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3 years ago

What is the 23rd term of the arithmetic sequence where a1 = 8 and a9 = 48?

Mathematics

1 answer:

joja [24]3 years ago

4 0

Answer:

23rd term of the arithmetic sequence is 118.

Step-by-step explanation:

In this question we have been given first term a1 = 8 and 9th term a9 = 48

we have to find the 23rd term of this arithmetic sequence.

Since in an arithmetic sequence

$T_{n}=a+(n-1)d$

here a = first term

n = number of term

d = common difference

since 9th term a9 = 48

48 = 8 + (9-1)d

8d = 48 - 8 = 40

d = 40/8 = 5

Now $T_{23}= a + (n-1)d$

= 8 + (23 -1)5 = 8 + 22×5 = 8 + 110 = 118

Therefore 23rd term of the sequence is 118.

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Write the expression in WORDS!<br><br> 5x + 3

Svet_ta [14]

The expression 5x+3 would be three more than five times a number! More than in this case would be addition - so if you get the same problem with subtraction you just change more to less!
Basically what it's tell you is that if x stood for 2 in this case 5*2 = 10 since it's 3 MORE than 5 times a number (x is in place of a number), you're adding 3 to 10 and that gives you 13!
I hope I simplified it a little more and you understand!
Good luck, rockstar! c: I hope this helped!

8 0

3 years ago

The area of<br>of a rectangle is (14x^4 + 7x^2) cm²<br>and its breadth is 7x^2 cm. Find its length.

NeTakaya

Answer:

2x^1+1

Step-by-step explanation:

Area=L X W

which means that (14x^4+7x^2) needs to be divided by 7x^2

factorise(14x^4+7x^2) which gives 7x(2x^2+1)

divide 7x(2x^2+1) by 7x^2

gives 2x^2 +1

7 0

3 years ago

Read 2 more answers

Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targete

icang [17]

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

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

In which:

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.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

In this question:

Fleet of 17 means that $N = 17$

4 are carrying nucleas weapons, which means that $k = 4$

9 are destroyed, which means that $n = 9$

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

$P(X > 1) = 1 - P(X \leq 1)$

In which

$P(X \leq 1) = P(X = 0) + P(X = 1)$

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

$P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294$

$P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412$

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588$

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

8 0

3 years ago

jess has $22 and saves $5 each week rosie has $10 and saves $8 each week how many weeks till they have the same amount of money

Lemur [1.5K]

Answer: 5 weeks

Explanation:
Jess starts with $22 and saves $5 per week, Rosie has $10 and saves $8 per week.

In order to find an equal amount of money between the two girls is by finding a common denominator.

Jess- 22, 27, 32, 37, 42
Rosie- 10, 18, 26, 34, 42

Since we found that they can both end up with $42, after a certain amount of weeks have passed, now you’ll want to count how many numbers are in each row to find the amount of weeks it took to get to an equal amount

4 0

3 years ago

How many quarts of pure antifreeze must be added to 5 quarts of a 40% antifreeze solution to obtain a 50% antifreeze solution

GarryVolchara [31]

Answer:

2 quarts of 100% antifreeze.

Step-by-step explanation:

5 quarts/ .40 * x/ 1

.40x= 5

x=2

6 0

3 years ago