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inn [45]
3 years ago
6

Find the value of the variables in the simplest form

Mathematics
1 answer:
STatiana [176]3 years ago
6 0

Answer:

x = 3

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° = \sqrt{3}

tan60° = \frac{opposite}{adjacent} = \frac{x}{\sqrt{3} } = \sqrt{3} ( multiply both sides by \sqrt{3} )

x = 3

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A box contains 5 red balls, 6 white balls and 9 black balls. Two balls are drawn at
valina [46]

Answer:

P(Same)=\frac{61}{190}

Step-by-step explanation:

Given

Red = 5

White = 6

Black = 9

Required

The probability of selecting 2 same colors when the first is not replaced

The total number of ball is:

Total = 5 + 6 + 9

Total = 20

This is calculated as:

P(Same)=P(Red\ and\ Red) + P(White\ and\ White) + P(Black\ and\ Black)

So, we have:

P(Same)=\frac{n(Red)}{Total} * \frac{n(Red) - 1}{Total - 1} + \frac{n(White)}{Total} * \frac{n(White) - 1}{Total - 1}  + \frac{n(Black)}{Total} * \frac{n(Black) - 1}{Total - 1}

<em>Note that: 1 is subtracted because it is a probability without replacement</em>

P(Same)=\frac{5}{20} * \frac{5 - 1}{20- 1} + \frac{6}{20} * \frac{6 - 1}{20- 1}  + \frac{9}{20} * \frac{9- 1}{20- 1}

P(Same)=\frac{5}{20} * \frac{4}{19} + \frac{6}{20} * \frac{5}{19}  + \frac{9}{20} * \frac{8}{19}

P(Same)=\frac{20}{380} + \frac{30}{380}  + \frac{72}{380}

P(Same)=\frac{20+30+72}{380}

P(Same)=\frac{122}{380}

P(Same)=\frac{61}{190}

4 0
3 years ago
Which expression represents this word phrase? seven less than the quotient of x and 9
KIM [24]
Required expression is x/9 - 7
4 0
2 years ago
Solve negative one equals negative two v plus two-thirds for v.
makkiz [27]
We write it out as an equation:

-1 = -2v + 2/3

Rearrange:
-1 -2/3 = -2v

Multiply by negative to equal positive
1 2/3 = 2v

Make 1 into a fraction
3/3 + 2/3 = 2v
5/3 = 2v
10/6 = 2v
5/6 = v

The answer is: v equals 5/6
3 0
3 years ago
mauricio estimates that the first module of the project could be completed in as few as 15 days or could take as many as 25 days
4vir4ik [10]

Answer:

<em>Most likely time, </em>according to PERT (Program evaluation and review technique).

Step-by-step explanation:

PERT is "a statistical tool used in <em>project management" (Program evaluation and review technique (2020), </em>in Wikipedia), and it is commonly used with CPM <em>(Critical Path Method)</em> to manage projects.

Inside PERT, there are different defined times to accomplished an activity in a project, that is:

  • An <em>optimistic time</em> or minimum time required to accomplished an activity, i.e., if everything goes better than normal, the activity is accomplished before expected.
  • A <em>pessimistic time, </em>a time quite the opposite to optimistic time.
  • A <em>most likely time</em>, or a time required to accomplished an activity if everything goes as expected or normally.
  • An <em>expected time</em>, an statistical estimation.

Considering the question, we have that the <em>time</em> when "the first module of the project could be completed":

  • "[...] in as few as 15 days"  is the <em>optimistic time</em>.
  • "[...] or could take as many as 25 days" is the <em>pessimistic time</em>.
  • "[...] but most likely will require 20 days" is the <em>most likely time</em>.

As a result, the <em>20-day estimate</em> is called the <em>most likely time</em> in the context of the PERT/CPM techniques.

3 0
3 years ago
Find an equation of the line l that passes through the point (x, y) = (−9, 2) and satisfies the condition. the x-intercept of l
spayn [35]
-9(2)+4=-16 you do -9 times 2 which is -18 then you subtract that to 4 which you get -16. hope this helps!

3 0
2 years ago
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