Question
In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by S(T) = 0.6T + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?
 The speed of sound, in meters per second, at 0°C
 The speed of sound, in meters per second, at 0.6°C
 The increase in the speed of sound, in meters per second, that corresponds to an increase of 1°C
 The increase in the speed of sound, in meters per second, that corresponds to an increase of 0.6°C
The correct answer is: The speed of sound, in meters per second, at 0°C
Solution:
Given : Speed of sound= S m/s
Temperature = T °C
S(T) = 0.6T + 331.4
We can compare this equation with the equation of straight line y= mx + c.
And T represents xaxis
We get yintercept, c= 331.4, when x= 0
Similarly , we will get S(T)= 331.4 when T=0
Therefore, the speed of sound in meters per second at 0°C will be 331.4 m/s
So, correct answer is Option A.
Related Questions to study
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?
 We have given that Jackie has two jobs. She works as a tutor and lifeguard.
 Payment as a tutor = $12 per hour
 x = Number of hours she tutors.
 Then amount as tutor will be calculate by multiplying number of hours, x and payment per hour, which will be 12x and same for lifeguard i. e 9.5y
 Minimum payment she requires= $220 per week.
 Maximum work in a week= 20 hours
Therefore, the correct option is C) 12x + 9.5y ≥ 220
x +y ≤ 20
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?
 We have given that Jackie has two jobs. She works as a tutor and lifeguard.
 Payment as a tutor = $12 per hour
 x = Number of hours she tutors.
 Then amount as tutor will be calculate by multiplying number of hours, x and payment per hour, which will be 12x and same for lifeguard i. e 9.5y
 Minimum payment she requires= $220 per week.
 Maximum work in a week= 20 hours
Therefore, the correct option is C) 12x + 9.5y ≥ 220
x +y ≤ 20
The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?
 For solving the above question,
 After the 40% discount, the price of the property became 0.6x dollars
 And after the additional 20% off the discounted price, the price of the property became 0.8(0.6x).
 Thus, in terms of the original price of the property, x, the purchase price of the property is 0.48x.
 It follows that
Solving this equation for x gives
x = 291,666.6 .
 Therefore, of the given choices, $291,700 best approximates the original price of the Glenview Street property.
 Option A is incorrect because it is the result of dividing the purchase price of the property by 0.4, as though the purchase price were 40% of the original price.
 Option C is incorrect because it is the closest to dividing the purchase price of the property by 0.6, as though the purchase price were 60% of the original price.
 Option D is incorrect because it is the result of dividing the purchase price of the property by 0.8, as though the purchase price were 80% of the original price.
The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?
 For solving the above question,
 After the 40% discount, the price of the property became 0.6x dollars
 And after the additional 20% off the discounted price, the price of the property became 0.8(0.6x).
 Thus, in terms of the original price of the property, x, the purchase price of the property is 0.48x.
 It follows that
Solving this equation for x gives
x = 291,666.6 .
 Therefore, of the given choices, $291,700 best approximates the original price of the Glenview Street property.
 Option A is incorrect because it is the result of dividing the purchase price of the property by 0.4, as though the purchase price were 40% of the original price.
 Option C is incorrect because it is the closest to dividing the purchase price of the property by 0.6, as though the purchase price were 60% of the original price.
 Option D is incorrect because it is the result of dividing the purchase price of the property by 0.8, as though the purchase price were 80% of the original price.
The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
The relationship between the monthly rental price r, in dollars, and the property’s purchase price p, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?
 We have given that the linear function that represents the relationship will be in the linerar form like
where a and b are constants
and r(p) = monthly rental price( in dollars) of a property
price = p thousands of dollars.
 According to the table, (70, 515) and (450, 3,365) are ordered pairs that should satisfy the function, which leads to the system of equations below.
 70a + b = 515
 450a + b= 3365
 Subtracting side by side the first equation from the second
380a = 2850;
 Solving for a gives
 Substituting 7.5 for a in the first equation of the system gives
 Solving for b gives
 Therefore, the linear function that represents the relationship is
Choices A, B, and C are incorrect because the coefficient of p, or the rate at which the rental price, in dollars, increases for every thousanddollar increase of the purchase price is different from what is suggested by these choices.
