Answer:
110 = 16 + 10h
110 - 16 = 10h
Step-by-step explanation:
Sylvie needs a total of $110, which is the number she is working towards.
She already has $16, which is what we call a constant, or a number that will not change in the equation.
We are told that if she works 10 hours, she will earn enough money to buy the concert ticket. The amount that she is paid per hour is the variable, which would be signified by the letter "h" in this case.
Set the equation:
(amount of hours) * (pay per hour) + (amount she starts out with) = (total she needs).
Or, to put into numerical & variable terms, plug in the corresponding number (or variable) to the corresponding part.
10 * h + 16 = 110
(10h) + 16 = 110
Another way to solve is to do the first step in isolating the variable, h. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation & =
Parenthesis
Exponents & roots
Multiplication
Division
Addition
Subtraction
First, subtract 16 from both sides:
10h + 16 (-16) = 110 (-16)
10h = 110 - 16
10h = 94
Next, divide 10 from both sides:
(10h)/10 = (94)/10
h = 94/10
h = 9.4
Mercury contamination of swordfish. Consumer Reports found widespread contamination of seafood in New York and Chicago supermarkets. For example, 40% of the swordfish pieces available for sale have a level of mercury above the Food and Drug Administration (FDA) limit. Consider a random sample of 20 swordfish pieces from New York and Chicago supermarkets.a. Use the normal approximation to the binomial to calculate the probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit. (The final answer is 0.0015) b. Use the normal approximation to the binomial to calculate the probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit. (The final answer is 0.1271) c. Use the binomial tables to calculate the exact probabilities in parts a and b. Does the normal distribution provide a good approximation to the binomial distribution? (0.0005 and 0.1275)
Answer:
Using the normal approximation to the binomial distribution
a) The probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x < 2) = 0.0015
b) The probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x > 10) = 0.1271
Using Binomial distribution formula for these same probabilities.
c) The probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x < 2) = 0.0005
The probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x > 10) = 0.1275
With the continuity correction factor added, the normal approximation to the binomial distribution problem is a good estimate of the binomial distribution, especially for variables close to the mean.
Step-by-step explanation:
To use the normal approximation to the binomial distribution problem, we need to compute the mean and the standard deviation.
With n = sample size = 20
p = proportion of the swordfish pieces available for sale have a level of mercury above the Food and Drug Administration (FDA) limit = 40% = 0.40
Mean = μ = np = 20 × 0.40 = 8
Standard deviation = σ = √[np(1-p)] = √(20×0.40×0.60) = 2.191
If X represents the number of swordfish pieces that have mercury levels exceeding the FDA limit
a) Probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit.
Introducing the continuity correction factor,
P(X < 2) becomes P(x < 2-0.5) = P(x < 1.5)
We first normalize or standardize 1.5.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (1.5 - 8)/2.191 = - 2.97
To determine the required probability
P(x < 1.5) = P(z < -2 97)
We'll use data from the normal distribution table for these probabilities
P(X < 2) = P(x < 1.5) = P(z < -2 97) = 0.00149 = 0.0015
b) Probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit
Adjusting with the continuity correction factor P(X > 10) = P(x > 10+0.5) = P(x > 10.5)
We first normalize or standardize 10.5
z = (x - μ)/σ = (10.5 - 8)/2.191 = 1.14
To determine the required probability
P(x > 10.5) = P(z > 1.14)
We'll use data from the normal distribution table for these probabilities
P(X > 10) = P(X > 10.5) = P(z > 1.14)
= 1 - P(z ≤ 1.14)
= 1 - 0.87286 = 0.12714 = 0.1271
c) Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of swordfishes to be examined = 20
x = Number of successes required = fewer than 2 and more than half, < 2 and > 10
p = probability of success = probability of a swordfish having mercury levels above the FDA limits = 0.40
q = probability of failure = probability of a swordfish NOT having mercury levels above the FDA limits = 1 - p = 1 - 0.40 = 0.60
P(X < 2) = P(X = 0) + P(X = 1) = 0.00052404938 = 0.0005
P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.12752124615 = 0.1275
With the continuity correction factor added, the normal approximation to the binomial distribution problem is a good estimate of the binomial distribution, especially for variables close to the mean.
