The coordinates of Δxyz ⇒⇒ x(1,1) y(2,3) z(3,2)
The coordinates of Δx'y'z' ⇒⇒ x'(2,-2) y'(4,2) z'(6,0)
1. Applying the transformation of the first sentence on Δxyz
The results are ⇒⇒⇒ (2,-2) (4,2) (6,0)
2. Applying the transformation of the second sentence on Δxyz
The results are ⇒⇒⇒ (12,14) (24,38) (36,28)
3. Applying the transformation of the third sentence on Δxyz
The results are ⇒⇒⇒ (12,-36) (24,-12) (36,-24)
4. Applying the transformation of the fourth sentence on Δxyz
The results are ⇒⇒⇒ (2,-6) (4,-2) (6,-4)
By comparing the results obtained with the coordinates of Δx'y'z'
So, the correct answer is the first sentence.
<span>dilation with respect to the origin by a scale factor of 2 followed by a translation of 4 units down</span>
The answer is choice B in the upper right hand corner.
Choice B is the graph that is a straight line and it's a single unbroken straight line. There are no gaps or jumps or any kinds of bends like choice A shows. Choice A is an absolute value graph, which is the result of gluing together two linear functions. Overall, graph A is considered nonlinear. Choices C and D are nonlinear as well.
Answer:
(1) $11955.38
(2) $12228.62
(3) $12293.527
(4) $12326.6
Step-by-step explanation:
Compound interest is given by
A= P( 1 + r/n)^n*t
A= Final amount
P = initial amount = 6000
r = interest rate = 9% = 0.09
n = number of times interest applied per time period
t = number of time periods elapsed
(1) Compounded annually
n = 1 , t = 8
A = 6000( 1+ 0.09/1) ^1*8
A = 6000( 1.09) ^8 = $11955.38
(2) compounded quarterly
n = 4 , t = 8
A = 6000( 1+ 0.09/4) ^4*8
= 6000( 1.0225)^32 = $12228.62
(3) compounded monthly
n = 12 , t = 8
A = 6000( 1+0.09/12)^12*8 = $12293.527
(4) compounded continuously
A = P* e^rt
r = 0.09 , t = 8
= 6000* e^0.09*8
= 6000* e^0.72 = $12326.6
I set it up as a ratio with hours on the top and the fraction of the job on the bottom. It looks like this: 5/(2/3) / x/1, because 1 is the whole job if 2/3 is only a fraction of it. Cross multiplying gives you 2/3x = 5. Solving for x gives you that it will take 7.5 hours to complete a whole job if it takes 5 hours to complete 2/3 of it.
Answer:
q1=11
q3= 33
Step-by-step explanation:
The data set has 44 number of students. The first quartile is 25 % of the numbers in the data set . So
25 % of 44 = 25/100 * 44= 0.25 *44 = 11
So the first quartile lies at 11.
Similarly the third quartile lies at the 75 % of the numbers of the data set . So
75 % of 44 = 75/100 * 44= 0.75 *44 = 33
So the third quartile lies at 33.
