Three competing brands of cerial are being sold in the school cafeteria. Brand z's weekly sales are affected by the sales of the other two proucts. For each $1 increase in brand z's sales, there is a decrease $0.80 in sales of brand z. Similarly, each $1 increase in brand y's sales, there is a increase $0.10 in sales of brand z. If the current sales for brand z, y, and z are $45.00, $69.00, and $76.00 respectively, write an equation for z's sales in terms of z and y.

Roland's Barber Shop and Charley's Barber Shop are both located in the business district of a certain town. Roland estimates that if he raises the price of a haircut by $1, he will increase his market share by 6% if Charley raises his price by the same amount; he will decrease his market share by 1% if Charley holds his price at the same level; and he will decrease his market share by 2% if Charley lowers his price by $1. If Roland keeps his price the same, he will increase his market share by 4% if Charley raises his price by $1; he will keep the same market share if Charley holds the price at the same level; and he will decrease his market share by 3% if Charley lowers his price by $1. Finally, if Roland lowers the price he charges by $1, his market share will increase by 5% if Charley raises his prices by the same amount; he will increase his market share by 3% if Charley holds his price at the same level; and he will increase his market share by 2% if Charley lowers his price by…

A manufacturer of skis produces two types: downhill and cross-country. The times required for manufacturing and finishing each ski are given in the table. The maximum total weekly hours available for manufacturing and finishing the skis are 108 hours and 20 hours, respectively. The profits per ski are $40 for downhill and $90 for cross-country. Determine how many of each kind of ski should be produced to achieve a maximum profit. Manufacturing time per ski Finishing time per ski Downhill 3 hours 0.5 hour Cross-country 2.5 hours 0.5 hour To achieve maximum profit, the manufacturer should produce downhill skis and cross-country skis. C

Each summer, a jet ski company rents both jet skis and water skis to its guests for a flat daily rate per jet ski and a flat daily rate per pairs of water skis. Four pairs of water skis and three jet skis will cost a family $300. Three pairs of water skis and six jet skis will cost a family $480. During a particularly slow season, the company announces a 5% discount on all water skis and jet skis. What would be the cost of renting two pairs of water skis and one jet skis if they were rented during this discounted period? ca

Benjamin currently pays $1,080 for his annual car insurance premium. He is in the marines and will be deployed for 9 months. Since his car will be used much less, there is less risk for the insurance company and it offers him a 66% discount for his annual premium while on deployment. What is the amount he just save each month while on deployment to be able to pay his discounted premium? When Benjamin returns, his premium will revert to the amount prior to deployment. What will his total premium be for the year?

Suppose Country A spent $50$⁢50 billion on national defense in 2012, which was 10%10% of total government spending. In 2013, Country A's total government spending increased by $60$⁢60 billion compared to 2012. Determine the value of healthcare expenditures in 2013 if they were 5%5% of total government spending.

In February, Apple stock rose from $120.69 to $164.85, while Tesla stock increased from $675.50 a share to $809.87. You've invested $1500 in Feb 2021 and sold them for $2802.83 in Feb 2022. How many shares of each stock did you purchase? Apple A 29.78% (1Y) T Tesla Buy Sell a 12.73% (1Y) S182.00 Buy Sell $1.230.00 $149.00 TW TY SY 10Y se97.00 Position Overview Transactions News TW TY SY 10Y Personal portfolio Value 0 $498.29 (a +27.10%) $106.24 Position Overview Transactions News Amount invested 0 $392.05 Share price O $809.87 % of portfolio 0 4% Today's change O A 1.14% Average price O $129.70 View more v Shares 0 3.02268

A student's course grade is based on one midterm that counts as 5% of his final grade, ono class project that counts as 10% of his final grade, a set of homework assignments that counts as 50% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 66, his project score is 80, his homework score is 93, and his final exam score is 80. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above least 80 but less than 90 is a B, and so on. an A, a mean of at His overall final score is (Type an integer or a decimal. Do not round.)

Travel agents for a company are paid 17% commission on their holiday sales. The company offers trips to New Zealand and customers can choose from standard, deluxe or luxury packages. During one week, George sells 3 standard, 1 deluxe and 1 luxury holiday. Shirl sells 1 standard, 4 deluxe and 1 luxury holiday. Robert sells 2 standard and 2 luxury holidays. For that week George’s commission was $10,223.46, Shirl’s was $14,005.96 and Robert’s was $9,311.92. Solve using Cramer’s Rule to find the price of each holiday.

A waterpark has a profit of $22,000 on sunny days, a profit of $11,500 on overcast days, but a loss of $4,000 on rainy days.  For the month of June, the weather is predicted to be 62% sunny, 23% overcast, and 15% rainy.  Find the expected daily profit for the waterpark in June.