Forming Inequalities from statement

Q.

Find the largest three consecutive natural numbers, such that the sum of one-third of first, one-fourth of second and one-fifth of the third is atmost $25$.

Q.

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

Q.

Jackie has two summer jobs. She works as a tutor, which pays $\$12$ per hour, and she works as a lifeguard, which pays $\$9.50$ per hour. She can work no more than 20 hours per week, but she wants to earn at least $\$220$ per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

1. $12x+9.5y\le 220;x+y\ge 20$
2. $12x+9.5y\le 220;x+y\le 20$
3. $12x+9.5y\ge 220;x+y\le 20$
4. $12x+9.5y\ge 220;x+y\le 20$

Q.

A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than $20\%$ of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p?

1. $p>0.20(300-36),wherep\le 150$
2. $p>0.20(300+36),wherep\le 150$
3. $p-36>0.20\left(300\right),wherep\le 150$
4. $p+36>0.20\left(300\right),wherep\le 150$

Q. Maria plans to rent a boat. The boat rental costs $\$60$ per hour, and she will also have to pay for a water safety course that costs $\$10$. Maria wants to spend no more than $\$280$ for the rental and the course. If the boat rental is available only for a whole number of hours, the maximum number of hours for which Maria can rent the boat is ___

Q.

Each morning, John jogs at 6 miles per hour and rides a bike at 12 miles per hour. His goal is to jog and ride his bike a total of at least 9 miles in less than 1 hour. If John jogs j miles and rides his bike b miles, which of the following systems of inequalities represents John’s goal?

1. $\frac{j}{6}+\frac{b}{12}\ge 1;j+b<9$
2. $6j+12b<1;j+b\ge 1$
3. $\frac{j}{6}+\frac{b}{12}<1;j+b\ge 9$
4. $6j+12b\ge 9;j+b<1$

Q.

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

1. $7.35d+6.2s\le 300;d\ge 2s$
2. $7.35d+6.2s\le 300;2d\ge s$
3. $14.7d+6.2s\le 300;2d\ge s$
4. $14.7d+6.2s\le 300;d\ge 2s$

Q.

Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal?

1. $\frac{240+310+320}{3}+x\ge 280$
2. $240+310+320\ge x\left(280\right)$
3. $\frac{240}{4}+\frac{310}{4}+\frac{320}{4}+x\ge 280$
4. $240+310+320+x\ge 4\left(280\right)$

Q.

On January 1, 2000, there were 175, 000 tons of trash in a landfill that had a capacity of 325, 000 tons. Each year since then, the amount of trash in the landfill increased by 7, 500 tons. If y represents the time, in years, after January 1, 2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?

1. $325,000\le 7500y$
2. $325,000-7500\le y$
3. $150,000\ge 7500y$
4. $175000+7500y\ge 325000$

Q.

A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let x be the number of 40-pound boxes and y be the number of 65-pound boxes. The forklift can carry up to either 45 boxes or a weight of 2, 400 pounds. Which of the following systems of inequalities represents this relationship?

1. $40x+65\le 2400;x+y\le 45$
2. $\frac{x}{40}+\frac{y}{65}\le 2400;x+y\le 45$
3. $40x+65\le 45;x+y\le 2400$
4. $40x+65\le 2400;x+y\le 2400$

Q. The cost, in cents, of manufacturing $x$ pencils, is $1200+20x$. The pencil sells for 50 cents each. What number of pencils need to be sold so that the revenue received is at least equal to the manufacturing cost?

1. 33
2. 36
3. 40
4. 27

Q.

A die is thrown three times. Let X be the 'number of twos seen', find the expectation of X.

Q. in combination problems why are we adding the total number of combinations if 'or' is given in the question and multiplying if 'and' is given.explain please.

Q.

There are $1000$ rabbits and chickens on a farm and together they have $3150$ legs.

How many rabbits and how many chickens are there on the farm?

Q.

A tub is $\frac{2}{5}$ full of water. If $10litres$ of water is taken out from it, then it is $\frac{3}{10}$ full. What is the capacity of the tub $?$

Q. More than 600 students travelled to a botanical garden for a college trip. The college allowed 7 students to travel by bike & the rest students on 12 buses, each of which held the same number of students. If there were x students in each bus, which inequality best represents this situation?

