A surveyor determines that the angle of elevation between herself and the top of an observation tower is 60^o. She determines that the distance between her position and the base of the tower is 20 meters. Approximately how tall is the tower?
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The volume of the figure is the amount of space in the figure

The volume of the figure is 10488 cubic inches

The figure is a composite figure, and it contains:

The volume (V1) of the rectangular prism is:

V1 = Length * Width * Height

V1 = 18 in * 23 in * 16 in

V1 = 6624 cubic inches

The volume (V2) of the triangular prism is:

V2 = 0.5 * Base * Width * Height

V2 = 0.5 * 23 in * 16 in * 21 in

V2 = 3864 cubic inches

Add the volumes of both figures

V =  V1 + V2

V = 6624 cubic inches + 3864 cubic inches

V = 10488 cubic inches

Hence, the volume of the figure is 10488 cubic inches

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Answer:

The answer is D: 10488

Step-by-step explanation:

The equivalent expression for the expression that represents the amount Carmen would earn is 5000(1.0005^12)^t.

Based on the expression given, Carmen's investment is compounded monthly.

The formula for calculating future value:

FV = P (1 + r)^nm

5000(1.0005)^12t

= 5000(1.0005^12)^t

50002.5^12t

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Answer:

Step-by-step explanation:

hours              Cost

  0                   $15

   1                    $15 + 2.50 = $17.50

   2                    $15 + 2.50(2) = $15 + 5 = $20

   3                     $15 + 2.50(3)= $15 + 7.50 = $22.50

   4.                     $15 + 2.50(4)= $15 + 10 = $25

Answer:

30% for chocolate

Step-by-step explanation:

9÷30= 30% 0.3 vanilla

9÷30=30% 0.3 chocolate

12÷30=40% 0.4 oatmeal

The probability of choosing chocolate is 0.30.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Number of total cookies = 30

Number of vanilla = 9

Number of chocolate = 9

Number of oatmeal = 12

The probability that chocolate is randomly selected is;

Probability of choosing a chocolate = Number of chocolate / Number of total cookies

Probability of chosen a chocolate = 9 / 30

Probability of chosen a chocolate = 3 / 10

Probability of chosen a chocolate = 0.30

Hence, the probability of choosing chocolate is 0.30.

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Step-by-step explanation:

X + Y = 90

Y = 24

X = 6x

X + 24 = 90

X = 66

x = X/6 = 66/6 = 11

Answer:

See below ↓

Step-by-step explanation:

We need to prove :

⇒ cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex] = tan⁻¹ [tex]\frac{56}{65}[/tex]

Let's simplify the LHS.

Convert the inverse cos and sin functions into inverse tan functions

Identity

Using this identity, we can simplify our earlier equation!

⇒ tan⁻¹ [(5/12 + 3/4)/(1 - (5/12 x 3/4))]

⇒ tan⁻¹ [(20 + 36) / (48 - 15)

⇒ tan⁻¹ (56/65)

⇒ RHS

⇒ Proved ∴√

[tex]\text{L.H.S}\\\\=\cos^{-1} \dfrac{12}{13} + \sin^{-1} \dfrac 35\\\\=\sin^{-1} \dfrac 5{13} + \sin^{-1} \dfrac 35\\\\[/tex]

[tex]=\sin^{-1}\left[\dfrac 5{13}\sqrt{1- \left(\dfrac 35 \right)^2} + \dfrac 35\sqrt{1-\left(\dfrac 5{13} \right)^2} \right]\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{1-\dfrac 9{25} }+\dfrac 35 \sqrt{1-\dfrac{25}{169}} \right)\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{\dfrac{16}{25}}+\dfrac 35 \sqrt{\dfrac{144}{169}} \right)\\\\=\sin^{-1} \left(\dfrac{5}{13} \cdot \dfrac 45 + \dfrac 35 \cdot \dfrac{12}{13} \right)\\[/tex]

