Answer: The correct selling price is $29.97.
Step-by-step explanation:
Since we have given that
Cost price of an item = $27
Mark up rate = 11%
So, Amount of mark up would be
So, Amount after mark up would be
Hence, the correct selling price is $29.97.
The manager's likely error is that he has put the selling price the mark up amount only i.e $2.9≈$3 instead of adding the mark up amount to the cost price.
It’s would be the second one aka it would be b
To find the critical value
![z_{\alpha/2}](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D)
that corresponds<span> to 97% confidence level</span>:
Step 1:
Subtract 0.97 from 1:
1 - 0.97 = 0.03
Step 2:
Divide 0.03 by 2:
0.03 / 2 = 0.015
Step 3:
Subtract 0.03 from 1:
1 - 0.015 = 0.985
Step 4:
From the normal distribution table, the z score that corresponds to a probability of 0.985 is 2.17.
Therefore, <span>the critical value that corresponds to 97% confidence level is 2.17.</span>
Answer:
Dimensions: 0.4 by 3.2 by 1.2
Step-by-step explanation:
I'm assuming here that we are cutting out squares out of each of the metal's corners:
Let x = the length of each cut-out square,
Each base (of the desired net square folded) is 4-2x, and 2-2x respectively,
Volume = x(4-2x)(2-2x)
= 4x^3 - 12x + 8x
Now we take the derivative:
![\frac{d}{dx}\left[4x^3-12x^2+8x\right]\\\\= \frac{d}{dx}\left(4x^3\right)-\frac{d}{dx}\left(12x^2\right)+\frac{d}{dx}\left(8x\right)\\\\= 12x^2-24x+8](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B4x%5E3-12x%5E2%2B8x%5Cright%5D%5C%5C%5C%5C%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%284x%5E3%5Cright%29-%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%2812x%5E2%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%288x%5Cright%29%5C%5C%5C%5C%3D%2012x%5E2-24x%2B8)
We equate to 0 (0 for max volume), and solve using the quadratic formula:
![12x^2-24x+8=0,\\\\x_{1,\:2}=\frac{-\left(-24\right)\pm \sqrt{\left(-24\right)^2-4\cdot \:12\cdot \:8}}{2\cdot \:12}\\\\= \frac{-\left(-24\right)\pm \:8\sqrt{3}}{2\cdot \:12}\\\\\mathrm{Separate\:the\:solutions}:\\\\x_1=\frac{-\left(-24\right)+8\sqrt{3}}{2\cdot \:12},\:x_2=\frac{-\left(-24\right)-8\sqrt{3}}{2\cdot \:12}\\\\x =\frac{3+\sqrt{3}}{3},\:x=\frac{3-\sqrt{3}}{3}\\\\x=1.57735\dots ,\:x=0.42264\dots](https://tex.z-dn.net/?f=12x%5E2-24x%2B8%3D0%2C%5C%5C%5C%5Cx_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-%5Cleft%28-24%5Cright%29%5Cpm%20%5Csqrt%7B%5Cleft%28-24%5Cright%29%5E2-4%5Ccdot%20%5C%3A12%5Ccdot%20%5C%3A8%7D%7D%7B2%5Ccdot%20%5C%3A12%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B-%5Cleft%28-24%5Cright%29%5Cpm%20%5C%3A8%5Csqrt%7B3%7D%7D%7B2%5Ccdot%20%5C%3A12%7D%5C%5C%5C%5C%5Cmathrm%7BSeparate%5C%3Athe%5C%3Asolutions%7D%3A%5C%5C%5C%5Cx_1%3D%5Cfrac%7B-%5Cleft%28-24%5Cright%29%2B8%5Csqrt%7B3%7D%7D%7B2%5Ccdot%20%5C%3A12%7D%2C%5C%3Ax_2%3D%5Cfrac%7B-%5Cleft%28-24%5Cright%29-8%5Csqrt%7B3%7D%7D%7B2%5Ccdot%20%5C%3A12%7D%5C%5C%5C%5Cx%20%3D%5Cfrac%7B3%2B%5Csqrt%7B3%7D%7D%7B3%7D%2C%5C%3Ax%3D%5Cfrac%7B3-%5Csqrt%7B3%7D%7D%7B3%7D%5C%5C%5C%5Cx%3D1.57735%5Cdots%20%2C%5C%3Ax%3D0.42264%5Cdots)
So we approximate the side lengths to be 1.6 and 0.4 respectively. But when we plug in 1.6 for x, we get the volume as negative. Therefore x has to be 0.4.
Side lengths: 0.4, 4-2(0.4) => 3.2, 2-2(0.4) => 1.2
Answer:
£13496.80
Step-by-step explanation:
We can ignore the £ sign for now, that is just units.
If we decrease a number by 4.5%, we will have to find
% of 14132.77.
We can easily do this by setting up a proportion.
![\frac{x}{14132.77} = \frac{95.5}{100}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B14132.77%7D%20%3D%20%5Cfrac%7B95.5%7D%7B100%7D)
Multiply 14132.77 by 95.5:
![14132.77\cdot95.5=1349679.535](https://tex.z-dn.net/?f=14132.77%5Ccdot95.5%3D1349679.535)
Divide by 100:
![1349679.535\div100=13496.79535](https://tex.z-dn.net/?f=1349679.535%5Cdiv100%3D13496.79535)
Rounding this to two decimal places, it simplifies to 13496.80.
Hope this helped!