Which expression is the least absolute value?<br> |0|<br> |12|<br> |13|<br> |-12|

If you roll a 6-sided die 4 times, what is the probability of one roll being a multiple of 3? A)2/3 B)16/81 C)145/1296 D)65/81 E

DerKrebs [107]

Answer:

671/1296

The probability of rolling at least one six is therefore 1 − 625/1296 = 671/1296 ≈ . 517.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Simplify (-2x^4y^-3)^4

elixir [45]

Answer:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = \frac{16 {x}^{16}}{ {y}^{12} }$

Step-by-step explanation:

We want to simplify:

$( - 2 {x}^{4} {y}^{ - 3} )^{4}$

We need to apply the exponential property for products of powers.

Recall that:

$( {a}^{m} \times {a}^{n} )^{p} = {a}^{mp} \times {a}^{np}$

We apply this rule to get:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = ( { - 2)}^{4} x \times {x}^{16} \times {y}^{ - 12}$

This simplifies to:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = 16 {x}^{16} \times {y}^{ - 12}$

We rewrite as positive index to get:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = \frac{16 {x}^{16}}{ {y}^{12} }$

7 0

4 years ago

Find the exact value of cos(sin^-1(-5/13))

son4ous [18]

bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

$\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}$

$\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}$

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

8 0

3 years ago

Find the number, d, if the sum of five times d and five times five is a<br> hundred.

Gelneren [198K]

The value of d from the given expression is 15

<h3>Word problem leading to equation</h3>

From the given statement the sum of five times d and five times five is a

hundred is interpreted as;

5d + 5(5) = 100

5d + 25 = 100

Subtract 25 from both sides

5d = 100 - 25

5d = 75

d =15

Hence the value of d from the given expression is 15

Learn more on word problem here: brainly.com/question/13818690

#SPJ1

6 0

2 years ago

4. A number m is such that when it is divided by 30, 36, and 45 the remainder is always 7,

Bezzdna [24]

Answer:

187

Step-by-step explanation:

A number m is such that when it is divided by 30, 36 and 45 the remainder is always 7.

We should first find the LCM of 30, 36 and 45

We get that the LCM of the three numbers is 280 (working attached).

So now;

$\frac{180}{30}$ = 6

$\frac{180}{36}$ = 5

$\frac{180}{45}$ = 4

But we need a number that leaves a remainder of 7 so we add 7 to 180 to get; 180 + 7 = 187.

5 0

4 years ago

Which expression is the least absolute value? |0| |12| |13| |-12|