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3 years ago

Determine whether each sequence is arithmetic or geometric. sequence 1: 32, 16, 0, –16, ... sequence 2: 32, 16, 8, 4, ...

1 answer:

6 0

S1.
32, 16, 0, -16, ...
It's an arithmetic sequence:

$a_1=32;\ d=16-32=-16\\\\a_n=a_1+(n-1)d\\\\a_n=32+(n-1)\cdot(-16)=32-16n+16=48-16n$

S2.
32, 16, 8, 4, ...
It's a geometric sequence:

$a_1=32;\ r=16:32=\dfrac{1}{2}\\\\a_n=a_1r^{n-1}\\\\a_n=32\cdot\left(\dfrac{1}{2}\right)^{n-1}$

Answer: <span>sequence 1 is arithmetic and sequence 2 is geometric.</span>

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Solve the literal equation for x. s=2r+3x

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3 years ago

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The number of flaws per square yard in a type of carpet material varies with mean 1.4 flaws per square yard and standard deviati

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According to the Central Limit Theorem, the distribution of the sample means is approximately normal, with the mean equal to the population mean (1.4 flaws per square yard) and standard deviation given by:
$\frac{\sigma}{ \sqrt{n} }=\frac{1.2}{ \sqrt{178} }=0.09$
The z-score for 1.5 flaws per square yard is:
$z=\frac{1.5-1.4}{0.09}=1.11$
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3 years ago

ANYONE PLZZZ THIS IS DUE IN AN HOUR. Will mark the brainliest

aleksley [76]

Answer:

0.96 in^3

Step-by-step explanation:

Are those the only three choices? Anyway, I hope this helps

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3 years ago

In a baseball tournament, teams get 5 points for a win, 3 points for a tie and 1 point for a loss Nathan’s team has 29 points ho

puteri [66]

Answer:

37 different combinations

Step-by-step explanation:

First of all, we will count the possible combinations that add up to 29.

-Losses only;

One possibility: 29 losses

-Ties & losses;

Nine possibilities: 1 tie and 26 losses; 2 ties and 23 losses; 3 ties and 20 losses;4 ties and 17 losses; 5 ties and 14 losses; 6 ties and 11 losses; 7 ties and 8 losses; 8 ties and 5 losses; 9 ties and 2 losses

-Wins & losses

Five possibilities: 1 win and 24 losses; 2 wins and 19 losses; 3 wins and 14 losses; 4 wins and 9 losses; 5 wins and 4 losses

Now, what we want to find from the question is number of possibilities for wins, ties, and losses all together. So, we will count up the ties and losses in the remainder for each case of a given number of wins.

Thus;

For 0 Wins: 0 ties and 29 losses; 1 tie and 26 losses; 2 ties and 23 losses; 3 ties and 20 losses;4 ties and 17 losses; 5 ties and 14 losses; 6 ties and 11 losses; 7 ties and 8 losses; 8 ties and 5 losses; 9 ties and 2 losses.

Which sums up to 10 possibilities

For 1 win; 0 ties and 24 losses; 1 tie and 21 losses........8 ties and 0 losses.

Which sums up to 9 possibilities

For 2 wins; 0 ties and 19 losses; 1 tie & 16 losses............ 6 ties and 1 loss.

Which sums up to 7 possibilities

For 3 wins; 0 ties and 14 losses; 1 tie and 11 losses ....... 4 ties and 2 losses.

Which sums up to 5 possibilities

For 4 wins; 0 ties & 9 losses; 1 tie and 6 losses....... 3 ties and 0 losses

Which sums up to 4 possibilities

For 5 wins; 0 ties and 4 losses; 1 tie and 1 loss

Which sums up to 2 possibilities

Thus;

Total number of possibilities of combinations of wins, ties and losses = 10 + 9 + 7 + 5 + 4 + 2 = 37

8 0

3 years ago

If Jefferson is drawing cards from a deck, and draws a 4 of hearts and a 10 of diamonds, what is this situation considered?

katrin2010 [14]

<h3>Answer: A) Outcome</h3>

==========================================================

Explanation:

We can rule out "theoretical probability" since that concept deals with doing the math on paper, rather than getting out an actual deck of cards to compute the probability. If your teacher stated "the probability of drawing an ace is 1/13", then s/he would be using theoretical probability. We have a 1 in 13 chance to theoretically pick an ace out of all 52 cards since 4/52 = 1/13. No cards are needed to do such calculations. But if you actually pull out a deck of cards and randomly select them, then you'd be leaning toward empirical or experimental probability.

So in short, we can rule out choice B.

We can also rule out "complement" since the two situations of "drawing a 4" and "drawing a 10" aren't opposite. If it said something like "drawing a red card or drawing a black card", then those two events are opposite. The two events fully compose all the deck of cards (sample space). You either will draw a red one, or a black one, but not both colors at the same time.

So we're down to the answer being either A) outcome or D) event. At first glance, these two terms seem almost identical. However, they mean slightly different things.

Let's pick apart what each of those terms mean.

----------------

The outcome is the result of an event. An event is some specific action that you may or may not want to happen, and it's usually phrased within the parameters your teacher set up.

For example, we can define the event "it rains outside". So we're setting up the specific action of raining. Whether we want it or not doesn't really matter. The outcome would be the actual result of if the event happens or not. So if it does truly rain on day 1, then the outcome "rain" is what is recorded for day 1. Then if its dry on day 2, then "no rain" is the outcome for that second day. And so on.

Going back to the cards, one event could be set up as "selecting a heart card" with the outcome being "selected a 4 of hearts". The event is the rule set up and the outcome is the result we observe. To compute the empirical or experimental probability, we divide the number of times we get a specific event to occur over the total number of possible

---------------

Let's look at another example.

We'll roll a single die that has 6 faces on it. The set of possible outcomes are {1,2,3,4,5,6}. Only one outcome is possible per roll.

If we roll the die and it lands on 5, then the outcome is 5. This is the final result of the trial or experiment.

We can define an event like "A = rolling an even number", and then ask the question "what is the probability event A occurs?" In other words, we would be asking "what is the probability of rolling an even number?"

---------------

I suppose now that I think about it, we can state,

outcome = some single action you observe
event = collection of outcomes (usually some pattern to it)

as a loose way of telling the difference between the two terms.

Ultimately, the observations of getting a 4 of hearts and 10 of diamonds are considered an outcome.

4 0

3 years ago