[tex]=\sin^{-1} \left(\dfrac 4{13} +\dfrac{36}{65}\right)\\\\=\sin^{-1} \left(\dfrac{20}{65} + \dfrac{36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{20+36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{56}{65} \right)\\\\=\text{R.H.S}[/tex]

y = 1

Step-by-step explanation:

X = 2y + 6

X³ - 8y³ - 36xy - 216 = 0

(subsitute)

(2y + 6)³ - 8y³ - 36(2y + 6)y -216 = 0

(concentrate on first part)

(2y + 6)(2y + 6)(2y + 6)

(4y² + 12y + 12y + 36)(2y + 6)

(4y² + 24y + 36)(2y + 6)

8y³ + 24y² + 48y² + 144y + 72y + 216

(back to full equation)

8y³ + 72y² + 216y + 216 - 8y³ - 36(2y + 6)y - 216 = 0

(factor the last part)

-36(2y + 6)y

y(-72y - 216)

-72y² - 216y

(back to main equation)

8y³ + 72y² + 216y + 216 - 8y³ - 72y² - 216y - 216 = 0

(start to cancel out)

8y³ and -8y³ cancel

72y² + 216y + 216 - 72y² - 216y - 216 = 0

72y² and -72y² cancel

216y + 216 - 216y - 216 = 0

216y and -216y cancel

216 - 216 = 0

those cancel

0y = 0

add 1 to both sides

y = 1.

(I hope this helped)

Answer:

5.1 cm

Step-by-step explanation:

The equation for the circumference of a circle is 2πr or πd.

So, we can plug in 16 and 3.14 to get 16 = 3.14×diameter.

Divide both sides by 3.14 to get approximately 5.1 cm.

Hope that helps! :)

Answer:

4442

Step-by-step explanation:

We Cant Read A Chair So We Exclude Chairs.

Therefore, 2345+1469+628

Which is equals to 4442

Answer:

I believe the correct answer is f^-1 (x) = x - 3/2

Answer:

[tex]\boxed{\sf{y=-50 \quad x=3}}[/tex]

Step-by-step explanation:

Isolate the term of x and y from one side of the equation.

First, you have to substitute.

[tex]\sf{y=-15x-5=11x-15x-5=-17}[/tex]

Then, you solve.

[tex]\sf{-4x-5=-17}[/tex]

Add by 5 from both sides.

-4x-5+5=-17+5

Solve.

-17+5=-12

-4x=-12

Divide by -4 from both sides.

-4x/-4=-12/-4

Solve.

-12/-4=3

x=3

y=-15*3-5

Solve.

PEMDAS stands for:

15*3=45

Rewrite the problem down.

y=-45-5

Solve.

y=-50

Therefore, the correct answer is y=-50 and x=3.

I hope this helps you! Let me know if my answer is wrong or not.  

Answer: AAS

Step-by-step explanation:

Answer:

630 inches³

Step-by-step explanation:

According to the question ,

we have to find the volume of rectangular prism

Volume of rectangular prism :- l × b × h

Putting the value ,

14 × 5 × 9 cubic inches

= 630 cubic inches

[tex]\rightarrow[/tex] Length(l) of prism = 14in.

[tex]\rightarrow[/tex] Width(w) of prism = 5in.

[tex]\rightarrow[/tex] Height(h) of prism = 9in.

[tex]\rightarrow[/tex] Volume of prism.

[tex]\rightarrow[/tex] Volume of rectangular prism = [tex]\sf{l×w×h}[/tex]

[tex]\rightarrow[/tex]Volume of prism = [tex]\sf{l×w×h}[/tex](putting the value of l, w and h from the above given)

[tex]\rightarrow[/tex] [tex]\sf{=\:14×5×9}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{= \: 630 in^3}[/tex]

Therefore, volume of the given prism [tex]\sf{= \: 630 in^3.}[/tex]

________________________________

Hope it helps you:)

- 5 + 5x = - 1 + 6x

- 5 + 5 + 5x = - 1 + 5 + 6x

5x = 4 + 6x

5x - 6x = 6x - 6x + 4

- x = 4

x = - 4

Answer:

The answer is that x = -4.