Hope this Helps!!!
Lisa surveyed 60 students at her school and found that 0.85 of the students she surveyed said their favorite class is math. Another 15% of the students she surveyed reported that their favorite class is science. How many more students in the survey prefer math over science?
Answer:
42
Step-by-step explanation:
Number of students whose favorite class is Math:
60*0.85=51
Number of students whose favorite class is Science:
15% is equal to 0.15.
60*0.15=9
Subtract number of students who like science from number of students who like math.
51-9=42
42 more students in the survey prefer math over science.
Answer:
42
Step-by-step explanation:
85% math
15% science
Subtract
85-15 = 70
The difference is 70 %
70% of 60 students
.70 * 60 = 42
There is a 42 student difference
A school district performed a study to find the main causes leading to its students dropping out of school. Thirty cases were analyzed, and a primary cause was assigned to each case. The causes included unexcused absences (U), illness (I), family problems (F), and other causes (O). The results for the thirty cases are listed below:
U U U I F O O U I F F O U I I F I I O U I F F U U I I O F U
Required:
Construct a table summarizing the frequency distribution of the primary causes leading to student dropout.
Answer:
See below for the table.
Step-by-step explanation:
The results for the thirty cases are listed below:
U U U I F O O U I F F O U I I F I I O U I F F U U I I O F U
The table summarizing the frequency distribution of the primary causes leading to student dropout is:
[tex]\left|\begin{array}{c|c}$Cause&$Frequency\\----------&----\\\\$Unexcused absences (U)&9\\$Illness (I)&9\\$Family problems (F)&7\\$Other causes (O)&5\\-----------&---\\$Total&30\end{array}\right|[/tex]
The volume of a cantaloupe is approximated by Upper V equals four thirds pi font size decreased by 5 r cubed . The radius is growing at the rate of 0.5 cm divided by week, at a time when the radius is 6.4 cm. How fast is the volume changing at that moment?
Answer:
308.67 cm ^ 3 / week
Step-by-step explanation:
A cantaloupe is approximately a sphere, therefore its approximate volume would be:
V = (4/3) * pi * (r ^ 3)
They tell us that dr / dt 0.5 cm / week and the radius is 6.4 cm
if we derive the formula from the volume we are left with:
dV / dt = (4/3) * pi * d / dr [(r ^ 3)]
dV / dt = (4/3) * pi * 3 * (r ^ 2) * dr / dt
dV / dt = 4 * pi * (r ^ 2) * dr / dt
we replace all the values and we are left with:
dV / dt = 4 * 3.14 * (6.4 ^ 2) * 0.6
dV / dt = 308.67
Therefore the volume is changing at a rate of 308.67 cm ^ 3 / week
50 random teenagers were asked how many hours a day they use their phone. They spent an average of 7 hours a day with a standard deviation of 1.3. Based on the results, what is the margin of error for the true mean number of hours a teenager spends on their phone?your margin of error on a 95% confidence level, round your answer to the nearest tenth
Answer:
The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.
Step-by-step explanation:
We have the standard deviation of the saple, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2\frac{1.3}{\sqrt{50}} = 0.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.
The graph below shows the solution to which system of inequalities?
Someone please help me I would appreciate the help
Answer:
y>=1/4x+4
y>3x
Step-by-step explanation:
16. How much money will I need to have at retirement so I can withdraw $60,000 a year for 20 years from an account earning 8% compounded annually? a. How much do you need in your account at the beginning b. How much total money will you pull out of the account? c. How much of that money is interest?
Answer:
starting balance: $636,215.95total withdrawals: $1,200,000interest withdrawn: $563,784.05Step-by-step explanation:
a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.
