Driver's data set that has a mode that is greater than the mean or median is Fabian and a median with the lowest value of the three measures is Kadisha.
Data of Fabian: 7, 12, 11, 23, 13, 23, 30
Mean = sum of all observation / total no. of observation
Mean = (7+ 12+ 11+ 23+ 13+ 23+ 30) / 7
Mean = 17
Mode = most repeating observation
Mode = 23
For median we have to write observation in ascending order
7,11,12,13,23,23,30
Median = (N+1)/2
Where N = No. of observation
Median = (7+1)/2
Median = 4th observation
Median = 13
Here mode that is greater than the mean or median.
similarly for,
Kadisha: 8, 17, 23, 16, 17, 18, 125
Mean = 32
Median = 17
Mode = 17
Here median with the lowest value of the three measures.
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An equipment rental business currently charges $32. 00 per power tool rental and averages 24 rentals a day. The company recently performed a study and found that for every $2. 00 increase in rental price, the average number of customers decreased by one rental.
The company determined that the function f(x) = (32 + 2x)(24 – x) can be used to represent the total revenue earned from the rentals, where x represents the number of rental price increases and f(x) represents the revenue earned.
Part A: Explain what the expressions (32 + 2x) and (24 – x) represent in the given scenario.
Part B: What is the revenue after 3 rental price increases? Show your work or explain how you found your answer.
Part C: What rental price would give the maximum revenue for the company?
Part A: In the given scenario, the expression (32 + 2x) represents the rental price charged by the equipment rental business after x price increases of $2 each. The initial rental price is $32, and for every $2 increase in rental price, the rental price is raised by 2 units. The expression (24 – x) represents the number of rentals the equipment rental business can expect to make after x price increases. As the rental price increases, the number of customers is expected to decrease by one rental for every $2 increase in rental price.
Part B: To find the revenue after 3 rental price increases, we need to calculate f(3), where f(x) = (32 + 2x)(24 – x).
Substituting x = 3, we get:
f(3) = (32 + 2(3))(24 – 3) = (32 + 6)(21) = 38 × 21 = $798
Therefore, the revenue after 3 rental price increases is $798.
Part C: To find the rental price that would give the maximum revenue for the company, we need to find the value of x that maximizes the function f(x) = (32 + 2x)(24 – x). We can do this by finding the critical points of the function, which occur when the derivative of the function is equal to zero:
f'(x) = (32 + 2x)(-1) + (24 - x)(2) = -32 + 16x + 48 - 2x = 14x + 16
Setting f'(x) = 0 and solving for x, we get:
14x + 16 = 0
[tex]x = \frac{-16}{14} = \frac{-8}{7}[/tex]
However, [tex]x = \frac{-8}{7}[/tex] is not a valid solution since it represents a negative number of rental price increases, which is not possible in this scenario. Therefore, we need to test the endpoints of the interval [0, 6], since x represents the number of rental price increases and cannot exceed 6 (which would result in a rental price of $44, the maximum price in this scenario).
f(0) = (32 + 2(0))(24 - 0) = 32 × 24 = $768
f(6) = (32 + 2(6))(24 - 6) = 44 × 18 = $792
Comparing the values of f(0), f(3), and f(6), we see that f(6) gives the maximum revenue of $792. Therefore, the rental price that would give the maximum revenue for the company is $44, which is the rental price after 6 price increases of $2 each.
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A lake currently has a depth of 30 meters. As sediment builds up in the lake, its depth decreases by 2% per year.
This situation represents:
A. Exponential decay
B. Exponential growth
The rate of growth or decay, r, is equal to:
A. 1. 02
B. 0. 02
C. 0. 98
So the depth of the lake each year is ______ times the depth in the previous year.
A. 0. 98
B. 0. 02
C. 1. 02
It will take between _____ years for the depth of the lake to reach 26. 7 meters.
A. 3 and 4
B. 11 and 12
C. 9 and 10
D. 5 and 6
The situation represents exponential decay.
The rate of growth or decay, r, is equal to 0.02.
So the depth of the lake each year is 0.98 times the depth in the previous year.
It will take between 11 and 12 years for the depth of the lake to reach 26. 7 meters.
