The vertices for the dilated image can be found by multiplying the coordinates of the original image by the scale factor. In this problem, the scale factor is 1/3.
(0,0) ⇒ 0 x 1/3 = 0 ; 0 x 1/3 = 0 ⇒ (0,0)
(27,0) ⇒ 27 x 1/3 = 9 ; 0 x 1/3 = 0 ⇒ (9,0)
(36,30) ⇒36 x 1/3 = 12 ; 30 x 1/3 = 10 ⇒ (12,10)
(9,30) ⇒ 9 x 1/3 = 3 ; 30 x 1/3 = 10 ⇒ (3,10)
Answer is choice D. (3,10)
Answer:
And rounded up we have that n=99
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that 
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We assume the value for 
since we don't have previous info. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=99
$20 minus $15 = $5 difference
$5 divided by $0.20 = 25 checks
*Now the accounts are even, except I haven't done the checks for the second account.*
25 checks times $0.10 = $2.50
$2.50 divided by $0.20 = 12.5 checks (round up in this case to 13)
*Now, you need to do 13 more checks on the second account*
13 checks times $0.10 = $1.30
$1.30 divided by $0.20 = 6.5 checks (round up in this case to 7)
*Now, you need to do 7 more checks on the second account*
7 checks times $0.10 = $0.70
$0.70 divided by $0.20 = 3.5 checks (round up in this case to 4)
*Now, you need to do 7 more checks on the second account*
4 checks times $0.10 = $0.40
$0.40 divided by $0.20 = 2 checks
*Now, you need to do 2 more checks on the second account*
2 checks times $0.10 = $0.20
$0.20 divided by $0.20 = 1 check
*Now, you need to do 1 more checks on the second account*
1 checks times $0.10 = $0.10
$0.10 divided by $0.20 = 0.5 checks (round up in this case to 1)
*Now, you need to do 1 more checks on the second account*
1 checks times $0.10 = $0.10
$0.10 divided by $0.20 = 0.5 checks
25 + 13 + 7 + 4 + 2 + 1 + 1 = 53 checks
Check your work!
Account #1- $15 + (53 times $0.20) = $25.60
Account #2- $20 + (53 times $0.10) = $25.30
Answer
53 checks
Answer:
46°
Step-by-step explanation:
Given that :
Angle, A = 66°
Angle B = 68°
The sum of angles in a triangle is given by :
A + B + C = 180° (sum if angles una triangle)
66° + 68° + C = 180°
134° + C = 180°
C = 180° - 134°
C = 46°
Hence, angle C is 46°
