Answer:
Explained below.
Step-by-step explanation:
The complete question is:
A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries. a. If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? b. If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? c. If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? d. If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? e. If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
Solution:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
Permutation is the number of ways to select k items from n distinct items in a specific order.
The formula to compute the permutation or arrangement of k items is:
[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
(a)
The number of ways to serve 3 bottles of zinfandel, with a specific order is:
[tex]^{8}P_{3}=\frac{8!}{(8-3)!}=\frac{8\times7\times6\times5!}{5!}=336[/tex]
(b)
The number of ways to select 6 bottles from the 30 is:
[tex]{30\choose 6}=\frac{30!}{6!(30-6)!}=\frac{30!}{6!\times 24!}=593775[/tex]
(c)
The number of ways to select two bottles of each variety is:
[tex]{8\choose 2}\times {10\choose 2}\times {12\choose 2}=\frac{8!}{2!\times6!}\times \frac{10!}{2!\times8!}\times \frac{12!}{2!\times10!}[/tex]
[tex]=\frac{12!}{(2!)^{3}\times 6!}\\\\=83160[/tex]
(d)
Compute the probability of selecting two bottles of each variety if 6 bottles are selected:
[tex]P(\text{2 bottles of each})=\frac{83160}{593775}=0.14[/tex]
(e)
Compute the probability of selecting the same variety of bottles, if 6 bottles are selected:
[tex]P(\text{Same Variety})=\frac{{8\choose 6}+{10\choose 6}+{12\choose 6}}{{30\choose 6}}[/tex]
[tex]=\frac{28+210+924}{593775}\\\\=0.0019570\\\\\approx 0.002[/tex]
Use 4's to create problems that will equal 1-12. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, Multiply or Divide, Add or Subtract.
Answer and Step-by-step explanation:
Solution:
Order of operations:
1- Parentheses
2- Exponent
3- Multiply
4- Divide
5- Subtract
By using these operations we can find out the solution of 4’s to create problems that will equal to 1 – 12.
1 = 44 / 44 or (4+4) / (4+4)
2= 4/4 + 4/4
3 = (4+4+4) /4
4 = 4 x (4 – 4) +4
5 = (4 x 4 + 4)/ 4
6 = 4 x .4 + 4.4
7 = 44 / 4 – 4
8 = 4 + 4.4 - .4
9 = 4/4 +4 +4
10 = 44 / 4.4
11= 4 / .4 + 4/4
12 = (44 + 4) / 4
If m<7 is 2x + 30 and m<28 is 3x - 10, find the
following:
Answer:
x = 32
m∠7 = 94
m∠8 = 86
m∠3 = 94
Step-by-step explanation:
(2x + 30) + (3x - 10) = 180
5x + 20 = 180
5x = 160
x = 32
m∠7 = 2(32) + 30 = 94
m∠8 = 3(32) - 10 = 86
or
m∠8 = 180 - 94 = 86
m∠3 ≈ m∠7 (corresponding angles)
PLEASE HELP I CANT DO MATH
Answer:
c
Step-by-step explanation:
the number line says less than 4 so if you solce for all the equations c will be x<4
Question:
7x^2 + 8x = x^2
Answer:
x1= -4/3 and x2= 0
Step-by-step explanation:
the first number in the pattern is 32 the rule is to add 27
Answer:
59
Step-by-step explanation:
Circle O has a circumference of approximately 44 in.
What is the approximate length of the diameter, d2
7 in
14 in
22 in
44 in
Answer:
14 in
Step-by-step explanation:
Given:
Circumference of circle = 44 in
Required:
The length of the diameter of the circle.
SOLUTION:
Circumference of circle = πd
Circumference = 44 in
π = 3.14
d = ?
Plug the values into the formula
44 = 3.14*d
Divide both sides by 3.14
44/3.14 = d
14.01 = d
d ≈ 14 in
|x |-8= -5
what's the answer
Answer:
|x |-7 = -5 ( x = -3 )
Step-by-step explanation:
A square patio has an area of 135 square feet. How long is each side of the patio to the nearest tenth?
Each side of the patio is approximately
feet long.
Which of the following lists of ordered pairs is a function?
