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Kgabo completed 2/5 of a job. The next day he completed 3/8 of the remaining job. The part of the job that




is still left, given as a fraction, is


aldo's shoes bought a shipment of 667 pairs of​ women's shoes for ​$36.00 per pair. The store sold 122 pairs at the regular selling price of $228.00 per​ pair, 78 pairs at a clearance sale at a discount of 35% and the remaining pairs during an inventory sale at a price that equals cost plus overhead. The​ store's overhead is 25% of cost.

​(a) What was the price at which the shoes were sold during the clearance​ sale?

​(b) What was the selling price during the inventory​ sale?

​(c) What was the total profit realized on the​ shipment?

​(d) What was the average rate of markup based on cost that was realized on the​ shipment?


Write the vector (1, −2, 5) as a linear combination of the vectors (1, 1, 1),(1, 2, 3)

and (2, −1, 1)


Consider the following systemof linear equations:



x+2y+2z=1,x+ay+3z=3,x+11y+az=b.




For which values of a does the system have a unique solution. and for which pairs of values (a,b) does the system have more than on solution?

the dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are apporoximately normally distributed with a mean 72 and a standard deviation of 4 based of this information,what is the probability that the mean score of a sample of 64 students it at least 73


An insulated rod of length has its ends A and B maintained at O^ C and 100 degrees * C respectively until steady state conditions prevailFind the steady -state temperature of the rod


Given that M is a singular matrix, evaluate x where;



6 7 -1



M = 3 x 5



9 11 x





A stone crushing company is planning to purchase a Wheel Loader to be used for conveying raw



stone to a large Stone Crushing Machine and loading crushed stone in trucks. A new Wheel loader



can be purchased directly from Caterpillar Company for $150,000. The new Wheel Loader will



reduce the annual cost by $25,500 and increase annual operating expenses by $4,500. The useful



life of the Wheel Loader is 20 years. After 20 years it will have a salvage value of $30,000. The



company uses straight line method of depreciation for all assets.




Does the sequence 3+ (-1)^n converge to 2. Justify

a deck has four cards - an ace of spades, an ace of hearts, an ace of diamonds and an ace of club. two cards will be drawn with replacement. let H denote the number of the ace of hearts is drawn

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