Answer:
chocolate: 6 poundsjelly: 4 poundsStep-by-step explanation:
Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...
10x +5(10 -x) = 80
5x +50 = 80
5x = 30
x = 6 . . . . . . . . pounds of chocolate
10 -x = 4 . . . . . pounds of jelly candy
6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.
help huryyyyyyyyyyyyy
Answer: 4
Step-by-step explanation:
Because %s can be expressed as fractions over 100, because 90 is 70% of x, 70% is 70% of 100. Thus, 90/x = 70/100.
Hope it helps <3
Answer:
4
Step-by-step explanation:
90 is 70% of x.
90 = 70% × x
90 = 70/100x
Divide both sides by x.
90/x = 70/100
If I set my alarm to read 8:10 when it is really 8:00 (i.e., it is 10 minutes fast) and the alarm goes off each day when it reads 8:10, it will be ___________ but not ___________.
Answer:
If I set my alarm to read 8:10 when it is really 8:00 (i.e., it is 10 minutes fast) and the alarm goes off each day when it reads 8:10, it will be reliable but not valid.
Step-by-step explanation:
If I set my alarm to wake me earlier than I need to be woken, it might be in order to give me enough time to adjust to the alarm, and be awake enough to get out of bed before the normal time I need to be out of bed. This method is very reliable, as there is a very little probability of me waking up late, since I have a 10 minutes head start everyday to get out of bed. The problem is that this method is not valid, since I now actually wake earlier than I am supposed to. The extra 10 minutes can actually lead to a disorientation with time.
Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?
Answer:
$252
Step-by-step explanation:
This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.
Jan's " give away " = Ami + 36, Jan - 108, Toy + 72
Toy's " give away " = Ami + 72, Jan + 36, Toy - 108
Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.
144 + 72 + 36 = 252 dollars ( in total )
Answer:
answer is 252
Step-by-step explanation:
Good luck :)
Hershel had 100 baseball cards that he labeled from 1-100. He started with number
one and marked every 5th card with an X, every 7th card with an O and every 10th
card with a V. What number card will be the first to have all 3 marks (XOV)?
Answer:
Hey there!
This question is basically asking for the least common multiple, or LCM of the three numbers.
If it is a multiple of 10, it has to be a multiple of 5. Thus, the only thing we need to do now, is find the LCM of 10 and 7, which is 70.
Thus, your answer is 70.
Hope this helps :)
Answer:
I think it is 70.
Step-by-step explanation:
I think that is the Lowest common Multiple of 5, 7 and 10:
10 = 2*5
7 = 7
5 = 5
So the LCM is 2 * 5 * 7 = 70.
Pls help asap What is the number of degrees in the acute angle formed by the hands of a clock at 6:44?
Answer:
264 degree angle
Step-by-step explanation:
f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).
Answer:
Step-by-step explanation:
Fog=2(g)+1
2(3x+2+4)+1
2{3x+6)+1
6x+12+1
=6x+13
Fog(-2)=6(-2)+13
-12+13
=1
Gof=3(f)+2+4
=3(2x+1)+6
6x+3+6
=6x+9
Gof(-2)=6(-2)+9
-12+9
=-3
Here is a sample distribution of hourly earnings in Paul's Cookie Factory:
Hourly Earning $6 up to $9 $9 up to $12 $12 up to $15
Frequency 16 42 10
The limits of the class with the smallest frequency are:_________
A) $6.00 and $9.00.
B) $12.00 and up to $14.00.
C) $11.75 and $14.25.
D) $12.00 and up to $15.00.
Answer:
The correct answer is:
$12.00 and up to $15.00 (D)
Step-by-step explanation:
Let us arrange the data properly in a tabular format.
Hourly Earnings($) 6 - 9 9 - 12 12 - 15
Frequency 16 42 10
The frequency of a distribution is the number of times that distribution occurs in a particular group of data or intervals.
