geno3141

You need to find invcos(.6018), which is also acos(.6016).

I don't get your answer; try again; if you still get your answer; re-post a question.

Draw a triangle:  Point C represents the initial position of the boat.

Directly below C is Point A, which represents the islands.

To the right of Point C is Point B, which represents the new position of the boat.

Angle C is a right angle. Angle B is 28.5°. The length of CB is 3.5 km.

You want to find the length of CA.

In relation to Angle B, CB is the adjacent side and CA is the opposite side.

tan = opposite/adjacent   --->   tan(B)  =  CA/CB   --->   tan(28.5°)  =  CA/3.5

--->   3.5·tan(28.5°)  =  CA   --->   CA  =  1.9 km

Cube both sides to get:  r³  =  h³ - 7r³

Add 7r³ to both sides:   8r³  =  h³

Divide both sides by 8h³:  r³/h³  =  1/8

Find the cube root of both sides:  r/h  =  1/2

You can try this:  tan(θ) + cot(θ)  

   =  tan(θ)  +  1/tan(θ)  

   =  tan²(θ)/tan(θ)  +  1/tan(θ)

   =  [tan²(θ) + 1] / tan(θ)  

   =   sec²(θ)/tan(θ)

or this:   tan(θ) + cot(θ)

=  sin(θ)/cos(θ)  +  cos(θ)/sin(θ)

=  [sin(θ)sin(θ)]/[sin(θ)cos(θ)]  +  [cos(θ)cos(θ)]/[sin(θ)cos(θ)]

=  sin²(θ)/[sin(θ)cos(θ)]  +  cos²(θ)/[sin(θ)cos(θ)]

=  [sin²(θ) + cos²(θ)]/[sin(θ)cos(θ)]

=  1/[sin(θ)cos(θ)]

The compound interest formula:  A  =  P(1 + r/n)^(n·t)

A  =  final amount         P  =  beginning amount         r  =  rate (as a decimal)

n  =  number of times compounded per year             t  =  number of years

1)  4 019 013  =  1 491 420(1 + r/1)^(1·11)   --->   4 019 013  =  1 491 420(1 + r)^(11)

   --->  (divide by 1 491 420)   --->   2.694 756(1 + r)^11

   --->   (take the 11th root)   --->   1.0943  =  1 + r     --->   r  =  0.094304365

2) If $73,376.39 was the interest earned on lending $101,000, this means that the final amount is $73,376.39 + $101,000  =  $174,376.39:

     174,376.39  =  101 000(1 + r/4)^(4·7)     --->     174,376.39  =  101 000(1 + r/4)^28

    --->  (divide by 101 000)   --->   1.726498911 =  (1 + r/4)^28

   --->   (take the 28th root)   --->   1.019694849  =  1 + r/4

   --->   0.019694849  =   r/4     --->   r  =  0.0787793946

3)  a)  Interest of $227,708.21 on a loan of $59,000 loan gives a final amount of $286,708.21.

   b)  286 708.21  =  59 000(1 + 0.074/2)^(2·n) 

--->   4.859461186  =  (1.037)^(2n)

--->  (find the log of both sides)   --->  log( 4.859461186 )  = log[ 1.037^(2n) ]

---> (exponents come out as multipliers)   --->   log( 4.859461186 )  = 2n · log[ 1.037 ]   

---> (divide by 2· log[ 1.037 ] )   --->   21.7567247 years

The best point-estimate for the mean of a population is the mean of the sample.

Since the mean of the sample is 7.2, the best point-estimate for the population is also 7.2.

95% --->  z(α/2)  = 1.96

E  =  z(α/2)√(p-hat·q-hat/n)   --->   E  =  1.96√(0.42·0.58/1500) 

--->  E  =  0.025

C.I.  =  p-hat ± E

--->  C.I.  =  0.42 ± 0.025

The sample proportion is the number of successes divided by the total number:  70/280  = 0.25

The standard deviation indicates the closeness of the data to the mean.

For Jamie, a mean of 37 and a standard deviation of 2 means that the greatest proportion of her output is 37 ± 2 mins.  This means that 68% of her output is between 35 and 39 minutes.

For Tara, a mean of 37 and a standard deviation of 5 means that the greatest proportion of her output is 37 ± 5 mins. This means that 68% of her output is between 32 and 42 minutes.

Therefore Jamie is the more consistent (the smaller the standard deviation, the greater the consistency).

It depends upon the other data; however, it will probablty be represented as 3 | 0

because the stem is the ten's value and the leaf is the unit's value.