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Mila [183]
3 years ago
13

Use the ratio of a 30-60-90 triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals

in simplest form. u= n=_____square root________

Mathematics
1 answer:
Lelu [443]3 years ago
6 0

Answer:

A. v = 19√3.

B. u = 38.

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 60°

Adjacent = 19

Opposite = v

Hypothenus = u

A. Determination of the value of 'v'

The value of v can be obtained by using Tan ratio as shown below:

Angle θ = 60°

Adjacent = 19

Opposite = v

Tan θ = Opposite /Adjacent

Tan 60 = v/19

Cross multiply

v = 19 × Tan 60

Tan 60 = √3

v = 19 × √3

v = 19√3

Therefore, the value of v is 19√3

B. Determination of the value of 'u'

The value of u can be obtained by using cosine ratio as shown below:

Angle θ = 60°

Adjacent = 19

Hypothenus = u

Cos θ = Adjacent /Hypothenus

Cos 60 = 19/u

Cos 60 = 1/2

1/2 = 19/u

Cross multiply

u = 2 × 19

u = 38

Therefore, the value of u is 38.

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anyanavicka [17]
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6 -> 20

7 -> 25

8 -> 30

9 -> 35

10 -> 40

then in ones:

after 41 would be 42 and 43


the elapsed time would be 43 minutes :)

hope this helps :)




8 0
3 years ago
For the given function, x can have what value?
Lyrx [107]

Answer:

x cannot be -4,-3, or 13

x can be anything else

Step-by-step explanation:

There are infinitely many values x can take where the relation above will be a function.

For it to be a function, you just need to make sure each x is only assigned one y value.

So x couldn't be -4 because it would by assigned to y=2 and y=0.

x couldn't be -3 because it would be assigned to y=1 and y=0.

x couldn't be 13 because it would be assigned to y=5 and y=0.

So as long as x is not chosen to be -4,-3, or 13 your relation here is a function.

5 0
3 years ago
Which kingdom was divided into provinces ruled by governors who reported to the king? a Ghana b Mali c Songhai
Vera_Pavlovna [14]

Answer: Songhai

explanation:

7 0
3 years ago
Read 2 more answers
The two-way table shows the number of books of each type in Eliza's home ​what is the probability that a randomly selected refer
Salsk061 [2.6K]

Answer:

B. 0.4

Step-by-step explanation:

Use the definition of the probability

Pr=\dfrac{\text{Number of all favorable outcomes}}{\text{Number of all possible outcomes}}

You have to find the probability that a randomly selected reference book is hard cover. Hence, from the table

  • Number of all possible outcomes = Number of Reference books = 25
  • Number of all favorable outcomes = Number of Hardcover Reference books = 10

So, the probability is

Pr=\dfrac{10}{25}=\dfrac{40}{100}=0.4

6 0
3 years ago
Read 2 more answers
A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye
Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 \mu_{x}=n\mu

And the standard deviation of the distribution of the sum of values of X is given by,  

 \sigma_{x}=\sqrt{n}\sigma

The information provided is:

<em>μ</em> = $970

<em>σ</em> = $129

<em>n</em> = 102

Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)

Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:

P (\sum X \leq  100,000) =P(\frac{\sum X-\mu_{x}}{\sigma_{x}}

                              =P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

6 0
3 years ago
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