The principal P that must be invested at rate r for n annual withdrawals of amount A is ...
P = A(1+r)(1 -(1 +r)^-n)/r
P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95
__
b) 20 withdrawals of $60,000 each total ...
20×$60,000 = $1,200,000
__
c) The excess over the amount deposited is interest:
$1,200,000 -636,215.95 = $563,784.05
The diagram shows the first four patterns of a sequence. Find an expression for the numbers of squares in the nth pattern of the sequence.
Answer:
n^2+3
Step-by-step explanation:
As we can see in the diagram
1st pattern consists from 1 square 1x1 +3 squares 1x1 each
2nd pattern consists from 1 square 2x2 +3 squares 1x1 each
3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each
4-th pattern consists from 1 square 4x4 + 3 squares 1x1 each
We can to continue :
5-th pattern consists from 1 square 5x5+3 squares 1x1 each
So the nth pattern consists from 1 square nxn+3 squares 1x1 each
Or total amount of 1x1 squares in nth pattern N= n^2+3
The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
What is nth term of a sequence?"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."
From the given diagram
We can see that every term is made up with a square which side is n and three small square side is 1.
So,
1st term is 1 × 1 + 3 = 4
2nd term is 2 × 2 + 3 = 4
3rd term is 3 × 3 + 3 = 12
4th term is 4 × 4 + 3 = 19
So, nth term is [tex]n^{2} +3[/tex]
Hence, The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
Learn more about nth term of a sequence here
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What is the measure of x?
Answer:
x= 9 inches
Step-by-step explanation:
Hello
I can help you with this.
in this case, we have two similar triangles, let's see
Step 1
identify the rigth triangles.
1) the first triangle has these dimensions
hypotenuse( remember, the longest side)= unknown=H
adjacent side(the horizontal)=6 +x
opposite side(the vertical)=10
2) the second triangle has these dimensions
hypotenuse( remember, the longest side)= unknown=h
adjacent side(the horizontal)=6
opposite side(the vertical)=4.
As these triangles keep the same proportion and in both cases we know the length of the legs, we can establish a relationship
Step 2
establish a relationship
let's compare the opposite side and the adjacent side
triangle 1 (the bigger)
[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{10}{6+x}[/tex]
Triangle 2
[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{4}{6}\\proportion=\frac{2}{3}[/tex]
were the proportions are equal, so
[tex]\frac{10}{6+x}=\frac{2}{3}[/tex]
at this point, just isolate x to find its value
Step 3
isolate x
[tex]\frac{10}{6+x}=\frac{2}{3}\\multiply\ both\ sides\ by\ 3\\\frac{10*3}{6+x}=\frac{2*3}{3}\\\frac{30}{6+x} =2\\\\Multiply\ both\ sides\ by (6+x)\\\frac{30(6+X)}{6+x} =2(6+x)\\30=12+2x\\30-12=2x\\18=2x\\so\\x=\frac{18}{2} \\x=9[/tex]
remember the units of measure ( Inches)
x= 9 inches
I really hope it helps, have a nice day.
HELP WITH THESE QUESTIONS!!
Create a bucket by rotating around the y axis the curve y=5 ln(x-2) from y=0 to y=4. If this bucket contains a liquid with density 760 kg/m3 filled to a height of 3 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity.
Answer:
The work will be "1909212.015 J". The further explanation is given below.
