What is the economic order quantity for zhou's airwing bicycle? a. 42 b. 68 c. 37 d. 79
Answers
The economic order quantity for Zhou Bicycle Company's Airwing bicycle is approximately 68. The answer is (b) 68.
To calculate the economic order quantity (EOQ) for Zhou Bicycle Company's Airwing bicycle, we need to use the following formula:
EOQ = √((2DS)/H)
where:
D = annual demand
S = cost of placing one order
H = holding cost per unit per year
First, we need to calculate the annual demand for Airwing bicycles. The table provided shows the sales data for the past two years:
Year 1: 300 Airwing bicycles sold
Year 2: 350 Airwing bicycles sold
Average annual demand = (300 + 350) / 2 = 325
Next, we need to calculate the cost of placing one order. The question states that each time an order is placed, ZBC incurs a cost of $65. Therefore, S = $65.
Finally, we must compute the annual holding cost per unit. According to the question, ZBC's inventory carrying cost is 1% per month (12% per year) of the purchase price. ZBC paid 60% of the suggested retail price of $170 for the purchase. Therefore, the purchase price paid by ZBC is 0.6 x $170 = $102.
Holding cost per unit per year = 12% x $102 = $12.24
Now we can plug these values into the EOQ formula:
EOQ = √((2 x 325 x $65)/$12.24) ≈ 68
Therefore, the economic order quantity for Zhou Bicycle Company's Airwing bicycle is approximately 68.
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Complete question:
Zhou Bicycle Company (ZBC), located in Seattle, is a wholesale distributor of bicycles and bicycle parts. Formed in 1981 by University of Washington Professor Yong-Pin Zhou, the firm’s primary retail outlets are located within a 400-mile radius of the distribution center. These retail outlets receive the order from ZBC within 2 days after notifying the distribution center, provided that the stock is available. However, if an order is not fulfilled by the company, no backorder is placed; the retailers arrange to get their shipment from other distributors, and ZBC loses that amount of business.
The company distributes a wide variety of bicycles. The most popular model, and the major source of revenue to the company, is the Airwing. ZBC receives all the models from a single manufacturer in China, and shipment takes as long as 4 weeks from the time an order is placed. With the cost of communication, paperwork, and customs clearance included, ZBC estimates that each time an order is placed, it incurs a cost of $65. The purchase price paid by ZBC, per bicycle, is roughly 60% of the suggested retail price for all the styles available, and the inventory carrying cost is 1% per month (12% per year) of the purchase price paid by ZBC. The retail price (paid by the customers) for the Airwing is $170 per bicycle.
ZBC is interested in making an inventory plan for 2019. The firm wants to maintain a 95% service level with its customers to minimize the losses on the lost orders. The data collected for the past 2 years are summarized in the following table. A forecast for Airwing model sales in 2019 has been developed and will be used to make an inventory plan for ZBC.
Related Questions
Leticia is running
a cross-country race. She runs the first
mile in 12 minutes. How many miles can
she run in 1 hour?
Answers
Answer:
Step-by-step explanation:
first, we convert the minutes into an hour
there are 60 minutes in an hour
so then we do 60 divided by 12
that equals to 5
so 5 miles is the answer
Is $9 : 4 visitors - $18 : 8 visitors proportional
Answers
Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.
To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.
The ratio of cost to the quantity of visitors for $9 and four visitors is:
$9/4 visitors = $2.25/ visitors
The ratio of value to the quantity of visitors for $18 and eight visitors is:
$18/8 visitors = $2.25/ visitors
We are able to see that both ratios are equal to $2.25 per visitor.
Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.
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The diagram shows a prism placed on a horizontal floor. The prism has a height of 5m and a volume of 30m cubed. The pressure on the floor due to to the prism is 55 newtons/m². Work out the force exerted by the prism on the floor.
Answers
Step-by-step explanation:
We can start by using the formula:
force = pressure x area
The pressure on the floor is given as 55 newtons/m². To find the area, we need to first calculate the base of the prism. We can do this by rearranging the formula for volume:
volume = base x height x depth
30 = base x 5 x depth
base = 6m² (dividing both sides by 5 x depth)
Now we can calculate the force exerted by the prism on the floor:
force = pressure x area
force = 55 x 6
force = 330 newtons
Therefore, the force exerted by the prism on the floor is 330 newtons.
Let B {bı, b2} and C = {c1, c2} be bases for R^2 where bı [-1;8]. b2 [1;-5], c1 = [1;4]. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B.
Answers
Answer:
Let B {bı, b2} and C = {c1, c2} be bases for R^2 where bı [-1;8]. b2 [1;-5], c1 = [1;4]. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B.