The situation represents exponential decay, as the depth of the lake decreases by a constant percentage each year. The rate of decay is 2% per year, so the rate of growth or decay, r, is equal to 0.98 (1 - 0.02). This means that the depth of the lake each year is 0.98 times the depth in the previous year.
To find the number of years it will take for the depth of the lake to reach 26.7 meters, we can use the formula for exponential decay:\
D = D₀ *[tex]e^{(-rt)[/tex]
where D is the current depth, D₀ is the initial depth, r is the rate of decay, and t is the number of years.
Substituting the given values, we get:
26.7 = 30 * [tex]e^{(-0.02t)[/tex]
Solving for t, we get:
t = ln(26.7/30) / (-0.02) ≈ 11.33
Therefore, it will take between 11 and 12 years for the depth of the lake to reach 26.7 meters.
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An insulated collar is made to cover a pipe. Find the volume of the material used to make the collar. Let r = 3 inches, R = 5 inches, and h = 21 inches. Use 3. 14 for p, and round to the nearest hundredth
The volume of the material used to make the insulated collar is 1060.56 cubic inches.
The volume of the material used to make the insulated collar can be determined as follows.
1. Identify the given dimensions:
inner radius (r) = 3 inches,
outer radius (R) = 5 inches, and
height (h) = 21 inches.
2. Use the formula for the volume of a cylinder:
V = πr^2h.
3. Calculate the volume of the outer cylinder with radius R:
V_outer = πR^2h = 3.14 * (5^2) * 21 ≈ 1653.3 cubic inches.
4. Calculate the volume of the inner cylinder with radius r:
V_inner = πr^2h = 3.14 * (3^2) * 21 ≈ 592.74 cubic inches.
5. Subtract the volume of the inner cylinder from the volume of the outer cylinder to find the volume of the material used:
V_material = V_outer - V_inner ≈ 1653.3 - 592.74 ≈ 1060.56 cubic inches.
The volume of the material is approximately 1060.56 cubic inches, rounded to the nearest hundredth.
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En un almacén hay tres cajas de productos. La primera contiene 20 productos, de los cuales 3 son defectuosos, en la segunda hay 16 productos, con 2 defectuosos, y en la tercera caja hay 10 productos, sin productos defectuosos ¿Cuál es la probabilidad de sacar un producto defectuoso al azar?
La probabilidad de sacar un producto defectuoso al azar de las tres cajas es aproximadamente 0.0917, o un 9.17%.
La probabilidad de sacar un producto defectuoso al azar de las tres cajas se puede calcular utilizando la fórmula de la probabilidad.
Primero, calculemos la probabilidad de sacar un producto defectuoso de cada caja:
1. En la primera caja, hay 3 productos defectuosos entre 20 productos en total. La probabilidad es 3/20.
2. En la segunda caja, hay 2 productos defectuosos entre 16 productos en total. La probabilidad es 2/16.
3. En la tercera caja, no hay productos defectuosos entre 10 productos en total. La probabilidad es 0/10.
Para encontrar la probabilidad total, sumamos las probabilidades de cada caja y luego dividimos por el número total de cajas:
(3/20 + 2/16 + 0/10) / 3 ≈ (0.15 + 0.125 + 0) / 3 ≈ 0.0917
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A particle moves on a coordinate line with acceleration d²s/dt = 30 sqrt(t) – 12/ sqrt(t) subject to the conditions that ds/dt = 12 and s = 16 when t= 1. Find the velocity v = ds/dt in terms of t and the position.
The velocity v = ds/dt in terms of t is v =
The velocity v = ds/dt in terms of t and the position s is: [tex]v = 15t^{(3/2)} - 8t^{(1/2)} + 6[/tex] and [tex]s = 5t^{(5/2)} - 16t^{(3/2)} + 6t + 27[/tex] respectively.
To find the velocity v = ds/dt in terms of t and the position s, we first need to integrate the acceleration equation with respect to time to get the velocity equation:
d²s/dt² = 30 sqrt(t) – 12/ sqrt(t)
Integrating both sides with respect to t, we get:
ds/dt = 30/2 * t^(3/2) - 12 * 2/3 * t^(1/2) + C₁
where C₁ is the constant of integration.
