Answer:
see attached
Step-by-step explanation:
Rotation 270° counterclockwise is equivalent to rotation 90° clockwise. The transformation of coordinates is ...
(x, y) ⇒ (y, -x) . . . . . . . rotation 270° CCW
This means the points are moved to ...
A(-2, 1) ⇒ A'(1, 2)
B( 1, 2) ⇒ B'(2, -1)
C(-2, 4) ⇒ C'(4, 2)
The rotated triangle is shown in the attachment. You may notice that A' and B are the same point.
Given the radius of 50 miles and the line joining the cities at (0, 56) and (58, 0), the transmitter signal can be picked during 59.24 miles of the drive.
<h3>How can the duration of signal reception be found?</h3>
Radius of broadcast of the transmitter = 50 miles
Location of starting point = 56 miles north of the transmitter
Location of destination city = 58 miles east of the transmitter
Therefore we have;
Slope of the line joining the two cities
= 56 ÷ (-58) = -0.966
Which gives the equation of the line as follows;
y = -0.966•x + 56
The equation of the circle is;
1.933156•x^2 - 108.192•x + 636 = 0
Which gives;
Therefore;
When x = 6.67, we have;
- y = -0.966 × 6.67 + 56 = 49.56
When x = 49.29, we have;
- y = -0.966 × 49.29 + 56 = 8.4
The length of the drive, during which the driver can pick the signal, <em>l</em>, is therefore;
l = √((49.56-8.4)^2 + (49.29-6.67)^2) = <u>59.24 miles</u>
- The length of the drive during which the signal is received is 59.24 miles
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Answer:
6x+20
c.
Step-by-step explanation:
If f(x)=6x+2 and you are asked to find f(x+3), then you just replace all the x's in f(x)=6x+2 with (x+3).
Doing this gives you:
f(x)=6x+2 with new input (x+3) in place of out input (x)
f(x+3)=6(x+3)+2
f(x+3)=6x+18+2
f(x+3)=6x+20
Answer:
no of sample within two percentage points is 5409
no of sample not use prior estimates is 8321
Step-by-step explanation:
Given data
E = 2% = 0.02
male m = 21.2 % = 0.212
female f = 19.7 % = 0.197
to find out
no of sample within two percentage points and if does not use any prior estimates
solution
first we calculate no of sample within two percentage points
we know Z critical value for 99% is 2.58
so no of sample will be
n = (Z / E )² × m(1-m) + f ( 1-f )
put all the value we get no of sample
n = (2.58 / 0.02 )² × 0.212 ( 1 - 0.212 ) + 0.197 ( 1 - 0.197 )
n = 16641 ×0.3250
no of sample within two percentage points is 5409
in 2nd part no of sample not use prior estimates
here than f and m will be 0.5
than
n = (Z / E )² × m(1-m) + f ( 1-f )
put all value
n = (2.58 / 0.02 )² × 0.5 ( 1 - 0.5 ) + 0.5 ( 1 - 0.5 )
n = 16641 × 0.5
no of sample not use prior estimates is 8321
Answer:
Step-by-step explanation: The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
What is an integer exponent?
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The question is incomplete.
The complete question is attached in the picture, please refer picture.
We have an expression:
Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
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