(-1, 2), (2, 3), (3, 1), (2, 5)
(1, 2), (4, 0), (3, 5), (4, 3)
(2, 5), (3, 6), (6, 9)
(2, 5), (3, 6), (2, 1)
Answer:
[tex](2,5), (3,6), (6,9)[/tex]
Step-by-step explanation:
Because the abscissa does not repeat with different ordinate (well, there's actually no repeating abscissa)
Answer:c
Step-by-step explanation:
Toby works at an amusement park. He loads 10 new passengers onto the roller coaster every
3/4
of a minute. At what rate does Toby load passengers?
Pleaseeee
Answer:
13 1/3
Step-by-step explanation:
im sure this is right btw
Delisa Corporation has two divisions: Division L and Division Q. Data from the most recent month appear below:
Total Company Division L Division Q
Sales $ 577,000 $ 158,000 $ 419,000
Variable expenses 347,300 104,280 243,020
Contribution margin 229,700 53,720 175,980
Traceable fixed expenses 124,110 38,710 85,400
Segment margin 105,590 $ 15,010 $ 90,580
Common fixed expenses 70,310
Net operating income $ 35,280
The break-even in sales dollars for Division Q is closest to: (Round your intermediate calculations to 2 decimal places.)
Multiple Choice
$318,530
$203,333
$268,466
$459,400
Answer:
$203,333
Step-by-step explanation:
Computation for the break-even in sales dollars for Division Q
First step is to compute the Segment Contribution Margin ratio
Using this formula
Segment Contribution Margin ratio = Segment contribution margin ÷ Segment sales
Let plug in the formula
Segment Contribution Margin ratio= $ 175,980÷ $ 419,000
Segment Contribution Margin ratio= 0.42
Last step is to find the break-even in sales dollars for Division Q using this formula
Break-even in sales dollars = Segment traceable fixed expenses ÷ Segment Contribution Margin ratio
Let plug in the formula
Break-even in sales dollars= $85,400÷ 0.42
Break-even in sales dollars=$203,333
Therefore the break-even in sales dollars for Division Q is $203,333
Find the focus and directrix of the parabola with the given equation. y^2-4x=0
Answer:
directrix: x=-1
focus: (1,0)
Step-by-step explanation:
Model a desert community where 48% of the area is covered with houses. Place houses on of the 100 squares to represent or 48% houses.
Answer:
100
Step-by-step explanation:
Answer:
Place houses on
48
of the 100 squares to
represent
48/100
or 48% houses.
Radio blackouts are among the most common space weather events to affect Earth. Minor radio blackouts occur, on average, twice per year. Use a Poisson process to model the phenomenon. (a) Given that 3 events have occurred in the first half of the year, what is that probability that 3 events will happen in the rest of the year? (b) How many radio blackouts do you expect to see in two years? (c) Starting from now, how long must we wait so that the probability of seeing the next radio blackout is at least 0.5? (d) Find the probability that the time to the 4th blackout is at most 2 years.
Answer:
a. P(x = 3) = 0.061313
b. The expected number of radio blackouts = 4
c. It is not possible to determine the next radio blackout
d. P(x = 4) = 0.19537
Step-by-step explanation:
From the given information:
Using a Poisson process to model the phenomenon:
Since minor radio blackouts occur, on average, twice per year.
Then:
[tex]\lambda = 2 \ years[/tex]
From question (a)
time t = 1/2 (i.e half of the year)
Let x be the random variable that denotes the probability that 3 events will happen in the rest of the year.
Then:
[tex]P(x = 3) = \dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!}[/tex]
[tex]P(x = 3) = \dfrac{e^{-2* 0.5} \times (2 * 0.5)^3}{3!}[/tex]
P(x = 3) = 0.061313
b).
The number of radio blackouts we expect to see in two years can be estimated as follows:
we know that:
t = 2 years
E(x) = λ × t
E(x) = 2 × 2
E(x) = 4
The expected number of radio blackouts = 4
c).
The amount of time we need to wait given that the probability of seeing the next radio blackout is at least 0.5 is as follows:
Here, the time (t) = ???