In the given problem, we have the bases B and C as follows:
B = {b1, b2} where b1 = [-1;8] and b2 = [1;-5]
C = {c1, c2} where c1 = [1;4] and c2 = [0;1]
We need to find the change-of-coordinates matrix from B to C and from C to B.
To find the change-of-coordinates matrix from B to C, we need to express the basis vectors of B in terms of the basis vectors of C. We can do this by solving the following equations:
b1 = x1c1 + y1c2
b2 = x2c1 + y2c2
where x1 , y1, x2, and y2 are the coefficients we want to find.
Substituting the given values, we get:
[-1;8] = x1*[1;4] + y1*[0;1]
[1;-5] = x2*[1;4] + y2*[0;1]
Solving these equations, we get:
x1 = -17/4, y1 = 1/4, x2 = 9/4, and y2 = -1/4
Therefore, the change-of-coordinates matrix from B to C is:
[-17/4 9/4]
[ 1/4 -1/4]
To find the change-of-coordinates matrix from C to B, we need to express the basis vectors of C in terms of the basis vectors of B. We can do this by solving the following equations:
c1 = a1b1 + a2b2
c2 = b1b1 + b2b2
where a1 , a2, b1, and b2 are the coefficients we want to find.
Substituting the given values and solving these equations, we get:
a1 = 4/17, a2 = -1/17, b1 = -1/17, and b2 = -5/17
Therefore, the change-of-coordinates matrix from C to B is:
[ 4/17 -1/17]
[-1/17 -5/17]
I hope this helps!
Step-by-step explanation:
for an integer $n$, the inequality \[x^2 nx 15 < 0\]has no real solutions in $x$. find the number of different possible values of $n$.
Answers
To solve this problem, we need to understand the conditions under which the inequality $x^2 nx 15 < 0$ has no real solutions. This inequality can be rewritten as $nx(x-15/n) < 0$, which tells us that either $n>0$ and $x<0$ or $x>15/n$, or $n<0$ and $x>0$ or $x<15/n$.
In either case, we have a product of two factors that must be negative, which means that either both factors are negative or both factors are positive.
Since we are looking for the number of different possible values of $n$, we need to consider all possible combinations of signs for $n$ and $x-15/n$. If $n>0$, then $x-15/n$ must also be positive, which means that $x>15/n$. If $n<0$, then $x-15/n$ must be negative, which means that $x<15/n$. In either case, we can see that $n$ must be either positive or negative, and that there is only one possible value of $n$ that satisfies the given condition: $n = \frac{15}{x^2}$.
To find the number of different possible values of $n$, we need to consider all possible values of $x$. If $x=0$, then the inequality is trivially true for any value of $n$. If $x\neq 0$, then we can see that $n$ can take any value in the interval $(0,\infty)$ or $(-\infty,0)$, which means that there are infinitely many possible values of $n$ that satisfy the given condition.
Therefore, the answer to the question is that there are infinitely many different possible values of $n$.
To find the number of different possible values of $n$ for which the inequality $x^2 + nx + 15 < 0$ has no real solutions in $x$, we first need to analyze the inequality.
Step 1: Find the discriminant of the quadratic inequality.
The discriminant, $D$, is given by the formula $D = b^2 - 4ac$, where $a$, $b$, and $c$ are the coefficients of the quadratic expression. In this case, $a = 1$, $b = n$, and $c = 15$.
So, $D = n^2 - 4(1)(15) = n^2 - 60$.
Step 2: Determine the condition for the inequality to have no real solutions.
For a quadratic inequality to have no real solutions, the parabola must not intersect the x-axis, which means the discriminant must be less than 0.
So, we need to solve the inequality $D < 0$:
$n^2 - 60 < 0$
Step 3: Solve the inequality for $n$.
To solve the inequality, find the range of values of $n$ that satisfy the inequality.
$(n - \sqrt{60})(n + \sqrt{60}) < 0$
Since $\sqrt{60}$ is between 7 and 8, we can rewrite the inequality as:
$-8 < n < 8$
Step 4: Count the number of possible integer values of $n$.
The inequality indicates that $n$ must be an integer between -8 and 8 (not inclusive). Therefore, the possible values of $n$ are -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, and 7.
There are 14 different possible values of $n$ for which the inequality $x^2 + nx + 15 < 0$ has no real solutions in $x$.
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x is less than or equal to -2 and x is less than -5 how to plot
Answers
The inequalities are x ≤ -2 and x <-5.