1. 7x + 12 > 600
2. 12x + 7 < 600
3. 7x + 12 < 600
4. 12x + 7 > 600

Q. A pollution filtering machine is installed in a factory, on a floor with area 2500 sq. feet. The machine is expected to filter at least 3500 liters of air and water. It filters air at the rate of 600 liters per hour and it filters water at the rate of 250 liter per hour. Which of the following inequalities represents the number of hours the machine should filter air (A) and water (W) to meet the expectation?

1. $600A+250W\ge 3500$
2. $600A+250W\le 3500$
3. $250A+600W\ge 3500$
4. $250A+600W\le 3500$

Q.

Henko is renting a car. The rental charge is $17.50perdayplus$0.16 per mile. Henko can spend at most $33 for the cost of the car rental. If Henko rents the car for one day, which of the following is one possible number of miles Henko can drive the rental car?

1. 53

2. 98

3. 110

4. 150

Q. Martin is ordering pizzas and cupcakes for a house party. He calls the Eat All bakery, and places order for x pizzas and y cupcakes. If a pizza costs $12\$$ and a cupcake costs $7\$$ and he had planned a budget of $90\$$ at the most, then which of the following inequalities models the situation in the best possible way?

1. $7x+12y>90$
2. $7x+12y\ge 90$
3. $12x+7y<90$
4. $12x+7y\le 90$

Q.

If the cost of $3$ dozens of banana is $Rs60$, then:

_____ dozens of banana can be bought for $Rs30$

Q.

You want to create a $95\%$ confidence interval with a margin of error of no more than $0.05$ for a population proportion.

The historical data indicate that population has remained constant at about $0.55$.

What is the minimum size random sample you need to construct this interval $?$

1. $223$

2. $324$

3. $378$

4. $381$

Q. If $\frac{x}{y}=\frac{15}{4}$ then find the value of $\frac{2y}{3x+2y}$

Q.

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Q.

If the entry fee to a fair is $\$5$ and each game at the fair costs $\$2$ to play, write an inequality for the total cost when a person plays n games and the maximum amount the person can spend is $\$25$.

1. $2n+5\le 25$
2. $5n+2\le 25$
3. $5n-2\le 25$
4. $2n-5\le 25$

Q. If $e^{x+y}-x=0$, prove that $\frac{dy}{dx}=\frac{1-x}{x}$

Q. A random variable $X$ takes the values $0,1$ and $2$. If $P(X=1)=P(X=2)$ and $P(X=0)=0.4$, then the mean value of the random variable $X$ is

1. $0.9$
2. $0.5$
3. $0.7$
4. $0.2$

Q. The least value of the expression $2{\log }_{10}x-{\log }_x\left(0.01\right)$ for $x>1$ is:

1. $1$
2. $2$
3. $3$
4. $4$

Q. A car travels $260$ km distance from a place $A$ to $B$, at a uniform speed $65$ km/hr passes through all thirteen green traffic signals, $4$ minutes at first signal, $7$ minutes at second signal, $10$ minutes at third signal and so on stops for $40$ minutes at thirteenth signal. How much total time it takes to reach at the place $B$? Solve by suitable Mathematical Method.

Q. A woman has m $\$20$ notes and n $\$50$ notes. The total amount of money in her possession cannot be less than $\$800$. Represent this as an inequality.

1. $20m+50n<800$
2. $20m+50n\le 800$
3. $20m+50n>800$
4. $20m+50n\ge 800$

Q. A beautician charges $\$15$ for a manicure. Her operating expense is $\$35$ per day (average). She calculates her profit by subtracting her operating costs from the money she earns from the manicure she gives. In a given day, the beautician expects to make a profit of at least $\$85$. If the beautician gives m manicure in a day. Which inequality best models this situation?

1. $15m-35\ge 85$
2. $15m+35\ge 85$
3. $15(m+35)\ge 85$
4. $15(m-35)\ge 85$