Answer:
(a) The total number of ways to select 4 officers from from 25 students is 12,650.
(b) The total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.
Step-by-step explanation:
(a)
It is provided that there are a total of <em>n</em> = 25 students.
Officers need to be elected for four positions:
President, Vice-President, Secretary, and Treasurer.
<em>k</em> = 4
In mathematics, the procedure to select <em>k</em> items from <em>n</em> distinct items, without replacement, is known as combinations.
The formula to compute the combinations of <em>k</em> items from <em>n</em> is given by the formula:
Compute the number of ways to select 4 students from from 25 as follows:
Thus, the total number of ways to select 4 officers from from 25 students is 12,650.
(b)
It is provided that of the 25 students, there are 13 girls and 12 boys in the class.
For the post of President and Treasurer only girls are selected.
For the post of Vice-President and Secretary only boys are selected.
Compute the number of ways to select 2 girls for the post of President and Treasurer as follows:
Compute the number of ways to select 2 boys for the post of Vice-President and Secretary as follows:
The number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is:
Thus, the total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.
<span>19/20 is a bigger fraction.</span>
<span>Vector Equation
(Line)</span>(x,y) = (x,y) + t(a,b);tERParametric Formx = x + t(a), y = y + t(b); tERr = (-4,-2) + t((-3,5);tERFind the vector equation of the line passing through A(-4,-2) & parallel to m = (-3,5)<span>Point: (2,5)
Create a direction vector: AB = (-1 - 2, 4 - 5)
= (-3,-1) or (3,1)when -1 (or any scalar multiple) is divided out.
r = (2,5) + t(-3,-1);tER</span>Find the vector equation of the line passing through A(2,5) & B(-1,4)<span>x = 4 - 3t
y = -2 + 5t
;tER</span>Write the parametric equations of the line passing through the line passing through the point A(4,-2) & with a direction vector of m =(-3,5)<span>Create Vector Equation first:
AB = (2,8)
Point: (4,-3)
r = (4,-3) + (2,8); tER
x = 4 + 2t
y = -3 + 8t
;tER</span>Write the parametric equations of the line through A(4,-3) & B(6,5)<span>Make parametric equations:
x = 5 + 4t
y = -2 + 3t ; tER
For x sub in -3
-3 = 5 + 4t
(-8 - 5)/4 = t
-2 = t
For y sub in -8
-8 = -2 + 3t
(-8 + 2)/3 = t
-2 = t
Parameter 't' is consistent so pt(-3,-8) is on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (-3,-8) on the line?<span>Make parametric equations:
x = 5 + 4t
y = -2 + 3t ; tER
For x sub in 1
-1 = 5 + 4t
(-1 - 5)/4 = t
-1 = t
For y sub in -7
-7 = -2 + 3t
(-7 + 2)/3 = t
-5/3 = t
Parameter 't' is inconsistent so pt(1,-7) is not on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (1,-7) on the line?<span>Use parametric equations when generating points:
x = 5 + 4t
y = -2 + 3t ;tER
X-int:
sub in y = 0
0 = -2 + 3t
solve for t
2/3 = t (this is the parameter that will generate the x-int)
Sub t = 2/3 into x = 5 + 4t
x = 5 + 4(2/3)
x = 5 + (8/3)
x = 15/3 + (8/3)
x = 23/3
The x-int is (23/3, 0)</span>What is the x-int of the line r = (5,-2) + t(4,3); tER?Note: if they define the same line: 1) Are their direction vectors scalar multiples? 2) Check the point of one equation in the other equation (LS = RS if point is subbed in)What are the two requirements for 2 lines to define the same line?
Answer:
B the 2 lb bread for 1.75
Step-by-step explanation:
The dollar per ounce for bread is $0.058 .
The dollar per ounce of bread is $0.055 .
b is the best buy .
Step-by-step explanation:
First part
As given
Bread, 1 lb. loaf for 96¢ would .
As
1 dollar = 100 cent
Now convert 96¢ into dollars .
= $0.96
As 1 pound = 16 ounce
Thus
Bread 16 ounce loaf for $0.96 .
Therefore the dollar per ounce for bread is $0.058 .
Second part
Bread, 2 lb. loaf for $1.75
As 1 pound = 16 ounce
2 pound = 2 × 16 ounce
= 32 ounce
Dollar per ounce = $ 0.055
Therefore dollar per ounce of bread is $0.055 .
Third part
As dollar per ounce for Bread, 2 lb. loaf for $1.75 is less as compared to Bread 1 lb. loaf for 96¢ .
Therefore b is the best buy .