Tutors Answer Your Questions about Linear-systems (FREE)
Question 1124074: The sum of three numbers is 10. The sum of twice the first number, 5 times the second number, and 6 times the third number is 53. The difference between 7 times the first number and the second number is 4.
Find the three numbers.
first number:
second number:
third number:
Click here to see answer by josgarithmetic(39780)  |
Question 1124074: The sum of three numbers is 10. The sum of twice the first number, 5 times the second number, and 6 times the third number is 53. The difference between 7 times the first number and the second number is 4.
Find the three numbers.
first number:
second number:
third number:
Click here to see answer by MathTherapy(10791)  |
Question 2732: I am studing the substitution Method.. and for some reason i can not seem to figure out how to do it. My teacher has been trying to work with me, but yet when I look at the problem I go blank on what to do.
I have an equation y = 2x + 7
y = 10x - 1 I dont understand how to do this...
Click here to see answer by MathTherapy(10791) |
Question 1180346: Will someone please help me with this problem?
A tree that is 8 feet tall is growing at a rate of 2 feet each year. Another tree that is 10 feet tall is growing at a rate of 1 foot each year. Determine how many years it will take for the two trees to reach the same height.
Click here to see answer by ikleyn(53724)  |
Question 1201131: Formulate a system of equations for the situation below and solve.
A private investment club has $400,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks, 6%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $40,000/year on the total investment. (Assume that all the money available for investment is invested.)
high-risk stocks $
medium-risk stocks $
low-risk stocks $
Click here to see answer by greenestamps(13318)  |
Question 1201131: Formulate a system of equations for the situation below and solve.
A private investment club has $400,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks, 6%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $40,000/year on the total investment. (Assume that all the money available for investment is invested.)
high-risk stocks $
medium-risk stocks $
low-risk stocks $
Click here to see answer by ikleyn(53724) |
Question 938535: Hello, I am having issues with my system of equations homework. I was wondering of you could help me. I generally know how to solve them but I cannot get mine to turn out.
The system is:
x+y+z+w=6
2x+3y-w=0
-3x+4y+z+2w=4
x+2y-z+w=0
Thanks in advance! :)
Click here to see answer by ikleyn(53724) |
Question 938535: Hello, I am having issues with my system of equations homework. I was wondering of you could help me. I generally know how to solve them but I cannot get mine to turn out.
The system is:
x+y+z+w=6
2x+3y-w=0
-3x+4y+z+2w=4
x+2y-z+w=0
Thanks in advance! :)
Click here to see answer by MathTherapy(10791) |
Question 429409: You invested money in two funds. Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330. This year, the first fund paid a 12% dividend and the second only 2% and you received a total of $1500. How much money did you invest in each fund?
Click here to see answer by ikleyn(53724) |
Question 1165132: Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing in Computer Studies of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato's Republic, Wishart and Leach found that about 26.1% of the five-syllable sequences are of the type in which two are short and three are long. Suppose that Greek archaeologists have found an ancient manuscript dating back to Plato's time (about 427 - 347 B.C.). A random sample of 317 five-syllable sequences from the newly discovered manuscript showed that 61 are of the type two short and three long. Do the data indicate that the population proportion of this type of five syllable sequence is different (either way) from the text of Plato's Republic? Use α = 0.01.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic.
Click here to see answer by CPhill(2189)  |
Question 1165134: Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.6%. A random sample of 10 bank stocks gave the following yields (in percents).
5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1
The sample mean is x bar = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use α = 0.01.
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value.
Click here to see answer by CPhill(2189) |
Question 1165201: Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.6%. A random sample of 10 bank stocks gave the following yields (in percents).
5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1
The sample mean is x bar = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use α = 0.01.
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
0.640
(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.
Click here to see answer by CPhill(2189) |
Question 1165202: Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.
3.7 2.9 3.8 4.2 4.8 3.1
The sample mean is x bar = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use α = 0.10
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.)
Click here to see answer by CPhill(2189) |
Question 1166583: Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft.
Write and solve a compound inequality to model the possible length of the dog run
This situation is modeled by the compound inequality 100 less than or equal to _____ less than or equal to 200.
(Use integers or decimals for any numbers in the expression. Do not include the $ symbol in your answer.)
Solving this compound inequality yields
_____ .
(Type a compound inequality. Use integers or decimals for any numbers in the expression.)
The dog run can be between
______ ft and
______ ft long.
(Type integers or decimals. Use ascending order.)
Click here to see answer by josgarithmetic(39780) |
Question 1209934: a firm hires 7 technicians and 3 apprentices for total daily wages of 820. if one apprentice is appointed to a technician, the total daily wages become 880. What are thr daily wages for a technician and an apprentice
Click here to see answer by ikleyn(53724) |
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