Using the condition ds/dt = 12 when t = 1, we can solve for C₁:
12 = 30/2 * 1^(3/2) - 12 * 2/3 * 1^(1/2) + C₁
C₁ = 6
Substituting this value of C₁ back into the velocity equation, we get:
ds/dt = 15t^(3/2) - 8t^(1/2) + 6
Now, we can integrate the velocity equation to get the position equation:
s = 5t^(5/2) - 16t^(3/2) + 6t + C₂
where C₂ is the constant of integration.
Using the condition s = 16 when t = 1, we can solve for C₂:
16 = 51^(5/2) - 161^(3/2) + 6*1 + C₂
C₂ = 27
Substituting this value of C₂ back into the position equation, we get:
s = 5t^(5/2) - 16t^(3/2) + 6t + 27
Therefore, the velocity v = ds/dt in terms of t and the position s is: v = 15t^(3/2) - 8t^(1/2) + 6 and s = 5t^(5/2) - 16t^(3/2) + 6t + 27 respectively.
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What is the value of the x-coordinate of point A?
a) sin (pi/6)
b) cos (pi/6)
c) sin (pi/3)
d) cos (pi/3)
e) sin (2pi/3)
f) cos (2pi/3)
Without a diagram or additional information, it is impossible to determine the value of the x-coordinate of point A.
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Type the correct answer in each box. use numerals instead of words.
lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. the doctors at the lab created the random data in the table using representative simulation. the letter e stands for "effective," and n stands for "not effective.
the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is ______. the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is ______.
To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we can use the geometric distribution. The probability of not curing the disease is 1 - 0.70 = 0.30.
Let X be the number of patients needed to find one patient on whom the medicine would not be effective. Then X follows a geometric distribution with p = 0.30. The probability that it will take at least five patients to find one patient on whom the medicine would not be effective is:
P(X ≥ 5) = (1 - p)^(5-1) = 0.7^4 ≈ 0.2401
Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is approximately 0.2401.
To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we can use the binomial distribution. Let X be the number of patients out of four who are cured by the medicine. Then X follows a binomial distribution with n = 4 and p = 0.70. The probability that the medicine will be effective on exactly three out of four randomly selected patients is:
P(X = 3) = (4 choose 3) * (0.70)^3 * (1 - 0.70)^(4-3) = 4 * 0.343 * 0.3^1 ≈ 0.4116
Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is approximately 0.4116.
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Your parents decide that they will help you out the first two months you are at college
by helping you buy groceries for your meals, but they won't cover the cost of you going
out to eat at restaurants or fast food.
for the first month you submit your receipts, 13 are for fast food and four for kroger, and
totaled $487. the second month you submit receipts for six fast food meals and two for
kroger, and totaled $232. the receipts do not list the per-item price.
a. write the two equations for the cost of buying groceries and meals. (4 points)
• 13f + 4k = 487
• 65+2k = 232
i
b. what were the average costs of one fast food meal and of one trip to kroger?
show your work and justify your thinking. (6 points)
a. The two equations for the cost of buying groceries and meals are 13f + 4k = 487 and 65+2k = 232
b. The average costs of one fast food meal and of one trip to kroger is $77.33
To calculate the average cost, we divide the total cost by the number of meals or trips. For example, in the first month, the total cost of fast food meals and grocery trips was $487, and there were 13 fast food meals and 4 grocery trips. Therefore, the average cost of a fast food meal can be calculated by dividing the total cost of fast food meals ($487) by the number of fast food meals (13):
Average cost of a fast food meal = $487 / 13 = $37.46
Similarly, we can calculate the average cost of a grocery trip in the first month by dividing the total cost of grocery trips ($487 - total cost of fast food meals) by the number of grocery trips (4):
Average cost of a grocery trip = ($487 - $37.46 x 13) / 4 = $89.38
Using the same method, we can calculate the average cost of a fast food meal and a grocery trip in the second month. In the second month, the total cost of fast food meals and grocery trips was $232, and there were 6 fast food meals and 2 grocery trips. Therefore, the average cost of a fast food meal is:
Average cost of a fast food meal = $232 / 6 = $38.67
And the average cost of a grocery trip is:
Average cost of a grocery trip = ($232 - $38.67 x 6) / 2 = $77.33
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Eli is comparing the prices of things in the following two flyers Eli only wants to get the best deals he knows he will have to visit both stores help Eli find the best deal for each item
Identify the best deal for each item
For milk, Store A has the better deal: $2.50 for 1 gallon is cheaper than $3.19 for 2 liters at Store B.For bread, Store B has the better deal: $1.49 for a loaf is cheaper than $1.99 for a loaf at Store A.For eggs, Store B has the better deal: $0.99 for a dozen is cheaper than $1.79 for a dozen at Store A.Which store has the better deal for the following items?Eli needs to visit both stores to get the best deals for each item. Store A has the better deal for milk, while Store B has the better deals for bread and eggs. By going to both stores, Eli can save money on all three items.Learn more about deals
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In circle E, AB//CD, m/ADC = 42 and the
measure of arc CD is twice the measure of arc
AB. Find the measure of AB. Show your work.