We have,
x is less than or equal to -2 and x is less than -5.
writing the inequality in mathematical expression as
x is less than or equal to -2 = x ≤ -2.
and, x is less than -5 = x <-5.
Now, for x ≤ -2 the number line start from -2 with closed dot and move towards -3, -4, -5, ....
and, for x < -5 the number line start from -5 with open dot move towards -6, -7, -8, ....
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Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
Answers
The event that will have a sample space of S = {h, t} is (a) Flipping a fair, two-sided coin
Which event will have a sample space of S = {h, t}?From the question, we have the following parameters that can be used in our computation:
Sample space of S = {h, t}
The sample size of the above is
Size = 2
Analyzing the options, we have
Flipping a fair, two-sided coin: Size = 2Rolling a six-sided die: Size = 6Spinning a spinner with three sections: Size = 3Choosing a tile from a pair of tiles, one with the letter A and one with the letter B: Probability = 1/2Hence, the event is (a)
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If the probability is 0.05 that a certain column will fail under a given load, what are the probabilities that among 16 such columns given that the failure of columns are independents a) At most two will fail.
Answers
The probability that at most 2 columns will fail is 0.98.
This is a binomial distribution problem, where the number of trials n = 16, the probability of success (a column failing) p = 0.05, and we want to find the probability of at most 2 columns failing.
To solve this, we need to calculate the probability of 0, 1, or 2 columns failing and add them up.
P(at most 2 columns failing) = P(0 columns failing) + P(1 column failing) + P(2 columns failing)
P(0 columns failing) = (n choose 0) * p^0 * (1-p)^(n-0) = (16 choose 0) * 0.05^0 * 0.95^16 = 0.45
P(1 column failing) = (n choose 1) * p^1 * (1-p)^(n-1) = (16 choose 1) * 0.05^1 * 0.95^15 = 0.38
P(2 columns failing) = (n choose 2) * p^2 * (1-p)^(n-2) = (16 choose 2) * 0.05^2 * 0.95^14 = 0.15
P(at most 2 columns failing) = 0.45 + 0.38 + 0.15 = 0.98
Therefore, the probability that at most 2 columns will fail is 0.98.
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A density graph for all of the possible temperatures from 60 degrees to 160
degrees can be used to find which of the following?
A. The probability of a temperature from 30 degrees to 90 degrees
B. The probability of a temperature from 90 degrees to 120 degrees
temperature from 90 degrees to 180 degrees
C. The probability of a
D. The probability of a temperature from 30 degrees to 120 degrees
Answers
Answer:
A. The probability of a temperature from 30 degrees to 90 degrees
Step-by-step explanation:
The range of the graph is from 60 to 160 degrees, so we're looking for options that fit within that range.
A. 30 degrees is lower than 60, outside the range
B. Fits
C. Need more information
D. 30 degrees is too low, outside the range
given three consecutive odd integers their sum is two times third number plus 25 what are the three numbers
Answers
The three consecutive odd integers are 27, 29, and 31.
Given that three consecutive odd integers their sum is two times third number plus 25
Let's call the first odd integer "x." Since the integers are consecutive odd numbers, therefore, the next two odd integers would be x+2 and x+4.
Now according to the problem, their sum is equal to two times the third number (x+4) plus 25:
x + (x+2) + (x+4) = 2(x+4) + 25
Simplifying the left side:
3x + 6 = 2x + 8 + 25
Next combining like terms:
3x + 6 = 2x + 33
Subtracting 2x and 6 from both sides:
x = 27
Therefore, the three consecutive odd integers are 27, 29, and 31.
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A candy company claims that the colors of the candy in their packages are distributed with the following percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% purple. If given a random sample of packages, using a 0.05 significance level, what is the critical value for the goodness-of-fit needed to test the claim?
A.11.071
B.12.592
C.12.833
D.15.822
Answers
The critical value for the goodness-of-fit needed to test the claim is A.11.071
How to solveGiven:
There are 6 colors.
Df= 6-1=5
Critical chi-square with 5 df at 0.05 level of significance = 11.071
Answer: 11.071
Chi-square serves as a statistical examination that analyzes whether there exists any noteworthy disparity between anticipated and witnessed frequencies present inside a categorical compilation of data.
By assessing the interrelationship between two independent variables, the tool determines the scope of association between them till they become independent.
After scrutinizing the differentiation within the outcome extracted from expected and actual observations, which is then evaluated against predetermined chi-square results, the derived p-value deduces the consequent decision concerning null hypothesis dismissal or affirmation in confirming an absence of interrelation between the two initial variable candidates.
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solve for x !
2x-6
4x+18
x = [?]
