Excell Computers promptly shipped two servers to its biggest client. The company profits RM5,000 on each one of these big systems. The shipping worker randomly selected the system without replacement that were delivered from 15 computers in stock. The system contain 4 refurbished computer, with 11 new computers in the warehouse.
If the client gets two new computers, Excell earns RM10,000 profit. If the client gets a refurbished computer, it’s coming back for replacement and Excell must pay the RM400 shipping fee, with leaves RM9,600 profit. If both computers shipped are refurbished, consequently the client will return both and cancel the order. As a result, Excell will be out any profit and left with RM8,000 in shipping cost. Let X be a random variable for the amount of the profit earned on the order.
Construct a probability distribution table and the amount of profit earned for the computer condition. (12 marks)
Calculate the expected profit then interpret the value. (3 marks)
Answers
Answer:
$9215.24
Step-by-step explanation:
Total Number of Computers=15
Number of New=11
Number of Refurbished Computers=4
P(New)=11/15P(Refurbished)=4/15[tex]P(NN)=\frac{11}{15} \times \frac{10}{14} = \frac{11}{21}\\P(NR)=\frac{11}{15} \times \frac{4}{14} = \frac{22}{105}\\P(RN)=\frac{4}{15} \times \frac{11}{14} = \frac{22}{105}\\P(RR)=\frac{4}{15} \times \frac{3}{14} = \frac{2}{35}[/tex]
Let X be the amount of profit earned on the purchase. The probability distribution of X is given as:
[tex]\left|\begin{array}{c|c|c|c|c}$Profit(X)& NN=\$10000 &NR=\$9600& RR=-\$800\\$P(X)&\dfrac{11}{21}&\dfrac{44}{105}&\dfrac{2}{35}\end{array}\right|[/tex]
(b) Expected Profit
[tex]\text{Expected Profit}=\sum X_iP(X_i)\\=(10000 \times \dfrac{11}{21}) +(9600 \times \dfrac{44}{105}) + (-800 \times \dfrac{2}{35})\\=\$9215.24[/tex]
The store is expected to make an average profit of $9215.24 on the order.
Answer:
Check the probability distribution table and the amount of profit earned is contained in the file attached.
Expected Profit, E(x) = RM9216.8
Explanation:
Probability that 1st computer is refurbished, P₁ = 4/15
Probability that 1st computer is not refurbished, q₁ = 11/15
Probability that 2nd computer is refurbished, P₂ = 3/14
Probability that 2nd computer is not refurbished, q₂ = 11/14
Excel makes a profit of X = RM10,000 if the two computers are new( i.e. none is refurbished)
P(X=RM10000) = q₁q₂ = 4/15 * 3/14
P(X=RM10000) = 0.52
Excel makes a profit of X = RM9600 if just one computer is refurbished
P(X=RM9600) = P₁q₂ + P₂q₁
P(X=RM9600) = (4/15 * 4/14) + (3/14 * 11/15) = 0.419
Excel makes a loss of RM800 ( X = -RM800) if the two computers are refurbished
P(X=-RM800) = P₁P₂
P(X=-RM800) = 4/15 * 3/14
P(X=-RM800) = 0.057
The table that contains the probability distribution and the amount of profit earned is attached as a file below.
2) Expected Profit
E(x) = Σ xP(x)
E(x) = (10000*0.524) + (9600*0.419) - (800 * 0.057)
E(x) = 5240 + 4022.4 - 45.6
E(x) = RM9216.8
Related Questions
Dermine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
The rankings of songs in the top 100.
a) Ordinal.
b) Ratio.
c) Interval.
d) Nominal.
Answers
Answer:
Option A Ordinal
Step-by-step explanation:
The most appropriate level of measurements for this category is ordinal measurements. The ordinal measurement allows for the ordering of the data but differences cannot be found for them or finding differences is completely useless using this measurements.
Khan academy : Sasha has been saving the money she earns from babysitting for several months. She has a total of $96.75 dollar saved. Round the amount of money to the nearest ten.
Answers
Answer:
$100.00
Step-by-step explanation:
If we are rounding to the nearest 10, then we only have to look at 96. Since 6 is bigger than 5, we round up to 100.