From the frequency table above the following observations can be made:
Highest frequency = 42 (hourly earnings of $9 - $12)
smallest frequency = 10 ( hourly earnings of $12 - $15)
This means that among a total of 68 workers (16 + 42 + 10), the people earning $12 - $15 form the smallest group (only 10 people), while 42 workers earn $9 - $12, forming the largest majority
For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}
(1) Number of terms
(2) Value of Sum
Answer:
Number of term N = 9
Value of Sum = 0.186
Step-by-step explanation:
From the given information:
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]
Number of term N = 9
The Value of the sum can be determined by using the expression for geometric series:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]
here;
m = 5
n = 9
r = 0.5
Then:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]
For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,
the responses are;
(1) The number of terms are 9
(2) The value of the sum is approximately 0.374
How can the geometric series be evaluated?The given geometric series is presented as follows;
3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³
(1) The number of terms in the series = 13 - 4 = 9
Therefore;
The number of terms in the series = 9 terms(2) The value of the sum can be found as follows;
The common ratio, r = 0.5
The sum of the first n terms of a geometric progression is presented as follows;
[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]
The sum of the first 4 terms are therefore;
[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]
The sum of the first 13 terms is found as follows;
[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]
Which gives;
The sum of the 5th to the 13th term = S₁₃ - S₄
Therefore;
[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]
The value of the sum of the terms of the series is approximately 0.374Learn more about geometric series here:
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The equation 6x2 - 132 +5 -0 has solutions of the form
NVD
M
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N.M and D. Do not worry about simplifying the VD yet in this part of the problem.
N = ]:D
M
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
Preview
Answer:
(A)
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B)
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
Step-by-step explanation:
The given equation is
[tex]6x^2 - 13x + 5 = 0[/tex]
The solution is of the form as given by
[tex]$x=\frac{N\pm\sqrt{D}}{M}$[/tex]
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the VD yet in this part of the problem.
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
The equations of N, M and D are
[tex]N = -b[/tex]
[tex]D =b^2 -4ac[/tex]
[tex]M = 2a[/tex]
The values of a, b and c are
[tex]a = 6 \\\\b = -13 \\\\c = 5[/tex]
So,
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
N = 13
D = 49
M = 12
[tex]$x=\frac{13\pm\sqrt{49}}{12}$[/tex]
[tex]$x=\frac{13\pm7}{12}$[/tex]
[tex]$ x=\frac{13+7}{12} $[/tex] and [tex]$ x=\frac{13-7}{12} $[/tex]
[tex]$ x=\frac{20}{12} $[/tex] and [tex]$ x=\frac{6}{12} $[/tex]
[tex]$ x=\frac{5}{3} $[/tex] and [tex]$ x=\frac{1}{2} $[/tex]
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
Solve the quadratic equation by factoring 9x^2 -16 = 0
Answer: x= - 4/3 and x = 4/3
Step-by-step explanation:
(3x-4) times (3x+4) = 0
Translate and solve: 3x less than two times the sum of 2X and one is equal to the sum of 2 and 5
Answer:
The answer is x = 5Step-by-step explanation:
The statement
3x less than two times the sum of 2X and one is written as
2( 2x + 1) - 3x
the sum of 2 and 5 is written as
2 + 5
Equate the two statements
We have
2( 2x + 1) - 3x = 2+5
Expand
4x + 2 - 3x = 7
Simplify
4x - 3x = 7 - 2
We have the final answer as
x = 5Hope this helps you
A radio transmission tower is feet tall. How long should a guy wire be if it is to be attached feet from the top and is tomake an angle of with the ground
Answer:
Length of guy wire is 590.6 ft
Step-by-step explanation:
The complete question is
A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of 20° with the ground. Give your answer to the nearest tenth of a foot.
height of tower = 210 ft
8 ft fro the top leaves 210 - 8 = 202 ft to the ground
This is an angle of elevation problem
the opposite is 202 ft
hypotenuse = ?
