Five friends share 3 bags of trail mix equally. What fraction of a bag of trail mix does each friend get? Please explain or show your work! :)

Answer:

Step-by-step explanation:

Well 7 is the only number that can be divided by itself and 1

Answer:

Hello!

Great question.

The correct answer would be "Prime Number."

Step-by-step explanation:

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.

Answer:

Part 5) [tex]x=50\°[/tex]

Part 6) [tex]x=15\°[/tex]

Step-by-step explanation:

Part 5) we know that

[tex](2x-10)\°+90\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)

solve for x

[tex]2x=180\°-80\°[/tex]

[tex]2x=100\°[/tex]

[tex]x=50\°[/tex]

Find the value of the labeled angle

[tex](2x-10)\°=2(50\°)-10\°=90\°[/tex] ----> is a right angle

Verify the answer

we know that

In a quadrilateral the sum of the internal angles must be equal to 360 degrees

so

[tex](2x-10)\°+90\°+(180-x)\°+x\°=360\°[/tex]

[tex](2x+260)\°=360\°[/tex]

substitute the value of x

[tex]2(50\°)+260\°=360\°[/tex]

[tex]360\°=360\°[/tex] ------> is true, therefore the value of x is correct

Part 6) we know that

[tex](8x+10)\°+(4x-10)\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)

solve for x

[tex]12x=180\°[/tex]

[tex]x=15\°[/tex]

Find the value of each labeled angle

[tex](8x+10)\°=8(15\°)+10\°=130\°[/tex]

[tex](4x-10)\°=4(15\°)-10\°=50\°[/tex]

[tex]130\°[/tex] and [tex]50\°[/tex] are supplementary angles

➷ Find the multiplier:

28/100 = 0.28

1 - 0.28 = 0.72

Multiply the total amount by this multiplier:

40,000 x 0.72 = 28,800

She will make $28,800

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

She will make 28,800 dollars after tax.

Step-by-step explanation:

just subtract 28 percent of 40,000.

Or even simpler just follow peachy's instructions cause she/he did her crud right. a percentage is the same as a decimal. 1 percent is 0.01. since 28 percent is 0.28 we subtract 0.28 from one, because 1 is 100 percent. Also,all of this is the same as subtracting 28 percent of 40,000 from 40,000 1 - 0.28= 0.72, and multiply 40,000 by 0.72.

All credit on this part is peachy's thank her/his answer and give her/him brainliest. :)

btw why i say him/her, he/she, and her/his is because I dot want to assume gender

Answer:

a) [tex]N_0=250\; k=0.15 [/tex]

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies [tex]t=0[/tex]. And [tex]N(0)=N_0[/tex]. The process is:

[tex]N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250[/tex]

b) After 2 days means [tex]t=48[/tex]. So, we just replace and operate:

[tex]N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}[/tex]

c) [tex]N(t_1)=4000; \;t_1=?[/tex]

[tex]N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\  \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h [/tex]

d) [tex]t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)[/tex]

[tex]N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h [/tex]

An example of dependent events is drawing a red marble from the same jar without replacing the first marble, which changes the probabilities for the second draw. This is known as sampling without replacement, which contrasts with independent events where the item is replaced and the probabilities remain unchanged.

An example of dependent events is drawing a red marble out of the same jar, without replacing the first marble. This creates a dependency because removing the first marble affects the outcome chances for the subsequent draw. If the jar starts with four blue and three white marbles and you draw one blue marble and do not replace it, the jar then contains three blue and three white marbles. Therefore, the probability of drawing another blue marble has changed from the original draw.

Dependent events are associated with sampling without replacement, which means once an item is drawn, it is not put back into the population from which it was taken, altering the probabilities of subsequent draws. In contrast, independent events, such as drawing and replacing a marble, do not affect the subsequent probabilities, since the composition of the jar remains unchanged with each draw.

Answer: 14 cars 4 left over

Step-by-step explanation:

74/5=14.8

14 x 5 = 70

4 wheels left over

Answer:THE ANSWER IS

300% PLEASE BRAINEST ME!

Answer:

The answer is D hope this helps

Step-by-step explanation:

Answer:

150 miles

Step-by-step explanation:

Find the unit rate (MPH) by dividing miles travlled by hours.

