Step-by-step explanation:
we do know that the area of a rectangle is length × width.
we know the total area and the width of the rug, so
12 = length × 3
length = 12/3 = 4 meters.
the perimeter of a rectangle is the whole way around it : 2 times the length and 2 times the width.
perimeter = 2×4 + 2×3 = 8 + 6 = 14 meters
The answer it’s a. Pretty sure if not sorry
Answer:
![h=2.4 hours \: 2hours\:24'](https://tex.z-dn.net/?f=h%3D2.4%20hours%20%5C%3A%202hours%5C%3A24%27)
Step-by-step explanation:
1)Rewriting it properly:
![Q(t)=28850*\left ( \left ( \frac{3}{4}\right )^{h} \right )^{\frac{t}{h}}\, if \left ( \frac{3}{4} \right )^{h}=\frac{1}{2}](https://tex.z-dn.net/?f=Q%28t%29%3D28850%2A%5Cleft%20%28%20%5Cleft%20%28%20%5Cfrac%7B3%7D%7B4%7D%5Cright%20%29%5E%7Bh%7D%20%5Cright%20%29%5E%7B%5Cfrac%7Bt%7D%7Bh%7D%7D%5C%2C%20if%20%5Cleft%20%28%20%5Cfrac%7B3%7D%7B4%7D%20%5Cright%20%29%5E%7Bh%7D%3D%5Cfrac%7B1%7D%7B2%7D)
2) Let's calculate the time (in hours), based on this relation:
![\left ( \frac{3}{4} \right )^{h}=\frac{1}{2} \Rightarrow log_{\frac{3}{4}}\frac{1}{2} \Rightarrow h \approx 2.4\: hours](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7B3%7D%7B4%7D%20%5Cright%20%29%5E%7Bh%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%5CRightarrow%20log_%7B%5Cfrac%7B3%7D%7B4%7D%7D%5Cfrac%7B1%7D%7B2%7D%20%5CRightarrow%20h%20%5Capprox%202.4%5C%3A%20hours)
3) Testing it. We must find something around the half of 28850, due to some rounding in logarithms.
![Q(t)=28850*\left ( \left ( \frac{3}{4}\right )^{h} \right )^{\frac{t}{h}}\, if \left ( \frac{3}{4} \right )^{h}=\frac{1}{2}\Rightarrow h=\\Q(t)=28850(\frac{1}{2})^{\frac{t}{h}}\Rightarrow Q(t)=28850(\frac{1}{2})^{\frac{t}{2.4}}\\28850(\frac{1}{2})^{\frac{t}{2.4}}=14425 \Rightarrow (\frac{1}{2})^{\frac{t}{2.4}}=\frac{14425}{28850}\Rightarrow (\frac{1}{2})^{\frac{t}{2.4}}=\frac{1}{2}\Rightarrow t=2.4\\Q(2.4)=28850*\left ( \left ( \frac{3}{4}\right )^{2.4} \right )^{\frac{2.4}{2.4}}\Rightarrow Q\approx14464](https://tex.z-dn.net/?f=Q%28t%29%3D28850%2A%5Cleft%20%28%20%5Cleft%20%28%20%5Cfrac%7B3%7D%7B4%7D%5Cright%20%29%5E%7Bh%7D%20%5Cright%20%29%5E%7B%5Cfrac%7Bt%7D%7Bh%7D%7D%5C%2C%20if%20%5Cleft%20%28%20%5Cfrac%7B3%7D%7B4%7D%20%5Cright%20%29%5E%7Bh%7D%3D%5Cfrac%7B1%7D%7B2%7D%5CRightarrow%20h%3D%5C%5CQ%28t%29%3D28850%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7Bh%7D%7D%5CRightarrow%20Q%28t%29%3D28850%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B2.4%7D%7D%5C%5C28850%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B2.4%7D%7D%3D14425%20%5CRightarrow%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B2.4%7D%7D%3D%5Cfrac%7B14425%7D%7B28850%7D%5CRightarrow%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B2.4%7D%7D%3D%5Cfrac%7B1%7D%7B2%7D%5CRightarrow%20t%3D2.4%5C%5CQ%282.4%29%3D28850%2A%5Cleft%20%28%20%5Cleft%20%28%20%5Cfrac%7B3%7D%7B4%7D%5Cright%20%29%5E%7B2.4%7D%20%5Cright%20%29%5E%7B%5Cfrac%7B2.4%7D%7B2.4%7D%7D%5CRightarrow%20Q%5Capprox14464)
4) So, h≈ 2.40 hours or 2 hours 24'
Let
be the weight of i-th player.
1. If the mean weight of 4 backfield members on the football team is 221 lb, then
![\dfrac{x_1+x_2+x_3+x_4}{4}=221\ lb.](https://tex.z-dn.net/?f=%5Cdfrac%7Bx_1%2Bx_2%2Bx_3%2Bx_4%7D%7B4%7D%3D221%5C%20lb.)
2. If the mean weight of the 7 other players is 202 lb, then
![\dfrac{x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}}{7}=202\ lb.](https://tex.z-dn.net/?f=%5Cdfrac%7Bx_5%2Bx_6%2Bx_7%2Bx_8%2Bx_9%2Bx_%7B10%7D%2Bx_%7B11%7D%7D%7B7%7D%3D202%5C%20lb.)
3. From the previous statements you have that
![x_1+x_2+x_3+x_4=221\cdot 4=884 \lb,\\ \\x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}=202\cdot 7=1414\ lb.](https://tex.z-dn.net/?f=x_1%2Bx_2%2Bx_3%2Bx_4%3D221%5Ccdot%204%3D884%20%5Clb%2C%5C%5C%20%5C%5Cx_5%2Bx_6%2Bx_7%2Bx_8%2Bx_9%2Bx_%7B10%7D%2Bx_%7B11%7D%3D202%5Ccdot%207%3D1414%5C%20lb.)
Add these two equalities and then divide by 11:
![x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}=884+1414=2298\ lb,\\ \\\dfrac{x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}}{11}=\dfrac{2298}{11}=208\dfrac{10}{11}\ lb.](https://tex.z-dn.net/?f=x_1%2Bx_2%2Bx_3%2Bx_4%2Bx_5%2Bx_6%2Bx_7%2Bx_8%2Bx_9%2Bx_%7B10%7D%2Bx_%7B11%7D%3D884%2B1414%3D2298%5C%20lb%2C%5C%5C%20%5C%5C%5Cdfrac%7Bx_1%2Bx_2%2Bx_3%2Bx_4%2Bx_5%2Bx_6%2Bx_7%2Bx_8%2Bx_9%2Bx_%7B10%7D%2Bx_%7B11%7D%7D%7B11%7D%3D%5Cdfrac%7B2298%7D%7B11%7D%3D208%5Cdfrac%7B10%7D%7B11%7D%5C%20lb.)
Answer: the mean weight of the 11-person team is ![208\dfrac{10}{11}\ lb.](https://tex.z-dn.net/?f=208%5Cdfrac%7B10%7D%7B11%7D%5C%20lb.)
Answer:
B
Step-by-step explanation:
Product refers to multiplication and B is the only one the uses multiplication with 8.