Answer:
Correct option is (C)
Step-by-step explanation:
we are given that -Tim design a pair of shorts,S, and T-shirts,t.
Tim sell Sorts for $12 and T-shirts for $8 each.
Tim can work atmost 18 hours a day so we can write ![time\leq 18](https://tex.z-dn.net/?f=time%5Cleq%2018)
Time taken to design a T-shirt is 30 minutes and for Shorts, it is 45 minutes.
![\frac{30}{60}t+\frac{45}{60}s\leq 18\\\text{Multiply both the sides by 60}\\30t+45s\leq 1080\\\text{Divide both the sides by 45}\\s+0.66t\leq 24\\\text{Subtract 0.66t from both the sides}\\s\leq 24-0.66t](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B60%7Dt%2B%5Cfrac%7B45%7D%7B60%7Ds%5Cleq%20%20%2018%5C%5C%5Ctext%7BMultiply%20both%20the%20sides%20by%2060%7D%5C%5C30t%2B45s%5Cleq%201080%5C%5C%5Ctext%7BDivide%20both%20the%20sides%20by%2045%7D%5C%5Cs%2B0.66t%5Cleq%2024%5C%5C%5Ctext%7BSubtract%200.66t%20from%20both%20the%20sides%7D%5C%5Cs%5Cleq%2024-0.66t)
He must design 12 itesm each day, so we can write ![t+s\geq 12](https://tex.z-dn.net/?f=t%2Bs%5Cgeq%2012)
Further it can be written as
![t+s\geq 12\\\text{Subtract t from both the sides}\\s\geq 12-t](https://tex.z-dn.net/?f=t%2Bs%5Cgeq%2012%5C%5C%5Ctext%7BSubtract%20t%20from%20both%20the%20sides%7D%5C%5Cs%5Cgeq%2012-t)
Also Tim can not design more than 30 items in one day, so we can write
![t+s\leq 30\\\text{Subtsract t from both the sides}\\s\leq 30-t](https://tex.z-dn.net/?f=t%2Bs%5Cleq%2030%5C%5C%5Ctext%7BSubtsract%20t%20from%20both%20the%20sides%7D%5C%5Cs%5Cleq%2030-t)
Hence from the above equations , its claer that
![s\geq 12-t,s\leq 30-t,s\leq 24-0.66t,s\geq 0,t\geq 0](https://tex.z-dn.net/?f=s%5Cgeq%2012-t%2Cs%5Cleq%2030-t%2Cs%5Cleq%2024-0.66t%2Cs%5Cgeq%200%2Ct%5Cgeq%200)
Answer: £535
Step-by-step explanation:
Herr is the complete question:
Tim and three friends go on holiday together for a week.
The 4 friends will share the costs of the holiday equally,
Here are the costs of the holiday.
£1280 for 4 return plane tickets
£640 for the villa
£220 for hire of a car for the week
Work out how much Tim has to pay for his share of the costs.
Firstly, we have to calculate the total cost of the holiday. This will be:
= £1280 + £640 + £220
= £2140
We are also told that they will share the costs equally. Since there are 4 people, Tim will have to pay:
= £2140 ÷ 4
= £535
Tim will pay £535
Answer:
Step-by-step explanation:
The $2,000 upfront payment by Hank means that the relationship between the total amount paid and the number of months elapsed is NOT linear. On the other hand, the girl's zero down payment indicates a linear, proportional relationship.
Answer:
x < 3
Step-by-step explanation:
![4x-7 < 5\\4x-7+7 < 5+7\\4x < 12\\\frac{4x}{4} < \frac{12}{4}\\x < 3](https://tex.z-dn.net/?f=4x-7%20%3C%205%5C%5C4x-7%2B7%20%3C%205%2B7%5C%5C4x%20%3C%2012%5C%5C%5Cfrac%7B4x%7D%7B4%7D%20%3C%20%5Cfrac%7B12%7D%7B4%7D%5C%5Cx%20%3C%203)
Answer:
<em>The uniform rate of depreciation is $56,333 per year, or 11% per year.</em>
Step-by-step explanation:
<u>Rate of Depreciation</u>
If some object has a certain value P and after some time t its value decreases to Q, the rate of depreciation is a measure of how much its value changed per unit time.
It can be calculated as:
![\displaystyle R=\frac{P-Q}{t}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20R%3D%5Cfrac%7BP-Q%7D%7Bt%7D)
It can also be expressed as a percentage, dividing the previous value by P.
The school bus reduces its value from $512,000 to $343,000 in 3 years, thus:
![\displaystyle R=\frac{512,000-343,000}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20R%3D%5Cfrac%7B512%2C000-343%2C000%7D%7B3%7D)
![\displaystyle R=\frac{169,000}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20R%3D%5Cfrac%7B169%2C000%7D%7B3%7D)
R = 56,333 $/year
Expressed as a percentage:
R = 56,333 / 512,000 = 0.11
R = 11%/year
The uniform rate of depreciation is $56,333 per year, or 11% per year.