Step-by-step explanation:

You first take away the parenthesis so it would look like this: -5+5x=-1+6x

Then, you add 5 to both sides of the problem: -5+5x+5=-1+6x+5

Then, you simplify it down: 5x=6x+4

You then subtract 6x from each side: 5x-6x=6x+4-6x

Then simplify again: -x=4

Then, divide both sides by -1: -x/-1 = 4/-1

Then simplify to get x = -4.

Answer:

20 2/5 cm

Step-by-step explanation:

4 ( 5 1/10)

4 × 51/10

2×51/5

0.4x51

=20 2/5

Answer:

7.744

Step-by-step explanation:

For this problem you have to work backwards

The equation for the volume is V = (area of circle) x height

So here, to solve the area of the circle, you need to divide the 235.5 by 5

So:

235.5 = (area of circle) x 5

Area of circle is 47.1

Then, you need to find the radius of the circle by using this equation for the area of a circle

[tex]A = \pi \cdot r^{2}[/tex]

So:

47.1 = π * [tex]r^{2}[/tex]

r = 3.872

This question is asking for the diameter, which is double the radius,

2 x 3.872 = 7.744

Answer: 81

Step-by-step explanation:

90% is the same as 0.9

We can multiply .9 by 90 to see how many students are enrolled in health

0.9×90=81.0

Answer:

[tex]\huge\boxed{\sf 81\ students }[/tex]

Step-by-step explanation:

Total students = 90

Enrolled in health:

= 90 % of 90

[Key: "of" means "to multiply" and "%" means "out of hundred"]

[tex]\displaystyle = \frac{90}{100} \times 90\\\\= 9 \times 9\\\\= 81[/tex]

So, 81 students are enrolled in health.

[tex]\rule[225]{225}{2}[/tex]

Answer:

nasa pic yung answer

Step-by-step explanation:

hope its help

correct me if im wrong

Answer:

x=-3 x=-3

Step-by-step explanation:

You have the equation x^2+6x+9=0. So we are tying to find two terms that add to 6 but multiply to 9. Those numbers are 3 and 3. So now we have x^2+3x+3x+9=0. Then factor it to get (x+3) and (x+3) then to isolate x do x+3=0, x=-3 (move 3 to the other side to get x=-3).

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 15000}}{\left( \cfrac{20}{100} \right)15000}\implies 30000[/tex]

Answer: If you want you can put 480 seconds or 8 minutes.

480 seconds = 8 minutes

Step-by-step explanation:

8 inches multiply by 60 feet

Answer:

Hello fellow Human! ^ω^

The answer is option D. 0.308

Step-by-step explanation:

We are going to Compare the digits starting with the greatest place value.

Therefore, the answer is Option D. 0.308

Hope this helps!

Have an Awesome Friday!

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}[/tex]

Answer:

22 tickets

Step-by-step explanation:

4/6 is 2/3
2/3 of 32 is 21 .3
Can't sell 0.3 of a ticket, so round up.
22 tickets

The 100th term of the sequence is -273

Arithmetic sequence is one derived from addition/subtraction of a constant term to find the next term. the constant term is usually called the common difference

first term a = 222

common difference, d = -5

nth term of an Arithmetic sequence. Tn = a + ( n - 1 ) d

T100 = a + ( 100 - 1 ) d

T100 = 222 + 99 * -5

T100 = -273

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Answer:

See below ↓

Step-by-step explanation:

Information we need

Solving

Answer:

hope it helps

also try to find out what 5power 10 is because I have no calculator with me

Answer:

48 ounce bag of granola per month.

T = 48x

Where 'x' represents the months.

Replace x with 12, because we want to know how many ounces she eats each year.

T = 48x

T = 48(12)

T = 576 ounces, she eats each year.