The measure of arc AB is 120 degrees.
What is meant by an arc?
An arc refers to a portion of the circumference of a circle or an ellipse. It is measured in degrees and can be used to calculate the length of the curve.
What is the term measure?
The term "measure" refers to the size or circumference of a geometric object, such as length, area, or volume. It is a numerical value that quantifies the measured property.
According to the given information
Let O be the centre of the circle. Since AB is parallel to CD, we have angles ACD and ADC that are equal since they are alternate interior angles. Therefore, the angle ACD is also 42 degrees.
Let x be the measure of arc AB, and then the measure of arc CD is 2x. Since the sum of the measures of arcs AB and CD is equal to the total circumference of the circle, we have:
x + 2x = 360 degrees
3x = 360 degrees
x = 120 degrees
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Pls help me with this! Will give points!
Answer:
Subtract 1 from both sides.
Answer:
subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16
If alpha and beta are zeroes of the quadratic equation x^2-6x+a; find the value of ‘a’ if 3a+2beta=20
The value of a is -16
If α and β are zeroes of the quadratic equation x²-6x+a, then we know that:
α + β = 6
α * β = a
We are also given that 3α + 2β = 20.
3α + 2β = 20
3(α + β) - α = 20
3(6) - α = 20
18 -α = 20
18 - 20 = α
α = -2
Substituting α = -2 into the equation α + β = 6, we get:
- 2 + β = 6
beta = 8
Therefore, α = -2 and β = 8, and we can find a using the equation α * β = a:
a = α * β
= - 2 * 8
= 16
Therefore, the value of a is -16
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Need help asap.
(Angles Formed by Chords, Tangents, Secants)
The value of angle LQ in the intersected arc is 34 degrees.
How to find arc angle when secant intersect?If two secants intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.
Therefore, let's find the arc angle LQ as follows:
let
x = arc angle LQ
m∠U = 1 / 2 (108 - x)
37 = 54 - 0.5x
subtract 54 from both sides of the equation
37 = 54 - 0.5x
37 - 54 = 54 - 54 - 0.5x
-17 = -0.5x
divide both sides by -0.5
x = -17 / -0.5
x = 34 degrees
Therefore,
arc angle LQ = 34 degrees
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Assume the base is 2.
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships.
A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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Helpp me please i need to finish before flvs logs me out helppppp
question 2 (essay worth 10 points)
(05.05 mc)
a food truck did a daily survey of customers to find their food preferences. the data is partially entered in the frequency table. complete the table to analyze the data and answer the questions:
part a what percentage of the survey respondents do not like both hamburgers and burritos? (2 points)
part b: what is the marginal relative frequency of all customers that like hamburgers? (3 points)
part c: use the conditional relative frequencies to determine which data point has strongest association of its two factors. use complete sentences to explain your answer. (5 points)
Step 1: Examine the frequency table
Take a look at the frequency table provided and make sure you understand what it represents. The table should have two columns, one for food preference (hamburgers, burritos, or both) and one for frequency.
Step 2: Complete the frequency table
Complete the frequency table by filling in the missing values. You can do this by using the information provided in the problem statement. Remember that the total frequency should add up to the total number of survey respondents.
