore, the right answers are D and G
At the halftime show, a marching band marched in formation. The lead drummer started at a point with coordinates (–2, –5) and moved 3 steps up and 1 step right.
a. Write a rule to describe the translation.
b. What were the coordinates of the drummer's final position? (3 points)
Answer:
a) The answer is: (x + a, y + b)
b) The answer is: (-1, -2)
The initial coordinates are:
(x, y) = (-2, -5)
should be the answer.
Let's find a and b.
a is a distance in x direction: a = 1
b is a distance in y direction: b = 3
The final position is:
(x + a, y + b) = (-2 + 1, -5 + 3) = (-1, -2)
Step-by-step explanation:
Find the amount of simple interest earned after 2 years on $480 invested at a 7% annual interest rate?
Using the simple interest formula, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.
Finding Simple Interest on an Investment
To calculate the simple interest earned after 2 years on a $480 investment at a 7% annual interest rate, you can use the simple interest formula: Interest = Principal times Rate times Time.
The principal (P) is the initial amount of money, which in this case is $480. The rate (R) is the annual interest rate expressed as a decimal, so 7% becomes 0.07. The time (T) is the number of years the money is invested or borrowed, which is 2 years in this scenario.
Using the simple interest formula:
Interest = 480 times 0.07 times 2
Interest = 33.6 times 2
Interest = $67.20
Therefore, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.
The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function:
What is the youngest age for which the average income of a lawyer is $450,000?
Round to the nearest year.
To find the youngest age for a lawyer to have an average income of $450,000, you solve the income function equation and round to the nearest year.
Explanation:The youngest age for which the average income of a lawyer is $450,000 can be found by solving the given function:
I(x) = 10000 + 2000x
Given I(x) = $450,000, the equation becomes:
450,000 = 10000 + 2000x2000x = 440,000x = 220Rounded to the nearest year, the youngest age would be 220 years old.
The polynomial given below has _____ root(s).
3x2 - 8x + 4
A. two positive
B. two negative
C. two complex
D. one positive and one negative
A comic book costs $3.99, including tax. It is marked up 45%. What is the final price of the comic book after it is marked up? $1.80 $4.44 $5.79 $6.15
the real answer is 5.79, the other person had had miscalculation
What is closer to 1/3 0.3 0.33 or 0.333
Find two consecutive whole numbers that /76 lies between.
3 out of 4 students surveyed in a school said they will vote for nuncio for class president predict how many of the 340 students in the school would vote for nuncio
To predict the number of votes for Nuncio for class president, multiply 3/4 (or 0.75) by the total number of students (340), resulting in a prediction that 255 students would vote for Nuncio.
To predict how many of the 340 students in the school would vote for Nuncio for class president, we need to understand the proportion that we got from the survey. Since 3 out of 4 students said they would vote for Nuncio, this is the same as 75% or 0.75 when expressed as a decimal.
We then apply this proportion to the total number of students in the school:
Convert the fraction 3/4 to a decimal: 3 ÷ 4 = 0.75.
Multiply the total number of students by the decimal: 340 students × 0.75 = 255 students.
Therefore, we predict that 255 of the 340 students would vote for Nuncio for class president.
Expressions cannot _____.
be evaluated
be solved
be simplified
have variables
Answer:
B. be solved
Step-by-step explanation:
The product of twenty-one negative integers is negative.
True
False
Naomi draws a portion of a figure as shown. She wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
Answer:
In FLVS it is the third option
Step-by-step explanation:
Hope this helps :)
What is the answer to the riddle 20 30 x 0 1 the real answer..?
PEMDAS- [Parenthese, Exponents, Multiplication, Division, Addition, Subtraction.]
Since there is no Parentheses, nor Exponents, you have to go straight to multiplication. Then to addition
30+30×0+1
30×0=0
30+0+1=31.
I hope my answer has come to your help. God bless and have a nice day ahead!
A bag of chips contains 145 calories per serving. Each bag of chips contain 3 servings.
How many calories are in 2 bags of chips?
A.145 calories
B.150 calories
C.435 calories
D.870 calories
Answer:
870 calories Option D.
Step-by-step explanation:
A bag of chips contains calories per serving = 145
If each bag contains servings = 3
so total calories per bag = 3 × 145
= 435
Now we have to calculate the total servings in 2 bags.
Number of calories in 1 bag = 435
Therefore, number of calories in 2 bags = 435 × 2
= 870 calories
Option D. 870 calories is the answer.
PLEASE HELP PLEASE PLEASE
The cost of 5 dresses and 2 belts is $48. The cost of 3 dresses and 2 belts is $32. Find the cost of a dress and a belt. Let x denote the cost of a dress and y denote the cost of a belt.
By setting up a system of linear equations and solving for x and y, we find that the cost of a dress is $8 and the cost of a belt is $4.
Explanation:To find the cost of a dress and a belt, we can set up a system of linear equations using the information given. Let x denote the cost of a dress and y denote the cost of a belt. We then have two equations:
5x + 2y = $48 (1)3x + 2y = $32 (2)Subtract equation (2) from equation (1) to eliminate y:
5x + 2y - (3x + 2y) = $48 - $32
2x = $16
Now we can solve for x:
x = $16 / 2
x = $8
Now that we know the cost of a dress (x), we can substitute this value into equation (2) to find the cost of a belt (y):
3(8) + 2y = $32
24 + 2y = $32
2y = $32 - $24
2y = $8
y = $8 / 2
y = $4
Therefore, the cost of a dress is $8 and the cost of a belt is $4.
Select all situations that could be represented by a constant rate.
A) the number of cars manufactured per day at a factory
B) the speed of a toy rocket as it is launched straight into the air the number of
C) rotations per minute made by a fan
D) the population increase of a bacteria colony in a petri dish
Use the stem and leaf plot shown to answer the following question.
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and x are related by the equation.
What is the change in the total cost for each book printed?
What is the cost to get started (before any books are printed)?
Equation: y=1250+25x
The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:
F = 9 over 5C + 32
Which of the following formulas correctly solves for C?
C = 5F − 32 over 9
C = 5 F over 9 − 32
C = 9 over 5(F − 32)
C = 5 over 9(F − 32)
Answer:
The correct option is 4.
Step-by-step explanation:
The relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F is defined by the given equation.
[tex]F=\frac{9}{5}C+32[/tex]
We need to find the formula for C.
Subtract 32 from both the sides.
[tex]F-32=\frac{9}{5}C+32-32[/tex]
[tex]F-32=\frac{9}{5}C[/tex]
Multiply both sides by 5.
[tex]5(F-32)=9C[/tex]
Divide both sides by 9.
[tex]\frac{5(F-32)}{9}=\frac{9C}{9}[/tex]
[tex]\frac{5}{9}(F-32)=C[/tex]
The formula for C is [tex]C=\frac{5}{9}(F-32)[/tex].
Therefore the correct option is 4.
WILL UPVOTE!
Factor the expression.
36c^2 −121