Step-by-step explanation:
The given values are:
Liquid's density
= 760 kg/m³
Height
= 3 meters
Gravity
g = 3.8 m/s²
Value of y is:
y = 5 log (x-2)
y = 0
y = 4
As we know,
⇒ [tex]\Delta V=\pi r^2 \Delta y[/tex]
⇒ [tex]y =5log(x-2)[/tex]
⇒ [tex]\frac{y}{5} =log (x-2)[/tex]
⇒ [tex]e^{\frac{y}{5}}=(x-2)[/tex]
⇒ [tex]x=e^{\frac{y}{5}}+2[/tex]
Now,
[tex]\Delta F=ma[/tex]
[tex]=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y[/tex]
So that,
⇒ [tex]\Delta W = \Delta F.distance[/tex]
[tex]=\Delta F(4-y)[/tex]
The required work will be:
⇒ [tex]W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy[/tex]
[tex]=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}][/tex]
[tex]=760\times 9.8 \pi[81.455][/tex]
[tex]=1909212.015 \ J[/tex]
Tanya can wash a car and vacuum its interior in 2 hours. Pat needs 5 hours to do this same job. If Tanya and Pat work together, how many hours will it take them to clean a car??
Answer:
It will take 1.43 hours for them to clean the car.
Step-by-step explanation:
The together rate is the sum of each separate rate.
In this problem:
Together rate: 1/x
Tanya's rate: 1/2
Pat's rate: 1/5
Together rate = Tanya's rate + Pat's rate
[tex]\frac{1}{x} = \frac{1}{2} + \frac{1}{5}[/tex]
[tex]\frac{1}{x} = \frac{5 + 2}{10}[/tex]
[tex]\frac{1}{x} = \frac{7}{10}[/tex]
[tex]7x = 10[/tex]
[tex]x = \frac{10}{7}[/tex]
[tex]x = 1.43[/tex]
It will take 1.43 hours for them to clean the car.
The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a maximum of 12.75 ounces of soda. Every can that has more than 12.75 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process?
Answer:
0.1587
Step-by-step explanation:
According to the situation, the solution and the data provided is as follows
mean = 12.45 ounces
Standard deviation = 0.30 ounces
maximum = 12.75 ounces
More than ounces of soda = 12.75
Based on the above information, the probability is
[tex]Z=\frac{X-\mu }{\sigma } \\\\Z=\frac{12.75-12.45 }{0.30 } \\\\\Z=\frac{0.30 }{0.30 } \\\\Z= 1 \\\\P(X> 12.75)=1-P(X< 12.75) \\\\\P(X> 12.75)=1-P(Z< 1) \\\\[/tex]
As we know that
P(Z<1) = 0.8413
So,
P (X > 12.75) = 1 - 0.8413
= 0.1587
I will Give brainliest to who ever can show me how to solve this killer!!!!!!! Using Descartes Rule and the rational zeros of polynomial equation, find the root (positive, negative and imaginary) of x^5-2x^4+x^3+x^2-2x+1=0
see if other people has already answered this question
Answer:
-1
1
1/2(1±i√3)
Step-by-step explanation:
x^5-2x^4+x^3+x^2-2x+1=0x^3(x^2-2x+1)+(x^2-2x+1)=0(x^3+1)(x-1)^2=0(x+1)(x^2-x+1)(x-1)^2=01. x+1=0 ⇒ x= -1
2. x-1= 0 ⇒ x= 1
3. x^2-x+1=0
x^2- 2*1/2x+1/4= -3/4(x-1/2)^2= -3/4x-1/2= ±√-3/4 ⇒ x-1/2=±i√3/2 ⇒ x= 1/2 ± i√3/2= 1/2(1± i√3)What is the length of Line segment M N?
58cm
75cm
88cm
116cm
Answer:
58
Step-by-step explanation:
use equations to get answers
Referring to a line segment with endpoints A and B, what does it mean to refer to AB with no line over it?
Answer: length of AB
Step-by-step explanation:
[tex]\overline{AB}[/tex] represents the line segment from point A to point B
[tex]\overrightarrow{AB}[/tex] represents ray from point A to infinity through point B
AB represents the length of the line segment from point A to point B.
Please answer question now
Answer:
[tex]\overrightarrow{VU}\text{ and }\overrightarrow{VW}[/tex]
Step-by-step explanation:
From the given figure it is clear that we two rays because both sides have one endpoint and goes on infinitely in only one direction.
