Answer: The total price of a bench is 1.008x.
Step-by-step explanation:
Since we have given that
Let the cost price be 'x'.
Mark up % = 120%
So, Mark up value would be
![\dfrac{120}{100}x\\\\=1.20x](https://tex.z-dn.net/?f=%5Cdfrac%7B120%7D%7B100%7Dx%5C%5C%5C%5C%3D1.20x)
Discount % = 20%
Amount of discount is given by
![\dfrac{20}{100}\times 1.2x\\\\=0.2\times 1.2x\\\\=0.24x](https://tex.z-dn.net/?f=%5Cdfrac%7B20%7D%7B100%7D%5Ctimes%201.2x%5C%5C%5C%5C%3D0.2%5Ctimes%201.2x%5C%5C%5C%5C%3D0.24x)
So, it becomes,
Amount after discount is given by
![1.2x-0.24x\\\\=0.96x](https://tex.z-dn.net/?f=1.2x-0.24x%5C%5C%5C%5C%3D0.96x)
Sales tax = 5%
Amount of sales tax would be
![\dfrac{100+5}{100}\times 0.96x\\\\=\dfrac{105}{100}\times 0.96x\\\\=1.05\times 0.96x\\\\=1.008x](https://tex.z-dn.net/?f=%5Cdfrac%7B100%2B5%7D%7B100%7D%5Ctimes%200.96x%5C%5C%5C%5C%3D%5Cdfrac%7B105%7D%7B100%7D%5Ctimes%200.96x%5C%5C%5C%5C%3D1.05%5Ctimes%200.96x%5C%5C%5C%5C%3D1.008x)
Hence, the total price of a bench is 1.008x.
Answer:
The age of the youngest friend is 9 years old.
Step-by-step explanation:
3a = 30 - 3
= 27 ÷ 3
= 9
= 9 + 10 + 11 = 30
= 9 is the smallest number. So, the youngest friend is 9 years old.
Change 212,514 into 215,000.
Change 396,705 into 400,000.
--------
Estimate:
215,000 + 400,000 = 615,000
Therefore:
212,514 + 396,705 ≈ 615,000
Answer:
yes what is it
Step-by-step explanation:
Answer:
The base is decreasing at 2 cm/min.
Step-by-step explanation:
The area (A) of a triangle is given by:
(1)
Where:
b: is the base
h: is the altitude = 10 cm
If we take the derivative of equation (1) as a function of time we have:
![\frac{dA}{dt} = \frac{1}{2}(\frac{db}{dt}h + \frac{dh}{dt}b)](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7Bdb%7D%7Bdt%7Dh%20%2B%20%5Cfrac%7Bdh%7D%7Bdt%7Db%29%20)
We can find the base by solving equation (1) for b:
![b = \frac{2A}{h} = \frac{2*120 cm^{2}}{10 cm} = 24 cm](https://tex.z-dn.net/?f=%20b%20%3D%20%5Cfrac%7B2A%7D%7Bh%7D%20%3D%20%5Cfrac%7B2%2A120%20cm%5E%7B2%7D%7D%7B10%20cm%7D%20%3D%2024%20cm%20)
Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:
![2 cm^{2}/min = \frac{1}{2}(\frac{db}{dt}*10 cm + 1 cm/min*24 cm)](https://tex.z-dn.net/?f=%202%20cm%5E%7B2%7D%2Fmin%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7Bdb%7D%7Bdt%7D%2A10%20cm%20%2B%201%20cm%2Fmin%2A24%20cm%29%20)
Therefore, the base is decreasing at 2 cm/min.
I hope it helps you!