An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to be 16.5 and 10.5 respectively. How long is the island ?

Answer:

c

Step-by-step explanation:

Answer:C

Step-by-step explanation:

Answer:

x>125

Step-by-step explanation:

Answer:

x > 125

Step-by-step explanation:

I hope this helps!

Answer:

[tex]4000(1.023)^t\\\\[/tex]

Step-by-step explanation:

Using this exponential growth equation we can get an equation that models the situation.

A= Principal Amount

R= Rate of Growth

T= Amount of time

[tex]A=4000\\R=2.3/100=.023\\T= Non[/tex]

[tex]A(1+R)^t\\4000(1+0.23)^t\\4000(1.023)^t\\\\[/tex]

Answer:

Let us check these out one at a time:

1. x + y is odd.  FALSE.  The sum of 2 odd numbers is even.

2. xy is odd.  TRUE.  The product of 2 odd numbers is odd.

3. x/y is odd.  TRUE.  The ratio of 2 odd numbers is odd, if the ratio is an integer.

4. x - y is odd.  FALSE.  The difference of 2 odd numbers is even.

Only statements 2 and 3 are TRUE, so that makes (C) the correct answer.

[tex]\\ \sf\longmapsto \left\{x|x \epsilon I,x\leqslant 3\right\}[/tex]

In listing

[tex]\\ \sf\longmapsto \left\{\dots,0,1,2,3\right\}[/tex]

Step-by-step explanation:

|- 9| + |- 3|

9 + 3

12

I hope this answers your question

Answer:

The 5th term of a sequence is defined as the term with n = 5.  So for this sequence, a sub 5 = 5/6

[tex]3\frac{16}{99} = \dfrac{313}{99}= 3.161616161616.....[/tex]

Answer:

1). x = 2.67 units

2). x = 4.80 units

3). x = 6.00 units

Step-by-step explanation:

1). By applying Pythagoras theorem,

 Hypotenuse² = [Leg(1)]² + [leg(2)]²

  12² = x² + b² [Let the base of both the triangles = b units]

  144 = x² + b² ------(1)

  Similarly, 13² = (x + 3)² + b²

  169 = x² + 6x + 9 + b²

  169 - 9 - 6x = x² + b²

  160 - 6x = x² + b² ------(2)

  From equation (1) and (2)

  144 = 160 - 6x

  6x = 160 - 144

  x = [tex]\frac{16}{6}[/tex]

  x = 2.67 units

2). By applying Pythagoras theorem,

  10² = x² + h² [Let the height of the triangle = h]

  100 = x² + h² ------(1)

  13² = (2x)² + h²

  169 = 4x² + h² -----(2)

  By substituting equation (1) from equation (2),

  169 - 100 = (4x² + h²) - (x² + h²)

  69 = 3x²

  x² = 23

  x = √23

  x = 4.795

  x ≈ 4.80 units

3). By applying Pythagoras theorem,

  9² = x² + h² [Let the height of the triangle = h units]

  81 = x² + h² ------(1)

  7² = (x - 4)² + h²

  49 = x² + 16 - 8x + h²

  49 - 16 = x² + h² - 8x

  33 + 8x = x² + h² -------(2)

  From equation (1) and (2)

  81 = 33 + 8x

  8x = 48

   x = 6.00 units

Answer: a. 0.4 × 0.15 = 0.060

Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.

For P(A):

P(A') = 1 - 0.6

P(A') = 0.4

For P(B):

P(B') = 1 - 0.85

P(B') = 0.15

To determine probability of A' and B':

P(A' and B') = P(A')*P(B')

P(A' and B') = 0.4*0.15

P(A' and B') = 0.06

Probability of the complement of the event is 0.060

Answer:

100 inches^3

Step-by-step explanation:

The volume of the back rectangle is

V = l*w*h

V = 8*5*1 = 40 inches ^3

The volume of the front rectangle is

V = 6*2*5 = 60 inches^3

Add the volumes

40+60 = 100 inches^3

Answer:

A

Step-by-step explanation:

Because of we pur all the points on the Cartesian plane and we "connect" all the points comes a rhombus

SORRY FOR MY BAD ENGLISH BUT I AM ITALIAN

Answer:

[tex]x> \frac{8}{51} [/tex]

Step-by-step explanation:

[tex]7x - \frac{5}{8} x + 3>4[/tex]

Bring constants to one side, simplify:

[tex] \frac{51}{8} x>4 - 3 \\ \frac{51}{8} x>1 \\ x>1 \div \frac{51}{8} \\ x>1 \times \frac{8}{51} \\ x> \frac{8}{51} [/tex]

*Note that the inequality sign only changes when you divide the whole inequality by a negative number.

Answer:

[tex]x>\frac{8}{51}[/tex]

Step-by-step explanation:

[tex]7x-\frac{5}{8}x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-\frac{5}{8}x+3-3>4-3\\\mathrm{Simplify}\\7x-\frac{5}{8}x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x\times \:8-\frac{5}{8}x\times \:8>1\times \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\\frac{51x}{51}>\frac{8}{51}\\\\x>\frac{8}{51}[/tex]

I hope it helps :)

Answer:

Step-by-step explanation:

This is a hypergeometric distribution

[tex]\frac{{3\choose2}*{3\choose1}}{{6\choose3}}[/tex]=.45

Answer:

Step-by-step explanation:

First you have to find the medians which is when you put the numbers in number order and find the one in the middle.

Class A: 60,65,70,70,75,80,80,85,90,90

=77.5

Class B: 75,85,85,85,90,90,90,90,95,100

=90

That the class B is more advanced, and they probably studied.