    300/6 = 50 MPH

    250/5 = 50 MPH

Multiply the hours on day 3 (3) by 50 MPH

    3*50 = 150 miles

Answer:

150 miles

Step-by-step explanation:

The relationship between speed, time and distance is such that the product of speed and time is distance.

Given that they drove the same speed throughout the trip

Speed on day one given that distance covered is 300 miles in 6 hours,

Speed = 300 miles/ 6 hours

= 50 miles per hour

Speed on day two given that distance covered is 250 miles in 5 hours

= 250 miles/ 5 hours

= 50 miles per hour

If on the third day, the speed is maintained and they drove for 3 hours,

Distance covered = 50 miles per hour × 3 hours = 150 miles

Answer:

B

Step-by-step explanation:

Since the d value is changed, we're talking about a vertical transformation. Since d > 0, the graph is shifted up.

Answer:

A second degree trinomial or a quadratic expression.

Step-by-step explanation:

The expression;

3x^2 -6x +10 , is a Quadratic expression or a second degree trinomial.

A Trinomial is a three term polynomial like the one above; that is,

3x^2 -6x +10.

A second degree trinomial  or polynomial is an expression of the form.

ax2 + bx + c , where a ≠ 0.

Answer:

B.   y = e^(-2/x).

Step-by-step explanation:

dy/dx = 2y / x^2

Separate the variables:

x^2 dy = 2y dx

1/2 * dy/y =  dx/x^2

1/2  ln y = = -1/x  + C

ln y = -2/x +  C

y = Ae^(-2/x)  is the general solution ( where A is a constant).

Plug in the given conditions:

e = A e^(-2/-2)

e = A * e

A = 1

So the specific solution is y = e^(-2/x).

Final answer:

The separable differential equation [tex]dy/dx = 2y/x^2[/tex] can be solved by separating variables, integrating both sides, and then applying the given initial condition y(-2) = e to find the specific solution, which is [tex]y = e^{-2/x},[/tex] corresponding to answer option B.

Explanation:

To solve the given separable differential equation [tex]dy/dx = 2y/x^2[/tex], we first separate the variables:

[tex]\( \frac{dy}{y} = \frac{2}{x^2}dx \)[/tex]

Next, we integrate both sides:

[tex]\( \int \frac{1}{y}dy = \int 2x^{-2}dx \)[/tex]

Which gives:

[tex]ln|y| = -2/x + C[/tex]

Now, we apply the initial condition y(-2) = e to find C:

ln(e) = [tex]-2/(-2) + C \Rightarrow 1 = 1 + C \Rightarrow C = 0[/tex]

Thus, the specific solution is:

[tex]y = e^{-2/x}[/tex]

So, the correct answer is option B, y equals e raised to the negative 2 over x power.

Answer:

j:19 days

s:23 days

23-19=4

4 days

Step-by-step explanation:

Answer:

Step-by-step explanation:

We must calculate the lateral area of a cylinder.

The formula is:

[tex]A=2\pi rH[/tex]

r - radius

H - height

We have H = 6 cm and r = 3.5.

Substitute:

[tex]A=2\pi(3.5)(6)=42\pi\ cm^2[/tex]

Use [tex]\pi\approx\dfrac{22}{7}[/tex]

[tex]A\approx42\left(\dfrac{22}{7}\right)=(6)(22)=132\ cm^2[/tex]

Answer:

x ≈ 5 years

Step-by-step explanation:

Given amount = A = 500 mg

Decay rate = r = 10% per year

Remaining amount = L = 295.25 mg

The formula to calculate remaining amount after x years decay =

L = A((100-r)/100)^x

By putting values in this formula, we get

295.25 = 500 ((100-10)/10)^x

295.25 = 500 (0.90)^x    

295.25/500 = 0.90^x

0.5905 = 0.90^x

0.90^x =0.5905

taking log on both sides

ln(0.90^x) =ln(0.5905)

x*ln(0.90) =ln(0.5905)  using property of log

x = ln(0.5905)/ln(0.90)

x = 4.9984

x ≈ 5 years

Answer:

C. 20

Step-by-step explanation:

The given limit is

[tex]\lim_{x \to 2} (3x^3 +x^2-8)[/tex]

This a limit of a polynomial function.

