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zheka24 [161]
2 years ago
9

* The nth term of sequence A is 3n − 2 The nth term of sequence B is 10 − 2n Sally says there is only one number that is in both

sequence A and sequence B. Is Sally right? You must explain your answer.
Mathematics
1 answer:
Nina [5.8K]2 years ago
7 0

Answer:

Sally is not right

Step-by-step explanation:

Given the two sequences which have their respective n^{th} terms as following:

Sequence A. 3n - 2

Sequence B. 10 - 2n

As per Sally, there exists only one number which is in both the sequences.

To find:

Whether Sally is correct or not.

Solution:

For Sally to be correct, we need to put the n^{th} terms of the respective sequences as equal and let us verify that.

3n-2=10-2n\\\Rightarrow 3n+2n=10+2\\\Rightarrow 5n=12\\\Rightarrow n = \dfrac{12}{5}

When we talk about n^{th} terms, n here is a whole number not a fractional number.

But as per the statement as stated by Sally n is a fractional number, only then the two sequences can have a number which is in the both sequences.

Therefore, no number can be in both the sequences A and B.

Hence, Sally is not right.

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Acar can travel 25 miles per gallon. Approximately how many gallons of fuel will the car need to travel 30
FrozenT [24]

Answer:

The gallons of fuel car need to travel 30 km is <u>0.75</u> approximately .

Step-by-step explanation:

Given:

The car can travel 25 miles per gallon. (1 mile = 1.6 km)

Now, we need to convert 25 miles into km .

25 miles = 25 × 1.6 km

              = 40 km

So, the car can travel 40 km per gallon.

Then, we find out in 1 km how many gallons are used:

40 km = 1 gallons

1\ km = \frac{1}{40}\ gallons

1\ km = 0.025\ gallons

Now, we find out how much gallons of fuel will the car need to travel 30 km:

Gallons of fuel the car need to travel 30 km = 30\times 0.025

                                                                         = 0.75 gallons.

Therefore, the gallons of fuel car need to travel 30 km is 0.75 approximately.

6 0
3 years ago
Find the value of y​
bulgar [2K]

Answer:

m\angle y=48^o

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc comprising

so

m\angle y=\frac{1}{2}[96^o]

m\angle y=48^o

6 0
2 years ago
4. In the spinner below, the pointer stopped on the blank region. What color should the blank region be so
Tju [1.3M]
Red because there are more reds
4 0
3 years ago
There is a bag filled with 3 blue and 4 red marbles.
tresset_1 [31]

Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.

The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • N is the size of the population.
  • n is the size of the sample.
  • k is the total number of desired outcomes.

In this problem:

  • There is a total of 3 + 4 = 7 marbles, hence N = 7.
  • Of those, 3 are blue, hence k = 3.
  • 2 marbles will be taken, hence n = 2.

The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,7,2,3) = \frac{C_{3,0}C_{4,2}}{C_{7,2}} = 0.2857

P(X = 2) = h(2,7,2,3) = \frac{C_{3,2}C_{4,0}}{C_{7,2}} = 0.1429

Hence:

p = P(X = 0) + P(X = 2) = 0.2857 + 0.1429 = 0.4286

0.4286 = 42.86% probability of getting 2 of the same colour.

You can learn more about the hypergeometric distribution at brainly.com/question/4818951

3 0
2 years ago
Aaron gets paid $152.80 for 8<br> hours of work. How much does he<br> make per hour?
lubasha [3.4K]

Answer: Aaron gets paid $19.10 per hour.

When you divide 152.80 by 8, you get 19.1 simplified. But in this case, it is in money so you need to put a 0 at the end.

3 0
2 years ago
Read 2 more answers
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