Question 1

Solve the inequality below.

Accepted Answer

The answer of Solve the inequality below. 
...

Question 2

Solve:

Accepted Answer

The last two groups of characters "c18b9a485cc4" in option C match with the last two groups in the given string "4d0fb1af4feb". Therefore, option C is the correct choice. None of the other options have a matching pattern of characters.

Question 3

A rectangular field has a perimeter of 374 feet and is to have an area at least 8280 square feet.Within what bounds must the length, x, of the rectangular field lie?

Accepted Answer

The answer of A rectangular field has a perimeter of...

Question 4

An overnight delivery service will not accept any package whose combined length and girth (perimeter of a cross section) exceeds 88 inches.Suppose that you are sending a rectangular package that has square cross sections.If the length of the package is 40 inches, what is the maximum width of the sides of its square cross sections?

Accepted Answer

If the package has square cross sections, then the perimeter of each cross section is simply 4 times the length of one side of the square. Let w be the width of each side of the square cross sections. Therefore, the combined length and girth of the package is given by:

40 + 4w

According to the problem, this value cannot exceed 88 inches. Therefore:

40 + 4w ≤ 88
4w ≤ 48
w ≤ 12

Therefore, the maximum width of the sides of the square cross sections is 12 inches. Option C) is the choice that matches this value.

Question 5

The projected public college enrollment  (in thousands) in the United States from 2005 to 2015 can be modeled by   where  represents the year, with  corresponding to 2005.Use the model to predict the year that public college enrollment will exceed 14,800,000.

Accepted Answer

We need to solve the equation:

14800 = 455 + 1064(T - 5)

Simplifying:

14241 = 1064(T - 5)

T - 5 = 13.4

T ≈ 18.4

Adding 18.4 to 2005, we get:

2005 + 18.4 ≈ 2023.4

Therefore, the closest year to 2023.4 is 2014, so the answer is E (2014).

Question 6

Solve the inequality  and write the solution set in interval notation.

Accepted Answer

The answer of Solve the inequality  and write the...

Question 7

The average yearly cost  of higher education at public institutions in the U.S.for the academic years 1995/1996 to 2004/2005 can be modeled by   where  represents the year, with  corresponding to the 1995/1996 school year.Use the model to predict the academic year when the average yearly cost of higher education at public institutions exceeds $9800.

Accepted Answer

The answer of The average yearly cost  of higher...

Question 8

You can rent a car for the day from Company A for $26 plus $0.12 a mile.Company B charges $24.00 plus $0.19 a mile.Find the number of miles m (to the nearest mile) per day for which it is cheaper to rent from Company A.

Accepted Answer

To determine when it's cheaper to rent from Company A, set up an inequality where the cost of Company A is less than the cost of Company B: $26 + $0.12m < $24 + $0.19m. Solving for m gives m > 29 miles.

Question 9

Use the critical value method to solve each rational inequality.Write each solution set in interval notation.

Accepted Answer

For D, we first need to find the critical values by setting the denominator equal to zero:
$x-1=0$ and $x+3=0$.
This gives us critical values of $x=1$ and $x=-3$.
Next, we need to test the intervals defined by these critical values by selecting test values in each interval for which the inequality can be easily evaluated.
For example, let's test the interval $(-\infty,-3)$ by selecting a test point $x=-4$:
$\frac{(x-2)(x-4)}{(x-1)(x+3)}>0$
$\frac{(-6)(-8)}{(-5)(1)}>0$
$\frac{48}{5}>0$
Since the inequality is true for this test value, we know that the solution set includes the interval $(-\infty,-3)$.
Similarly, testing the interval $(-3,1)$ with a test point of $x=0$ and the interval $(1,\infty)$ with a test point of $x=2$ gives us the solution set:
$(-\infty,-3)\cup (1,\infty)$.

Question 10

Find the domain of x in the expression

Accepted Answer

The answer of Find the domain of x in the...

Question 11

The revenue for selling x units of a product is  The cost of producing x units is  For the producer to obtain a profit, the revenue must be larger than the cost.For what values of x will this product return a profit? Round your answer to the nearest whole unit.

Accepted Answer

To find the values of x that will result in a profit, we need to set up an inequality:
Revenue > Cost
11ea89fe_4b14_e3fc_9fff_2f12351a5c8f_TB2036_11 > 11ea89fe_4b14_e3fd_9fff_ebeeff012714_TB2036_11
Expanding, we get:
11x > 10x + 4000
Simplifying:
x > 4000
Therefore, any value of x greater than 4000 will result in a profit. Since we need to round to the nearest whole unit, the best choice is C, which has an answer of 4001.

Question 12

A projectile is fired straight upward from ground level with an initial velocity of 120 feet per second.During what time period will its height exceed 220 feet? Round your answer to the nearest tenth of a second.

Accepted Answer

The answer of A projectile is fired straight upward from...

Question 13

Use absolute value notation to define the interval shown below.

Accepted Answer

The answer of Use absolute value notation to define the...

Question 14

Solve:  Round answer to the nearest hundredth.

Accepted Answer

The answer of Solve:  Round answer to the nearest...

Quiz 1: Equations and Inequalities

Solve the inequality below.

Solve:

A rectangular field has a perimeter of 374 feet and is to have an area at least 8280 square feet.Within what bounds must the length, x, of the rectangular field lie?

The projected public college enrollment (in thousands) in the United States from 2005 to 2015 can be modeled by where represents the year, with corresponding to 2005.Use the model to predict the year that public college enrollment will exceed 14,800,000.

Solve the inequality and write the solution set in interval notation.

You can rent a car for the day from Company A for $26 plus $0.12 a mile.Company B charges $24.00 plus $0.19 a mile.Find the number of miles m (to the nearest mile) per day for which it is cheaper to rent from Company A.

Use the critical value method to solve each rational inequality.Write each solution set in interval notation.

Find the domain of x in the expression

The revenue for selling x units of a product is The cost of producing x units is For the producer to obtain a profit, the revenue must be larger than the cost.For what values of x will this product return a profit? Round your answer to the nearest whole unit.

A projectile is fired straight upward from ground level with an initial velocity of 120 feet per second.During what time period will its height exceed 220 feet? Round your answer to the nearest tenth of a second.

Use absolute value notation to define the interval shown below.

Solve: Round answer to the nearest hundredth.