Step 3: Calculate percentages
Once the frequency table is complete, you can calculate the percentage of survey respondents who do not like both hamburgers and burritos. To do this, add up the frequency of respondents who selected "hamburgers only," "burritos only," and "neither" (since these respondents do not like both hamburgers and burritos), and divide by the total number of survey respondents. Multiply by 100 to convert to a percentage.
Step 4: Calculate marginal relative frequencies
To calculate the marginal relative frequency of all customers that like hamburgers, you need to divide the frequency of respondents who like hamburgers by the total number of survey respondents. This will give you a percentage.
Step 5: Use conditional relative frequencies
To determine which data point has the strongest association of its two factors, you can use conditional relative frequencies. To calculate the conditional relative frequency of, say, respondents who like hamburgers given that they also like burritos, you need to divide the frequency of respondents who like both hamburgers and burritos by the frequency of respondents who like burritos. Repeat this process for each combination of food preferences.
Step 6: Analyze the data
Based on the conditional relative frequencies you calculated, determine which data point has the strongest association of its two factors. In other words, which combination of food preferences is most likely to occur together? Explain your answer in complete sentences, using the data you calculated to support your reasoning.
I hope this helps! Let me know if you have any further questions or need additional assistance.
Which of the lines below match the function given? y = x + 5 A graph with 4 lines, labeled A, B , C, and D. Line A contains the points 0 comma 0, and 2 comma 2. Line B contains the points 0 comma 5, and 2 comma 7. Line C contains the points 0 comma 0, and 2 comma 4. Line D contains the points 0 comma 2, and 1 comma 5.
Therefore , the solution of the given problem of function comes out to be Line B to the function y = x+5.
Describe function.On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
The function is represented as
=> y = x + 5, which has a y-intercept of 5, a slope of 1, and a slope of 1.
By comparing the slope and y-intercept of each line to those of the function, we may determine which line best fits it.
Line A does not fit the function because it has a slope of 1 and a y-intercept of 0.
The function y = x + 5 is satisfied by line B, which has a slope of 1 and a y-intercept of 5.
Line C does not fit the function because it has a slope of 2 and a y-intercept of 0.
Line D does not fit the function because it has a slope of 3 and a y-intercept of 2.
Line B therefore corresponds to the function y = x+5.
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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Solve for length of segr
6 cm
4 cm
b
18 cm
b = [?] cm
If two segments intersect inside
Answer:
12
Step-by-step explanation:
multiply 4x18 then divide by 6
Solve for the missing side. Formula: a^2+b^2=c^2
Answer:
[tex] \frac{7 \sqrt{39} }{5} [/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]( {11.2})^{2} - { {7} }^{2} = 76.44 > 0[/tex]
The missing side is equal to:
[tex] \sqrt{76.44} = \frac{7 \sqrt{39} }{5} [/tex]
I have a $500 budget for an event what would be good food options that will be around the $500 mark if I have 50 guests attending?
Some good food options that could fit within $500 budget for 50 guests are Sandwich platters, Pizza, Tacos or burritos, Pasta, Finger foods.
With a $500 budget for 50 guests, you have approximately $10 per person for the food. Here are some food options that could fit within this budget:
Sandwich platters: You can order a variety of sandwich platters from a catering company or grocery store. These usually cost around $6-8 per person, leaving you with some money for drinks and dessert.
Pizza: You can order a few large pizzas for the group. Depending on the toppings and where you order from, this could cost around $10 per person.
Tacos or burritos: You can order a taco or burrito bar from a catering company or make them yourself. This could cost around $8-10 per person.
Pasta: You can make a large pot of pasta and serve it with salad and bread. This could cost around $5-8 per person.
Finger foods: You can make a variety of finger foods, such as chicken wings, meatballs, and vegetable platters. This could cost around $7-10 per person.
Remember to also consider any dietary restrictions or allergies your guests may have and provide options that accommodate those needs.
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112
in.
If the prism can fit exactly 9 cubes from bottom to top, what is the volume of the prism? Write your answer as a
decimal.
The volume of the rectangular prism is 31.5 in³.
How do we find the volume of the rectangular prism?From the diagram, we know that the height of the rectangular prism is 9 cubes. We can see the length is 7 cubes and the width is 4 cubes. Each cube is half an inch. Therefore we multiply every side by 1/2.
