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larisa86 [58]
3 years ago
11

A tourist standing on the New York City coast sees the Statue of Liberty, which is 305 feet tall. She must tilt her head 9 degre

es upwards to look at its head. How far away is she from the base of the statue? Round your answer to the nearest whole foot.
Mathematics
1 answer:
mixer [17]3 years ago
4 0

Given:

Height of the Statue of Liberty = 305 feet

Angle of elevation = 9 degrees

To find:

The between the tourist and the Statue of Liberty.

Solution:

Using the given information, draw a figure as shown below.

In a right triangle,

\tan \theta=\dfrac{Perpendicular}{Base}

In the triangle ABC,

\tan 9^\circ=\dfrac{305}{x}

x=\dfrac{305}{\tan 9^\circ}

x=1925.6942

x\approx 1926

Therefore, the tourist is standing 1926 feet from the Statue of Liberty.

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Answer:

The slope is \frac{-1}{3}.

Step-by-step explanation:

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Horizontal Change             3

Slope                                   \frac{-1}{3}

8 0
3 years ago
5.5 + 2.1x + 3.8x – 4.1
lozanna [386]

Answer:

5.9x + 1.4

Step-by-step explanation:

5.5 + 2.1x + 3.8x - 4.1

= 5.9x + 1.4

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Miranda has a bag of marbles with 5 blue marbles, 1 white marbles, and 1 red marbles. Find the following probabilities of Mirand
kvasek [131]

Answer:

(a)\frac{5}{7},\frac{1}{6} (b)\frac{1}{7},\frac{1}{6} (c)\frac{5}{7},\frac{2}{3},\frac{3}{5}

Step-by-step explanation:

GIVEN: Miranda has a bag of marbles with 5 blue marbles, 1 white marbles, and

TO FIND: a) A Blue, then a red Preview

,b)A red, then a white Preview

,c) A Blue, then a Blue, then a Blue.

SOLUTION:

Total marbles in bag =7

(a)

Probability of drawing blue marble =\frac{\text{total blue marble}}{\text{total marbles}}

                                                          =\frac{5}{7}

As marble is not returned to bag,

Probability of drawing red marble  =\frac{\text{total red marble}}{\text{total marbles}}

                                                         =\frac{1}{6}

(b)

Probability of drawing red marble =\frac{\text{total red marble}}{\text{total marbles}}

                                                          =\frac{1}{7}

As marble is not returned to bag,

Probability of drawing white marble  =\frac{\text{total white marble}}{\text{total marbles}}

                                                         =\frac{1}{6}

(c)

Probability of drawing blue marble =\frac{\text{total blue marble}}{\text{total marbles}}

                                                          =\frac{5}{7}

As marble is not returned to bag,

Probability of drawing second blue marble  =\frac{\text{total blue marble}}{\text{total marbles}}

                                                                         =\frac{4}{6}=\frac{2}{3}

As marble is not returned to the bag

Probability of drawing third blue marble   =\frac{\text{total blue marble}}{\text{total marbles}}

                                                                    =\frac{3}{5}

8 0
3 years ago
Graph this rational equation. Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asy
irakobra [83]

Step-by-step explanation:

We have given,

A rational function : f(x) = \frac{x-2}{x-4}

W need to find :

Point of discontinuity : - At x = 4, f(x) tends to reach infinity, So we get discontinuity point at x =4.

For no values of x, we get indetermined form (i.e \frac{0}{0}), Hence there is no holes

Vertical Asymptotes:

Plug y=f(x) = ∞ in f(x) to get vertical asymptote   {We can us writing ∞ = \frac{1}{0}}

i.e ∞ = \frac{x-2}{x-4}

or \frac{1}{0}=\frac{x-2}{x-4}

or x-4 =0

or x=4, Hence at x = 4, f(x) has a vertical asymptote

X -intercept :

Plug f(x)=0 , to get x intercept.

i.e 0 = \frac{x-2}{x-4}

or x - 2 =0

or x = 2

Hence at x=2, f(x) has an x intercept

Horizontal asymptote:

Plug x = ∞ in f(x) to get horizontal asymptote.

i.e f(x) = \frac{x-2}{x-4} = \frac{x(1-\frac{2}{x} )}{x(1-\frac{4}{x} )}

or f(x) = \frac{(1-\frac{2}{∞} )}{(1-\frac{4}{∞} )}

or f(x) = 1 = y

hence at y =f(x) = 1, we get horizontal asymptote





4 0
3 years ago
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