Thus:
P(x =1) = 0.5
[tex]P(x = 1) = \dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5[/tex]
[tex]\dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5[/tex]
Thus, it is not possible to determine the probability (50%) of seeing the next radio blackout.
d)
The probability that the time to the 4th blackout is at most 2 years can be computed as follows:
Here;
x =4 , t = 2
Thus:
[tex]P(x = 4) = \dfrac{e^{-4 } \times (4)^4}{4!}[/tex]
P(x = 4) = 0.19537
Seventeen less than a number
is negative two. What is that
number?
Answer:15
Step-by-step explanation:
15-17=-2
Answer:
15
Step-by-step explanation:
15
What place value is the 5 in the following number, 123.465? earn 100 points!!!
Answer:
it will be in the thousands place for sure
Step-by-step explanation:
hope that helps =) i forgot there were a decimal point
Answer:
The place value of 5 in "123.465" is the thousandths
Step-by-step explanation:
The reason for this is because the "5" is 3 points behind the decimal, making it in the thousanths place.
Somebody tell me whats the answer and how do i find the oder pair thing
Answer:
( 2,0)
Step-by-step explanation:
The line crosses the Y intercept at the coordinates at (2,0)
Answer:
the y-intercept of the graph is 2
the ordered pair is (0,2)
Step-by-step explanation:
The y-intercept is the point where the line crosses the "y" line. Ordered pair are written (x,y) (the x is always in the front)
So, if we look at the "y" line we can see they y point is a 2, and if we look at line "x", the 2 is "above" the point 0 on the line labeled x.
The table shows the unit prices (per pound) of tomatoes
at different stores.
Store
Tomato Unit Prices
Jamal needs to buy 3.25 lb of tomatoes. If Jamal only
has $10, from which store(s) could he purchase his
tomatoes? Check all that apply.
Store A
Store B
Store C
Store D
Store E
A
$3.10 per pound
B
$3.02 per pound
с
$2.97 per pound
D
$3.07 per pound
E
$3.09 per pound
Answer:
store B, C, and D
Step-by-step explanation:
Adam’s weight to the nearest kilogram is 65 kg what is the greatest possible value of his weight
Answer:
65kg=143.30047 pounds and 1kg=2.20462262 pounds
Can only polygons be rotated
Answer: no
hope this helps!!!!!!! lol i suck
find the slope from the table
Answer:
5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
10 Given a || b. Find the value of z that makes ; || k.
Turned in
+27)
id document
(4:+3y)
N
submit
57
**/y+ :)
z=228
z=11.25
2 = 17.25
2= 48
maybe try quizzlet that would really help i swear
What is the y-intercept of the line?
YA
2
-2
-2
0
Answer:
1 the line hits the y line at 1
Finding the Slope of a Line from a Table What is the slope of the linear function represented in the table?
-7
-1/7
1/7
7
Find the equation of the line khan academy slope intercept equation from the graph
PLEASE HELP!!!
Evaluate the expresions -8-14÷2+5
Answer:
-10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation:
Pendiente 6 y puntos (5, -2)
Step-by-step explanation:
I need help the instructions say go left to right
five ninths minus two sixths equals blank what is the answer
In Evans history class, 10 out of 100 key terms will be randomly selected to appear on the final exam; Evan must then choose 7 of those 10 to define. Since he knows the format of the exam in advance, Evan is trying to decide how many key terms he should study. (a) Suppose that Evan decides to study s key terms, where s is an integer between 0 and 100. Let X be the number of key terms appearing on the exam that he has studied. What is the distribution of X? Give the name and parameters, in terms of s. (b) Calculate the probability that Evan knows at least 7 of the 10 key terms that appear on the exam, assuming that he studies s = 75 key term
Answer:
(a) Hypergeometric distribution
(b) 0.785384...
Step-by-step explanation:
(a) looking at the question, we see that [tex]X = \in \{0, ... , 10 \}[/tex], suppose Evans studied s key terms, this implies that he has not studied 100 - s key terms. Suppose [tex]k = \in \{0, ... , 10 \}[/tex] if X = k, then k out of the s key terms he had studied appeared. But 10 - k out of 100 - s key terms he hasn't studied appeared. Thus X is an Hypergeometric distribution, X~HGeom(s, 100 - s, 10) with PMF:
[tex]P_{x}(k) = P(X = k)[/tex]