Giving 30 points to the right person

Which of the following shows the correct work and solution to the exponential equation 5x - 1=25

olga_2 [115]

We have the expression:

$5^{x-1}=25$

And we need to solve this for x.

Let's solve this expression and then see which of the options is the correct one.

The first step to solve this is that we need for the two sides of the equation to have the same base. (the number 5 on the left side is the base, so we need to also have a 5 as the base on the right side).

We do this by noting that:

$25=5^2$

We know that 25 is equal to 5 squared (because 5x5 is 25)

So the first step is to substitute 25 for 5 squared:

$5^{x-1}=5^2$

Since we have the same base on both sides (5), we follow the rule:

• If we have the same base on both sides of an equation, the exponents have to be equal

Thus, the second step to solve is to equal the exponents:

$x-1=2$

Finally, to solve this equation for x, we just need to add 1 to both sides to get rid of the -1 on the left side:

$\begin{gathered} x-1+1=x=2+1 \\ \end{gathered}$

And the third step is:

$x=3$

As we can see, these three steps are represented in the third option In which we get the same result of x=3.

Answer: x=3

8 0

1 year ago

There are 9 students in a class: 2 boys and 7 girls. If the teacher picks a group of 4 at random, what is the probability that e

notsponge [240]

Answer:

<h2>28% probability that every student in the group is a girl.</h2>

Step-by-step explanation:

In this problem we have independent events, that is, the event "picking a girl" doesn't affect an "picking a boy", also, picking picking a girl doesn't affect the probability of the other subjects.

So, the probability when the first girl is being picked is:

$P_{1}=\frac{7 \ girls}{9 \ students}$

Because among the total 9 students, there are 7 girls.

Now, after picking one girl, there remains 6 girls and 8 students to be picked. So, the probability of the second girl would be:

$P_{2}=\frac{6 \ girls}{8 \ students}$

Then, the probability of the third girl:

$P_{3}=\frac{5 \ girls}{7 \ students}$

The fourth girl probability:

$P_{3}=\frac{4 \ girls}{6 \ students}$

Therefore, the probability of picking all 4 girls would be the product of each probability, because events are independent (we use product when they are independent):

$P=\frac{7 \ girls}{9 \ students} \times \frac{6 \ girls}{8 \ students} \times \frac{5 \ girls}{7 \ students} \times \frac{4 \ girls}{6 \ students}\\P=\frac{5}{18}=0.28 \ (or \ 28\%)$