Answers
Answer:
-12
Step-by-step explanation:
First substitute
2x-6 and 4x+18Then after evaluating collect the like terms
2x-6=4x+18After collecting the like terns simplify the Numbers
2x-4x=18+6And finally evaluate the answer
-2x=24 x=-12Answer: 2x-64x+18x = –44x
Step-by-step explanation:
you are hiking on a 3 mile long trail to get to the peak of a mountain. the trailhead sits at 3,874 ft, and the mountain peak sits at 9,262 ft. calculate the gradient of this path in ft/mi. type out your math work.
Answers
The gradient of the path from the trailhead to the mountain peak can be calculated by dividing the change in elevation (in feet) by the length of the trail (in miles). i.e., Gradient = (Change in Elevation) / (Trail Length)
To calculate the elevation change, we can subtract the elevation at the trailhead from the elevation at the mountain peak:
Change in Elevation = Peak Elevation - Trailhead Elevation
Change in Elevation = 9,262 ft - 3,874 ft
Change in Elevation = 5,388 ft
To calculate the length of the trail in miles, we simply divide the length in feet by the number of feet in a mile:
Trail Length = 3 miles
Now we can calculate the gradient:
Gradient = (Change in Elevation) / (Trail Length)
Gradient = 5,388 ft / 3 miles
Gradient = 1,796 ft/mi
Therefore, the gradient of the path from the trailhead to the mountain peak is 1,796 ft/mi. This means that for every mile traveled along the path, there is an increase in elevation of 1,796 feet. The steepness of this path may pose a challenge to hikers, especially those who are not accustomed to hiking at high elevations. Hikers need to be prepared and take appropriate safety precautions when hiking in mountainous terrain.
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38. A 10-year-old boy (weighing 30 kg) has been prescribed Rimactane 150mg capsules (rifampicin) for the management of brucellosis at a dose of 10 mg/kg twice daily for 4 weeks. How many of these capsules should be dispensed for this patient to cover the 4 weeks? A 108 capsules B 110 capsules C 112 capsules D 114 capsules E 116 capsules 41. Arnold, a 5-year-old boy (weight 18 kg) with epilepsy, currently takes Epanutin suspension (phenytoin 30 mg/5 ml) at a dose of 5 mg/kg twice daily. How many millilitres of Epanutin suspension will Arnold take during the month of October? You can assume that he is fully compliant and no spillages or medication loss occurs during the month of October. A 155 ml B 450 mL C 465 ml. D 900 mL E 930 ml
Answers
a) The total number of capsules needed for 4 weeks is C, 112 capsules.
b) The total milliliters needed for the month of October is C, 465 ml.
a) To determine the number of Rimactane 150mg capsules needed for a 10-year-old boy weighing 30 kg, who has been prescribed a dose of 10 mg/kg twice daily for 4 weeks, follow these steps:
1. Calculate the total daily dose: 30 kg * 10 mg/kg = 300 mg/day
2. Determine the number of daily doses: 300 mg/day / 150 mg/capsule = 2 capsules/day
3. Calculate the total number of capsules needed for 4 weeks: 2 capsules/day * 7 days/week * 4 weeks = 112 capsules
The answer is C, 112 capsules.
b) To calculate the number of milliliters of Epanutin suspension (phenytoin 30 mg/5 ml) that a 5-year-old boy weighing 18 kg with epilepsy will take at a dose of 5 mg/kg twice daily during the month of October, follow these steps:
1. Calculate the total daily dose: 18 kg * 5 mg/kg = 90 mg/day
2. Determine the number of milliliters needed for each daily dose: 90 mg/day * (5 ml/30 mg) = 15 ml/day
3. Calculate the total milliliters needed for the month of October: 15 ml/day * 31 days = 465 ml
The answer is C, 465 ml.
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find the median of the lower half
17,18,19,20,21,24,25,27
Answers
Answer:
18.5
Step-by-step explanation:
Make sure the numbers are in order from least to greatest!
To define the median of the lower half, you must first divide the data set in half. Then, find the median of the first half.
17, 18, 19, 20 | 21, 24, 25, 27
To find the median, locate the number(s) in the middle of the data set.
17, 18, 19, 20
There are two numbers in the middle: 18 and 19.
When you have two medians, add the numbers, then divide the sum by 2.
[tex]18+19=37\\37/2=18.5[/tex]
The median of the lower half is 18.5.
A restaurant's delivery person can determine the number of miles he can drive in x hours by the function f (x) = x2 + 3x. The number of gallons of gasoline that the delivery person uses for driving y miles can be determined by the function g of y is equal to y over 18 period If the delivery person works a 9-hour shift, how many gallons of gasoline will he need in his tank?3456
Answers
The delivery person will need 6 gallons of gasoline in his tank for a 9-hour shift.