Someone pls answer this question
Answers
Answer:
[tex]9^2-x^2[/tex] and [tex]x(9-x)+9(9-x)[/tex]
Step-by-step explanation:
The area of the larger square is 9*9=9^2. The area of the smaller square inside of it is x*x=x^2. The area of the light shaded gray is therefore 9^2-x^2, which is also equivalent to x(9-x)+9(9-x). Hope this helps!
f(n) = 5n for n = 2
Answers
Answer:
10
Step-by-step explanation:
F(2) = 5 * 2 = 10
Answer:
f(2) =10
Step-by-step explanation:
f(n) = 5n
Let n=2
f(2) = 5*2
f(2) =10
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answers
Answer:
2 is the answer
Step-by-step explanation:
area=1/2*base*height
as height = 2*base and area =4 it comes
1/2*2*base*base=4
so base *base=4
so base = 2
The function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold. Determine the vertex, and explain what it means in the context of the problem. (6, 10); The vertex represents the maximum profit. (6, 10); The vertex represents the minimum profit. (8, 4); The vertex represents the minimum profit. (8, 4); The vertex represents the maximum profit.
Answers
Answer:
A.
f is a quadratic function, which means it's graph is a parabola.
Notice that the coefficient of is negative, so the parabola opens downwards.
the x-coordinate of a parabola is always determined by the formula:
where a is coefficient of the term, and b is the coefficient of the x term.
Thus, x-coordinate of the vertex of the graph of f is :
the y-coordinate of the vertex is f(8)=-8*8+16*8-60=4.
The vertex is (8, 4).
This means that the maximum daily profit is when exactly 8 candles are sold.
B.
The x-intercepts are the values of x such that f(x)=0,
so to find these values we solve:
complete the square:
so x-8=2 or x-8=-2
the roots are x=10 and x=6, are the roots.
This means that when the shop sells exactly 6 or 10 candles, it makes no profit.
Answer: d (8, 4); The vertex represents the maximum profit.
Explanation: i got it right on the test
A box contains 16 transistors, 4 of which are defective. if 4 are selected at random, find the probability that
a. all are defective.
b. none are defective.
Answers
Answer:
(a)0.0005
(b)0.2720
Step-by-step explanation:
Total Number of Transistors = 16
To find the probability that 4 selected at random are defective (or non-defective), we find the probability of the 1st, 2nd, 3rd, and 4th defective (or non-defective) items in that order, Note that the selection is without replacement.
(a)Probability that all are defective
Number of Defective Transistors =4
P(all are defective) [tex]=\dfrac{4}{16} \times \dfrac{3}{15} \times \dfrac{2}{14} \times \dfrac{1}{13}[/tex]
=0.0005
(b)Probability that none are defective
Number of Non-Defective Transistors =16-4=12
P(none are defective) [tex]=\dfrac{12}{16} \times \dfrac{11}{15} \times \dfrac{10}{14} \times \dfrac{9}{13}[/tex]
=0.2720
En una encuesta sobre preferencias entre los deportes Tenis (T), Surf (S) y Golf (G) se sabe que:
90 personas fueron encuestadas
15 personas prefieren Golf
10 no prefieren ninguno de estos deportes
ninguno de los que prefiere los deportes Tenis ó Surf prefieren Golf
30 prefieren sólo Surf
20 prefieren sólo Tenis
a) ¿Cuántas personas prefieren dos de estos deportes?
b) ¿Cuántos prefieren sólo uno de estos deportes?
Answers
Answer:
a) 15
b) 65
Step-by-step explanation:
Adjunto se encuentra el diagrama asociado a esta situación. Comenzamos por ubicar aquellas afirmaciones que relacionan todos los deportes. Sabemos que 10 personas no prefieren ningún deporte. Luego, ubicamos 10 fuera de los conjuntos mostrados. Sabemos que 30 personas prefieren sólo surf y 20 personas prefieren sólo Tenis. Es decir, hay 30 personas en el conjunto S que no intersectan a los otros dos. En este momento, hemos ubicado a 60 personas. Nos hacen falta 30 personas. La afirmación "15 personas prefieren Golf" significa que la suma de los números dentro del conjunto G es 15. La afirmación "ninguno de los que prefieren los deportes Tenis o Surf prefieren el golf. Es decir, que la intersección de G con T y con S son vacías. Es decir que las 15 personas que prefieren golf, lo prefieren únicamente. Esto nos deja con 15 personas por ubicar. El único lugar donde podemos ubicar a dichas 15 personas es en en la intersección de T y S.
a). ¿cuántas personas prefieren dos de estos deportes? Por el diagrama, son aquellas personas que prefieren Tenis o Surf. Es decir, 15.
b) ¿Cuánto prefieren sólo uno de estos deportes? Es la suma de aquellos que prefieren sólo un deporte. Es decir, sólo G, sólo T o sólo S. Es decir 15+20+30 = 65.
