To determine the amount of juice you will need you will multiply the number of students by how much juice each student will get. This is the idea of grouping. We will need 30 groups of 12 ounces.
30 x 12 = 360 ounces.
You will need 360 ounces of juice.
Answer:
A = 384 inches^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 ( 32) *(24)
A = 384 inches^2
Answer:
![x=-30;\quad \:I\ne \:0](https://tex.z-dn.net/?f=x%3D-30%3B%5Cquad%20%5C%3AI%5Cne%20%5C%3A0)
Step-by-step explanation:
![In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)](https://tex.z-dn.net/?f=In%5Ccdot%20%5C%3A4%2BIn%5Cleft%284x-15%5Cright%29%3DIn%5Cleft%285x%2B19%5Cright%29)
![\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\](https://tex.z-dn.net/?f=%5C%3A4%2BIn%5Cleft%284x-15%5Cright%29%3A%5Cquad%20-11nI%2B4nxI%5C%5CIn%5Ccdot%20%5C%3A4%2BIn%5Cleft%284x-15%5Cright%29%5C%5C%3D4nI%2BnI%5Cleft%284x-15%5Cright%29%5C%5C%5C%5C%5C%3AIn%5Cleft%284x-15%5Cright%29%3A%5Cquad%204nxI-15nI%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Adistributive%5C%3Alaw%7D%3A%5Cquad%20%5C%3Aa%5Cleft%28b-c%5Cright%29%3Dab-ac%5C%5Ca%3DIn%2C%5C%3Ab%3D4x%2C%5C%3Ac%3D15%5C%5C%3DIn%5Ccdot%20%5C%3A4x-In%5Ccdot%20%5C%3A15%5C%5C%3D4nxI-15nI%5C%5C%3DIn%5Ccdot%20%5C%3A4%2B4nxI-15nI%5C%5C%5Cmathrm%7BSimplify%7D%5C%3AIn%5Ccdot%20%5C%3A4%2B4nxI-15nI%3A%5Cquad%20-11nI%2B4nxI%5C%5CIn%5Ccdot%20%5C%3A4%2B4nxI-15nI%5C%5C%5Cmathrm%7BGroup%5C%3Alike%5C%3Aterms%7D%5C%5C%3D4nI-15nI%2B4nxI%5C%5C%5Cmathrm%7BAdd%5C%3Asimilar%5C%3Aelements%3A%7D%5C%3A4nI-15nI%3D-11nI%5C%5C%3D-11nI%2B4nxI%5C%5C)
![\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\](https://tex.z-dn.net/?f=%5Cmathrm%7BExpand%5C%3A%7DIn%5Cleft%285x%2B19%5Cright%29%3A%5Cquad%205nxI%2B19nI%5C%5CIn%5Cleft%285x%2B19%5Cright%29%5C%5C%3DnI%5Cleft%285x%2B19%5Cright%29%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Adistributive%5C%3Alaw%7D%3A%5Cquad%20%5C%3Aa%5Cleft%28b%2Bc%5Cright%29%3Dab%2Bac%5C%5Ca%3DIn%2C%5C%3Ab%3D5x%2C%5C%3Ac%3D19%5C%5C%3DIn%5Ccdot%20%5C%3A5x%2BIn%5Ccdot%20%5C%3A19%5C%5C%3D5nxI%2B19nI%5C%5C%5C%5C-11nI%2B4nxI%3D5nxI%2B19nI%5C%5C%5C%5C%5Cmathrm%7BAdd%5C%3A%7D11nI%5Cmathrm%7B%5C%3Ato%5C%3Aboth%5C%3Asides%7D%5C%5C-11nI%2B4nxI%2B11nI%3D5nxI%2B19nI%2B11nI%5C%5CSimplify%5C%5C4nxI%3D5nxI%2B30nI%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D5nxI%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C4nxI-5nxI%3D5nxI%2B30nI-5nxI%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C-nxI%3D30nI%5C%5C)
![\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D-nI%3B%5Cquad%20%5C%3AI%5Cne%20%5C%3A0%5C%5C%5Cfrac%7B-nxI%7D%7B-nI%7D%3D%5Cfrac%7B30nI%7D%7B-nI%7D%3B%5Cquad%20%5C%3AI%5Cne%20%5C%3A0%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5Cfrac%7B-nxI%7D%7B-nI%7D%3D%5Cfrac%7B30nI%7D%7B-nI%7D%5C%5C%5Cmathrm%7BSimplify%5C%3A%7D%5Cfrac%7B-nxI%7D%7B-nI%7D%3A%5Cquad%20x%5C%5C%5Cfrac%7B-nxI%7D%7B-nI%7D%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7B-a%7D%7B-b%7D%3D%5Cfrac%7Ba%7D%7Bb%7D%5C%5C%3D%5Cfrac%7BnxI%7D%7BnI%7D%5C%5C%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3An%5C%5C%3D%5Cfrac%7BxI%7D%7BI%7D%5C%5C%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3AI%5C%5C%3Dx%5C%5C%5Cmathrm%7BSimplify%5C%3A%7D%5Cfrac%7B30nI%7D%7B-nI%7D%3A%5Cquad%20-30%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A)
![\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0](https://tex.z-dn.net/?f=%5Cquad%20%5Cfrac%7Ba%7D%7B-b%7D%3D-%5Cfrac%7Ba%7D%7Bb%7D%5C%5C%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3An%5C%5C%3D%5Cfrac%7B30I%7D%7BI%7D%5C%5C%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3AI%5C%5C%3D-30%5C%5Cx%3D-30%3B%5Cquad%20%5C%3AI%5Cne%20%5C%3A0)
Answer:
-4 3/4, -4 1/2, -4 1/4
Step-by-step explanation:
Dear Jazzy870, John uses 161-162 lb of coffee a. Use the equation 655.70/4.05≈161.901.