To find the gallons of gasoline needed for a 9-hour shift, we will use the given functions f(x) and g(y).
Find the number of miles driven in 9 hours using the function f(x) = x^2 + 3x.
f(9) = 9^2 + 3(9) = 81 + 27 = 108 miles
Calculate the gallons of gasoline used for driving 108 miles using the function g(y) = y/18.
g(108) = 108/18 = 6 gallons
So, the delivery person will need 6 gallons of gasoline in his tank for a 9-hour shift.
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Bridgeton University claims to accept 42% of applicants. In a random sample of 1,000 Bridgeton University applicants, 392 were accepted. Calculate the 95% confidence interval and evaluate whether Bridgeton's claim seems accurate.
The interval is from 36.7% to 41.7%. Since the value of 42% does not lie in the interval, Bridgeton's claimed acceptance rate does not seem accurate.
The interval is from 36.2% to 42.2%. Since almost 40% of the sample was accepted, Bridgeton's claimed acceptance rate seems accurate.
The interval is from 36.2% to 42.2%. Since the value of 42% lies in the interval, Bridgeton's claimed acceptance rate seems accurate.
The interval is from 36.7% to 41.7%. Since only 40% of the sample was accepted, Bridgeton's claimed acceptance rate does not seem accurate.
Answers
If random sample of 1000 applicants, 392 applicants were accepted, then (c) interval is from 36.2% to 42.2%. Since value of 42% lies in interval, Bridgeton's claimed acceptance rate is accurate.
The "Confidence-Interval" is defined as "range-of-values" which contain the "true-value" of a population parameter with a certain probability.
To calculate the 95% confidence interval, we use the formula:
⇒ CI = p ± z × √((p(1-p))/n),
where : p = sample proportion (accepted applicants / total applicants)
⇒ z is = z-score associated with desired "level-of-confidence" (95% corresponds to z = 1.96)
⇒ n is = sample size = (1,000),
First, we calculate the "sample-proportion" (p) :
⇒ p = 392 / 1000 = 0.392,
Substituting the values,
We get,
⇒ CI = 0.392 ± 1.96 × √((0.392(1-0.392))/1000),
⇒ 0.392 ± 0.030,
So, the 95% confidence interval for the proportion of accepted applicants at Bridgeton University is (0.362, 0.422) = 36.2% to 42.2%.
Next, To evaluate whether Bridgeton's claim of accepting 42% of applicants seems accurate, we can check if the claim falls within the confidence interval.
The claim of 42% falls within the 95% confidence interval of (0.362, 0.422). So, acceptance rate claimed by Bridgeton is accurate.
Therefore, the correct option is (c).
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The given question is incomplete, the complete question is
Bridgeton University claims to accept 42% of applicants. In a random sample of 1,000 Bridgeton University applicants, 392 were accepted. Calculate the 95% confidence interval and evaluate whether Bridgeton's claim seems accurate.
(a) The interval is from 36.7% to 41.7%. Since the value of 42% does not lie in the interval, Bridgeton's claimed acceptance rate does not seem accurate.
(b) The interval is from 36.2% to 42.2%. Since almost 40% of the sample was accepted, Bridgeton's claimed acceptance rate seems accurate.
(c) The interval is from 36.2% to 42.2%. Since the value of 42% lies in the interval, Bridgeton's claimed acceptance rate seems accurate.
(d) The interval is from 36.7% to 41.7%. Since only 40% of the sample was accepted, Bridgeton's claimed acceptance rate does not seem accurate.
#4 Which series of transformations correctly show that △CAT≅△DOG?
Select all that apply.
Answers
The series of transformations correctly show that △CAT≅△DOG is rotate ACAT 180° about the origin, the correct option is A.
We are given that;
△CAT≅△DOG
Now,
To show that ACAT and ADOG are congruent, we need to find a sequence of rigid transformations that maps one onto the other.
One possible sequence is:
This will map A to D, C to O, A to G, and T to O.
Translate the image 2 units left. This will align the image with ADOG.
Therefore, by transformation the answer will be rotate ACAT 180° about the origin.
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Is (x + 7) a factor of f(x) = x^3 − 3x^2 + 2x − 8? Explain your reasoning. and show work
Answers
Answer:
No, it is not. See justification in the diagram.
Step-by-step explanation:
You have to do polynomial long division. My math is shown in the picture below and if you have any questions, please let me know.
At the end, (x+7) does not go into 468.
