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Factorize algebraic expressions: 15xy+2y-3x²y
In a right-angled triangle the altitude to the hypotenuse is 8 cm high. The hypotenuse is 20 cm long. Find the lengths of the segements of the hypotenuse (Hint: let the length of the segment be x.)
In a right-angled triangle, the median to the hypotenuse is 6.4 cm. What is the length of the hypotenuse?
A bridge crosses a river at an angle of 60°. If the length of the bridge is 170 m, what is the width of the river?
If you deposit 6 500 FRW com-pounded monthly into an account paying 8% annual interest compounded monthly, how much money will be in the account after 7 years?
If you deposit 8 000 FRW into anaccount paying 7% annual interest compounded quarterly, how long will it take to have 12 400 FRW in the account?
A car hire company with 24 cars uses 2 940 litres of petrol in 5 days. How long would 4 116 litres of petrol last if the company had 28 cars and the consumption rate does not change?
A new car falls in value by 30% a year. After a year, it is worth 84 000 FRW. Find the price of the car when it was new.
Miguel’s basketball team is down seven points from their opponent if they make a two point shot how many more points do they need to tie the game justify your answer by writing a number sentence to represent the situation
how to convert quintal number 13242 to octal
encode the following words using a 6-bit BCD code, with odd parity showing clearly each alphabet represented:
(a) Banele
(b) Shabangu
Use supply and demand curves to illustrate how each of the following events would
affect the price of KitKat chocolate bar and the quantity of Kitkat bought and sold:
a. An increase in the price of Cadbury chocolate bar.
b. An increase in the price of Chocolate.
c. A decrease in average income levels.
d. Pandemic has caused cocoa harvest to drop drastically.
A grid... 10 x 10 fill in the correct % red 25% yellow 50% blue 15% green 15%, now if alice buys 10% of orange how many squares would that cover with whats left available
Determine the y-intercept, the zeros, the number of turning points, and the behavior of the graph and sketch the graph of the following polynomial functions.
1. P(x) = x3 + 6x2 + 11x + 6
Note: 1. Answer all questions in space provided
2. Show your work [calculations and/or calculator inputs] to receive
full marks.
3. Be sure to upload your completed work as Word Document; no other
format will be accepted including .pages.
Question 1:
A firm manufactures a product that sells for $12 per unit. Variable cost per unit is $8 and fixed cost per month is $1200. Capacity is 1000 units per month.
a. How much is the contribution margin? __________
b. How much is the contribution rate? __________
c. How many units must they sell per month in order to break even? __________
d. How many units must they sell in order to have a profit of $2,500 per month? __________
Question 2:
The following data pertain to the operating budget of Harrow Seed and Fertilizers which projects sales of $120,000. The total of its variable costs is estimated at $48,000 while fixed costs are $43,200.
a. How much is the contribution margin? __________
b. How much is the contribution rate? __________
c. What is the firm’s break-even point expressed in dollars of revenue? __________
Question 3:
ABC Corp. lists a product for $440.00 less discounts of 25% and 15%.
a. What is the net price? __________
b. What is the total amount of the discount? __________
c. Suppose a competitor sells the same product for $229.00. What additional rate of discount must ABC Corp. offer to meet the competitor’s price? __________
Question 4:
The SKI SHOPPE purchased Rossignol skis for $492 per pair and priced them to give a 40% rate of markup on selling price. When this model was discontinued, the store marked down its remaining stock by 30%. What was the sale price after the markdown? __________
The End
The radius of a circle is 18. Find the length of the perimeter and the apothem of a regular (a) inscribed quadrilateral, and (b) circumscribed hexagon.
