Answer:
0.184
Step-by-step explanation:
There are 38 seniors, of which 7 prefer evening classes.
7/38 ≈ 0.184
Slope of line = tan(120) = -tan(60) = - √3
Distance from origin = 8
Let equation be Ax+By+C=0
then -A/B=-√3, or
B=A/√3.
Equation becomes
Ax+(A/√3)y+C=0
Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/√3)y+C)/sqrt(A^2+(A/√3)^2))
Substitute coordinates of origin (x,y)=(0,0) =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
8=C/√(4/3) => C=8*2/√3 = (16/3)√3
Therefore one solution is
x+(1/√3)+(16/3)√3=0
or equivalently
√3 x + y + 16 = 0
Check:
slope = -1/√3 .....ok
distance from origin
= (√3 * 0 + 0 + 16)/(sqrt(√3)^2+1^2)
=16/2
=8 ok.
Similarly C=-16 will satisfy the given conditions.
Answer The required equations are
√3 x + y = ± 16
in standard form.
You can conveniently convert to point-slope form if you wish.
F=5 dollar bills
t=twent dollar bills
38 total bills
f+t=38
400 in bills
400=5f+20t
we have
f+t=38
5f+20t=400
multipy first equation by -5 and add to second equation
-5f-5t=-190
5f+20t=400 +
0f+15t=210
15t=210
divide both sides by 15
t=14
subsitute
t+f=38
15+f=38
f=23
23 five dolar bills
15 twenty dollar bills
The last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.
A few fundamental principles apply to density curves:
- A density curve's area beneath it represents probability.
- A density curve's area under it equals one.
- Base x height in a uniform density curve equals one.
- The likelihood that x = a will never occur.
- The likelihood that x < a is the same as that of x ≤ a.
Following the rules above, we can see from graph B that the curve is above the horizontal axis. That shows that the probabilities are positive which is a necessity. Moreover, the area under the curve must also be 1. That is also satisfied.
Hence, the last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.
Learn more about density curves here-
brainly.com/question/18345488
#SPJ10
Answer:
<h2><em><u>Option</u></em><em><u> </u></em><em><u>B</u></em><em><u>:</u></em></h2><h2>
</h2>
Step-by-step explanation:
<em><u>Given</u></em><em><u>,</u></em>
Number of numbers of each side of the cube
= 4, 5, 6, 7, 8 and 9
= 6 numbers
Number of sides of cube having the number 5
= 1
<em><u>Therefore</u></em><em><u>,</u></em><em><u> </u></em>
Probability of getting a side of the cube of no. 5 is