Find , 2 Cu, 3V, V - u, and 2u + 5v. 3 u = (8, 3), v = (6, -7) (a) 2 a u 3 (b) 3v (c) V — u (d) 2u + 5v
Answers
The solutions are:
(a) 2Cu = (16C, 6C)
(b) 3v = (18, -21)
(c) V - u = (-2, -10)
(d) 2u + 5v = (46, -29)
To find the given values, we need to perform basic vector operations using the given vectors u and v.
(a) 2Cu
We need to multiply the vector u by 2C.
2Cu = 2C(8, 3)
= (16C, 6C)
So, 2Cu = (16C, 6C).
(b) 3v
We need to multiply the vector v by 3.
3v = 3(6, -7)
= (18, -21)
So, 3v = (18, -21).
(c) V - u
We need to subtract the vector u from the vector v.
V - u = (6, -7) - (8, 3)
= (-2, -10)
So, V - u = (-2, -10).
(d) 2u + 5v
We need to multiply vector u by 2 and vector v by 5 and then add the two vectors.
2u + 5v = 2(8, 3) + 5(6, -7)
= (16, 6) + (30, -35)
= (46, -29)
So, 2u + 5v = (46, -29).
Therefore, the solutions are:
(a) 2Cu = (16C, 6C)
(b) 3v = (18, -21)
(c) V - u = (-2, -10)
(d) 2u + 5v = (46, -29)
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A T-shirt stand on the boardwalk recently sold 6 purple shirts and 9 shirts in other colors. What is the experimental probability that the next shirt sold will be purple?
Write your answer as a fraction or whole number.
Answers
The experimental probability that the next shirt sold will be purple is [tex]2/5[/tex].
What is experimental probability on purple shirt?The experimental probability means ratio of the number of times the event occurs to the total number of trials or observations.
In this case, the event is the sale of a purple shirt and the trials are the total number of shirts sold.
So, total number of shirts sold is:
= 6 purple shirts + 9 other color shirts
= 15 shirts
The number of purple shirts sold is 6.
The experimental probability of selling a purple shirt on the next sale will be:
= Number of purple shirts sold / Total number of shirts sold
= 6 / 15
= 2 / 5.
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Final Practice - Part 3
A population of 40 foxes in a wildlife preserve quadruples in size
every 10 years. The function y=40. 4*, where x is the number of
10-year periods, models the population growth. How many foxes
will there be after 20 years?
What are we Show work:
substituting
for x?
Answer:
Answers
After 20 years, the value of the fox population will be 640.
What is the population of the fox after 20 years?The population of the fox after 20 years is calculated as follows;
The given function is;
y = 40 x 4ˣ
Where;
x is the number of 10-year periodshow many 10 years period make up 20 years?
x = 2
The value of the fox population is calculated as follows
y = 40 x 4²
y = 40 x 16
y = 640
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30°
X
y
29.5
Hey i have a math test coming
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The values of x and y in the attached triangle using trigonometric ratios are: x = 59 and y = 51.1
How to use trigonometric ratios?The three primary trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, to find the values of x and y in the attached triangle using trigonometric ratios, we have:
29.5/y = tan 30
y = 29.5/tan 30
y = 51.1
Similarly:
29.5/x = sin 30
29.5/0.5 = x
x = 59
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Jeremy has a cylindrical case for his toothbrush that has a diameter of 30 millimeters and a height of 15 centimeters. Which of the following would be an appropriate unit of measure to describe the surface area of the case?
a. millimeters
b. square centimeters
c. cubic millimeters
d. cubic centimeters
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A rental car company charges $20 per day to rent a car and $0.10 for every mile driven. Addison wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $80 to spend.
Write and solve an inequality which can be used to determine xxx, the number of days Addison can afford to rent while staying within her budget.
Answers
Answer:
Let xxx be the number of days Addison can afford to rent.
The cost of renting the car for xxx days is 20*x.
The cost of driving 100 miles is 0.10*100 = 10.
The total cost of renting the car and driving is 20*x + 10.
Addison wants to spend at most $80, so we have the inequality 20*x + 10 <= 80.
Solving for xxx, we get x <= 3.
Therefore, Addison can afford to rent the car for at most 3 days.
