Put numbers in order: 4,5,6,6,7,8,9,9,10,10,12,12,14,15
Cut the list into two equal parts: 4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Find middle numbers: 4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Lower quartile: 6
Upper quartile: 12
The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6
Answer:
219 + 159 <= x <= 369 + 309
378 <= x <= 678
Step-by-step explanation:
Answer:
hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to
Answer: v = 5v + 4u + 1.5sin(3t),
Step-by-step explanation:
u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1
v represents the "velocity function" i.e v = u'(t)
As v = u'(t)
<em>u' = v</em>
since <em>u' = v </em>
v' = u"
v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )
= 5v + 4u + 1.5sin(3t) ( noting that v = u' )
so v' = 5v + 4u + 1.5sin(3t)
d/dt ![\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Du%26%5C%5Cv%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%26%5C%5C4%265%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ ![\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26%5C%5C1.5sin%283t%29%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Given that u(1) = 1 and u'(1) = 2.5
since v = u'
v(1) = 2.5
note: the initial value for the vector valued function is given as
![\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Du%281%29%26%5C%5Cv%281%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}1\\2.5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C2.5%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Answer:
Paasche's Index= 168.63= 169
Step-by-step explanation:
<em><u>Products</u></em>
<em><u>Base-Period Current Period</u></em>
Quantities Mean Shipping Quantities Mean Shipping
(Year 1) Cost per Unit ($) (Year 5) Cost per Unit ($)
A 1,500 10.50 4000 15.90
B 5,000 16.25 3000 33.00
C 6,500 12.20 8000 18.40
D 2,500 20.00 3000 35.50
Paasche's Index= ∑ pn.qn/∑po.qn* 100
Where pn is the price of the current year and qn is the quantity of the current year and po. is the price of the base year and qo. is the quantity of the base year.
Paasche's Index is the percentage ratio of the aggregate of given period prices weighted by the quantities sold or consumed in the given period to the aggregate of the base period prices weighted by the given period quantities.
Multiplying the current year prices with the current year quantities and the base year price with the current year quantities we get.
Product pn.qn po.qn
A 15.90* 4000 10.50* 4000
= 63600 =42000
B 33.00*3000 16.25 * 3000
= 99000 = 48750
C 18.40* 8000 12.20 *8000
=147200 =97600
D 35.50* 3000 20.00*3000
<u> =</u><u>106500 60,000 </u><u> </u>
<u>∑ 416300 248350 </u>
<u />
Paasche's Index= ∑ pn.qn/∑po.qn= <u> </u>416300/ 248350 *100 = 1.676=1.68= 168.63= 169
<u />
Answer:
The line equation is y = 1.5x + 3
Fill the first space with '1.5' and the second with '3'
Step-by-step explanation:
The generic model for a line equation is:
y = ax + b
To find the parameters 'a' and 'b', we can use two points of the graph in the equation.
Using the point (0, 3), we have:
3 = 0*a + b
b = 3
Using the point (-2, 0) and the value of b above, we have:
0 = -2*a + b
2a = 3
a = 1.5
So the line equation is y = 1.5x + 3
