Which sum does the model below represent?

What is the simplified value of the exponential expression 27}? оооо 3 9 1/3 1/9

iVinArrow [24]

Note: Your exponential expression seems a little unclear. Because 27 is not an exponential expression.

But, I am assuming that your exponential expression is:

$\:27^{\frac{1}{3}}$

The reason is that my solution would still clear your concept about this topic, no matter what the question is.

Answer:

The simplified value of the exponential expression is:

$27^{\frac{1}{3}}=3$

Step-by-step explanation:

Assuming the exponential expression

$\:27^{\frac{1}{3}}$

$\mathrm{Factor\:the\:number:\:}\:27=3^3$

$=\left(3^3\right)^{\frac{1}{3}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0$

$\left(3^3\right)^{\frac{1}{3}}=3^{3\cdot \frac{1}{3}}$

$=3^{3\cdot \frac{1}{3}}$

$=3^1$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a$

$=3$

Therefore, the simplified value of the exponential expression is:

$27^{\frac{1}{3}}=3$

4 0

3 years ago

Please help!!!!!!!!!!

Lena [83]

Answer:

30 ways

Step-by-step explanation:

10 x 3 = 30

7 0

3 years ago

A regular 6-sided die is tossed 5 times what is the probability that in two of those tosses we get a number less than 3

kipiarov [429]

In probability and statistics, there is an equation used for repeated trials. In this equation, you find the probability of getting 'r' successful events out of 'n' trials. Moreover, you should incorporate the probability of the success per trial. For a 6-sided face, each side has a probability of success of 1/6. On the other hand, the probability of each side not appearing is 5/6, because when you add these two, it would sum up to 1 as always.

Now, the equation for repeated trials is:

Total Probability = n!/r!(n-r)! * p^(n-r) * q^r

where
n = 5 tosses
r = 1 and 2 (since you want to see the probability of a side less than 3)
p = 1/6
q = 5/6

So, you add the individual probability when r=1, and when r=2.

Total Probability = 5!/1!(5-1)! * (1/6)^(5-1) * (5/6)^1 + 5!/2!(5-2)! * (1/6)^(5-2) * (5/6)^2
Total Probability = 50/243 or 20.58%

7 0

3 years ago

Find the domain and range of f(x). Please explain your answer. f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

4 0

2 years ago

Find the unit rate: 297 words in 5.5 minutes

MArishka [77]

Answer:

54 words per minute

Step-by-step explanation:

the ratio of 297:5.5 is equivalent to 54:1

7 0

3 years ago