Shantel offers online tutorial services. She charges $25.00 an hour per student. Her budget tracker reflects a total of $3,200.00 monthly expenses. How many hours must Shantel work each month to earn a monthly profit of at least $600.00?(1 point)
Let's calculate Shantel's monthly expenses first: $3200
Next, let's determine her desired profit: $600
Now, let's find the total cost of her expenses and desired profit: $3200 + $600 = $<<3200+600=3800>>3800
To find the number of hours Shantel must work, we need to divide the total cost by her hourly rate: $3800 / $25 = <<3800/25=152>>152 hours
Therefore, Shantel must work at least 152 hours each month to earn a monthly profit of at least $600.
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La’Shondra solves the inequality 6+3x≤24. She begins by subtracting 6 from both sides of the inequality and then divides both sides of the equivalent inequality by a number. What is the number?(1 point)
To solve the inequality 6 + 3x ≤ 24, La'Shondra subtracts 6 from both sides:
6 + 3x - 6 ≤ 24 - 6
This simplifies to:
3x ≤ 18
To isolate x, La'Shondra then divides both sides of the inequality by 3:
3x/3 ≤ 18/3
This simplifies to:
x ≤ 6
So the number La'Shondra divided both sides of the inequality by is 3.
Solve the inequality Rx>10, where R is a number greater than 0.(1 point)
To solve the inequality Rx > 10, where R is a number greater than 0, we divide both sides by R:
Rx/R > 10/R
Simplifying, we get:
x > 10/R
Since R is a number greater than 0, dividing by R does not change the direction of the inequality. Therefore, the solution is:
x > 10/R
Solve the inequality Ay+3<12, where A is a number greater than 0.(1 point)
To solve the inequality Ay + 3 < 12, where A is a number greater than 0, we can subtract 3 from both sides of the inequality:
Ay + 3 - 3 < 12 - 3
This simplifies to:
Ay < 9
Next, we need to divide both sides of the inequality by A. Since A is a number greater than 0, dividing by A does not change the direction of the inequality. Therefore, the solution is:
y < 9/A
So, for any value of A that is greater than 0, the inequality Ay + 3 < 12 is satisfied when y is less than 9/A.
Jorelle is planning a 5-day vacation. The trip will cost him $1,300.00 for airfare, food, and itineraries. He plans to stay in a hotel room for $80.00 per night. He only has $950.00 in savings, but he earns $25.00 per hour from his online tutoring services. Create a linear inequality in one variable that would best translate the problem. Determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip.
Let's start by breaking down the total cost of Jorelle's trip:
Airfare, food, and itineraries cost: $1,300.00
Hotel cost per night: $80.00
Number of nights staying in a hotel: 5
The total cost of hotel accommodations would be: $80.00 * 5 = $<<80*5=400.00>>400.00
Jorelle only has $950.00 in savings, so his available funds can be represented by: $950.00
The total amount Jorelle can spend on the trip is the sum of his savings and earnings from tutoring: $950.00 + ($25.00 * h), where 'h' represents the number of hours he tutors.
Therefore, the linear inequality that represents this scenario is:
$950.00 + ($25.00 * h) ≥ $1,300.00 + $400.00
Simplifying this inequality further, we get:
$25.00 * h ≥ $1,700.00
To determine the minimum number of hours Jorelle must tutor to have enough money for the trip, we need to isolate 'h'. Divide both sides of the inequality by $25.00:
h ≥ $1,700.00 / $25.00
This simplifies to:
h ≥ 68
So, the minimum number of hours Jorelle must tutor to have enough money for the trip is 68 hours.
Jorelle is planning a 5-day vacation. The trip will cost him $1,300.00 for airfare, food, and itineraries. He plans to stay in a hotel room for $80.00 per night. He only has $950.00 in savings, but he earns $25.00 per hour from his online tutoring services. Create a linear inequality in one variable that would best translate the problem. Determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip.(1 point)
Responses
A. 950+25x≥1,700; at least 30 hours
B. 950+25x≥1,300; at least 14 hours
C. 950+25x≤1,300; at most 14 hours
D. 950+25x≤1,700; at most 30 hours
To create a linear inequality based on the given information, we need to consider Jorelle's savings of $950, his earnings of $25 per hour from tutoring, and the total cost of the trip, which is $1,300.
Since Jorelle's earnings are added to his savings, the linear inequality is: 950 + 25x ≥ 1,300.
To determine the minimum number of hours Jorelle must tutor, we need to solve this inequality for 'x' (the number of hours).
Let's solve it:
950 + 25x ≥ 1,300
Subtract 950 from both sides:
25x ≥ 1,300 - 950
25x ≥ 350
Divide both sides by 25:
x ≥ 350/25
x ≥ 14
Based on the inequality, the minimum number of hours Jorelle must tutor so he can have enough money for the trip is at least 14 hours.
Therefore, the correct answer is:
B. 950 + 25x ≥ 1,300; at least 14 hours
Mary Ann solves the inequality −3x≥12. Justify the steps Mary Ann takes to find the solution set.(1 point)
Responses
A. Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
B. Mary Ann adds −3 to both sides of the inequality to get x≥9.
C. Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9.
D. Mary Ann divides both sides of the inequality by −3 to get x≥−4.
To solve the inequality −3x ≥ 12, Mary Ann needs to isolate x on one side of the equation.
To do this, she divides both sides of the inequality by -3. However, when dividing by a negative number, the inequality symbol needs to be changed.
Therefore, the correct step is:
A. Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x ≤ −4.
So, the solution set for the inequality −3x ≥ 12 is x ≤ -4.
Kirk solves the inequality 5<12y−7. Which statement explains the steps he uses to find the solution set of the inequality?(1 point)
Responses
A. Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16)<y.
B. Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1>y.
C. Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y.
.
D. Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1<y.
To solve the inequality 5 < 12y - 7, Kirk needs to isolate y on one side of the inequality.
To do this, he starts by adding 7 to both sides of the inequality:
5 + 7 < 12y - 7 + 7
This simplifies to:
12 < 12y
Next, Kirk divides both sides of the inequality by 12:
12/12 < 12y/12
This simplifies to:
1 < y
Therefore, the correct statement explaining Kirk's steps to find the solution set is:
D. Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
So, the solution set for the inequality 5 < 12y - 7 is y > 1.
Which of the following shows how to solve the linear inequality with a letter coefficient Hy<7, where H is a number greater than 0?(1 point)
Responses
A. y<7
B. y<7H
C. Hy<7
D. y<7H
To solve the linear inequality Hy < 7, where H is a number greater than 0, we can divide both sides of the inequality by H. Since H is a positive number, the direction of the inequality does not change.
Therefore, the correct solution is:
D. y < 7H
Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
Responses
1. B.
2. 72
3. x
4. Bx
The term in the inequality that is a letter coefficient is:
4. Bx