How would I solve this problem. A researcher wishes to estimate the mean height of women aged between 60 and 65 in the U.S. She desires a margin of error of 0.3 inches. Past studies suggest that a population standard deviation of 3.3 inches is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
Answers
Answer:
465
Step-by-step explanation:
Margin of error = critical value × standard error
ME = CV × SE
Assuming 95% confidence, CV = z = 1.96.
Standard error is:
SE = σ / √n
SE = 3.3 / √n
Given margin of error of 0.3:
0.3 = 1.96 × 3.3 / √n
n = 465
A bucket that has a mass of 30 kg when filled with sand needs to be lifted to the top of a 30 meter tall building. You have a rope that has a mass of 0.3 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 15 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building. Find the work done lifting the bucket (sand and rope) to the top of the building.
Answers
Answer:
765 J
Step-by-step explanation:
We are given;
Mass of bucket = 30 kg
Mass of rope = 0.3 kg/m
height of building= 30 meter
Now,
work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand
Or W = W1 + W2
Work done in lifting the rope is given as,
W1 = Force x displacement
W1 = (30,0)∫(0.2x .dx)
Integrating, we have;
W1 = [0.2x²/2] at boundary of 30 and 0
W1 = 0.1(30²)
W1 = 90 J
work done in lifting the sand is given as;
W2 = (30,0)∫(F .dx)
F = mx + c
Where, c = 30 - 15 = 15
m = (30 - 15)/(30 - 0)
m = 15/30 = 0.5
So,
F = 0.5x + 15
Thus,
W2 = (30,0)∫(0.5x + 15 .dx)
Integrating, we have;
W2 = (0.5x²/2) + 15x at boundary of 30 and 0
So,
W2 = (0.5 × 30²)/2) + 15(30)
W2 = 225 + 450
W2 = 675 J
Therefore,
work done lifting the bucket (sand and rope) to the top of the building,
W = 90 + 675
W = 765 J
Please answer this correctly
Answers
Answer:
10.71
Step-by-step explanation:
The arc length is
2*3*3.14/4 = 4.71
Add to the two side lengths to get the perimeter
4.71+3+3 = 10.71
[tex]answer = 10.71 \: millimeters \\ solution \\ radius = 3 \: millimeters \\ perimeter \: of \:quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 3}{4} + 2 \times 3\\ = \frac{18.84}{4} + 6 \\ = \frac{18.84 + 6 \times 4}{4} \\ = \frac{18.84 + 24}{4} \\ = \frac{42.84}{4} \\ = 10.71 \: millimeters \\ hope \: it \: helps[/tex]
What is the solution to 4 x + 6 less-than-or-equal-to 18?
Answers
Answer:
a
Step-by-step explanation:
edge 2020-2021 <3333
(have an amazing day lovely)
winnie and kevin like to create their own triathlon courses to challenge each other. last weekend, winnie created a course that included a swim of 3/4 of a mile, a bike ride of 57/4 miles and a run of 13/4 miles. how long was the course winnie created?
Answers
3+57+13= 73
Then you would divide that number by 4
73/4= 18.25
So the course would be 18.25 or 18 1/4 miles long.
You are playing a game called cornhole and let’s assume that you are reallygood at it with the winning probability is 0.8. For the following parts, find (a) the name ofthe appropriate probability distribution and correct parameters, (b) the expected value and (c) the variance of Y.
A. Y = the number of games it takes you to lose one time.
B. Y = the number of games it takes you to lose four times.
C. Y the number of times you win out of 100 games.
Answers
Answer:
Step-by-step explanation:
Given that :
The probability of winning is 0.8
i.e P(winning) = 0.8
Then P(losing) = 0.2
a) Y ~ Geometric distribution
[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]
b) Y ~ Negative Binomial Distribution
[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]
c) Y ~ Binomial Distribution;
n = 100 ; P = 0.8
[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]
Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the standard deviation of the speeds in Excel file Q-14.xlsx.