Answer:

10 wide 30 long

Step-by-step explanation:

1. Start guess and check.

2. When you get to 10 follow this:

10x3=30. 30+30+10+10=80

80=80

Answer:

Percentage of home team supporters =65%

Percentage of visiting team supporters =35%

Step-by-step explanation:

Total attendees=2,000 people

Home team supporters=1,300

Visiting team supporters=700

What percentage of people attending supported the home team?

Percentage of people attending who supported the home team = home team supporters / total attendees × 100

=1,300/2,000 × 100

=0.65 × 100

=65%

Visiting team supporters = visiting team supporters / total attendees

× 100

=700/2000 × 100

=0.35 × 100

=35%

Alternatively,

Visiting team supporters = percentage of total attendees - percentage of home team supporters

=100% - 65%

=35%

Answer:

D, 49.42

Step-by-step explanation:

ΔVFT=180-90-43=47

formula

a/sin A = b/sin B/ = c/sin C

So,

FV/sin90=53/sin47

FV=72.4684

FT=√(72.4684)^2-(53)^2

FT=49.4234

Ans:D

The length FT in the given right-angle triangle is 49.42.

So option D is the correct answer.

We are given a right-angle triangle and to find the length of any side we can use Pythagoras theorem or trigonometric identities.

In the triangle, we see that TV = 53 and ∠ FVT = 43°

We will find the length FT by using Pythagoras theorem or trigonometric identities.

What are trigonometric functions?

There are some commonly used trigonometric identities:

SinФ = Perpendicular / hypotenuse

Cos Ф = Base / hypotenuse

Tan Ф =  Perpendicular / Base

We will use Tan Ф =  Perpendicular / Base to find the length FT.

Because we need to use trigonometric identities that have TV and FT.

Tan Ф = FT / TV

Tan 43° = FT / 53

FT = Tan 43° x 53

FT = 0.932515 X 53

FT = 49.42

Thus we got FT = 49.42 using the tan function.

Learn more about trigonometric functions here:

https://brainly.com/question/14746686

$SPJ2

Answer:

$270

Step-by-step explanation:

Price after markup was 1.20($250) = $300

Price after discounting:  (1.00 - 0.10)($300) = $270

Answer:

[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]

I hope I helped you^_^

Answer:

Infinite amount of solutions

Step-by-step explanation:

Parallel lines have no solution

Same lines have infinite solutions

Intersecting lines have 1 solution

Step 1: Write out equation

-14(x - 5) = -14x + 70

Step 2: Distribute -14

-14x + 70 = -14x + 70

Here we see that we have 2 exact same lines. Therefore, we have infinite amount of solutions.

Alternatively, we can plug in any number x and it would work. So then we would have infinite amount of solutions as well.

Answer:

2  c an of blue and 5 can of yellow

Step-by-step explanation:

Answer:

[tex]\boxed{345,600 mL}[/tex]

Step-by-step explanation:

Hey there!

Well first we need to find the amount of seconds in a day,

24hrs in a day * 60 min in an hour

= 1440 minutes in a day

1440 min • 60 secs in a minute

= 86,400 seconds in a day

So now we do 2*86400 = 172800

172800 mL in a day

172800 * 2

= 345600 mL in 2 days

Hope this helps :)

Answer:

288

Step-by-step explanation:

Area of two triangles=2(½bh)

=bh

=8×6

=48

For the rectangles=lb + lb +lb

l(b+b+b)

=12(8+6+6)

=12×20

=240

Total area=240 +48=288

Answer:

2y^3-7y^2+7y

Step-by-step explanation:

7y - 2y^3 + 5y^2 - (  12y^2 – 4y^3)

Distribute the minus sign

7y - 2y^3 + 5y^2 - 12y^2 + 4y^3

Combine like terms

2y^3-7y^2+7y

Answer:

46

Step-by-step explanation:

(14+x)/4 = 15

14 + x = 60

x = 46

Answer:

46

Step-by-step explanation:

Let a to d be number 1 to 4 respectively.

15 = (a + b + c + d) / 4

(a + b + c + d) = 60 ------> total sum of the 4 numbers

Since the sum of 3 numbers (assuming a to c) is 14,

Fourth number (d) = 60 - 14

= 46

That's how I would do it, hope this helps :)

Answer:

Step-by-step explanation:

Given the function f(x) = 8x³ − 12x² − 48x, the critical point of the function occurs at its turning point i,e at f'(x) = 0

First we have to differentiate the function as shown;

[tex]f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\ \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\[/tex]

[tex]Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1[/tex]

Hence the critical numbers of the function are (2, -1)

Answer:

  C.  70°

Step-by-step explanation:

The inscribed angle marked 15° intercepts an arc that is double that measure, so the intercepted arc on the right is 2×15° = 30°.

The external angle marked 20° is half the difference of the intercepted arcs, so is ...

  20° = (1/2)(x - 30°)

  40° = x - 30° . . . . . . multiply by 2

  70° = x . . . . . . . . . . . add 30°

The value of x is 70°.

Answer:

5.215 units (rounded up to three decimal places)

Step-by-step explanation:

To find the distance between points (3.1 , 0.3) and (2.7, -4.9)

We use the Pythagoras Theorem which states that for a right triangle of sides a,b and c then;

a² + b²  = c² ,  Where c is the hypotenuse.

In our case, the distance between the two points is the hypotenuse of triangle formed by change in y-axis and change in x-axis.

The distance (hypotenuse) squared = (-4.9 - 0.3)² + (2.7 - 3.1)² = 27.04 + 0.16 = 27.2

Hypotenuse (the distance between) = [tex]\sqrt{27.2}[/tex] = 5.215 units (rounded up to three decimal places)