Answer:
Z must equal 22° because it will add up to 180° it is an acute scalene triangle
Answer:
• From trigonometric ratios:
![{ \rm{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\](https://tex.z-dn.net/?f=%7B%20%5Crm%7B%20%5Csin%28%20%5Ctheta%29%20%3D%20%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%20%20%7D%7D%20%5C%5C%20)
→ theta is 41°
→ opposite is y
→ hypotenuse is 26 ft
![{ \tt{ \sin(41) = \frac{y}{26} }} \\ \\ { \tt{y = 26 \sin(41) }} \\ \\ { \boxed{ \tt{ \: y = 17.06 \: \: ft}}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7B%20%5Csin%2841%29%20%20%3D%20%20%5Cfrac%7By%7D%7B26%7D%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Ctt%7By%20%3D%2026%20%5Csin%2841%29%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Cboxed%7B%20%5Ctt%7B%20%5C%3A%20y%20%3D%2017.06%20%5C%3A%20%20%5C%3A%20ft%7D%7D%7D)
Answer:
3,360
Step-by-step explanation:
so, to start with, there are 8 over 5 permutations (the sequence of the picked beads matters, but no repetitions of beads are possible) to pick 5 items out of 8 available ones.
that is
8! / ((8-5)!) = 8! / 3! = 8×7×6×5×4 = 6,720
rotations and reflections are the same thing here for a 1- dimensional sequence.
1 2 3 4 5 rotated around the middle (3) is
5 4 3 2 1
a reflection is again
5 4 3 2 1
so, we need to consider that instead of 8 beads for the first choice we have only 4 beads to choose from to leave the other 4 beads as choices for the last position.
once we have this established, it is sure that the first and the last position cannot have mirrored beads in any permutation. and therefore rotational or reflectional permutations are impossible.
in other words, half of the possible permutations would be rotations/reflections, and we need to eliminate them.
so, the calculation is
4×7×6×5×4 = 8×7×6×5×4/2 = 6,720/2 = 3,360
Answer:
Part A: y = $250 + $45x
Part B: U = y * 0.75 or U = ($250 + $45x) * 0.75
Part C: $390
Step-by-step explanation:
Part A: In this scenario, we have fixed costs for the treatment and two variables, one of which is the number of appointments which is represented by the letter x and the total amount of costs which is represented by the letter y in the following equation...
y = $250 + $45x
Part B: Now we have the equation for the total cost we can update it to add the 25% discount. Since this is a discount it means that it is being subtracted from the 100% original price. Therefore, we need to multiply the total cost by the decimal form of 75% (100 - 25) which we can get by dividing the percentage by 100 like, which gives us 0.75. Now we multiply this value by the total cost in order to get the updated cost (U).
U = y * 0.75 or U = ($250 + $45x) * 0.75
Part C: Now we can substitute the number of appointments variable (x) by 6 and solve for U.
U = ($250 + $45x) * 0.75
U = ($250 + $45(6)) * 0.75
U = ($250 + $270) * 0.75
U = $520 * 0.75
U = $390