Resources

Resources

Interpret parts of quadratic expressions: word problems

1.08 s+1.02 b

predicts the end-of-year value of a financial portfolio where

s

is the value of stocks and

b

is the value of bonds in the portfolio at the beginning of the year.

\newline

What is the predicted end-of-year value of a portfolio that begins the year with

\$ 200

\$ 100

\newline

\$

6

\$ 6.60

\newline

Which equation would help determine the cost of

3

\newline

1

\newline

\frac{3}{x}=\frac{\$ 6.60}{6}

\newline

\frac{3}{6}=\frac{\$ 6.60}{x}

\newline

\frac{x}{3}=\frac{6}{\$ 6.60}

\newline

\frac{x}{3}=\frac{\$ 6.60}{6}

\newline

(E) None of the above

Elena is solving the following equation for

x

\newline

\sqrt[3]{3 x-5}+2=7

\newline

Her first few steps are given below.

\newline

\begin{aligned} \sqrt[3]{3 x-5} & =5 \\ (\sqrt[3]{3 x-5})^{3} & =(5)^{3} \\ 3 x-5 & =125 \end{aligned}

\newline

Is it necessary for Elena to check her answers for extraneous solutions?

\newline

1

\newline

\newline

Antonio is solving the following equation for

y

\newline

-1=\sqrt{y+11}-y

\newline

His first few steps are given below.

\newline

\begin{aligned} y-1 & =\sqrt{y+11} \\ (y-1)^{2} & =(\sqrt{y+11})^{2} \\ y^{2}-2 y+1 & =y+11 \end{aligned}

\newline

Is it necessary for Antonio to check his answers for extraneous solutions?

\newline

1

\newline

\newline

Dubai, United Arab Emirates set a record temperature for

49^{\circ} \mathrm{C}

\newline

What does the number

49

\newline

1

\newline

(A) Dubai's record high temperature is

49^{\circ} \mathrm{C}

\newline

(B) Dubai's record high temperature is

49^{\circ} \mathrm{C}

Credit card companies use negative balances to represent when the credit card company owes the customer money and positive balances to represent when the customer owes the credit card company money.

\newline

Sneha has a balance of

0

dollars with her credit card company.

\newline

What does a balance of

0

dollars represent?

\newline

1

\newline

(A) Sneha owes the credit card company money.

\newline

(B) Neither Sneha nor the credit card company owes money.

\newline

(C) The credit card company owes Sneha money.

The elevation of Death Valley, CA is

-86 \mathrm{~m}

\newline

What does the number

-86

\newline

1

\newline

(A) Death Valley is located

86 \mathrm{~m}

below sea level.

\newline

(B) Death Valley is located

86 \mathrm{~m}

above sea level.

When discussing temperature, meteorologists talk about temperature as it relates to the freezing point. The freezing point is

0{ }^{\circ}

\newline

On Monday, it is

4^{\circ}

\newline

On Tuesday, it is

2^{\circ}

\newline

On Wednesday, it is

1^{\circ}

\newline

On Thursday, it is

4^{\circ}

\newline

Which two days are the same distance from the freezing point?

\newline

1

\newline

(A) Monday and Tuesday

\newline

(B) Wednesday and Thursday

\newline

(C) Monday and Thursday

\newline

(D) Tuesday and Wednesday

Four friends are on vacation in Hawaii.

\newline

Leilani is hiking in Oahu at

952 \mathrm{~m}

\newline

Keanu is snorkeling at

-2 \mathrm{~m}

\newline

Kiah is scuba diving at

608 \mathrm{~m}

\newline

Kanoa is enjoying a picnic at

4 \mathrm{~m}

\newline

Which friend is closest to sea level?

\newline

1

\newline

\newline

\newline

\newline

A submarine is diving toward the bottom of the ocean.

\newline

D

of the submarine, in feet below sea level, after

t

minutes have elapsed is given by the function

D(t)=20+16 t

\newline

P

, in pounds per square inch, exerted on the submarine at a depth of

x

feet is given by the function

\newline

P(x)=14.7+0.445 x \text { }

\newline

Which expression models the pressure exerted on the submarine as a function of the elapsed time,

t

\newline

1

\newline

235.2+27.12 t

\newline

23.6+7.12 t

\newline

255.2+7.12 t

\newline

8.9+21.82 t

Moses has a bakery, and he is expecting a new shipment of flour today.