angle is 20°
using sin ∅ = opp/hyp
sin 20° = 202/hyp
0.342 = 202/hyp
hyp = 202/0.342 = 590.6 ft this is the length of the guy wire
can y’all help please
Answer: 0 ft, maximum, 11.6 ft, 6.8 ft, 13.6 ft
Step-by-step explanation:
y = -0.25x² + 3.4x
a= -0.25 b = 3.4 c = 0
"c" is the initial height = 0
"a" is negative ⇒ ∩-shaped parabola ⇒ vertex is a maximum
Axis of Symmetry (horizontal distance at maximum):
[tex]x=\dfrac{-b}{2a}=\dfrac{-(3.4)}{2(-0.25)}=\dfrac{-3.4}{-0.5}\quad = \large\boxed{6.8}[/tex]
Maximum: (heighth at maximum)
y = -0.25(6.8)² + 3.4(6.8)
= -11.56 + 23.12
= 11.56
Zeros (when the ball is on the ground):
0 = -0.25x² + 3.4x
0 = x(-0.25x + 3.4)
0 = x 0 = -0.25x + 3.4
-3.4 = -0.25x
[tex]\dfrac{-3.4}{-0.25}=x[/tex]
13.6 = x
x = 0 is where the ball started
x = 13.6 is where the ball landed
6 is what percentage of 10?l
Answer:
Hello! The answer will be below!
Step-by-step explanation:
The answer is 60, steps will be below....
Steps:
6 divided by 10
=0.6
And than we do (0.6 x 100)%
Which will give us 60%
Hope this helps! :)
⭐️Have a wonderful day!⭐️
There are five questions listed below. Each question includes the quantity 22. Match
the 22 in each question on the left to which part of the problem it represents on the right
-- the base, percent, or amount. Some answer options on the right will be used more
than once.
What percent of 22 is 3?
percent
22 is what percent of 164?
base
What is 4% of 22?
amount
8 is 22% of what number?
What is 5% of 22?
Using concepts of percentage,
3 is 16.63% of 22.
22 is 13.41% of 164.
0.88 is 4% of 22.
8 is 22% of 36.36.
1.1 is 5% of 22.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Let 3 be x% of 22.
[tex]=\frac{x}{100} *22 = 3\\\\=x = \frac{3*100}{22} = 13.63%[/tex]
3 is 13.63% of 22.
Let 22 be y % of 164.
[tex]=\frac{y}{100} *164 = 22\\\\=y = \frac{22*100}{164} = 13.41%[/tex]
13.41% of 164 is 22.
4% of 22 = 0.88
[tex]\frac{4}{100}*22 = 0.88[/tex]
Let 8 is 22% of z.
[tex]\frac{22}{100}*z = 8\\ \\z = \frac{8*100}{22} = 36.36[/tex]
5% of 22 = 1.1
[tex]\frac{5}{100}*22 = 1.1[/tex]
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Which point is a solution to y<=3x-4?
Answer:
(3, 1)
Step-by-step explanation:
Plug-in points and see which one works. (x, y). <= means less than or equal to.