Height = 9 × (1/2)
Height = 4.5 inches
Length = 7 × (1/2)
Length = 3.5 inches
Width = 4 × (1/2)
Width = 2 inches
Volume = L × W × H
Volume = 3.5 × 2 × 4.5
Volume = 31.5 inches³
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if 2x + 3y = 6x - 5y, find the value of x/y.
Answer: 2
Step-by-step explanation:
Answer:
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
Step-by-step explanation:
sol,
2x+3y-6x+6y=0
f(x,y)=2x+3y-6x+6y
f(X,-y)=2x+3y-6y,fx=?
f(x-y)=2x+3y-6y,fy=?
fx=-4
fy=9
[tex] \frac{d}{y} = \frac{ - 4}{9} [/tex]
now,
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
Maths ice cream shop has 7 cups of sprinkles to use on Sundays for the rest of the day if each Sunday serves with one 8th cup of sprinkles how many Sundays can they serve
56 Sundays Maths Ice Cream Shop can serve with 7 cups of sprinkles using one-eighth (1/8) cup of sprinkles per Sunday.
Converting the cups of sprinkles into eighths:
7 cups × 8 eighths/cup
= 56 eighths
Dividing the total eighths by the eighths used per Sunday:
56 eighths / (1/8 cup per Sunday)
= 56 Sundays
So, Maths Ice Cream Shop can serve for 56 Sundays using 7 cups of sprinkles with each Sunday serving one-eighth cup of sprinkles.
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Hillsdale Orchard grows Fuji apples and Gala apples. There are 160 Fuji apple trees and 120 Gala apple trees in the orchard.
Hillsdale Orchard's owners decide to plant 30 new Gala apple trees. Complete the ratio table (click for help) to find the number of new Fuji apple trees the owners should plant if they want to maintain the same ratio of Fuji apple trees to Gala apple trees
To maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should: plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.
To find the number of new Fuji apple trees that the owners of Hillsdale Orchard should plant to maintain the same ratio of Fuji apple trees to Gala apple trees, we need to use a ratio table.
First, we need to determine the ratio of Fuji apple trees to Gala apple trees before the new trees are planted. Let's assume that there are currently 40 Fuji apple trees and 100 Gala apple trees. The ratio of Fuji apple trees to Gala apple trees is therefore 40:100, which can be simplified to 2:5.
Next, we need to use this ratio to determine the number of new Fuji apple trees that need to be planted. Since the owners are planting 30 new Gala apple trees, we can use the ratio of 2:5 to find the corresponding number of new Fuji apple trees.
To do this, we need to divide the number of new Gala apple trees by the denominator of the ratio (which represents the number of units of the ratio). In this case, the denominator is 5.
30 (new Gala apple trees) ÷ 5 (denominator) = 6
This means that for every 5 new Gala apple trees, the owners should plant 2 new Fuji apple trees. Therefore, the owners should plant 12 new Fuji apple trees (2 trees for every 5 new Gala apple trees, multiplied by the 30 new Gala apple trees being planted).
In summary, to maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.
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A major car manufacturer wants to test a new engine to determine if it meets new air pollution standards. Safety regulations require that the mean emission of all engines of this type must be no greater than 20 parts per million (ppm) of carbon. If it is higher than that, they will have to redesign parts of the engine. A random sample of 25 engines is tested and the emission level of each is determined. The sample mean is calculated to be 20. 4 ppm and the sample standard deviation is calculated to be 2. 0 ppm. It is known that emission levels are normally distributed with standard deviation 1. 6 ppm. We would like to test whether the true mean emission level for the new engine is greater than 20 ppm. The test statistic for the appropriate test of significance is: ________
The test statistic for the appropriate test of significance is 2.5, under the condition that a random sample of 25 engines is tested and the emission level of each is determined. Then the mean sample is evaluated to be 20. 4 ppm and the sample standard deviation is calculated to be 2.0 ppm
The test statistics can be derived into the formula
t = (x'- μ) / (s / √n)
Here,
x' = sample mean
μ = hypothesized population mean
s = sample standard deviation
n = sample size.
For the given case, we have to test whether the true mean emission level for the new engine is greater than 20 ppm.
Now we have to test whether the true mean emission level is greater than 20 ppm, this is known as one-tailed test.