\newline

The number of loaves,

N

, that Moses will bake today given that he receives

k

kilograms of flour is given by the function

\newline

N(k)=10+3 k \text {. }

\newline

I

, in dollars, that Moses makes from baking

x

loaves of bread is given by

I(x)=6 x

\newline

Which expression models Moses's income for the day if he receives

k

kilograms of flour?

\newline

1

\newline

60+3 k

\newline

10+9 k

\newline

60+18 k

\newline

10+18 k

Pluto's distance from the sun varies in a periodic way that can be modeled approximately by a trigonometric function.

\newline

Pluto's maximum distance from the sun (aphelion) is

7

4

billion kilometers. Its minimum distance from the sun (perihelion) is

4

4

billion kilometers. Pluto last reached its perihelion in the year

1989

, and will next reach its perihelion in

2237

\newline

Find the formula of the trigonometric function that models Pluto's distance

D

from the sun (in billion

\mathrm{km}

t

2000

. Define the function using radians.

\newline

D(t)=\square

\newline

How far will Pluto be from the sun in

2022

? Round your answer, if necessary, to two decimal places.

\newline

\mathrm{km}

Wei is standing in wavy water and notices the depth of the waves varies in a periodic way that can be modeled by a trigonometric function. He starts a stopwatch to time the waves.

\newline

1

1

seconds, and then again every

3

seconds, the water just touches his knees. Between peaks, the water recedes to his ankles. Wei's ankles are

12 \mathrm{~cm}

off the ocean floor, and his knees are

55 \mathrm{~cm}

off the ocean floor.

\newline

Find the formula of the trigonometric function that models the depth

D

t

seconds after Wei starts the stopwatch. Define the function using radians.

\newline

D(t)=\square

After a certain medicine is ingested, its concentration in the bloodstream changes over time.

\newline

The relationship between the elapsed time,

t

, in minutes, since the medicine was ingested, and its concentration in the bloodstream,

C_{\text {minute }}(t)

\mathrm{mg} / \mathrm{L}

, is modeled by the following function:

\newline

C_{\text {minute }}(t)=61 \cdot(0.96)^{t}

\newline

Complete the following sentence about the hourly rate of change in the medicine concentration. Round your answer to two decimal places.

\newline

Every hour, the medicine concentration decays by a factor of

\square

The chemical element einsteinium

253

naturally loses its mass over time. When a sample of einsteinium

-253

was initially measured, it had a mass of

15

\newline

The relationship between the elapsed time

t

, in weeks, and the mass,

M_{\text {week }}(t)

, left in the sample is modeled by the following function:

\newline

M_{\text {week }}(t)=15 \cdot(0.79)^{t}

\newline

Complete the following sentence about the daily rate of change in the mass of the sample.

\newline

Round your answer to two decimal places.

\newline

Every day, the mass of the sample decays by a factor of

Laurent invested some money in a bank account.

\newline

The relationship between the elapsed time,

t

, in decades, since Laurent invested the money, and the total amount of money in the account,

M_{\text {decade }}(t)

, in dollars, is modeled by the following function:

\newline

M_{\text {decade }}(t)=4900 \cdot(1.5)^{t}

\newline

Complete the following sentence about the yearly rate of change in the amount of money in the account.

\newline

Round your answer to two decimal places.

\newline

Every year, the amount of money in the account increases by a factor of

Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish.

\newline

The relationship between the elapsed time,

t

, in days, since an ocean sunfish is born, and its mass,

M_{\text {day }}(t)

, in milligrams, is modeled by the following function:

\newline

M_{\text {day }}(t)=3.5 \cdot(1.05)^{t}

\newline

Complete the following sentence about the weekly rate of change in the mass of the sunfish.

\newline

Round your answer to two decimal places.

\newline

Every week, the mass of the sunfish increases by a factor of

Ocean sunfish are well-known for rapidly gaining a lot of weight on a diet based on jellyfish.

\newline

The relationship between the elapsed time,

t

, in days, since an ocean sunfish is born, and its mass,

M(t)

, in milligrams, is modeled by the following function:

\newline

M(t)=(1.34)^{\frac{t}{6}+4}

\newline

Complete the following sentence about the daily rate of change in the mass of the sunfish.

\newline

Round your answer to two decimal places.