If a ray has end point at A and goes on infinitely in only one direction towards point B, then ray is denoted as [tex]\overrightarrow{AB}[/tex].
For first side, we have point V as end point and ray goes goes on infinitely in only one direction towards point U. So, first side is [tex]\overrightarrow{VU}[/tex].
For second side, we have point V as end point and ray goes goes on infinitely in only one direction towards point W. So, second side is [tex]\overrightarrow{VW}[/tex].
Therefore, the sides are [tex]\overrightarrow{VU}\text{ and }\overrightarrow{VW}[/tex].
Suppose that the lenghth between 911 calls to a ceration police stattion is exponentially distribution with an average of 5 minutes between calls. What is the probability that they receive 10 calls in the next hours?
Answer:
0.1048
Step-by-step explanation:
The computation of probability that they receive 10 calls in the next hours is shown below:-
Average which is given in the question 5 minutes between calls = 5/60 calls an hour so it becomes 12 calls per hour
So,
P(X = 10)
[tex]= \frac{e^{-12}12^{10}}{10!}[/tex]
= 0.1048
Therefore for computing the probability that they receive 10 calls in the next hours we simply applied the above formula.
An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 51% of passengers have no checked luggage, 33% have one piece of checked luggage and 16% have two pieces. We suppose a negligible portion of people check more than two bags.
Required:
a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.
b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation? Note any assumptions you make and if you think they are justified.
Answer:
The average revenue per passenger is about $13.85
μ = $13.85
The corresponding standard deviation is $14.51
σ = $14.51
The airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.
Expected revenue = $1,662 ± 14.51
Step-by-step explanation:
An airline charges the following baggage fees:
$25 for the first bag and $35 for the second
Suppose 51% of passengers have no checked luggage,
P(0) = 0.51
33% have one piece of checked luggage and 16% have two pieces.
P(1) = 0.33
P(2) = 0.16
a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.
The average revenue per passenger is given by
μ = 0×P(0) + 25×P(1) + 35×P(2)
μ = 0×0.51 + 25×0.33 + 35×0.16
μ = 0 + 8.25 + 5.6
μ = $13.85
Therefore, the average revenue per passenger is about $13.85
The corresponding standard deviation is given by
σ = √σ²
Where σ² is the variance and is given by
σ² = (0 - 13.85)²×0.51 + (25 - 13.85)²×0.33 + (35 - 13.85)²×0.16
σ² = 97.83 + 41.03 + 71.57
σ² = 210.43
So,
σ = √210.43
σ = $14.51
Therefore, the corresponding standard deviation is $14.51
b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation?
For 120 passengers,
Expected revenue = 120×$13.85
Expected revenue = $1,662 ± 14.51
Therefore, the airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.
Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?
Answer:
65%
Step-by-step explanation:
Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?
3 gallons of 80% juice solution contains this amount of juice:
80% * 3 gal = 0.8 * 3 gal = 2.4 gal
1 gallon of 20% juice solution contains this amount of juice:
20% * 1 gal = 0.2 * 1 gal = 0.2 gal
The total amount of juice in the final juice solution is
2.4 gal + 0.2 gal = 2.6 gal
The total amount of juice solution made is 3 gal + 1 gal = 4 gal
The 4 gal juice solution contains 2.6 gallons of juice.
2.6 gallons is what percent of 4 gallons?
2.6/4 * 100% = 0.65 * 100% = 65%
Answer: 65%
Answer:
65% i got the answer right on the question
Step-by-step explanation:
Can someone help me with this
Answer:
Y is 90 degrees.
Step-by-step explanation:
This is an equalterial triangle which means all of the angles are the same. The angle for the upper part of the triangle is 60 as well. We can do 2x=60 because they add up to the angle which is 60. This gives us x=30. If x=30 and the other angle is 60, then the other angle has to be 90 because all triangle has an angle sum of 180. So 30 +60 + 90= 180. Hope this helps!
Answer:
y=90 degrees.