We plug in the limit directly to obtain;

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(2)^3+(2)^2-8[/tex]

We simplify to get;

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(8)+4-8[/tex]

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=24+4-8[/tex]

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=20[/tex]

The correct choice is C

Answer:log(x-3)

Step-by-step explanation:

log(A)-log(B) is log(A/B) then this would be log[(x^2-9)/(x+3)]

x^2-9 is (x-3)(x+3) then the answer is log(x-3)

Answer:

6√3 cm

Step-by-step explanation:

The hypotenuse of a right triangle is 12 centimeters, and the shorter leg is 6 centimeters then the other leg is 6√3

Answer: Defualt

Step-by-step explanation: Dan

15 Answer:  S₁ = 1       S₂ = 4        S₃ = 13        S₄ = 40       Sum = NO            

Step-by-step explanation:

1 + 3 + 9 + 27 + ...    [tex]\implies\sum^{\infty}_{n=1}3^{n-1}\implies\sum^{\infty}_{n=1}\dfrac{3^n}{3}\\\\\bullet S_1=1\\\bullet S_2=1+3=4\\\bullet S_3=1+3+9=13\\\bullet S=1+3+9+27=40\\\\\\ \lim_{n \to \infty} \dfrac{3^n}{3} \implies\dfrac{3^{\infty}}{3}\implies\infty\\\\\text{The series diverges so there is no sum.}[/tex]

16 Answer:      [tex]\bold{S_1=\dfrac{1}{2}\qquad S_2=\dfrac{2}{3}\qquad S_3=\dfrac{13}{18}\qquad S_4=\dfrac{39}{54}\qquad Sum=YES}[/tex]        

Step-by-step explanation:

[tex]\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{162}+...\implies \sum^{\infty}_{n=1}\dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\\\\\\\bullet S_1=\dfrac{1}{2}\\\\\bullet S_2=\dfrac{1}{2}+\dfrac{1}{6}=\dfrac{2}{3}\\\\\bullet S_3=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{13}{18}\\\\\bullet S_4=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}=\dfrac{39}{54}[/tex]

[tex]\lim_{n \to \infty} \dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\implies \dfrac{1}{2}\lim_{n \to \infty} \dfrac{1}{3^{\infty-1}}\implies \dfrac{1}{\infty}=0\\\\\\\text{The series converges so it does have a sum.}[/tex]

Tommy has 3 and 1/3 jars but 3 of them are full .

Okay so 5*2/3 =10/3 which is 3 1/3

Answer:

The number of banana splits sold was [tex]28[/tex]

Step-by-step explanation:

Let

x-----> the number of sundaes sold

y-----> the number of banana splits sold

we know that

[tex]2x+3y=156[/tex] -----> equation A

[tex]x=y+8[/tex] ----> equation B

substitute equation B in equation A and solve for y

[tex]2(y+8)+3y=156[/tex]

[tex]2y+16+3y=156[/tex]

[tex]5y=156-16[/tex]

[tex]5y=140[/tex]

[tex]y=28[/tex]

Answer:

x=2

Step-by-step explanation:

The formula for inverse variation is

xy = k

We know x = 4 and y = 8

4*8= k

32 = k

xy = 32

We want to find x when y = 16

x*16 = 32

Divide each side by 16

16x/16 = 32/16

x =2

Answer:

xy=32

16x=32

x=2

Answer:

True

Step-by-step explanation:

We have the serie:

[tex]\frac{1}{25}+ \frac{1}{36} + \frac{1}{49}+...[/tex]

To test whether the series converges or diverges first we must find the rule of the series

Note that:

[tex]5^2 = 25\\\\6^2 = 36\\\\7^2 = 49[/tex]

Then we can write the series as:

[tex]\frac{1}{5^2}+ \frac{1}{6^2} + \frac{1}{7^2}+...[/tex]

Then:

[tex]\frac{1}{5^2}+ \frac{1}{6^2} + \frac{1}{7^2}+... = \sum_{n=5}^{\infty}\frac{1}{n^2}\\\\\sum_{n=5}^{\infty}\frac{1}{n^2} = \sum_{n=1}^{\infty}\frac{1}{(n+4)^2}[/tex]

The series that have the form:

[tex]\sum_{n=1}^{\infty}\frac{1}{n^p}[/tex]

are known as "p-series". This type of series converges whenever [tex]p > 1[/tex].