Answer:
D. (3,1) is the correct answer
Step-by-step explanation: Just graph this question on a graph, and you will find that (3,1) is in the shaded region, which means it is part of the solution
6x-5<2x+11. plz helpppppp
Answer:
x < 4 or x = ( -∞, 4)
Step-by-step explanation:
6x - 5 < 2x + 116x - 2x < 11 + 54x < 16 x < 16/4x < 4or
x = ( -∞, 4)
[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]
Simplify the expression:
– 10x + – 4 – 8 + 7x
Answer:
-3x-12
Step-by-step explanation:
-10x-4-8+7x
-3x-4-8
-3x-12
Answer:
-3x-12
Step-by-step explanation:
– 10x + – 4 – 8 + 7x
Combine like terms
-10x +7x -4-8
-3x -12
The manager of a grocery store took a random sample of 100 customers. The avg. length of time it took the customers in the sample to check out was 3.1 minutes with a std. deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly > 3 min. At 95% confidence, it can be concluded that the mean of the population is
Answer:
Step-by-step explanation:
The data given are;
sample size n = 100
sample mean x = 3.1
standard deviation σ = 0.5
mean = 3
The value for Z can be determined by using the formula:
[tex]Z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{3.1 - 3.00}{\dfrac{0.5}{\sqrt{100}}}[/tex]
[tex]Z = \dfrac{0.1}{\dfrac{0.5}{10}}}[/tex]
Z = 0.2
At 95% Confidence interval, level of significance ∝ = 0.05
From the z table ;P- value for the test statistics at ∝ = 0.05
P = 0.0228
We can see that the P-value is < ∝
Decision Rule:
Reject the null hypothesis [tex]H_o[/tex] if P-value is less than ∝
Conclusion:
At 0.05 level of significance; we conclude that the mean of the population is significantly > 3 min
Which is the simplified form of m Superscript negative 8 p Superscript 0? StartFraction 1 Over m Superscript 8 Baseline p EndFraction StartFraction 1 Over m Superscript 8 EndFraction StartFraction p over m Superscript 8 EndFraction m Superscript 8 PLS HELPP
Answer:
Correct Option is : StartFraction 1 Over m Superscript 8 EndFraction
Step-by-step explanation:
=> [tex]m^{-8} p^0[/tex]
According to law of exponents [tex]a^0 = 1[/tex]
=> [tex]m^{-8} (1)[/tex]
Using Law of exponents [tex]a^{-m} = \frac{1}{a^m}[/tex]
=> [tex]\frac{1}{m^8}[/tex]
The simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].
The question is not well formatted the question might be as follows:
Which is the simplified form of [tex]m^{-8}p^0[/tex]?
[tex]\frac{1}{m^8p}[/tex][tex]\frac{1}{m^8}[/tex][tex]\frac{p}{m^8}[/tex]m⁸What are exponents?Exponents are numbers that say how many times a number is to be multiplied. For example, 2⁸ means 2 is multiplied 8 times.
How to solve the problem?[tex]m^{-8}p^0[/tex] = [tex]m^{-8}[/tex] since, p⁰=1.
⇒[tex]m^{-8}[/tex] = [tex]\frac{1}{m^8}[/tex] .
Hence, the simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].
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Assume that there is a 6% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? four a. With two hard disk drives, the probability that catastrophe can be avoided is . (Round to four decimal places as needed.) b. With four hard disk drives, the probability that catastrophe can be avoided is . (Round to six decimal places as needed.)
Answer: 0.9964
Step-by-step explanation:
Consider,
P (disk failure) = 0.06
q = 0.06
p = 1- q
p = 1- 0.06,
p = 0.94
Step 2
Whereas p represents the probability that a disk does not fail. (i.e. working entire year).
a)
Step 3
a)
n = 2,
let x be a random variable for number...
Continuation in the attached document
PLEASE PLEASE PLEASE HELP TIMEDCan you prove that DE F = HGF Justify your answer. A. Yes, the triangles are congruent by SAS. B. Yes, the triangles are congruent by SSS. C. Yes, the triangles are congruent by SSA. D. No, not enough information is given.
Answer:
A. Yes, the triangles are congruent by SAS.
Step-by-step explanation:
EF = FG and DF = FH-> Given
angle EFD = angle HFG -> Vertical angles are congruent
DE F = HGF -> SAS Triangle Congruence Theorem
We can prove ∠DE F = ∠HGF by SAS congruency.
Hence option A is correct.
In the given triangle,
DE = GE
DF = FH
We know that,
SAS congruency stands for "Side-Angle-Side" congruence,
Which is a rule used in geometry to prove that two triangles are congruent or equal in size and shape.
This rule states that if two sides and the angle between them of one triangle are congruent to the corresponding two sides and angle of another triangle, then the two triangles are congruent.
Since the triangles
DE,GE and DF, FH are the corresponding sides and
DE = GE
DF = FH
Since DEF and FHG are congruent.
Therefore,
∠DE F = ∠HGF
Hence proved.
