Answer:

Step-by-step explanation:
Given

Rotation = +270 degrees
Required
Determine the new coordinates of Q (i.e. Q')
When a point (x,y) is rotated +270° about the origin, the new coordinates is: (y,−x)
So:

Where:
and 
Q' will be:

So since the kitchens long is wide x 2 if you add the 2 longs it makes a wide so you end up with 3 wides technically. So you divide 84 by 3 and u get 28 so make your 2 wides 28. Then u divide 28 by 2 to get 14 so your longs are 14 and your wides are 28 if u add it all together it’s 84.
The hypotenuse of the triangle would be the diameter of the semi circle.
Using the Pythagorean theorem you can find that.
8^2 + 6^2 = x^2
64 +36 = x^2
100 = x^2
x = √100
x = 10
The diameter is 10, now find the circumference.
Circumference = diameter x PI = 10 x 3.14 = 31.4
Since it is a semi circle, the circumference would be 1/2 of that.
31.4 / 2 = 15.7
The perimeter would be 8 + 6 + 15.7 = 29.7
Answer:
The correct answer is a. $2275.28; b. 17.04 years
Step-by-step explanation:
Principal to be invested is $2000
Interest rate (r) per year is 6.5 quarterly.
Interest is calculated compoundly.
a. Time (t) for the investment is given to be 2 years.
Amount after two years is = Principal ×
where the value of n is 4.
⇒ A = 2000 × 
⇒ A = $2275.28.
b. Now the value of A is given to be triple the principal = $ (3 × 2000).
Therefore we need to find the value of t.
⇒ 3 × 2000 = 2000 × 
⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)
⇒ t = 17.04
Therefore it would take 17.04 years for the principal to triple.
Answer:
mean=4.44
standard deviation=1.67
Step-by-step explanation:
The mean and standard deviation for the number of erroneous returns per batch can be calculated using binomial distribution. The binomial distribution is used because
i) There are one of two possible outcomes( error or no error) that can be categorized into success and failure.
ii) The experiment is repeated fix number of times 12.
iii) The probability of success remains constant at each trial i.e. 37%
iv) The trails are independent.The mean and standard deviation of binomial distribution are np and √npq
Here, n=12, p=0.37 and q=1-0.37=0.63
mean=12*0.37=4.44
standard deviation=√12*0.37*0.63=√2.8=1.67