Is 4 a solution of 3x+8=4 ? complete the statement

Find the sum of the first six terms of a geometric progression .

Dominik [7]

Question:

Find the sum of the first six terms of a geometric progression.

1,3,9,....

Answer:

$S_6 = 364$

Step-by-step explanation:

For a geometric progression, the sum of n terms is:

$S_n = \frac{a(r^n - 1)}{r - 1}$

In the given sequence:

$a = 1$

$r = 3/1 =3$

$n = 6$

So:

$S_n = \frac{a(r^n - 1)}{r - 1}$

$S_6 = \frac{1 * (3^6 - 1)}{3 - 1}$

$S_6 = \frac{3^6 - 1}{2}$

$S_6 = \frac{728}{2}$

$S_6 = 364$

8 0

3 years ago

A track star runs two races on a certain day. The probability thathe wins the first race is 0.7, the probability that he wins th

NARA [144]

Answer:

a) 80% probability that he wins at least one race.

b) 30% probability that he wins exactly one race.

c) 20% probability that he wins neither race.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that he wins the first race.

B is the probability that he wins the second race.

C is the probability that he does not win any of these races.

We have that:

$A = a + (A \cap B)$

In which a is the probability that he wins the first race but not the second and $A \cap B$ is the probability that he wins both these races.

By the same logic, we have that:

$B = b + (A \cap B)$

The probability that he wins both races is 0.5.

This means that $A \cap B = 0.5$

The probability that he wins the second race is 0.6

This means that $B = 0.6$

$B = b + (A \cap B)$

$0.6 = b + 0.5$

$b = 0.1$

The probability that he wins the first race is 0.7.

This means that $A = 0.6$

$A = a + (A \cap B)$

$0.7 = a + 0.5$

$a = 0.2$

A) he wins at least one race.

This is

$P = a + b + (A \cap B) = 0.2 + 0.1 + 0.5 = 0.8$

There is an 80% probability that he wins at least one race.

B) he wins exactly one race.

This is

$P = a + b = 0.2 + 0.1 = 0.3$

There is a 30% probability that he wins exactly one race.

C) he wins neither race

Either he wins at least one race, or he wins neither. The sum of these probabilities is 100%.

From a), we have that there is an 80% probability that he wins at least one race.

So there is a 100-80 = 20% probability that he wins neither race.

6 0

3 years ago

The functions r and s are defined as follows. R(x)=x-1. And. S(x)=-x squared. Find the value of r(s(-2))

Iteru [2.4K]

Answer:

-5

Step-by-step explanation:

"r(s(-2))" is a composition of functions. To evaluate this, we need to plug in "-2" into the function S(x) and then take that value and further plug it into R(x).

First, s(-2):

$S(x)=-x^2\\S(-2)=-(-2)^2\\S(-2)=-4$

Now, we take the value (-4) and put it into R(x) to get our final answer:

$R(x)=x-1\\R(-4)=-4-1\\R(-4)=-5$

Hence, r(s(-2)) = -5

3 0

3 years ago

Solve the following pair of simultaneous: <img src="https://tex.z-dn.net/?f=%205x%20%2B%202y%20%3D%20%20-%202%20%20%20%20%20%

Vladimir [108]

Answer:

x = -2 , y = 4

Step-by-step explanation:

given:

5x + 2y = -2 *4

4x + 3y = 4 *5

Solving simultaneously,

20x + 8y = -8 ....eq 1

(-) 20x +15y = 20 ...eq 2

.............................................

-7y = -28

y = -28 / -7

y = 4

if y = 4

using equation 2,

20x +15(4) = 20

20x = -40

x = -2

8 0

3 years ago

Can someone please help me out

Oksi-84 [34.3K]

Answer:

A/ 0

B/ 6

C/

$3 {x}^{2} + 6x - 18$

D/ 77

E/ 33

8 0

3 years ago