\newline

Every day, the mass of the sunfish is multiplied by a factor of

A large open meadow near your city is shrinking in size because developers have started building new homes there.

\newline

The relationship between

A

, the area of the meadow, in hectares, and

t

, the elapsed time, in months, since the construction began is modeled by the following function.

\newline

A=1562.5 \cdot 10^{-0.1 t}

\newline

How many months of construction will there be before the area of the meadow decreases to

500

\newline

Give an exact answer expressed as a base

-10

\newline

A pot of piping hot stew has been removed from the stove and left to cool.

\newline

The relationship between the elapsed time,

m

, in minutes, since the stew was removed from the stove, and the temperature of the stew,

T(m)

{ }^{\circ} C

, is modeled by the following function.

\newline

T(m)=20+50 \cdot 10^{-0.04 m}

\newline

How many minutes will it take for the stew to cool to a temperature of

30^{\circ} \mathrm{C}

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

Aditi is participating in a walkathon fundraiser. Two anonymous donors agree to donate money according to the distance she walks. The money,

A

, in dollars, that she receives from the first donor for walking

d

kilometers is given by the formula

A(d)=12 d

. The total money,

T

, in dollars, that she receives from both donors for walking

d

kilometers is given by the formula

T(d)=d^{2}+20 d

\newline

B

be the money that Aditi receives from the second donor for walking

d

\newline

Write a formula for

B(d)

A(d)

d

0

\newline

B(d)=

\newline

Write a formula for

B(d)

d

\newline

B(d)=\square

Devorah is filling a pool with a hose. The volume,

H

, in liters, of water coming out of the hose in

m

minutes is given by the function

H(m)=17.4 m

. However, it is a sunny day, and water is also evaporating from the pool. Therefore, the volume,

V

, in liters, of water in the pool

m

minutes after Devorah started filling it is given by

V(m)=17 m

\newline

E

be the volume of water, in liters, that has evaporated from the pool

m

minutes after Devorah started filling it.

\newline

Write a formula for

E(m)

H(m)

m

0

\newline

E(m)=

\newline

Write a formula for

E(m)

m

\newline

E(m)=

Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money,

A

, in dollars, that he receives from the first donor given that he walks

d

kilometers is given by the formula

A(d)=10 d

B

, in dollars, that he receives from the second donor given that he walks

d

kilometers is given by the formula

B(d)=2 d+d^{2}

\newline

T

be the total money that Onur raises from those donors by walking

d

kilometers in the walkathon.

\newline

Write a formula for

T(d)

A(d)

d

0

\newline

T(d)=

\newline

Write a formula for

T(d)

d

\newline

T(d)=\square

Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of

15 \frac{1}{2} \mathrm{~m}^{2}

. Gabriel wants it to be

7 \frac{3}{4} \mathrm{~m}

\newline

How wide does the planter box need to be?

\newline

Skylar is a lifeguard at a swimming pool. Last week, they worked

3 \frac{3}{4}

equal-length shifts, because rain closed the pool early one day. Those shifts totaled

11 \frac{1}{4}

\newline

How long is a single shift?

\newline

An electrician plans to install solar panels on a rectangular section of roof with an area of

69 \mathrm{~m}^{2}

\newline

69 \div 7 \frac{1}{10}

could represent the length of the section if the roof is

7 \frac{1}{10} \mathrm{~m}

\newline

69 \div 7 \frac{1}{10}

could represent the number of solar panels that would fit if each panel was

7 \frac{1}{10} \mathrm{~m}

\newline

Whose interpretation makes sense in this context?

\newline

1

\newline

(A) Tyriq's only

\newline

(B) Corbin's only

\newline

(C) Both Tyriq's and Corbin's

A class collected

2,650 \mathrm{~L}

of materials to recycle.

\newline

Reginald said that

2,650 \div 49 \frac{1}{10}

could represent the volume of each bag if the class filled

49 \frac{1}{10}

bags with material to recycle.

\newline

2,650 \div 49 \frac{1}{10}

could represent the number of containers the class filled if each container holds

49 \frac{1}{10} \mathrm{~L}

\newline

Whose interpretation makes sense in this context?

