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2 years ago

Evaluate the expression. Write your answer as a fraction in simplest form. Thank you so much!

Mathematics

1 answer:

ziro4ka [17]2 years ago

7 0

Answer:

$\frac{1}{27}$

Step-by-step explanation:

Using the rule of exponents

$\frac{a^{m} }{a^{n} }$ with n > m

= $\frac{1}{a^{(n-m)} }$ , thus

$\frac{3^{5} }{3^{8} }$ = $\frac{1}{3^{(8-5)} }$ = $\frac{1}{3^{3} }$ = $\frac{1}{27}$

You might be interested in

Use the discriminant to determine the number of solutions to the quadratic equation 3x^2+5x=-1

kari74 [83]

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

Background of the Discriminant

The discriminant $b^2-4ac$ applies to quadratic equations when they are organised in standard form: $ax^2+bx+c=0$ .

All quadratic equations can be solved with the quadratic formula: $x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}$ .

When $b^2-4ac$ is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

Solving the Problem

$3x^2+5x=-1$

We're given the above equation. It hasn't been organised completely in $ax^2+bx+c=0$ , but we can change that by adding 1 to both sides to make the right side equal to 0:

$3x^2+5x+1=0$

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

$D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13$

Therefore, because the discriminant is positive, the equation has two real, distinct solutions.

I hope this helps!

4 0

2 years ago

What number would represent the outlier in the following set of data?

Rom4ik [11]

Answer:

What number would represent the outlier in the following set of data?

10, 13, 9, 29, 15, 11, 14, 8, 10, 11, 17, 14, 12

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A circle has a diameter of 100 cm. which of these is closest to its area? show or explain your reasoning

patriot [66]

Answer:31r

Step-by-step explanation:

Formula=πd

22/7 × 100

3.14 × 100

314 cm square

7 0

3 years ago

Make up two equations, one that is true and one that is false. do not state which equation is true and which is false.

Sophie [7]

3 + 6 = 9 - 1
4x3=36/3

4 0

3 years ago

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean

EastWind [94]

Using the normal distribution, it is found that 7.64% of of sample means are greater than 8.8 hours.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

The parameters are given as follows:

$\mu = 8.4, \sigma = 1.77, n = 40, s = \frac{1.77}{\sqrt{40}} = 0.2799$

The proportion of sample means greater than 8.8 hours is one subtracted by the p-value of Z when X = 8.8, hence:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.8 - 8.4}{0.2799}$

Z = 1.43

Z = 1.43 has a p-value of 0.9236.

1 - 0.9236 = 0.0764.

7.64% of of sample means are greater than 8.8 hours.

More can be learned about the normal distribution at brainly.com/question/25800303

#SPJ1

6 0

2 years ago