Let the five terms be: a, a + d, a + 2d, a + 3d, a + 4d, then
a + a + d + a + 2d + a + 3d + a + 4d = 5a + 15d = 40
i.e. a + 3d = 8
Also, (a + 2d)(a + 3d)(a + 4d) = 224
(a + 3d - d)(a + 3d)(a + 3d + d) = 224
(8 - d)(8)(8 + d) = 224
(8 - d)(8 + d) = 224/8 = 28
64 - d^2 = 28
d^2 = 64 - 28 = 36
d = sqrt(36) = 6
But a + 3d = 8
a + 3(6) = 8
a = 8 - 18 = -10
Therefore, the term of the sequence is: -10, -10 + 6, -10 + 2(6), -10 + 3(6), -10 + 4(6)
= -10, -4, -10 + 12, -10 + 18, -10 + 24
= -10, -4, 2, 8, 14
hi so for the first exercise it’s the 3rd and for the second exercise it’s the first
Step-by-step When you have to find the inverses of numbers the sign ( -or+ ) never change see: the inverse of 2 is 1/2 or the inverse of (x+7)/(3x-5) is (3x-5)(x+7), hope you’ll understand : )
<u>Construct potential hypotheses</u><u> or research questions to relate the </u><u>variables </u><u>in each of the following examples - </u>
<u>Political party and support of the affordable care act -</u>
- Given this, there can be a relationship between the ideological group and the support of the moderate consideration act.
- that various ideological groups may support various types of government disability conspiracies and might have various goals.
- A few gatherings might focus on a list of topics or problems and might provide serious thought at some random time.
- which might facilitate the implementation of the Affordable Care Act, while others would be gradually forgiving toward such arrangements.
- The implementation and success of the Affordable Care Act may depend on the rise of certain ideological movements.
and their ability to express what they think about the Act's purpose.
Learn more about hypotheses
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The experimental probability is 1/6, and the theoretical probability is 1/4. The theoretical probability is greater than the experimental probability in this trial.-------------------Explanation:
Theoretical probability is the mathematically calculated probability of the circumstances occurring.
There is a 1/2 chance of rolling an even number, and a 1/2 chance of flipping a coin on heads.
Since the question asks for the possibility of both happening, multiply those together to find the probability:
The theoretical probability of rolling an even number and then flipping a head is 1/4.
Now we'll focus on Taka's trials.
Experimental probability is the probability that is taken from results of a trial.
Take the results, and see if they match the criteria of rolling an even number and flipping heads.
The results that are bolded fit the criteria:1 H, 4 T, 1 H, 5 T, 2 H, 3 T, 6 T, 2 H, 3 T, 5 T, 3 H, 4 T
Taka managed to roll and flip the coin to fit the criteria 2 times out of 12. Converted into a fraction, it is 2/12. Simplified, the experimental probability is 1/6
Answer:
66%
Step-by-step explanation:
- First, add 20 + 10 = 30. This will give you the total amount of games.
- Now, make this into a fraction for won games. This should be 20/30.
- Next, take 20/30 and simplify it. You should get 2/3 as a fraction.
- Now, take 2 and divide by 3. (2/3) You should get .66 repeating. This is equal to 66%.
- Therefore 66% is the answer.
- Hope this helps! If you need a further explanation please let me know.