\newline

1

\newline

(A) Reginald's only

\newline

(B) Peni's only

\newline

(C) Both Reginald's and Peni's

2013

, the population of Nevada and North Carolina were each growing at a rate of approximately

3.3 \%

per year. In addition, the US Census Bureau estimated that the population of Nevada and North Carolina was

2

8

9

8

million people, respectively. If the population growth rates in each of these states remained the same, approximately how many more people were living in North Carolina compared to Nevada in

2014

\newline

1

\newline

7

0

\newline

7

2

\newline

9

3

\newline

\mathbf{1 3 . 0}

Daniela has a three-season acting contract for a new TV show. Her pay for Season

1

p

dollars. Then, her pay will increase by

5

percent from Season

1

2

10

percent from Season

2

3

. Which of the following represents Daniela's Season

3

pay in terms of

p

\newline

1

\newline

1.15 p

\newline

\frac{p}{1.15}

\newline

(1.05)(1.1) p

\newline

\frac{p}{(1.05)(1.1)}

r=\frac{-181 k\left(T_{\mathrm{t}}-T_{\mathrm{w}}\right)}{200}

\newline

The formula gives the temperature change

r

, in degrees Celsius per minute, of tortellini while it is being cooked, given the initial temperatures of the tortellini,

T_{\mathrm{t}}

, and the water,

T_{\mathrm{w}}

, in degrees Celsius, and a heat conductivity of the tortellini of

k

joules per square centimeter per second. Which equation correctly gives the heat conductivity of the tortellini in terms of the temperature change per minute and the initial temperatures of the water and tortellini?

\newline

1

\newline

k=\frac{200\left(r+T_{\mathrm{w}}\right)}{-181 T_{\mathrm{t}}}

\newline

k=\frac{200 r}{-181\left(T_{\mathrm{t}}-T_{\mathrm{w}}\right)}

\newline

k=\frac{200 r+T_{\mathrm{W}}}{-181 T_{+}}

Aiden is a taxi driver.

\newline

M(n)

models Aiden's fee (in dollars) for his

n^{\text {th }}

drive on a certain day.

\newline

What does the statement

M(8)<M(4)

\newline

1

\newline

(A) Aiden earned less money for his

8^{\text {th }}

than he earned for his

4^{\text {th }}

\newline

(B) Aiden earned

\$ 8

for fewer drives than the number of drives for which he earned

\$ 4

\newline

(C) Aiden earned

\$ 8

for a drive that was earlier than a drive for which he earned

\$ 4

Aiden is a taxi driver.

\newline

M(n)

models Aiden's fee (in dollars) for his

n^{\text {th }}

drive on a certain day.

\newline

What does the statement

M(8)<M(4)

\newline

1

\newline

(A) Aiden earned less money for his

8^{\text {th }}

than he earned for his

4^{\text {th }}

\newline

(B) Aiden earned

\$ 8

for a drive that was earlier than a drive for which he earned

\$ 4

\newline

(C) Aiden earned

\$ 8

for fewer drives than the number of drives for which he earned

\$ 4

Mustafa is staring at a pizza spinning on a wheel in a glass case.

\newline

The pizza is cut into four even slices. The distance

P(t)

\mathrm{cm}

) between the center of the tastiest looking slice and the door of the glass case as a function of time

t

(in seconds) can be modeled by a sinusoidal function of the form

a \cdot \cos (b \cdot t)+d

\newline

t=0

, the center of the tastiest looking slice is farthest from the door, at a distance of

30 \mathrm{~cm}

2 \pi

seconds, it is closest to the door, at a distance of

10 \mathrm{~cm}

\newline

P(t)

\newline

t

should be in radians.

\newline

P(t)=

Aditya's dog routinely eats Aditya's leftovers, which vary seasonally. As a result, his weight fluctuates throughout the year.

\newline

The dog's weight

W(t)

\mathrm{kg}

) as a function of time

t

(in days) over the course of a year can be modeled by a sinusoidal expression of the form

a \cdot \cos (b \cdot t)+d

\newline

t=0

, the start of the year, he is at his maximum weight of

9.1 \mathrm{~kg}

. One-quarter of the year later, when

t=91.25

, he is at his average weight of

8.2 \mathrm{~kg}

\newline

W(t)

\newline

t

should be in radians.

\newline

W(t)=

2019

, the population of the United Kingdom was approximately

66

7

million. According to a randomized poll,

41 \%

of the poll respondents approved of the country's leadership. If the poll participants were representative of the entire population of the United Kingdom, approximately how much of the population, in millions of people, approved of the country's leadership?