Step-by-step explanation:
find the value of x
m<2= x + 122
Answer:
x= -14
Step-by-step explanation:
Please see attached picture for full solution.
What is the slope of the line on the graph below? On a coordinate plane, a line goes through points (negative 2, negative 3), (negative 1, negative 1), (0, 1) and (1, 3). –One-half One-half 1 2 plz
Answer:
slope = 2
Step-by-step explanation:
All four points lie on the same line.
Taking the first and fourth points, the slope can be found by the formula
slope, m = (y2-y1)/(x2-x1) = (3- -3) / (1- -2) = 6/3 =2
See attached diagram.
Answer:
2
Step-by-step explanation:
edge 2020
If AB= X and x=4, then the transitive property states
Answer:
AB=4
Step-by-step explanation:
The transitive property states if A=B and B+C than A+C Next substitute
AB=x and x=4 so AB=4
Hope this helps, if it did, please give me brainliest, it helps me a lot. :)
Have a good day!
Crane Company reports the following for the month of June.
Date
Explanation
Units
Unit Cost
Total Cost
June 1 Inventory 150 $4 $600
12 Purchase 450 5 2,250
23 Purchase 400 6 2,400
30 Inventory 80
Assume a sale of 500 units occurred on June 15 for a selling price of $7 and a sale of 420 units on June 27 for $8.
Calculate cost of goods available for sale.
Calculate Moving-Average unit cost for June 1, 12, 15, 23 & 27. (Round answers to 3 decimal places, e.g. 2.525.)
Answer:
Crane CompanyJune Financial Reports
a) Cost of goods available for sale = $5,250
b) Moving-Average unit cost for:
i) June 1: = $5
ii) 12: = $4.75
iii) 15: = $4.75
iv) 23: = $5.75
v) 27: = $5.25
Step-by-step explanation:
a) Calculations:
Date Explanation Units Unit Cost Total Cost Moving Average Cost
June 1 Inventory 150 $4 $600 $4.000
12 Purchase 450 5 2,250 4.750
15 Sale 500 7 3,500 4.750
23 Purchase 400 6 2,400 5.750
27 Sale 420 8 3,360 5.250
30 Inventory 80
Cost of goods available for sale = Cost of Beginning Inventory + Cost of Purchases = $5,250 + ($600 + 2,250 + 2,400)
b) Moving-Average unit cost for:
i) June 1: Cost of goods available/Units of goods available = $5 ($600/150)
ii) 12: Cost of goods available/Units of goods available = $4.75 ($600 + 2,250/600)
iii) 15: Cost of goods available/Units of goods available = $4.75 ($475/100)
iv) 23: Cost of goods available/Units of goods available = $5.75 ($475 + 2,400)/500
v) 27: Cost of goods available/Units of goods available = $5.25 ($420/80)
In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each participant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree," and these are assigned the numbers 1 or −1, respectively. Participant’s responses to the survey are encoded as a vector in R4, where coordinates correspond to their answers to each question. Here are the questions:
The question is incomplete. Here is the complete question.
In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:
Question #1: I prefer outdoor activities, rather than indoor activities.
Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.
Question #3: I prefer texting, rather than talking on the phone.
Question #4: I prefer living in a small town, rather than in a big city.
Here are the results for the questionaire, with a group of 5 participants:
Question1 Question2 Question3 Question4
participant A 1 1 -1 -1
participant B -1 1 1 1
participant C -1 -1 1 1
participant D 1 -1 -1 -1
participant E 1 -1 1 1
Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".
(a) Which pairs of paricipants are compatible?
(b) Which pairs of participants are incompatible?
(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only
allowing "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?
Answer: (a) Participants A and D; B and C; C and E.
(b) Participants A and B; A and C; A and E; B and D; C and D;
Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.
Vectors form angles between themselves and can be found by the following formula:
cos α = [tex]\frac{A.B}{||A||.||B||}[/tex]
which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.