In this case, [tex]p = 2[/tex] and [tex]2 > 1[/tex]. Then the series converges

(2l+2w) is that right

In spherical coordinates, we set

[tex]x=\rho\cos\theta\sin\varphi[/tex]

[tex]y=\rho\sin\theta\sin\varphi[/tex]

[tex]z=\rho\cos\varphi[/tex]

so that the volume element under this transformation becomes

[tex]\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]

The region [tex]E[/tex] is given by the set

[tex]\left\{(\rho,\theta,\varphi)\mid0\le\rho\le1,0\le\theta\le2\pi,0\le\varphi\le\dfrac\pi3\right\}[/tex]

so that the integral is

[tex]\displaystyle\iiint_Ey^2z^2\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^6\sin^2\theta\sin^3\varphi\cos^2\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]

[tex]\displaystyle=\left(\int_0^{\pi/3}\sin^3\varphi\cos^2\varphi\,\mathrm d\varphi\right)\left(\int_0^{2\pi}\sin^2\theta\,\mathrm d\theta\right)\left(\int_0^1\rho^6\,\mathrm d\rho\right)[/tex]

[tex]=\dfrac{47}{480}\cdot\pi\cdot\dfrac17=\dfrac{47\pi}{3360}[/tex]

The volume of the solid using the triple integral [tex]\mathbf{\iiint_E y^2z^2 dV \ \ is \ \ = \dfrac{47 \pi}{3360}}[/tex]

Given that;

Then the spherical coordinates can be expressed as:

where;

Now, the expression for the solid E in the spherical coordinates can be computed as:

[tex]\mathbf{E = \Big \{ ( \rho , \theta, \phi )\Big| 0 \leq \rho \leq 1, 0 \leq \phi \leq \dfrac{\pi}{3}, 0 \leq \theta \leq 2 \pi \Big \} }[/tex]

and the volume of the solid using the triple integral is calculated as:

[tex]\mathbf{\iiint_E y^2z^2 dV = \iiint _E \ y^2 z^2 \ dx dy dz }[/tex]

[tex]\mathbf{\implies \iiint _E \ y^2 z^2 \ dx dy dz = \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \int ^1_0 \ (\rho sin \phi sin \theta )^2 ( \rho cos \phi )^2 \rho^2 sin \phi d \rhod \phi d \theta }[/tex]

[tex]\mathbf{\implies \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi sin^2 \theta \ \int^1_0 \ \rho^6 d \rho d \phi d \theta }[/tex]

[tex]\mathbf{\implies \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi sin^2 \theta \Big [ \dfrac{\rho^7}{7} \Big]^1_0 \ d \phi d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi \ d \phi d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta \int ^{\dfrac{\pi}{3}}_{0} \ sin \phi( 1- cos^2 \phi)cos^2 \phi \ d \phi d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \phi}{5}- \dfrac{cos ^3 \phi}{3} \Bigg ] ^{\dfrac{\pi}{3}}_{0} d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \dfrac{\pi}{3}}{5}- \dfrac{cos ^3 \dfrac{\pi}{3}}{3}- \dfrac{cos^5 0}{5}+ \dfrac{cos^3 0}{3} \Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{2}{15}- \dfrac{17}{480} \Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{(480\times 2) -(15\times 17)}{15\times 480}\Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{705}{15\times 480}\Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \int ^{2 \pi}_{0} 2sin ^2 d \theta}[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \int ^{2 \pi}_{0} (1-cos 2\theta) \ d \theta}[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \Bigg [\theta - \dfrac{sin 2 \theta }{2}\Bigg] ^{2 \pi}_{0}}[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \Bigg [2 \pi\Bigg] }[/tex]

[tex]\mathbf{\iiint_E y^2z^2 dV = \dfrac{47 \times 2 \pi}{6720}} }[/tex]

[tex]\mathbf{\iiint_E y^2z^2 dV = \dfrac{47 \pi}{3360} }[/tex]