Answers
Answer and Step-by-step explanation: Standard Deviation is the measure of how diferent a number is from the mean of the data set. It is the spread of a data set. To calculate it manually:
1) Find the mean of the data set. Mean, represented by μ, is the sum of all the values divided by the total number of elements forming the set;
2) Subtract each number with the Mean and square the result;
3) Add the differences and divide it by the total number of elements of the set;
4) Take the square root of the result and that is the Standard Deviation.
The calculations can be done by a calculator like Excel:
1) In each cell of a same column, write the data you want to know the deviation.
2) On the last cell, write: =stdev.p(A1:A10) or =stdev.s(A1:A10).
3) Press Enter. The deviation will appeared on the same cell.
The function STDEV.P is used when the data represents the entire population, whereas STDEV.S is used when the data is for a sample of the population. Inside the parenthesis, put the cells where your data is. For example, if you put your data in the column A, from cell 1 to cell 10, you write like it's written above.
Four whole nuber are each rounded to the nearest 10 the sum of the four rounded numbers is 90 what is the possible maximum sum of the four original numbers
Answers
Answer:
[tex]106[/tex]
Step-by-step explanation:
Let's try guessing...
[tex]45+45=90\\30+30+30=90\\10+20+30+30=90[/tex]
All the units place has to be 4, if it is higher than 4 then the answer will not be 90 (the sum of the four rounded numbers).
[tex]14 + 24 + 34 + 34= 106[/tex]
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answers
Answer:
true
is the answer
Average serving size is 500mls which is 1050kj.
What is the total number of kJs of energy in a 1.25 litre bottle of Lemon Squash?
Answers
Answer:
2625 kJ
Step-by-step explanation:
We assume the energy is proportional to the volume:
energy/volume = 1050 kJ/(500 mL) = E/(1250 mL)
Multiply by 1250 mL:
E = (1250/500)(1050 kJ) = 2625 kJ
The number of kJ in 1.25 L of Lemon Squash is 2625 kJ.
Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally
symmetric if the grid can be rotated 90, 180, or 270 degrees to achieve the same pattern.
Two colorings are called rotationally distinct if neither can be rotated to match the
other. How many rotationally distinct ways are there for Sam to color the grid such
that the colorings are not rotationally symmetric?
Answers
Answer:
65,280
Step-by-step explanation:
Consider the 4×4 grid ...
[tex]\left[\begin{array}{cc}a&b\\d&c\end{array}\right][/tex]
where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.
The same will be true of 270° rotational symmetry, for the same reason.
__
For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)
__
The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...
65,536 -256 = 65,280 . . . . colorings not rotationally symmetric
Please answer this correctly.I want expert people or genius people to answer this
Answers
Answer:
298.5 cm^2.
Step-by-step explanation:
The area of the triangular base
= 1/2 * base * height
= 1/2 * 10 * 8.7 cm^2
There are 3 other triangular sides all withe the same area and each of them as area = 1/2 * 10 * 17
So the total surface area of the pyramid
= 1/2 * 10 * 8.7 + 3 * 1/2 * 10 * 17
= 5 * 8.7 + 3 * 85
= 298.5 cm^2.
Question 2 of 10
2 Points
What is the sum of the rational expressions below?
2x+3/3x+x/x+1
Answers
Answer:
5x^2+5x+3/3x^2+3x
Step-by-step explanation:
What is the measure of <6?
Answers
Answer: Choice B. 54degrees
Step-by-step explanation:
Angles 1 4 5 8 are equal and angles 2 3 6 7 are also equal. These two sets of angles of supplementary(you‘d get 180 by adding them).
so
13x+9=180-(5x+9)
by simplifying the equation youll get
18x+18=180
x=9
so angle 7(and therefore angle 6) equals
5*9+9=54
Solve 3(xx)+x-5 using the first principle
Answers
Answer:
[tex]3x^2+x-5[/tex]
Step-by-step explanation:
[tex]3\left(xx\right)+x-5[/tex]
Remove parenthesis
[tex]3xx+x-5[/tex]
Multiply [tex]x \times x=x^2[/tex]
[tex]3x^2+x-5[/tex]
Answer:
3x²+x-5
Step-by-step explanation:
= 3(xx)+x-5
According to the rule, when bases are same powers are to be added.
= 3(x¹x¹)+x-5
= 3(x¹⁺¹)+x-5
= 3x²+x-5
Yellow card or no in soccer rules if a player leaves the field?
Answers
The end points of wx are w (-5,-1) and x (2,6) What is the length of wx
Answers
Answer:
9.90 units (3 s.f.)