The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
The relationship between the monthly rental price r, in dollars, and the property’s purchase price p, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?
 We have given that the linear function that represents the relationship will be in the linerar form like
where a and b are constants
and r(p) = monthly rental price( in dollars) of a property
price = p thousands of dollars.
 According to the table, (70, 515) and (450, 3,365) are ordered pairs that should satisfy the function, which leads to the system of equations below.
 70a + b = 515
 450a + b= 3365
 Subtracting side by side the first equation from the second
380a = 2850;
 Solving for a gives
 Substituting 7.5 for a in the first equation of the system gives
 Solving for b gives
 Therefore, the linear function that represents the relationship is
Choices A, B, and C are incorrect because the coefficient of p, or the rate at which the rental price, in dollars, increases for every thousanddollar increase of the purchase price is different from what is suggested by these choices.
In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one
of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated
professional activity is research?
After analysis of table given in the question according to the table, 74 orthopedic surgeons indicated that research is their major professional activity.
Since a total of 607 surgeons completed the survey, it follows that the probability that the randomly selected surgeon is an orthopedic surgeon whose indicated major professional activity is research is 74 out of 607,
Options B, C, and D are incorrect and may be the result of finding the probability that
 For option B the randomly selected surgeon is an orthopedic surgeon whose major professional activity is teaching .
 For option C an orthopedic surgeon whose major professional activity is either teaching or research.
 For option D a general surgeon or orthopedic surgeon whose major professional activity is research.
In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one
of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated
professional activity is research?
After analysis of table given in the question according to the table, 74 orthopedic surgeons indicated that research is their major professional activity.
Since a total of 607 surgeons completed the survey, it follows that the probability that the randomly selected surgeon is an orthopedic surgeon whose indicated major professional activity is research is 74 out of 607,
Options B, C, and D are incorrect and may be the result of finding the probability that
 For option B the randomly selected surgeon is an orthopedic surgeon whose major professional activity is teaching .
 For option C an orthopedic surgeon whose major professional activity is either teaching or research.
 For option D a general surgeon or orthopedic surgeon whose major professional activity is research.
The system of equations above has solution (x, y). What is the value of x ?
Solution:
 We have given two equations
(2x + y) = (1)
y = 2x (2)
 We can solve this by Substitution method, Substitute value of y from equation 2 in equation 1
2x + 2x =
 Further solving we get
4x =
 Divide both sides by 4 we gwt,
x =
 Substituting value of x in equation 2 we get,
y = 21 × =
 Therefore
x=
y=
 Therefore value of x is .
The system of equations above has solution (x, y). What is the value of x ?
Solution:
 We have given two equations
(2x + y) = (1)
y = 2x (2)
 We can solve this by Substitution method, Substitute value of y from equation 2 in equation 1
2x + 2x =
 Further solving we get
4x =
 Divide both sides by 4 we gwt,
x =
 Substituting value of x in equation 2 we get,
y = 21 × =
 Therefore
x=
y=
 Therefore value of x is .
In State X, Mr. Camp’s eighthgrade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighthgrade classes and there are 1,800 eighthgrade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?
 We have given that 34.6% of 26 students in Mr. Camp’s class reported that they had at least two siblings.
there must have been 9 students in the class who reported having at least two siblings and remaining 26 9 = 17 students who reported that they had fewer than two siblings.
 It is also given that the average eighthgrade class size in the state is 26 and that Mr. Camp’s class is representative of all eighthgrade classes in the state. This means that in each eighthgrade class in the state there are about 17 students who have fewer than two siblings. Therefore, the best estimate of the number of eighthgrade students in the state who have fewer than two siblings is
or 17 × 1,800 = 30,600.
 Option A is incorrect because 16,200 is the best estimate for the number of eighthgrade students in the state who have at least, not fewer than, two siblings.
 siblings, more than half of the students in each eighthgrade class in the state have fewer than two siblings, too.
