Maths-
SAT
Easy
Question
The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?
- 25,000 > (4,334 − 2,712) t
- 25,000 < (4,334 − 2,712) t
- 25,000 − 4,334 > 2,712t
The correct answer is: 25,000 < (4,334 − 2,712) t
Estimated cost to install a geothermal heating system is $25,000
The actual average annual energy cost is $4,331. Estimated average annual energy cost is $2,712.
The homeowner estimate is lesser than the actual average. That is, the homeowner estimates (4334 - 2712) less than the actual
For t years, the difference between the actual and estimated average becomes: (4334 – 2712) t.
The actual cost to install a geothermal heating system is (4334 - 2712) t greater than the estimate $25,000 Thus, 25,000 < (4334 - 2712) t
Related Questions to study
Maths-
Which of the following is a value of x for which the expression 
is undefined?
Which of the following is a value of x for which the expression is undefined?
Maths-SAT
Maths-
If 
= x, where a > 0, what is a in terms of x?
If = x, where a > 0, what is a in terms of x?
Maths-SAT
Maths-
If 
, what is the value of
If , what is the value of
Maths-SAT
Maths-
The graph of the equation ax + ky = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2, -6) and (0, -3), what is the value of k?
The graph of the equation ax + ky = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2, -6) and (0, -3), what is the value of k?
Maths-SAT
Maths-
Which of the following is an equivalent form of 
, where f > 0 and k > 0?
Which of the following is an equivalent form of , where f > 0 and k > 0?
Maths-SAT
Maths-
f(x) = -500x2 + 25,000x
The revenue f (x), in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of y = f (x) in the xy-plane intersects the x-axis at 0 and a. What does a represent?
f(x) = -500x2 + 25,000x
The revenue f (x), in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of y = f (x) in the xy-plane intersects the x-axis at 0 and a. What does a represent?
Maths-SAT
Maths-
If x is a solution to the given equation, which of the following is a possible value of x + 5 ?
If x is a solution to the given equation, which of the following is a possible value of x + 5 ?
Maths-SAT
Maths-
For the linear function f ,the table above gives some values of x and their corresponding values f (x), where c is a constant. Which of the following equations defines f?
For the linear function f ,the table above gives some values of x and their corresponding values f (x), where c is a constant. Which of the following equations defines f?
Maths-SAT
Maths-
0.8p = t
At a store, a coat originally priced at p dollars is on sale for t dollars, and the relationship between p and t is given in the equation above. What is p in terms of t?
0.8p = t
At a store, a coat originally priced at p dollars is on sale for t dollars, and the relationship between p and t is given in the equation above. What is p in terms of t?
Maths-SAT
Maths-
A fashion buyer for a large retail store purchased 315 items directly from the manufacturer for a total of $6000. Some of the items were dresses purchased for $25 each, and the rest were shirts purchased for $10 each. How many more dresses than shirts did the buyer purchase?
A purchase price is the economic value, usually expressed in fiat currency at the time of purchase, for which a buyer pays for a product, service, or asset. The compensation for this value can be in the form of fiat currency or something else, such as services as payment or benefits in kind.
A purchase formula is a formula that is used to calculate the invoice amount, including discounts and taxes. The default Purchase formula is not always useful to users because the invoice amount calculation varies for different suppliers depending on the type of origin of the arrived goods, tax, and other charges levied on the purchased items.
The basic amount is the gross amount. It is the sum that includes only the purchase price of the items.
Gross Amount = Quantity * Purchase Price
A fashion buyer for a large retail store purchased 315 items directly from the manufacturer for a total of $6000. Some of the items were dresses purchased for $25 each, and the rest were shirts purchased for $10 each. How many more dresses than shirts did the buyer purchase?
Maths-SAT
A purchase price is the economic value, usually expressed in fiat currency at the time of purchase, for which a buyer pays for a product, service, or asset. The compensation for this value can be in the form of fiat currency or something else, such as services as payment or benefits in kind.
A purchase formula is a formula that is used to calculate the invoice amount, including discounts and taxes. The default Purchase formula is not always useful to users because the invoice amount calculation varies for different suppliers depending on the type of origin of the arrived goods, tax, and other charges levied on the purchased items.
The basic amount is the gross amount. It is the sum that includes only the purchase price of the items.
Gross Amount = Quantity * Purchase Price
Maths-
If x
1, what is the value of 
?
If x1, what is the value of ?
Maths-SAT
Maths-
When 9 is increased by 3x, the result is greater than 36, What is the least possible integer value for x?
When 9 is increased by 3x, the result is greater than 36, What is the least possible integer value for x?
Maths-SAT
Maths-
Thomas is making a sign in the shape of a regular hexagon with 4-inch sides, which he will cut out from a rectangular sheet of metal, as shown in the figure above. What is the sum of the areas of the four triangles that will be removed from the rectangle?
Thomas is making a sign in the shape of a regular hexagon with 4-inch sides, which he will cut out from a rectangular sheet of metal, as shown in the figure above. What is the sum of the areas of the four triangles that will be removed from the rectangle?
Maths-SAT
Maths-
A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?
A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?
Maths-SAT
Maths-
The figure above shows that the shaded triangular region with a hypotenuse of 5 centimeters (cm) has been removed from a rectangular tile with dimensions x cm by y cm. Of the following, which best approximates the area, in square centimeters, of the tile before the piece was removed?
The figure above shows that the shaded triangular region with a hypotenuse of 5 centimeters (cm) has been removed from a rectangular tile with dimensions x cm by y cm. Of the following, which best approximates the area, in square centimeters, of the tile before the piece was removed?
Maths-SAT
