17% of the total number of students are in 1st grade
→0.17×500=85 students in 1st grade
19% of the total number of students are in 4th grade
→0.19×500=95 students in 4th grade
<span>The number of 3rd-grade students is 9 less than the number of 4th-grade students.
→95-9=86 students in 3rd grade
</span><span>The number of 2nd-grade students is 10 less than the number of 5th-grade students.
1st grade+4th grade+3rd grade=85+95+86=266
500-266=234=total number of students in 2nd grade and 5th grade
Let x=2nd grade students
Let y=5th grade students
x+y=234
2nd grade students is 10 less than the number of 5th grade students
→x=y-10
Since x=y-10 so we substitute y-10 for x
→y-10+y=234
→2y-10=234
+10 +10
→2y=244
→2y/2=244/2
→y=122 students in 5th grade
x+y=234
→x+122=234
→x=112 students in 2nd grade
ANSWERS:
1st: 85
2nd: 112
3rd: 86
4th: 95
5th: 122
</span>
Question, I that the Algebra nation book????
Answers:
1.)
C - Final exams: midterm = Q3 92 - Q1 80 = 12 and finals = Q3 85 - Q1 78 = 7, so finals exam has the smaller IQR.
2.)
B - exam median is much higher than the class median: refer to the attached image of class and exam box and whisker graph
3.)
A - <span>
IQR is a better measure of spread for movies than it is for basketball games: because the data for movies are quite wide or apart from each other than the data in the basketball games
4.)
A - </span><span>
mean for April is higher than October's mean: mean in April is 67 and mean in October is 60
5.)
A - </span><span>
Neither data set has suspected outliers: meaning there's no data that is further apart from the group or set
6.)
B - </span>
There is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical
<span>
7.)
C - </span>
college spread is best described by the IQR. The high school spread is best described by the standard deviation: this is because of the wide range of data in the college than the data in the high school.
keeping in mind that the vertex is between the focus point and the directrix, in this cases we have the focus point above the directrix, meaning is a vertical parabola opening upwards, Check the picture below, which means the "x" is the squared variable.
now, the vertical distance from the focus point to the directrix is
, which means the distance "p" is half that or 1/8, and is positive since it's opening upwards.
since the vertex is 1/8 above the directrix, that puts the vertex at
, meaning the y-coordinate for the vertex is 2.
![\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvertical%20parabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%204p%28y-%20k%29%3D%28x-%20h%29%5E2%20%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bfocus~point%7D%7B%28h%2Ck%2Bp%29%7D%5Cqquad%20%5Cstackrel%7Bdirectrix%7D%7By%3Dk-p%7D%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22p%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22p%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \begin{cases} h=-4\\ k=2\\ p=\frac{1}{8} \end{cases}\implies 4\left(\frac{1}{8} \right)(y-2)=[x-(-4)]^2\implies \cfrac{1}{2}(y-2)=(x+4)^2 \\\\\\ y-2=2(x+4)^2\implies \blacktriangleright y = 2(x+4)^2+2 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20h%3D-4%5C%5C%20k%3D2%5C%5C%20p%3D%5Cfrac%7B1%7D%7B8%7D%20%5Cend%7Bcases%7D%5Cimplies%204%5Cleft%28%5Cfrac%7B1%7D%7B8%7D%20%5Cright%29%28y-2%29%3D%5Bx-%28-4%29%5D%5E2%5Cimplies%20%5Ccfrac%7B1%7D%7B2%7D%28y-2%29%3D%28x%2B4%29%5E2%20%5C%5C%5C%5C%5C%5C%20y-2%3D2%28x%2B4%29%5E2%5Cimplies%20%5Cblacktriangleright%20y%20%3D%202%28x%2B4%29%5E2%2B2%20%5Cblacktriangleleft)