 Option D is incorrect because 46,800 is the estimated total number of eighthgrade students in the state.
In State X, Mr. Camp’s eighthgrade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighthgrade classes and there are 1,800 eighthgrade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?
 We have given that 34.6% of 26 students in Mr. Camp’s class reported that they had at least two siblings.
there must have been 9 students in the class who reported having at least two siblings and remaining 26 9 = 17 students who reported that they had fewer than two siblings.
 It is also given that the average eighthgrade class size in the state is 26 and that Mr. Camp’s class is representative of all eighthgrade classes in the state. This means that in each eighthgrade class in the state there are about 17 students who have fewer than two siblings. Therefore, the best estimate of the number of eighthgrade students in the state who have fewer than two siblings is
or 17 × 1,800 = 30,600.
 Option A is incorrect because 16,200 is the best estimate for the number of eighthgrade students in the state who have at least, not fewer than, two siblings.
 siblings, more than half of the students in each eighthgrade class in the state have fewer than two siblings, too.
 Option D is incorrect because 46,800 is the estimated total number of eighthgrade students in the state.
Which of the following is equivalent to the sum of the expressions a^{2}  1 and a + 1 ?
 Given two equations are a^{2 } 1 and a + 1.
 We have to find equivalent sum of both the expressions.
 Lets X be the sum of both the sums,
 Lets put the values of A and B in the equation
X = a^{2 }– 1 + a + 1
 We can see that there are two terms 1 and 1, if we add both of them their sum will be 0.
 Therefore, the correct option is (A) a^{2} + a
Which of the following is equivalent to the sum of the expressions a^{2}  1 and a + 1 ?
 Given two equations are a^{2 } 1 and a + 1.
 We have to find equivalent sum of both the expressions.
 Lets X be the sum of both the sums,
 Lets put the values of A and B in the equation
X = a^{2 }– 1 + a + 1
 We can see that there are two terms 1 and 1, if we add both of them their sum will be 0.
 Therefore, the correct option is (A) a^{2} + a
Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?
We have to find the power, in watts, is equal to 2 horsepower.
For solving this question,
Let us take x be the number of watts that is equal to 2 horsepower.
Since we have given that 5 horsepower is equal to 3730 watts,
5 horse power ~ 3730 watts
So, 2 horse power = x watts
This follows,
Multiplying both sides of equation by 3730
x = 1492
Therefore, 2 horsepower equals 1492 watts.
Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?
We have to find the power, in watts, is equal to 2 horsepower.
For solving this question,
Let us take x be the number of watts that is equal to 2 horsepower.
Since we have given that 5 horsepower is equal to 3730 watts,
5 horse power ~ 3730 watts
So, 2 horse power = x watts
This follows,
Multiplying both sides of equation by 3730
x = 1492
Therefore, 2 horsepower equals 1492 watts.
2(p + 1) + 8(p  1) = 5p
What value of p is the solution of the equation above?
2(p+1)+8(p1) = 5p
 Lets solve the brackets first
2p + 2 + 8p – 8 = 5p [ a(b + c) = ab + ac ]
 Adding the like terms
10p – 6 = 5p [2p + 8p=10p , 2 – 8 =  6]
 Subtract 5p from both sides
5p – 6 = 0
 Add 6 from both sides
5p = 6
 Divide both sides by 5
p = 6/5
 Therefore the value of p is 6/5
2(p + 1) + 8(p  1) = 5p
What value of p is the solution of the equation above?
2(p+1)+8(p1) = 5p
 Lets solve the brackets first
2p + 2 + 8p – 8 = 5p [ a(b + c) = ab + ac ]
 Adding the like terms
10p – 6 = 5p [2p + 8p=10p , 2 – 8 =  6]
 Subtract 5p from both sides
5p – 6 = 0
 Add 6 from both sides
5p = 6
 Divide both sides by 5
p = 6/5
 Therefore the value of p is 6/5
In the equation above, if a is negative and b is positive, which of the following must be true?
 We have given the equation
 The equation can be rewritten as ,
or .  Since and , it follows that
 And as b/a < 0

 1c < 0, or equivalent to c > 1.
