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Sharon has a total of $230,000 to invest in three types of mutual funds: growth, balanced, and income funds. Growth funds have a rate of return of 12%/year, balanced funds have a rate of return of 10%/year, and income funds have a return of 6%/year. The growth, balanced, and income mutual funds are assigned risk factors of 0.1, 0.06, and 0.02, respectively. Sharon has decided that at least 50% of her total portfolio is to be in income funds and at least 25% of it in balanced funds. She has also decided that the average risk factor for her investment should not exceed 0.05. How much should Sharon invest in each type of fund in order to realize a maximum return on her investment? Hint: The constraint for the average risk factor for the investment is given by 0.1x + 0.06y + 0.02z ≤ 0.05(x + y + z).growth funds $: balanced funds $: income funds $: What is the maximum return?
General
2 months ago
An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown. 110, 130, 150, 170, ...Which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned?a f(n + 1) = f(n) + 20b f(n + 1) = f(n) + 110c f(n + 1) = f(n + 1) + 20d f(n + 1) = f(n + 1) + 110
General
2 months ago
Your classmate wants you to check her work. She is working on a math question that asks her to determine the slope of a line given on a graph. You can see that the graph is a line, and that the line is increasing. Your classmate says that it’s a positive slope but you are not sure of the explanation. She tells you that she went down 5 units and to the left 3 units to the next point on the line to determine the slope. Determine if your classmate is correct and explain why or why not.
General
2 months ago
A polynomial function has a root of –5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true?The graph of the function is positive on (infinity, –5)The graph of the function is negative on (–5, 3).The graph of the function is positive on (infinity, 1).The graph of the function is negative on (3, infinity)
General
2 months ago
An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and the artist wants the words to all be horizontal in the final mosaic.The world tiles come in two sizes: the smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide.if the small tiles cost $3:00 each and the large tiles cost $4.50 each,how many of each should be used to minimize the cost? What is the minimum cost?
General
2 months ago
The weight of a bucket of fish was more than 23 pounds. Doria wants to write an inequality for the weight of the bucket of fish. She uses the variable w to represent the weight. Which inequality should Doria write?
General
2 months ago
What is the solution to the system of equations graphed below
General
2 months ago
The volume of a rectangular box is found by multiplying its length, width, and height: V = lwh. A certain box has a volume of b 3 + 3b 2 - 4b - 12. Factor the four-term polynomial to find the dimensions of the box. Hint: Use factoring by grouping to factor the four term polynomial first.
General
2 months ago
the elevation of Denver Colorado is 13 times greater than that of waikapu. hawaii.the sum of their elevations is 5600 ft. find the elevation of each city
General
2 months ago
Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).
General
2 months ago
A fabric store sells two types of ribbon. One customer buys 3 rolls of the satin ribbon and had a total of 120 yards of ribbon. Another customer buys 2 rolls of lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon. How many yards are on one rolls and one roll of satin ribbon?
General
2 months ago
A sine function has the following key features:Period = 12Amplitude = 4Midline: y = 1y-intercept: (0, 1)The function is not a reflection of its parent function over the x-axis.How would this graph look??
General
2 months ago
Determine if x + 2 is a factor of p(x) = x ^4 + 3x^ 3 + 4x ^2 - 8 and explain why.
General
2 months ago
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5).Write the equation of this cubic polynomial function. Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?-5The linear factors of the cubic are
General
2 months ago
Kiera wanted to find the approximate number of historical books at the library she works at. She used the computer to randomly take a sample of 80 books and found that 6 of them were considered historical books. There are 21,360 books at this library. What is the best estimate of the amount of historical books at this library?
General
2 months ago
Which graph shows a system of equations with a solution at (–1, 1)?
General
2 months ago
please help idk this one !!Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.(–2, 0)(–2, 0) and (2, 0)(–2, 0) and (3, 5)no solutions
General
2 months ago
Dana wants to make two types of dog treats. She has 10 cups of peanut butter and 12 cups of flour. Her dog bone treat recipe uses 3 cups of peanut butter and 2 cups of flour to make one tray. A tray of her oatmeal dog treat recipe uses 1 cup of peanut butter and 4 cups of flour. She plans to sell trays of dog treats at the town festival and charge $6 for a tray of dog bone treats and $7 for a tray of oatmeal treats. Dana wants to maximize her income from selling the dog treats. When writing constraints for the problem, what is the most reasonable definition for the variables x and y?A) Let x represent the number of cups of peanut butter used and y represent the number of cups of flour used. B) Let x represent the number of cups of peanut butter used and y represent the number of trays of dog bone treats made. C) Let x represent the number of dog bone treats made and y represents the number of cups of flour used. D) Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.
General
2 months ago
Given: g ∥ h and ∠2 ≅ ∠3Prove: e ∥ f Statements Reasons1. g || h 1. given2. ∠1 ≅ ∠2 2. corresponding angles theorme3. ∠2 ≅ ∠3 3. given4. ∠1 ≅ ∠3 4. transitive property5. e || f 5. ?What is the missing reason in the proof?A. vertical angles theoremB. alternate exterior angles theoremC. converse corresponding angles theoremD. converse alternate interior angles theorem
General
2 months ago
Henry lives in Mississippi, which has a sales tax of 7%. He just bought a bed whose full price was $1600, but he got 30% off, because the store was having a sale. What was the total amount that Henry paid?A.) $1120.00B.) $1198.40C.) $1934.40D.) $1712.00
General
2 months ago
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