Answer:
Option A. 52°
Step-by-step explanation:
From the figure attached,
JEFH is a parallelogram and ΔFGH is a scalene right triangle.
If m∠JEF = 142°
m∠JHF = 142° [Since opposite angles of the parallelogram are equal]
m∠FHG + m∠JHF = 180°
m∠FHG + 142° = 180°
m∠FHG = 180 - 142
= 38°
In the given scalene right triangle FGH,
m∠FHG + m∠HFG + m∠HGF = 180°
38° + m∠HFG + 90° = 180°
m∠HFG = 180° - 128°
m∠HFG = 52°
Option A. will be the answer.
Answer:
The amount Dave got after 3 wins and 2 loose is $843.75. The order of win and loose doesn't matter.
Step-by-step explanation:
- We are given with a word problem
- We are asked to find the amount he had after 5 hands
- We can do this in two steps
Step 1 : Identifying the percentages
Step 2 : Finding the amount left
Step 1 of 2
We are given with a word problem. He bets 50% of his money. If he wins he get his bet, if he loose he will loose the money too. If he wins he will get the money as 150%.
That is, 1.5
If he loose he will loose money by 50%
That is, 0.50
Step 2 of 2
The amount got after 5 hands with 3 wins and 2 loose is,
![$$\begin{gathered}1000 \times(1.5)^{3} \times(0.5)^{2}=1000 \times 3.375 \times 0.25 \\1000 \times 0.84375=843.75\end{gathered}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Bgathered%7D1000%20%5Ctimes%281.5%29%5E%7B3%7D%20%5Ctimes%280.5%29%5E%7B2%7D%3D1000%20%5Ctimes%203.375%20%5Ctimes%200.25%20%5C%5C1000%20%5Ctimes%200.84375%3D843.75%5Cend%7Bgathered%7D%24%24)
Answer:
The slope is 4/5
Step-by-step explanation:
The line goes over the point (5,6) so we can use that to help us find the slope. Since slope is rise/run, the rise would be 4 and the run would be 5. Thus the slope is 4/5
Given:
In an arithmetic sequence,
![a_1=2](https://tex.z-dn.net/?f=a_1%3D2)
![a_i=a_{i-1}-3](https://tex.z-dn.net/?f=a_i%3Da_%7Bi-1%7D-3)
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
...(i)
Where, d is the common difference.
We have,
...(ii)
On comparing (i) and (ii), we get
![d=-3](https://tex.z-dn.net/?f=d%3D-3)
The sum of first i terms of an arithmetic sequence is:
![S_i=\dfrac{i}{2}[2a+(i-1)d]](https://tex.z-dn.net/?f=S_i%3D%5Cdfrac%7Bi%7D%7B2%7D%5B2a%2B%28i-1%29d%5D)
Putting
, we get
![S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B2%282%29%2B%28335-1%29%28-3%29%5D)
![S_{335}=\dfrac{335}{2}[4+(334)(-3)]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B4%2B%28334%29%28-3%29%5D)
![S_{335}=\dfrac{335}{2}[4-1002]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B4-1002%5D)
![S_{335}=\dfrac{335}{2}(-998)](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%28-998%29)
On further simplification, we get
![S_{335}=335\times (-499)](https://tex.z-dn.net/?f=S_%7B335%7D%3D335%5Ctimes%20%28-499%29)
![S_{335}=-167165](https://tex.z-dn.net/?f=S_%7B335%7D%3D-167165)
Therefore, the sum of the first 335 terms in the given sequence is -167165.
I am assuming you meant "Roll a sum of 10".
First find all the combinations:
1st dice 2nd dice
4 + 6
5 + 5
6 + 4
Next, calculate the probability of rolling a 4,5, or 6: 3/6 => 1/2 on first dice
Then, calculate the probability of rolling a number on the second dice that adds up with the first number to make 10.
Note: once you roll the first number only 1 other number will make a match, so the probability on the second dice is: 1/6 on second dice
Finally, multiply the two fractions together: 1/2 x 1/6 = 1/12
Your probability is: 1/12 in fraction form, .083 in decimal form, and 8.33% in percent form.
Hope this helps and May the Force Be With You!
-Jabba