A beam of microwaves is incident normally on a pair of identical narrow slits S1 and S2 Not to scale 1. 181m microwave transmitter 1. 243m When a microwave receiver is initially placed at W which Is equidistant from the slits_ maximum in intensity is observed, The receiver is then moved towards Z along a line parallel to the slits Intensity maxima are observed at X and with one minimum between them W,X and Y are consecutive maxima (a) Explain why intensity maxima are observed at X and The distance from S1 to Y is 1. 243m and the distance from S2 to Y (s 1. 181m_ (b) Determine the frequency of the microwaves. (c) Outline one reason why the maxima observed at W, X and Y will have different intensities from each other:
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(a)This is because the distance between the slits is such that the waves from S1 and S2 arrive at Y in phase, resulting in constructive interference and a maximum in intensity. (b) The frequency of microwaves is [tex]1.94x10^8 Hz[/tex]. (c)One reason why the maxima observed at W, X, and Y will have different intensities from each other is due to the phenomenon of diffraction.
(a) The pattern of intensity maxima and minima observed in the double-slit experiment can be explained by the principle of interference. The microwaves from S1 and S2 interfere with each other as they propagate through the slits and form a pattern on the screen where they are detected. When the receiver is initially placed at W, it is equidistant from both slits and therefore the path lengths for the waves from each slit are equal, resulting in constructive interference and a maximum in intensity.
As the receiver is moved towards Z, the path length from S1 to the receiver decreases while the path length from S2 to the receiver increases. At X, the path lengths from S1 and S2 differ by one wavelength, resulting in constructive interference and a maximum in intensity. At Y, the path lengths from S1 and S2 differ by half a wavelength, resulting in destructive interference and a minimum in intensity.
The distance from S1 to Y is 1.243m, which is equal to the wavelength of the microwaves, while the distance from S2 to Y is 1.181m, which is also equal to the wavelength of the microwaves. This is because the distance between the slits is such that the waves from S1 and S2 arrive at Y in phase, resulting in constructive interference and a maximum in intensity.
(b) The frequency of the microwaves can be determined using the equation for the wavelength of a wave, which is given by[tex]λ = c/f[/tex], where[tex]λ[/tex]is the wavelength, c is the speed of light, and f is the frequency. We know that the wavelength of the microwaves is 1.243m, so we can rearrange the equation to solve for the frequency: f =[tex]c/λ[/tex] = 2.41 ×[tex]10^8[/tex]m/s ÷ 1.243m =[tex]1.94x10^8 Hz[/tex].
(c) As the waves pass through the narrow slits, they spread out and interfere with each other, creating a diffraction pattern. The intensity of the pattern is determined by the amount of interference, which depends on the size of the slits and the wavelength of the waves.
The intensity of the maxima will be affected by the width of the slits, with narrower slits producing a more intense diffraction pattern. The intensity will also be affected by the distance from the slits to the screen, with further distances producing a less intense diffraction pattern. Therefore, the maxima observed at different points on the screen will have different intensities due to variations in the diffraction pattern.
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A factory
produces cylindrical metal bar. The production process can be
modeled by normal distribution with mean length of 11 cm and
standard deviation of 0.25 cm.
In order to minimize the chance of the production cost of a metal bar to be more expensive than $1000, the senior manager decides to adjust the production process of the metal bar. The mean length is fixed and can’t be changed while the standard deviation can be adjusted. Should the process standard deviation be adjusted to (I) a higher level than 0.25 cm, or (II) a lower level than 0.25 cm? (Write down your suggestion, no explanation is needed in part (e)).
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To answer the question about whether the process standard deviation of the cylindrical metal bar production should be adjusted to (I) a higher level than 0.25 cm or (II) a lower level than 0.25 cm to minimize the chance of production costs exceeding $1000, the suggestion is to adjust the standard deviation to (II) a lower level than 0.25 cm.
By reducing the standard deviation, the variation in the lengths of the produced metal bars will decrease, resulting in more consistent and controlled production. This will ultimately help minimize the chances of the production cost of a metal bar exceeding the $1000 threshold. A lower standard deviation ensures that the production process has fewer outliers and deviations from the mean length of 11 cm, leading to cost efficiency and reduction of waste or rework due to bars not meeting the desired specifications.
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150 adults complete a survey 80 are women write the ratio men : women in its simplest form
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Answer: 7:8
Step-by-step explanation: just subtract 150-80 and you get 70
80 is the women
The remaining 70 is the men
Now arrange it to men:women
70:80
Now simplify
7:8
Hope that helps :)
A nationwide award for high school students is given to outstanding students who are sophomores, juniors, or seniors (freshmen are not eligible). Of the award-winners, 65 percent are SENIORS, 24 percent JUNIORS, and 11 percent are SOPHOMORES. Note: Your answers should be expressed as decimals rounded to three decimal places.
(a) Suppose we select award-winners one at a time and continue selecting until a SENIOR is selected. What is the probability that we will select exactly three award-winners? (b) Suppose we select award-winners one at a time and continue selecting until a JUNIOR is selected. What is the probability that we will select at least three award-winners?