\newline

(Give your answer to the nearest tenth of a million. For example, if the answer is

11

2

11

2

If the price of a

7

-pound bag of dried black beans is

\$ 9.80

, which of the following statements is true?

\newline

1

\newline

A The price of the dried black beans is

\$ 1.00

\newline

(B) The price of the dried black beans is

\$ 1.40

\newline

(C) The price of the dried black beans is

\$ 2.80

\newline

D The price of the dried black beans is

\$ 68.60

The strength of a magnetic field is measured in teslas. One tesla is equal to one weber per square meter, as follows:

\newline

1 \mathrm{~T}=1 \frac{\mathrm{Wb}}{\mathrm{m}^{2}}

\newline

Divya is building a circuit for her physics class. Point

P

on one of her wires has a magnetic field strength of

6 \cdot 10^{6}

webers per square megameter, where

1

megameter is equal to

10^{6}

meters. What is the magnetic field strength in teslas?

\newline

1

\newline

6 \cdot 10^{-6}

\newline

6 \cdot 10^{0}

\newline

6 \cdot 10^{12}

\newline

6 \cdot 10^{18}

The kinetic energy, measured in kilogram meters squared per second squared

\left(\frac{\mathrm{kg} \cdot \mathrm{m}^{2}}{\mathrm{~s}^{2}}\right)

, of the International Space Station is approximately:

\newline

13,340,250,000,000 \frac{\mathrm{kg} \cdot \mathrm{m}^{2}}{\mathrm{~s}^{2}}

\newline

1

(\mathrm{J})

1 \frac{\mathrm{kg} \cdot \mathrm{m}^{2}}{\mathrm{~s}^{2}}

1

(\mathrm{TJ})

10^{12} \mathrm{~J}

, what is the approximate kinetic energy of the Space Station in terajoules to the nearest hundredth?

\newline

1

\newline

0.1334

\mathrm{TJ}

\newline

1.334

\mathrm{TJ}

\newline

13.34

\mathrm{TJ}

\newline

13.34 \cdot 10^{12}

\mathrm{TJ}

Creep is the ratio of elongation to original length that occurs in materials over time. For a particular steel structure, for the first

50

days the creep increases by

6 \times 10^{-6}

per day. After the

50

th day, when the creep is

3 \times 10^{-4}

, the creep triples every

62

days. After the

236

th day, how much less would the creep be if it had continued to grow linearly after the

50

\newline

1

\newline

1.1 \times 10^{-3}

\newline

1.4 \times 10^{-3}

\newline

6.7 \times 10^{-3}

\newline

8.1 \times 10^{-3}

The cumulative costs of a tankless water heater and tank water heater are

\$ 4,090

each at the end of the

7^{\text {th }}

year of use. The cumulative costs of the tankless heater increase

\$ 180

per year, but for the tank heater, they increase by

11 \%

per year. By the end of the

10^{\text {th }}

year, about how much more will the cumulative costs of the tank heater be than those of the tankless heater?

\newline

1

\newline

\$ 964

\newline

\$ 1,504

\newline

\$ 4,625

\newline

\$ 5,723

2000

0

025

phone subscriptions per person in Africa for both mobile and land-line phones. After that, the land-line phone subscriptions steadily increased by

0

01

7

years, while the mobile phone subscriptions grew

48 \%

per year. What was the total number of phone subscriptions per person in

2002

\newline

1

\newline

0

027

\newline

0

034

\newline

0

073

\newline

0

083

A cereal company wants to enlarge the volume of the cylindrical container used for one of its products by enlarging the radius of the cylinder. The height must be

20

centimeters. The new volume of the cylinder is given by the equation

V(x)=20 \pi(5+x)^{2}

x

is the additional length of the radius in centimeters. Which of the following equivalent expressions displays the current volume of the cylinder as a constant or coefficient?

