Answer:
Step-by-step explanation:
a) Frequency table:
Category Frequency
Dog 4
Cat 3
Fish 2
Hamster 1
b) Relative frequencies of each animal type
Dog: 4/10 = 0.4
Cat: 3/10 = 0.3
Fish: 2/10 = 0.2
Hamster: 1/10 = 0.1
c) Popularity
Dog is the most popular because it has the highest relative frequency.
Hamster is the least popular because it has the lowest relative frequency.
Consider the coordinate plane:
1. The origin is the point where Sharon and Jacob started - (0,0).
2. North - positive y-direction, south - negetive y-direction.
3. East - positive x-direction, west - negative x-direction.
Then,
- if Jacob walked 3 m north and then 4 m west, the point where he is now has coordinates (-4,3);
- if Sharon walked 5 m south and 12 m east, the point where she is now has coordinates (12,-5).
The distance between two points with coordinates 
and 
can be calculated using formula
Therefore, the distance between Jacob and Sharon is
Answer:
119.05°
Step-by-step explanation:
In general, the angle is given by ...
θ = arctan(y/x)
Here, that becomes ...
θ = arctan(9/-5) ≈ 119.05°
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<em>Comment on using a calculator</em>
If you use the ATAN2( ) function of a graphing calculator or spreadsheet, it will give you the angle in the proper quadrant. If you use the arctangent function (tan⁻¹) of a typical scientific calculator, it will give you a 4th-quadrant angle when the ratio is negative. You must recognize that the desired 2nd-quadrant angle is 180° more than that.
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It may help you to consider looking at the "reference angle." In this geometry, it is the angle between the vector v and the -x axis. The coordinates tell you the lengths of the sides of the triangle vector v forms with the -x axis and a vertical line from that axis to the tip of the vector. Then the trig ratio you're interested in is ...
Tan = Opposite/Adjacent = |y|/|x|
This is the tangent of the reference angle, which will be ...
θ = arctan(|y| / |x|) = arctan(9/5) ≈ 60.95°
You can see from your diagram that the angle CCW from the +x axis will be the supplement of this value, 180° -60.95° = 119.05°.
Answer:
4/9 * 7 =3.11111111
Step-by-step explanation:
4/9 * 7 =3.11111111
Solution:
<u>Given:</u>
<u>Solve the equation by isolating the variable.</u>
- => 18 = 2b
- => 2b/2 = 18/2
- => b = 9
The value of b is 9.
Hoped this helped!