Step-by-step explanation:
distance formula
[tex] = \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]
Length of WX
[tex] = \sqrt{(2 - ( - 5))^{2} + (6 - ( - 1)^{2} } \\ = \sqrt{(2 + 5)^{2} + (6 + 1)^{2} } \\ = \sqrt{7 ^{2} + 7^{2} } \\ = \sqrt{98} \\ = 9.90 \: units \: (3 \: s.f.)[/tex]
Answer:
The answer is 7 square root 2
Step-by-step explanation:
trust
Which set of sides will NOT make a triangle?
2 cm, 3 cm, 4 cm
12 cm, 7 cm, 5 cm
Il cm, 13 cm, 3 cm
19 cm, 14 cm, 7 cm
Answers
Answer:
Set number 2: 12 cm, 7cm, 5cm
Step-by-step explanation:
Here’s why:
12+7 is greater than 5 (that’s good)
12+5 is greater than 7 (that’s good)
7+5 is equal to 12. That is not good because the 2 opposite sides must add together to be greater than the third side, in this case 12. If the 2 sides are less than or equal to the third side, then the triangle will not be formed. I hope this helps, and good luck.
What is the answer to this question
— 44 + 24 =
Answers
Answer:
-20
Step-by-step explanation:
the inverse of the equation (flipping all the signs except for the equal sign) would be 44-24=20. So flip the signs back and you get -44 + 24 = -20
gary mixes a solution using two types of concentration of sale: .70 gallons of 5% and .30 gallons of 22% salt. what is the concentration of the mixed solutions
Answers
Answer:
10.1%
Step-by-step explanation:
The first thing we should do is calculate the total volume of the solution when mixing them would be:
0.7 + 0.3 = 1
Now, we have that the resulting concentration (x) would be equal to the sum of the multiplications between the volumes and the concentrations to be mixed, as follows:
x * 1 = 0.7 * 0.05 + 0.3 * 0.22
x = 0.035 + 0.066
x = 0.101
That is, the concentration of the resulting mixture would be 10.1% (0.101 * 100)
4x2 - 14x + 6
x3 - 7x2 + 12x
What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common
factors.
Answers
Answer:
Answer is given below.
Step-by-step explanation:
let us solve the numerator first
=4x²-14x+6
=2(2x²)+2(-7x)+2(3)
= GCF of the terms of the numerator is 2.
denominator
x³-7x²+12x
x(x²)+x(-7x)+x(12)
GCF of the terms of the denominator is x.
factorise the numerator
4x²-14x+6
4x²-2x-12x + 6 (by splitting the middle term; the numbers should produce the product 4*6 and when the no.s are added they should give -14)
(4x²-2x) + (-12x+6)
2x(2x-1) -6(2x-1)
(2x-6)(2x-1)
factors are
(2x-6), (2x-1)
denominator
this can also be done by splitting the middle term
x³-7x²+12x
x³-3x²-4x²+12x
(x³-3x²) + (-4x²+12x)
x²(x-3) -4x(x-3)
(x²-4x)(x-3)
factors are
(x²-4x), (x-3)
Jar A contains four liters of a solution that is 45% acid. Jar B contains five liters of a solution that is 48% acid. Jar C contains one liter of a solution that is k % acid. From jar C, 2/3 liters of the solution is added to jar A, and the remainder of the solution in jar C is added to jar B. At the end both jar A and jar B contain solutions that are 50% acid. Find k.
Answers
Answer:
k = 79%
Step-by-step explanation:
Jar A - 45% acid and 55% water - "a" liters
Jar B - 48% acid and 52% water - "b" liters
Jar C - k% acid and (100% - k%) water - "c" liters
0,45 . 4 = 1,8 l acid jar A
0,48 . 5 = 2,4 l acid jar B
2/3 + 4 = a ----> a = 14/3 liters
1/3 + 5 = b -----> b = 16/3 liters
14/3 * 50% = 14/6 = 7/3 acid jar A = 2,33 l acid jar A
16/3 * 50% = 16/6 = 8/3 acid jar B = 2,66 l acid jar B
2,33 - 1,8 = 0,53 add in jar A
2,66 - 2,4 = 0,26 add in jar B
0,53 + 0,26 = 0,79 liters acid jar C
1 - 0,79 = 0,21 liters water jar C
(0,79/1) * 100% = 79% acid in jar C
So: k% acid is 79%