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4 years ago

A regular die is rolled 60 times. What is a reasonable prediction for the number of times it will land on 5?

Mathematics

1 answer:

anyanavicka [17]4 years ago

4 0

Answer:

dice is rolled 60 times and it has a chance to land on a 5 10times due to 6 sides to the die

Step-by-step explanation:

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If cos⁡ x=−45, and 180° < x < 270°, what is tan⁡(2x)?

iVinArrow [24]

$Tan2x =\frac{-24}{7}$

Step-by-step explanation:

Here we have , cos x = -4/5 ( corrected as given -45 which is not possible ) ,

180° < x < 270° i.e. in third quadrant . We need to find tan⁡(2x) . Let's find out:

⇒ $Tan\alpha = \frac{sin\alpha }{cos\alpha }$

⇒ $Tan\alpha = \frac{\sqrt{1-(cos\alpha)^2} }{cos\alpha }$

⇒ $Tan\alpha = \frac{\sqrt{1-(\frac{-4}{5})^2} }{\frac{-4}{5} }$

⇒ $Tan\alpha = \frac{-5}{4}\sqrt{1-(\frac{16}{25}) }$

⇒ $Tan\alpha = \frac{-5}{4}\sqrt{(\frac{25-16}{25}) }$

⇒ $Tan\alpha = \frac{-5}{4}(\frac{3}{5}) }$

⇒ $Tan\alpha = \frac{-3}{4}$ , since in third quadrant . $Tan\alpha = \frac{-3}{4}$ remains same .

Now , $Tan2x = \frac{2tanx}{1-(tanx)^{2}}}$

⇒ $Tan2x = \frac{2tanx}{1-(tanx)^{2}}}$

⇒ $Tan2x = \frac{2(\frac{-3}{4})}{1-(\frac{-3}{4})^{2}}}$

⇒ $Tan2x = \frac{-3}{2}(\frac{16}{7})$

⇒ $Tan2x =\frac{-24}{7}$

Therefore, $Tan2x =\frac{-24}{7}$ .

5 0

4 years ago

Find the slope: x y 13 10 15 17

Dimas [21]

Answer:

Step-by-step explanation:

17_10

15_13

2. =3.5

7 0

3 years ago

The function rule of 8 less than one third of x is y

choli [55]

This should be it y=(x/3)−8

Hope this helped

4 0

3 years ago

A quadrilateral has vertices at A (-5, 5), B (1, 8), C (4, 2), and D (-2, -2). Use slope to determine if the quadrilateral is a

gladu [14]

Answer:

not a rectangle

Step-by-step explanation:

There are several ways to determine whether the quadrilateral is a rectangle. Computing slope is one of the more time-consuming. We can already learn that the figure is not a rectangle by seeing if the midpoint of AC is the same as that of BD. (It is not.) A+C = (-5+4, 5+2) = (-1, 7). B+D = (1-2, 8-2) = (-1, 6). (A+C)/2 ≠ (B+D)/2, so the midpoints of the diagonals are different points.

___

The slope of AB is ∆y/∆x, where the ∆y is the change in y-coordinates, and ∆x is the change in x-coordinates.

... AB slope = (8-5)/(1-(-5)) = 3/6 = 1/2

The slope of AD is computed in similar fashion.

... AD slope = (-2-5)/(-2-(-5)) = -7/3

The product of these slopes is (1/2)(-7/3) = -7/6 ≠ -1. Since the product is not -1, the segments AB and AD are not perpendicular to each other. Adjacent sides of a rectangle are perpendicular, so this figure is not a rectangle.

___

Our preliminary work with the diagonals showed us the figure was not a parallelogram (hence not a rectangle). For our slope calculation, we "magically" chose two sides that were not perpendicular. In fact, this choice was by "trial and error". Side BC is perpendicular to AB, so we needed to choose a different side to find one that wasn't. A graph of the points is informative, but we didn't start with that.

5 0

3 years ago

Hannah is filling a 15 gallon cooler with water. The cooler is filling at a rate of 2.5 gallons every 90 seconds. At this rate h

Elan Coil [88]

Answer:

540

Step-by-step explanation:

divide 15 by 2.5 then multiply that answer by 90

3 0

3 years ago