 Option B is incorrect. If c = 1, then a – b = a, or b = 0. But it is given that b > 0, so c = 1 cannot be true.
 Option C is incorrect. If c = 1, then a  b = a, or 2a = b. But this equation contradicts the premise that a < 0 and b > 0, so c = 1 cannot be true.
 Option D is incorrect. For example, if c = 2, then a  b = 2a, or 3a = b. But this contradicts the fact that and have opposite signs, so c < 1 cannot be true.
In the equation above, if a is negative and b is positive, which of the following must be true?
 We have given the equation
 The equation can be rewritten as ,
or .  Since and , it follows that
 And as b/a < 0

 1c < 0, or equivalent to c > 1.
 Option B is incorrect. If c = 1, then a – b = a, or b = 0. But it is given that b > 0, so c = 1 cannot be true.
 Option C is incorrect. If c = 1, then a  b = a, or 2a = b. But this equation contradicts the premise that a < 0 and b > 0, so c = 1 cannot be true.
 Option D is incorrect. For example, if c = 2, then a  b = 2a, or 3a = b. But this contradicts the fact that and have opposite signs, so c < 1 cannot be true.
In the equation above, k is a constant. If x = 9, what is the value of K ?
 Given equation is .
 k is constant and x = 9
 Lets solve the equation, add x to both sides of equation, we get,
 As the value of x is given we will put it into the equation to find the value of k.
 Squaring on both sides we get,
 Subtract 2 from both sides we get,
 Therefore the value of k is 79, correct option is (D)79.
In the equation above, k is a constant. If x = 9, what is the value of K ?
 Given equation is .
 k is constant and x = 9
 Lets solve the equation, add x to both sides of equation, we get,
 As the value of x is given we will put it into the equation to find the value of k.
 Squaring on both sides we get,
 Subtract 2 from both sides we get,
 Therefore the value of k is 79, correct option is (D)79.
What value of x satisfies the equation above?
(We make sure that both the square roots are not on the same side o the equation.)
Squaring both sides, we get
Since,
Expanding the above equation, we get
Simplifying, we have
Dividing both sides by 3, we get
x = 8
Hence, the value of x which satisfies the given equation is 8.
Thus, the correct option is A).
What value of x satisfies the equation above?
(We make sure that both the square roots are not on the same side o the equation.)
Squaring both sides, we get
Since,
Expanding the above equation, we get
Simplifying, we have
Dividing both sides by 3, we get
x = 8
Hence, the value of x which satisfies the given equation is 8.
Thus, the correct option is A).
y ≤3x +1
x – y >1
Which of the following ordered pairs ( x, y)satisfies the system of inequalities above?
Method 1:
We have given two inequalities
y ≤3x +1
x – y >1
Any point (x, y) that is a solution to the given system of inequalities must
satisfy both inequalities in the system. Since the second inequality in the system can be rewritten as y < x − 1, the system is equivalent to the following system.
y ≤3x +1
x – y >1
Since , 3x + 1 > x − 1 for x > −1
and 3x + 1 ≤ x − 1 for x ≤ −1,
it follows that y < x − 1 for x > −1 and y ≤ 3x + 1 for x ≤ −1. Of the given choices,
only (2, −1) satisfies these conditions because −1 < 2 − 1 = 1
Method 2:
Substituting (2, −1) into the first inequality gives
−1 ≤ 3(2) + 1, or −1 ≤ 7,
which is a true statement.
Substituting (2, −1) into the second inequality gives
2 − (−1) > 1, or 3 > 1,
which is a true statement.
Therefore, since (2, −1) satisfies both inequalities,
it is a solution to the system.
 If we considered Option A , it is incorrect because substituting −2 for x and −1
 If we considered option B , it is incorrect because substituting −1 for x and 3 for
 If we considered option C, it is incorrect because substituting 1 for x and 5 for
y ≤3x +1
x – y >1
Which of the following ordered pairs ( x, y)satisfies the system of inequalities above?