\newline

1

\newline

\pi\left(20 x^{2}+200 x+500\right)

\newline

20 \pi\left(x^{2}+10 x+10\right)+3

\newline

20 \pi\left(x^{2}+10 x+25\right)

\newline

20 \pi x^{2}+200 \pi x+500 \pi

\left[H^{+}\right]=10^{-\mathrm{pH}}

\newline

\mathrm{pH}

is a measure of the hydrogen ion concentration,

\left[\mathrm{H}^{+}\right]

, measured in moles per liter, of a solution. Solutions with a high concentration of hydrogen ions have a low

\mathrm{pH}

and solutions with a low concentration of hydrogen ions have a high

\mathrm{pH}

. The relationship between

\left[\mathrm{H}^{+}\right]

\mathrm{pH}

is shown in the equation. What is the effect on

\mathrm{pH}

if the hydrogen ion concentration is multiplied by

10

\newline

1

\newline

\mathrm{pH}

1

\newline

\mathrm{pH}

is multiplied by

10

\newline

\mathrm{pH}

10

\newline

\mathrm{pH}

1

h

, in feet, of a baseball

t

seconds after Tobin hit it with a baseball bat can be modeled by the equation:

\newline

h(t)=-16 t^{2}+64 t+4

\newline

Which of the following equivalent expressions displays the value of the baseball's maximum height as a constant or coefficient?

\newline

1

\newline

-16(t-2)^{2}+68

\newline

-4 t(4 t-16)+4

\newline

-16\left(t^{2}-4 t-\frac{1}{4}\right)

\newline

-16\left(t^{2}-4 t\right)+4

In one hour, the distance,

d(s)

, in kilometers that a ferry can travel up and down a river flowing with a constant speed,

s

, in meters per second is:

\newline

d(s)=10.7-1.2 s^{2}

\newline

s

d(s)

are positive. Which of the following equivalent expressions for

d(s)

contains the speed of the river in meters per second, as a constant or coefficient, for which the ferry can travel a distance of

8

kilometers in one hour?

\newline

1

\newline

8-1.2(s-1.5)(s+1.5

\newline

8+1.2\left(2.25-s^{2}\right)

\newline

8\left(1-0.15 s^{2}\right)+2.7

\newline

11.9-1.2(s-1)^{2}-2.4

A surveyor discovers that the total combined length of all roads, in miles (mi), of a particular city was

500

at the beginning of

1950

and increased by

125 \mathrm{mi}

every ten years. Additionally, the number of cars driven in the city was

50

000

at the beginning of

1950

and increased by

20

percent every ten years. What was the difference between the number cars driven in the city per mile of city road at the beginning of

1950

and at the beginning of

1990

\newline

1

\newline

3

68

\newline

10

\newline

\mathbf{1 0 7 . 3 6}

\newline

\mathbf{1 0 3 . 6 8}

Huang Yi works as a paleontologist and a sculptor.

\newline

P

represent the number of months Huang Yi must work as a paleontologist and

S

represent the number of months she must work as a sculptor to make at least

\$ 50,000

\newline

5500 P+4500 S \geq 50000

\newline

Huang Yi worked for

6

months as a paleontologist this year. What is the minimum number of months that she must work as a sculptor to reach her goal?

\newline

1

\newline

(A) Huang Yi must work as a sculptor for at least

3

\newline

(B) Huang Yi must work as a sculptor for at least

4

\newline

(C) Huang Yi must work as a sculptor for at least

5

\newline

(D) Huang Yi must work as a sculptor for at least

6

A publishing company prints newspapers and magazines.

\newline

N

represent the number of newspapers and

M

represent the number of magazines the company can print with its daily supply of ink cartridges.

\newline

0.5 N+2.5 M \leq 6000

\newline

The company wants to print

8000

newspapers daily. How many magazines at most can the company print daily with the remaining number of ink cartridges?

\newline

1

\newline

(A) The company can print

800

magazines at most.

\newline

(B) The company can print

2500

magazines at most.

\newline

(C) The company can print

6000

magazines at most.

\newline

(D) The company can print

8000

magazines at most.

Choo Kheng must travel at least

288

kilometers in a submarine in order to reach her destination.

\newline

S

represent the number of hours the submarine can travel on the water's surface and

U

represent the number of hours it can travel underwater in order to reach Choo Kheng's destination.

\newline

36 S+64 U \geq 288

\newline

The submarine travels for

2 \frac{2}{3}

hours on the water's surface. What is the least number of hours the submarine must travel underwater in order for Choo Kheng to reach her destination?

\newline

1

\newline

(A) The submarine must travel for at least

1

\newline

(B) The submarine must travel for at least

2

\newline

(C) The submarine must travel for at least

3

\newline

(D) The submarine must travel for at least

4

...