Can anyone help me please I’m struggling and I don’t know the answer?

2. Find the 20th term of an arithmetic sequence if its 6th term is 14 and 14th term is 6.

Fudgin [204]

Answer:

$\sf t_{20}= 0$

Step-by-step explanation:

<h3>Arithmetic sequence:</h3>

$\sf \boxed{\bf n^{th} \ term = a + (n-1)d}\\\\\text{Here, a is the first term ; d is the common difference }$

6th term is 14 ⇒ $\sf t_6 = 14$

a + (6 - 1)d = 14

a + 5d = 14 --------------(I)

14th term is 6 ⇒ $\sf t_{14} = 6$

a + (14-1)d = 6

a + 13d = 6 ----------------(II)

Subtract equation (II) from equation(I)

(I) a + 5d = 14

(II) a + 13d = 6

-8d = 8

d = 8 ÷(-8)

$\sf \boxed{\bf d= (-1)}$

Plugin d = -1 in equation (I)

a + 5(-1) = 14

a -5 = 14

a = 14 + 5

$\sf \boxed{\bf a = 19}$

20th term:

$\sf t_{20}= 19 + 19*(-1)$

= 19 - 19

$\sf \boxed{\bf t_{20} = 0}$

8 0

1 year ago

Read 2 more answers

Which algebraic expression represent the verbal expression "5 less than a number"?

andriy [413]

Answer: n - 5

Step-by-step explanation:

8 0

3 years ago

Find the value of x in the isosceles triangle shown below.

Reptile [31]

Answer:

x=10

Step-by-step explanation:

We can use the Pythagorean theorem to find x

The height meets the base at a right angle

The base is bisected ( cut in half) so the base is 6 the height is 8

a^2 + b^2 = c^2

6^2 + 8^2 = x^2

36+64 = x^2

100 = x^2

Taking the square root of each side

sqrt(100) = sqrt(x^2)

10 = x

4 0

2 years ago

Read 2 more answers

In a list of households, own homes and do not own homes. Five households are randomly selected from these households. Find the p

hichkok12 [17]

Answer:

The probability of success for this case would be:

$p =\frac{9}{15}= 0.6$ representing the proportion of homes that are own homes

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=15, p=0.6)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

And we want this probability:

$P(X=3)$

And uing the probability mass function we got:

$P(X=3)= 15C3 (0.6)^3 (1-0.6)^{15-3}= 0.00165$

Step-by-step explanation:

Adduming the following info: In a list of 15 households, 9 own homes and 6 do not own homes. Five households are randomly selected from these 15 households. Find the probability that the number of households in these 5 own homes is exactly 3.

Round your answer to four decimal places

P (exactly 3)=

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

The probability of success for this case would be:

$p =\frac{9}{15}= 0.6$ representing the proportion of homes that are own homes

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=15, p=0.6)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

And we want this probability:

$P(X=3)$

And uing the probability mass function we got:

$P(X=3)= 15C3 (0.6)^3 (1-0.6)^{15-3}= 0.00165$

4 0

3 years ago

Please please please help.

saul85 [17]

Answer:

Step-by-step explanation:

(-5,-3) is a point on the graph.

f⁻¹(-3) = -5

7 0

3 years ago