Method 1:
We have given two inequalities
y ≤3x +1
x – y >1
Any point (x, y) that is a solution to the given system of inequalities must
satisfy both inequalities in the system. Since the second inequality in the system can be rewritten as y < x − 1, the system is equivalent to the following system.
y ≤3x +1
x – y >1
Since , 3x + 1 > x − 1 for x > −1
and 3x + 1 ≤ x − 1 for x ≤ −1,
it follows that y < x − 1 for x > −1 and y ≤ 3x + 1 for x ≤ −1. Of the given choices,
only (2, −1) satisfies these conditions because −1 < 2 − 1 = 1
Method 2:
Substituting (2, −1) into the first inequality gives
−1 ≤ 3(2) + 1, or −1 ≤ 7,
which is a true statement.
Substituting (2, −1) into the second inequality gives
2 − (−1) > 1, or 3 > 1,
which is a true statement.
Therefore, since (2, −1) satisfies both inequalities,
it is a solution to the system.
 If we considered Option A , it is incorrect because substituting −2 for x and −1
 If we considered option B , it is incorrect because substituting −1 for x and 3 for
 If we considered option C, it is incorrect because substituting 1 for x and 5 for
The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is the corresponding original dimension, what is the height of the reproduction, in inches ?
Reproduction made has dimensions rd of corresponding original dimensions so ,
The reproduction’s height is of the original height.
Reproduction height= original height / 3
=
= 9.6
Height of the reproduction is or in decimals 9.66 or 9.67 can be taken as the correct answer.
The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is the corresponding original dimension, what is the height of the reproduction, in inches ?
Reproduction made has dimensions rd of corresponding original dimensions so ,
The reproduction’s height is of the original height.
Reproduction height= original height / 3
=
= 9.6
Height of the reproduction is or in decimals 9.66 or 9.67 can be taken as the correct answer.
Which of the following is an example of a function whose graph in the xyplane has no xintercepts?
Lets consider option A, it says that A linear function whose rate of change is not zero.
 Rate of change = Slope of the line
In the question we have given that function has no xintercept. That means it should not intersect the xaxis. i.e.it should be parallel to the xaxis.
Now, xaxis is the line such that its slope, m= 0 and yintercept, c=0.
But as in the given option rate of change is not zero that means slope m≠0. So the line will not be parallel to xaxis. Hence, it will have xintercept at some point.
So, Option A is not correct.
Lets consider option B, it says that a quadratic function with real zero,
We know that, A zero or root of a function is the value of x at which the function is zero.
So, when we draw graph then, (x, y) = (x, f(x))
So, at real zero value of x is (x_{1 }, 0) where x_{1 }is real zero.
If the function has real zeros it will intersect xaxis at some point because function will be equal to zero at the value of the real zero.
So, Option B is not correct.
Lets consider option C, it says that a quadratic function with no real zeroes.
So, function with no real zeroes, will not be equal to 0 at any real value of x. Hence there will be no xintercept.
So, Option C is Correct .
Reason for option D will be same as of Option B.
Which of the following is an example of a function whose graph in the xyplane has no xintercepts?
Lets consider option A, it says that A linear function whose rate of change is not zero.
 Rate of change = Slope of the line
In the question we have given that function has no xintercept. That means it should not intersect the xaxis. i.e.it should be parallel to the xaxis.
Now, xaxis is the line such that its slope, m= 0 and yintercept, c=0.
But as in the given option rate of change is not zero that means slope m≠0. So the line will not be parallel to xaxis. Hence, it will have xintercept at some point.
So, Option A is not correct.
Lets consider option B, it says that a quadratic function with real zero,
We know that, A zero or root of a function is the value of x at which the function is zero.
So, when we draw graph then, (x, y) = (x, f(x))
So, at real zero value of x is (x_{1 }, 0) where x_{1 }is real zero.
If the function has real zeros it will intersect xaxis at some point because function will be equal to zero at the value of the real zero.
So, Option B is not correct.
Lets consider option C, it says that a quadratic function with no real zeroes.
So, function with no real zeroes, will not be equal to 0 at any real value of x. Hence there will be no xintercept.
So, Option C is Correct .
Reason for option D will be same as of Option B.