Cos theta would be (adjacent side) / (hypotenuse), or 8/29.
Thus, the angle theta would be the inverse cosine of 8/29, which is
1.291 radians or 73.987 degrees.
Given this result, just take the sine of this angle.
Answer:
(1) .20 (2) .40 (3) .12 (4) Less than
Step-by-step explanation:
You have to look at the table. There are 5 columns with 10 rows. 5x10=50
Then simply count the boxes that have the correct number of currency for instance, if they are asking for EXACTLY 1 dime then you rule out the ones that have 2 or 3 dimes and only the count the ones that have a single dime. So you count PDN but you would not count PDD. There are 20 boxes that have a single dime in them. 20 out of the 50 boxes. 20/50=.40 (answer 2)
The estimated probability that exactly two of the three coins Avery randomly picked are nickels is .
20
The estimated probability that exactly one of the three coins Avery randomly picked is a dime is .
40
The estimated probability that all three coins Avery randomly picked are pennies is .
12
The answer to #1 is .20 or 20% and the answer to #2 is .40 or 40%. 20% is less than 40% so...
The estimated probability that exactly two of the three coins Avery randomly picked are nickels is LESS THAN the estimated probability that exactly one of the three coins Avery randomly picked is a dime.
Pick 2 pairs of equations t<span>hen use addition and subtraction to eliminate </span>the same variable<span> from both pairs of equations then it is left with 2 variables
</span>Pick two pairs
<span><span>4x - 3y + z = - 10</span><span>2x + y + 3z = 0
</span></span>eliminate the same variable from each system
<span><span>4x - 3y + z = - 10</span>
<span>2x + y + 3z = 0</span>
<span>4x - 3y + z = - 10</span>
<span>-4x - 2y - 6z = 0</span>
<span>-5y - 5z = - 10</span>
<span>2x + y + 3z = 0</span>
<span>- x + 2y - 5z = 17</span>
<span>2x + y + 3z = 0</span>
<span>-2x + 4y - 10z = 34</span>
<span>5y - 7z = 34
</span></span>Solve the system of the two new equations:
<span><span>-5y - 5z = - 10</span>
<span>5y - 7z = 34</span>
<span>-12z = 24</span>
which is , <span>z = - 2</span>
<span>-5y - 5(- 2) = - 10</span>
<span>-5y = - 20</span>
wich is , <span>y = 4
</span></span>substitute into one of the original equations
<span>- x + 2y - 5z = 17</span>
<span>- x + 2(4) - 5(- 2) = 17</span>
<span>- x + 18 = 17</span>
<span>- x = - 1</span>
<span>x = 1</span>
<span>which is , </span><span>(x, y, z) = (1, 4, - 2)</span><span>
</span>Does 2(1) + 4 + 3(- 2) = 0<span> ? Yes</span><span>
</span>
Answer:
y = x-2
Step-by-step explanation:
y = mx + b as an equation
m = slope
slope = (change in y) / (change in x) = (y₂-y₁)/(x₂-x₁) = (y₁-y₂)/(x₁-x₂) = (2-(-2))/(4-0) = 4/4 = 1
y = 1*x + b
plug a value in, e.g. (0, -2)
-2 = 1 * 0 + b
-2 = b
our equation is thus
y = x - 2