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Which two statements describe domestic stocks? They are directly affected by exchange rate fluctuations. They are always traded in local currency. They are likely to be unfamiliar to investors. They are based in the investor’s country of residence. They form an important part of foreign trade.
Answer:
They are based in the investor’s country of residence
They are always traded in local currency.
Step-by-step explanation:
Stocks, in general, indicate ownership shares of a company and domestic stocks as the name suggests are stocks that are based in the investor's home country.
These domestic stocks are almost always traded in local currency and they are a great help to local investors because it eliminates the currency risk because of exchange rates which can change at any time.
Answer
They are based in the investor’s country of residence
They are always traded in local currency.
Step-by-step explanation:
Stocks, in general, indicate ownership shares of a company and domestic stocks as the name suggests are stocks that are based in the investor's home country.
These domestic stocks are almost always traded in local currency and they are a great help to local investors because it eliminates the currency risk because of exchange rates which can change at any time.
The regular octagon below has a perimeter of 80m What is the length of one side of the octagon?
Answer:
10 m
Step-by-step explanation:
Since all of the side lengths of a regular octagon are equal and there are 8 sides on an octagon, the answer would be 80 / 8 = 10 m.
For the functions f(x)=8 x 2 +7x and g(x)= x 2 +2x , find (f+g)(x) and (f+g)(3)
Answer:
(f+g)(x)= 9x² + 9x
(f+g)(3) = 108
Step-by-step explanation:
f(x)=8x² +7x
g(x)= x² +2x
(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x
(f+g)(x)= 9x² + 9x
(f+g)(3)= 9*3² + 9*3 = 108
If f is a function f: X Y, then Y is called (a) Domain (b) Co-domain (c) Range (d) None of these
Answer:
y is the range
Step-by-step explanation:
the y is the range
x isthe domain
Please help ASAP! Do not understand how to conduct problem!
Answer:
AB =-4 24 25
-5 15 15
BC= -5
4
10
2BC = -10
8
20
THE Operation AB -2BC cannot be performed because the unequality of the arrays
Step-by-step explanation:
AB=first row (3*2)+(1/2*0)+(5*-2), (3*-4)+(1/2*2)+(5*7), (3*0),(1/2*0),(5*5)
Second row ((1*1)+(-1*0)+(3*-2),(1*-4)+(-1*2)+(3*7), (1*0)+(-1*0)+(3*5)
AB =-4 24 25
-5 15 15
BC =FIRST ROW (1*1)+(-4*2)+(0*0)
SECOND ROW (0*1)+(2*2)+(0*0)
THIRSD ROW (-2*2)+(7*2)+(5*0)
BC= -5
4
10
2BC = -10
8
20
THE Operation AB -2BC cannot be performed because the unequality of the arrays
A runner can run 3 miles in 18 minutes. At this rate, how many miles can he run in 54
minutes?
6
9
12
I
18
Answer:
9 miles
Step-by-step explanation:
54 divided by 18
=
3.
3 x 3 (miles per 18 min)
=
9 miles
Answer:
9 miles in 54 minutes
Step-by-step explanation:
Create proportions
Do it miles:minutes
In this case it would be
3:18
Then divide both sides of the proportion by three to get
1 : 6
or the statement "It takes the runner 6 minutes to run a mile."
Now create another proportion
x: 54
If he can run a mile in 6 minutes,
he can run x miles in 54 minutes.
In this case divide 54 and 6 to get 9 miles in 54 minutes.
Hope this helps!
Two jokers are added to a $52$ card deck and the entire stack of $54$ cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answer:
52/3.
Step-by-step explanation:
There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.
Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:
For jokers: JJ---... there are 0 cards between. This will be the case also for ...
-JJ---...
--JJ---...
and so on, down to ...
...---JJ
The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.
__
For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.
__
Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...
[tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]
A lottery ticket has a grand prize of $31 million. The probability of winning the grand prize is .000000018. Determine the expected value of the lottery ticket.
Answer:
$0.558
Step-by-step explanation:
The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:
Win $31 millionWin $0Then our expected value can be calculated as:
[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]