Learn more about triple integral here:

https://brainly.com/question/2289273?referrer=searchResults

Answer:

[tex]1\frac{2}{3}\ kg[/tex]

Step-by-step explanation:

we know that

To find out how much the guests ate, multiply the total amount of kg of mashed potatoes by the 4/12 fraction

so

[tex]5(\frac{4}{12})=\frac{20}{12}\ kg[/tex]

convert to mixed number

[tex]\frac{20}{12}=\frac{12}{12}+\frac{8}{12}=1\frac{8}{12}\ kg[/tex]

simplify

[tex]1\frac{8}{12}=1\frac{2}{3}\ kg[/tex]

The guests consumed 1.67 kilograms of the 5 kilograms of mashed potatoes that the chef had made.

To solve this problem, we need to multiply the total amount of mashed potatoes made by the fraction that the guests consumed.

Given that the chef cooked 5 kilograms of mashed potatoes and the guests ate 4/12 (which simplifies down to 1/3) of this amount, we multiply these two together.

So, the calculation would be 5 × 1/3 = 1.67 kilograms.

Therefore, the guests ate 1.67 kilograms of mashed potatoes.

https://brainly.com/question/23715562

#SPJ3

Answer:

3975

Step-by-step explanation:

fog functions are basically f(g(o)).

So for this problem, it would be f(g(-7)).

Plug in -7 to the g(x) equation first, and you should get -63.

Then plug -63 into the f(x) equation, and you should finish with 3975.

Answer:

See below  

Step-by-step explanation:

7)

AT² = 11² + 4² = 121 + 16 = 137

AT = √137

sinA = DT/AT = 11/√137 = (11√137)/137

cosA = AD/AT = 4/√137 = (4√137)/137

tanA = DT/AD                 = 11/4

sinT = AD/AT = 4/√137 = (4√137)/137

cosT = DT/AT = 11/√137 = (11√137)/137

tanT = AD/DT                 = 4/11

9)

AT² = 8² + 3² = 64 + 9 = 73

AT = √73

sinA = LT/AT = 8/√73 = (8√73)/73

cosA = AL/AT = 3/√73 = (3√73)/73

tanA = LT/AL                = 8/3

sinT = AL/AT = 3/√73 = (3√73)/73

cosT = LT/AT = 8/√73 = (8√73)/73

tanT = AL/LT                = 3/8

11)

    6² =  4² + RT²

  36 = 16  + RT²

RT² = 20

RT =√20 = √(4× 5) = 2√5

 sinA = RT/AT = (2√5)/6 = (√5)/3

cosA = AR/AT = 4/6        = 2/3

tanA = RT/AR = (2√5)/4 = (√5)/2

 sinT = AR/AT = 4/6        = 2/3

cosT = RT/AT = (2√5)/6 = (√5)/3

tanT = AR/RT = 4/(2√5)  = (2√5)/5

Answer:

84 feet to the nearest foot.

Step-by-step explanation:

We have a right angled triangle with adjacent side (A) = 100 and you want to find the height of the tower, the opposite side (O).

A = 100 , O = ? so we need the tangent , (from SOH-CAH-TOA).

tan 40 = O/ 100

O = 100 tan 40

= 83.9 feet.

Final answer:

To determine the height of the tower, we can use the tangent of the angle of elevation, 40 degrees, multiplied by the distance, 100 feet, which results in approximately 84 feet.

Explanation:

To find the height of a tower with an angle of elevation of 40°, observed from 100 feet away, you can use trigonometric functions. Specifically, the tangent function, which is defined as the ratio of the opposite side (the height of the tower we're looking for) to the adjacent side (the distance from the tower).

We have:

The angle of elevation (θ) = 40°

The distance from the tower (adjacent side) = 100 feet

The height of the tower can be calculated as:

height = tan(θ) × adjacent side
= tan(40°) × 100 feet

Using a calculator, we find:

height = tan(40°) × 100
= 0.8391 × 100
≈ 84 feet (to the nearest foot)

Therefore, the tower is approximately 84 feet high.

The side length of the canvas is best found by using the quadratic formula

because the equation is prime. Solving the equation produces two

approximate measurements, and one must be discarded for being

unreasonable.

I took the test and this was correct.