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Sphinxa [80]
3 years ago
8

Which of the following ratios correctly describes the tangent function? a. opp/adj b. opp/hyp c. adj/hyp

Mathematics
2 answers:
Elena L [17]3 years ago
7 0
A. opp/adj because the the tangent is the hypotenuse so it eliminates all equations that require the hypotenuse.
Lera25 [3.4K]3 years ago
5 0

Answer: a.opp/adj


Step-by-step explanation:

The tangent function, along with sine and cosine, is one of the three most common trigonometric functions.

For any given angle x

\tan\ x=\frac{\sin\ x}{\cos\ x}=\frac{\frac{\text{side opposite to x}}{\text{hypotenuse}}}{\frac{\text{side adjacent to x}}{\text{hypotenuse}}}\\\Rightarrow\tan\ x=\frac{\text{side opposite to x}}{\text{side adjacent to x}}

thus, opp/adj  correctly describes the tangent function.



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stellarik [79]

Answer:

add 17 to both sides

Step-by-step explanation:

as it cancels itself

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3 years ago
A manufacturer produces bolts of a fabric with a fixed width. A quantity q of this fabric (measured in yards) that is sold is a
BigorU [14]

Answer:

R'(20) = 2000

Step-by-step explanation:

We are given the following in the question:

Quantity, q

Selling price in dollars per yard, p

q=f(p)

Total revenue earned =

R(p)=pf(p)

f(20)=13000

This means that 13000 yards of fabric is sold when the selling price is 20 dollars per yard.

f′(20)=−550

This means that increasing the selling price by 1 dollar per yards there is a decrease in fabric sales by 550.

We have to find R'(20)

Differentiating the above expression, we have,

R'(p) = \displaystyle\frac{d(R(p))}{dp} = \frac{d(pf(p))}{dp} = f(p) + pf'(p)

Putting the values, we get,

R'(p) = f(p) + pf'(p)\\\\R'(20) = f(20) + 20(f'(20))\\\\R'(20) = 13000 + 20(-550) = 2000

7 0
3 years ago
When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distributio
disa [49]

Answer:

The  Decision Rule

Fail to reject the null hypothesis

The conclusion

 There is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi

Step-by-step explanation:

From the question we are told that

   The data is  

      Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8

     Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4

      The  level of significance \alpha = 0.05

 Generally the null hypothesis  is  H_o  :  \mu_1 - \mu_2  = 0

                  the alternative hypothesis is   H_a  :  \mu_1 - \mu_2 >  0

Generally the sample mean for the age of  cars is mathematically represented as

        \= x_1 = \frac{\sum x_i }{n}

=>     \= x_1 = \frac{4+ 0+ 8 +11 + \cdots + 8
}{27}

=>     \= x_1 = 5.56

Generally the standard deviation of age of  cars

     \sigma _1  = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }

=>  \sigma _1  = \sqrt{\frac{(4 - 5.56)^2 + (0 - 5.56)^2+ (8 - 5.56)^2 + \cdots + 8}{ 27} }

=>  \sigma _1  =  3.88

Generally the sample mean for the age of taxi is mathematically represented as

        \= x_2 = \frac{\sum x_i }{n}

=>     \= x_2 = \frac{8 +8 +0  + \cdots + 4
}{20}

=>     \= x_2 = 5.85

Generally the standard deviation of age of  taxi

\sigma _2  = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }

=>  \sigma _2  = \sqrt{\frac{(8 - 5.85)^2 + (8 - 5.85)^2+ (0 - 5.85)^2 + \cdots + 8}{ 20} }

=>  \sigma _2  = 2.83

Generally the test statistics is mathematically represented as

   t = \frac{(\= x_ 1 - \= x_2 ) - 0}{\sqrt{\frac{\sigma^2_1}{n_1}  + \frac{\sigma^2_2}{n_2} }  }

=> t = \frac{(5.56 - 5.85 ) - 0}{\sqrt{\frac{(3.88)^2}{27}  + \frac{(2.83)}{20} }}  

=> t = -0.30  

Generally the degree of freedom is mathematically  represented as

   df =  n_1 + n_2 -2

    df =  27 +  20 -2

    df =  45

From the t distribution table  the P(t >  t ) at the obtained degree of freedom = 45 is  

   P(t >  -0.30 ) = 0.61722067

So  the  p-value  is

    p-value  =  P(t >  T) =  0.61722067

From the obtained values we see that the  p-value  >  \alpha hence we fail to reject the null hypothesis

Hence the there is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi

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Answer:

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Step-by-step explanation:

Given that:

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The cost of pepper =75 cents / scoop = $ 0.75 / scoop

Let he buys x scoops of salt and y scoops of pepper.

As he plans to bring home no more than 8 scoops of seasoning, so

x+y\leq8\cdots(i)

The total cost of x scoops of salt and y scoops of pepper = 0.5x+0.75y

As he wants to spend less than $5, so

0.5x+0.75y

Here, x\geq 0, y \geq 0 and x,y are counting numbers.

On plotting the graph of equations (ii) and (ii), the possible solution is the integral values in the shaded as shown in the figure.

The maximum possible integral values, for expances less than $5, are (x,y)=(3,4), (4,3).

Hence, he can buy 3 scoops of salts and 4 scoops of pepper or 4 scoops of salts and 3 scoops of pepper to spent maximum.

5 0
3 years ago
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Step-by-step explanation:

Answer in attached image...

hope it helps

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3 years ago
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