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3 years ago

Explain how a product of two Powers with the same base simplifies

Mathematics

2 answers:

defon3 years ago

7 0

Answer:

Add the powers.

Step-by-step explanation:

Let's say that we have:

$3^2*3^3$

The "Product Rule" of exponents states that if you are multiplying powers that have the base, then you would have to add the powers.

$a^n*a^m=a^{n+m}$

So, to solve the expression we have to apply the rule:

$3^2*3^3\\\text{Apply Product Rule: } a^n*a^m=a^{n+m}\\\rightarrow 2+3=5\\\boxed{3^2*3^3=3^5}$

Hope this helps.

lions [1.4K]3 years ago

5 0

Answer:

a^(b(c))

Step-by-step explanation:

(a^b)^c

a^(b(c))

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Which of the following describes the probability distribution below?

Verdich [7]

Answer: A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.

It is clear that most of the data (around 75%) is consist of value 1, which is the leftmost part of the data. Since it was more than 50% of the data, the median should be 1.

if 75% data is 1, it need 25% data with value at least 5 to make the means equal to 2. The means would be bigger than 1 but less than 2, so most(75% data is 1) of the data would be on the left of the mean

8 0

3 years ago

Read 2 more answers

School is making digital backups of old reels of film in its library archives the table shown approximate run Times of the films

Gemiola [76]

One technique that you can apply when solving such a problem is trial and error. We try to use each equation to prove that a given value of x on the table given will correspond to the value of y on the table.

a) Let's try to put x = 3 for the first equation and we must get an answer equal to 2.25.

$y=7.72(3)-29.02=-5.86_{}$

Since the value of y is not equal to 2.25 and the deviation is too large. this equation is not a good model,

b) We put x = 3 on the second equation and solve for y

$y=-7.52(3)^2+0.19(3)+3.26=-63.85$

Since the value of y is not equal to 2.25 and the deviation is too large. this equation is not a good model,

c) We put x = 3 on the third equation and solve for y,

$y=0.4(3)^2+0.79(3)-4.93=1.04$

Again, the value that we get is not equal to 2.25, hence, this equation is not a good model. But since its value is close to 2.25, we try to other values of x. If x = 5, we get

$y=0.4(5)^2+0.79(5)-4.93=9.02$

which has a slight deviation on the given value of y on the table for x = 5. let's try for x = 7. We have

$y=0.4(7)^2+0.79(7)-4.93=20.2$

and the answer has a small deviation compared to the actual value given. The other values of x can again be put on the equation and check their corresponding value of y, and the resulting values are as follows

$\begin{gathered} y=0.4(8)^2+0.79(8)-4.93=26.99 \\ y=0.4(12)^2+0.79(12)-4.93=62.15 \\ y=0.4(14)^2+0.79(14)-4.93=84.53 \end{gathered}$

And as you can see, the deviation of values from the table to calculated becomes smaller. Hence, this is the best model.

d) We put x = 3 on the third equation and solve for y,

$y=4.19(1.02)^3=4.45_{}_{}$

Again, the value that we get is not equal to 2.25, hence, this equation is not a good model. But since its value is close to 2.25, we try to other values of x. If x = 5, we get

$y=4.19(1.02)^5=4.63$

where the answer's deviation is too large compared to the value of y if x = 5 on the table given.

Based on the calculations used above, the best equation that can be a good model is equation 3.

5 0

1 year ago

The length of triangle base is 26. A line, which is parallel to the base divides the triangle into two equal area parts. Find th

Yanka [14]

Answer:

Step-by-step explanation:

It is given that the length of triangle base is 26, then let ABC be the triangle and BC be the base of the triangle=26.Let DE be the parallel line to the base that divides triangle ABC into two equal area parts.

Now, Let AD=a, DB=b, DE=c, AE=d and EC=e, then

Since, triangle ABC is similar to triangle ADE, thus using basic proportions, we get

$\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}$