(c) Suppose we select award-winners one at a time continue selecting until a SOPHOMORE is selected.
What is the probability that we will select 2 or fewer award-winners?
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(a) The probability of selecting a senior on any given selection is 0.65. The probability of selecting a non-senior (either a junior or a sophomore) is 0.35. To select exactly three award-winners until a senior is selected, we need to select two non-seniors followed by a senior. The probability of this sequence is:
0.35 * 0.35 * 0.65 = 0.080
So the probability of selecting exactly three award-winners until a senior is selected is 0.080.
(b) The probability of selecting a junior on any given selection is 0.24. The probability of selecting a non-junior (either a senior or a sophomore) is 0.76. To select at least three award-winners until a junior is selected, we need to select two or more non-juniors followed by a junior. The probability of this sequence is:
(0.76 * 0.76 * 0.24) + (0.76 * 0.24) + (0.24) = 0.334
So the probability of selecting at least three award-winners until a junior is selected is 0.334.
(c) The probability of selecting a sophomore on any given selection is 0.11. The probability of selecting a non-sophomore (either a senior or a junior) is 0.89. To select 2 or fewer award-winners until a sophomore is selected, we need to select 1 or 2 non-sophomores followed by a sophomore. The probability of these sequences is:
(0.89 * 0.89 * 0.11) + (0.89 * 0.11) + (0.11) = 0.214
So the probability of selecting 2 or fewer award-winners, until a sophomore is selected, is 0.214.
(a) To find the probability that we will select exactly three award-winners, and the third one is a SENIOR, we need to consider the following probabilities:
1. First student is not a senior (i.e., a junior or a sophomore)
2. Second student is not a senior (i.e., a junior or a sophomore)
3. Third student is a senior
Probability (not a senior) = 1 - Probability (senior) = 1 - 0.65 = 0.35
Probability (exactly 3 award-winners with the third being a senior) = 0.35 * 0.35 * 0.65 ≈ 0.079625
(b) To find the probability that we will select at least three award-winners until a JUNIOR is selected, we can find the probability of selecting 1 or 2 award-winners and subtract it from 1.
Probability (1 award-winner and it's a junior) = 0.24
Probability (2 award-winners, first is not a junior and second is a junior) = (1-0.24) * 0.24 = 0.1816
Total probability (1 or 2 award-winners) = 0.24 + 0.1816 = 0.4216
Probability (at least 3 award-winners) = 1 - 0.4216 ≈ 0.5784
(c) To find the probability that we will select 2 or fewer award-winners until a SOPHOMORE is selected:
Probability (1 award-winner and it's a sophomore) = 0.11
Probability (2 award-winners, first is not a sophomore and second is a sophomore) = (1-0.11) * 0.11 ≈ 0.0989
Total probability (2 or fewer award-winners) = 0.11 + 0.0989 ≈ 0.2089
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Mr. Wells always buys a big container of erasers before school starts each year. On the first day of school, he gives each of his students an eraser he has randomly chosen from the container. School started today, and so far he has handed out 3 blue, 5 yellow, 4 purple, 2 red, and 7 green erasers.
Based on the data, what is the probability that the next eraser Mr. Wells hands out will be blue?
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Answer:
We can use the concept of probability to determine the likelihood of Mr. Wells handing out a blue eraser next.
The probability of an event happening is equal to the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is Mr. Wells handing out a blue eraser, and the total number of possible outcomes is the total number of erasers in the container.
To find the total number of erasers in the container, we can add up the number of erasers in each color:
3 + 5 + 4 + 2 + 7 = 21
Therefore, there are 21 erasers in the container.
To find the number of blue erasers in the container, we need to use the information given in the problem. We know that Mr. Wells has already handed out 3 blue erasers, so there must be some blue erasers left in the container. However, we do not know how many blue erasers are left.
Since we do not have enough information to determine the exact number of blue erasers left, we can assume that all the remaining erasers in the container are equally likely to be handed out next. This is known as the principle of equally likely outcomes.
Therefore, the probability of Mr. Wells handing out a blue eraser next is equal to the number of blue erasers in the container divided by the total number of erasers in the container:
P(blue eraser) = number of blue erasers / total number of erasers
We do not know the exact number of blue erasers, but we know that there are some blue erasers left. Therefore, the probability of Mr. Wells handing out a blue eraser next is greater than zero.
So, the answer to the question is:
The probability that the next eraser Mr. Wells hands out will be blue is greater than zero, but we cannot determine the exact probability without knowing the number of blue erasers left in the container.