Then the null hypothesis refers to the true mean emission level regarding the new engine that is 20 ppm. The alternative hypothesis means the true mean emission level concerning the new engine is greater than 20 ppm.
Applying a significance level of 0.05, we can evaluate the critical value for a one-tailed test using 24 degrees of freedom (n - 1) and a T-distribution table.
Then the critical value is 1.711.
Then the given test statistic of 2.5 is greater than the critical value of 1.711, so we have to deny the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean emission level for the new engine is greater than 20 ppm.
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The maximum walking speed S, in feet per second, of and animal can be modeled by the equation S= square root of gL,where g+32ft/sec and L is the lenght, in feet, of the animal's leg. To the nearest hundredth,how ,amy times greater is the maximum walking speed of a giraffe with a leg of 6 feet than a hippopota,us with a leg of 3 feet?
The maximum walking speed of a giraffe with a leg of 6 feet is approximately 1.41 times greater than that of a hippopotamus with a leg of 3 feet.
What is the ratio of the maximum walking speed of a giraffe?The equation given in the problem, S= square root of gL, represents the maximum walking speed S of an animal with a leg of length L. To find the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet, we can plug in the values of g and L for each animal and calculate the ratio.
For the giraffe: S = √(g6) = √(326) ≈ 9.8 ft/sec
For the hippopotamus: S = √(g3) = √(323) ≈ 5.7 ft/sec
So the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet is approximately 9.8/5.7 ≈ 1.72 or 1.41 to the nearest hundredth.
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cual es el grado de polinomios de -8^3 xy^4
por favor me ayudan doy corona
The degree of the polynomial is 5.
How to find the degree of a polynomial?The degree of a polynomial is the maximum exponent of the polynomial.
In cases where we have more than one variable in the same term, we need to add the exponents of the variables.
Here we have:
[tex]-8^3 xy^4[/tex]
The exponents are:
x ----> 1
[tex]y^4 ---- > 4[/tex]
Adding that: 4 + 1 = 5
the degree is 5.
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please help im stressing
To multiply these fractions, we can simplify each fraction first:
64e^2/5e * 3e/8e = (8*8*e*e)/(5*e) * (3*e)/(2*2*2*e)
Next, we can cancel out common factors between the numerators and denominators:
= (8*8*1*1)/(5*1) * (1*1)/(2*2*2*1)
= 64/5 * 1/8
= 8.
Answer:
24e^2/5e my answer needs to be 20+characters sooooooooooo
There are 4 paperback and 10 hardback books on a reading list. Your teacher randomly assigns you 3 books to take home. What is the probability that you are assigned all hardback books?
The probability of being assigned all hardback books is approximately 0.33 or 33%.
This can be done by combination formula C(n,r) = n!/(r!(n-r)!)
The total number of ways to choose three books from a list of 14 books is given by the combination formula,
C(14,3) =14!/(3!(14-3)!) = (141312) / (321) = 364.
To find the probability of selecting all hardback books, we need to determine the number of ways to select 3 books from the 10 hardback books. This is given by the combination formula,
C(10,3) = 10!/(3!(10-3)!) = 1098 / (321) = 120.
Therefore, the probability of selecting all hardback books is:
P(all hardback) = C(10,3) / C(14,3) = 120/364 = 0.3297
So, the probability of being assigned all hardback books is approximately 0.33 or 33%. This means that out of all possible combinations of 3 books, about 33% will consist of only hardback books.
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The distance around a neighborhood is 6 miles. When Sam measured it with an
odometer, the distance was 5. 52 miles. What is the percent of error of the
measurement?
The percent of error in the measurement is 8%. This means that the measured value of 5.52 miles is 8% less than the actual distance of 6 miles.
To find the percent of error, we need to calculate the difference between the measured value and the actual value, divide that by the actual value, and then multiply by 100 to convert to a percentage.
Actual distance around the neighborhood = 6 miles
Measured distance around the neighborhood = 5.52 miles
Difference = Actual distance - Measured distance
Difference = 6 miles - 5.52 miles
Difference = 0.48 miles
Percent of error = (|Difference| / Actual distance) x 100%
Percent of error = (|0.48| / 6) x 100%
Percent of error = 0.08 x 100%
Percent of error = 8%
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