For the compatibility test, find the angle between vectors:
1) The vectors magnitude:
Magnitude of a vector is given by:
||x|| = [tex]\sqrt{x_{i}^{2} + x_{j}^{2}}[/tex]
Since all the vectors have value 1, they have the same magnitude:
||A|| = [tex]\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}[/tex] = 2
||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2
2) The dot product of vectors:
A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{1}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]
The angle that has cosine equal -1/2 is 120°, so incompatible
A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4
cos [tex]\alpha _{2}[/tex] = -1
Angle = 180° --------> incompatible
A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2
cos [tex]\alpha _{3}[/tex] = 1/2
Angle = 60° ---------> COMPATIBLE
A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{4}[/tex] = -1/2
Angle = 120° --------> incompatible
B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha _{5}[/tex] = 1/2
Angle = 60° -------------> COMPATIBLE
B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4
cos[tex]\alpha_{6}[/tex] = -1
Angle = 180° -----------> incompatible
B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0
cos[tex]\alpha _{7}[/tex] = 0
Angle = 90° -------------> may or may not
C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2
cos[tex]\alpha_{8} =[/tex] -1/2
Angle = 120° ---------------> Incompatible
C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha_{9}[/tex] = 1/2
Angle = 60° ---------------> COMPATIBLE
D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0
cos [tex]\alpha_{10}[/tex] = 0
Angle = 90° -----------------> may or may not
(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.
A student's course grade is based on one midterm that counts as 1010% of his final grade, one class project that counts as 1515% of his final grade, a set of homework assignments that counts as 4040% of his final grade, and a final exam that counts as 3535% of his final grade. His midterm score is 6767, his project score is 8888, his homework score is 9191, and his final exam score is 7272. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Answer:
His overall final score is 81.5
He earned a B
Step-by-step explanation:
To find his overall grade, we multiply each of his grades by it's weight.
Grades:
67 on the midterm, which counts for 10% = 0.1
88 on the project, which counts for 15% = 0.15
91 on homework assignements, which counts for 40% = 0.4
72 on the final exam, which counts for 35% = 0.35.
What is his overall final score?
67*0.1 + 88*0.15 + 91*0.4 + 72*0.35 = 81.5
His overall final score is 81.5
At least 80 and less than 90 has a letter grade of B. 81.5 is in this range. So he earned a B
There are 3 white counters and 1 black counters in a bag I take one of the counters at random what is the probability??
Answer:
0.25
Step-by-step explanation:
Out of the 4 counters only 1 is black so the probability is 1/4 or 0.25.
Answer:
0.25
Step-by-step explanation:
Since there are four marbles 100/4 =25 in this 100 is 1 thus the answer is 0.25
Jaime finished analyzing a set of data with an explanatory variable x and a response variable y. He finds that the mean and standard deviation for x are 5.43 and 1.12, respectively. The mean and standard deviation for y are 10.32 and 2.69, respectively. The correlation was found to be 0.893.
Select the correct slope and y-intercept for the least-squares line.
Answer:
The slope is m=2.145.
The y-intercept is b=-1.33.
Step-by-step explanation:
We have this data:
- The mean and standard deviation for x are 5.43 and 1.12, respectively.
- The mean and standard deviation for y are 10.32 and 2.69, respectively.
- The correlation is 0.893.
We have to calculate the slope and the y-intercept of the least-squares line.
With the given data, we can calculate the slope m as:
[tex]m=r\;\dfrac{s_y}{s_x}=0.893\;\dfrac{2.69}{1.12}=2.145[/tex]
Then, the y-intercept is calculated as:
[tex]b=\bar y-m\cdot \bar x=10.32-2.145\cdot 5.43=10.32-11.65=-1.33[/tex]
Clara did not want to tell Carl how old she was. All she said was that every year on her birthday, her Mom put as many coins in her money box as how old she turned that day. Carl roughly estimated the number of coins in the box as not less than 110 but not more than 130 coins. How old is Clara?