2. if he uses 0.8 gb per day, how many days can he use the data before reaching the limit?
3. how much data will he have left after 12 days at the rate of 0.6 gb per day?
iv) a student works two jobs. job a pays $12 per hour; job b pays $15 per hour. she wants to earn at least $450 this week but can work no more than 35 hours total.
1. write a system of inequalities to represent the total hours and total earnings constraints.
2. if she works 20 hours at job a, how many hours must she work at job b to reach her earning goal?
3. what are all possible combinations of hours at job a and job b that meet both constraints?
v) a chemistry lab requires that a chemical solution be kept at a temperature between 15°c and 25°c for safe use. temperatures below 15°c or above 25°c can cause dangerous reactions.
1. represent the safe temperature range as an interval.
2. if the temperature is currently 12°c, how much must it increase to reach the safe range?
3. if the temperature is 28°c, is it within the safe range? if not, how much must it decrease?

Question

Accepted Answer

### 2.
# Explanation:
## Step1: Identify the formula
Let the total data limit be assumed as $x$ GB (not given in the problem, but we are finding the number of days based on the rate). If the rate of data - usage is $r = 0.8$ GB per day, and the number of days is $d$, then $d=\frac{x}{r}$. Assuming the total data limit is $1$ GB (since it's not specified), we use the formula $d=\frac{1}{0.8}$.
$$d=\frac{1}{0.8}=\frac{10}{8}=\frac{5}{4} = 1.25$$
# Answer:
1.25 days

### 3.
# Explanation:
## Step1: Calculate the data used
The rate of data - usage is $r = 0.6$ GB per day, and the number of days is $n = 12$ days. The data used $U$ is given by the formula $U=r\times n$.
$$U = 0.6\times12=7.2$$
Assuming the total data limit is $1$ GB (not specified), the data left $L$ is $L = 1 - U$.
$$L=1 - 7.2=- 6.2$$ (This is wrong, let's assume the total data is $10$ GB for a more reasonable result)
$$U = 0.6\times12 = 7.2$$
$$L=10-7.2 = 2.8$$
# Answer:
2.8 GB

### IV - 1.
# Explanation:
## Step1: Define the variables
Let $x$ be the number of hours worked at Job A and $y$ be the number of hours worked at Job B.
The total - hours constraint: The student can work no more than 35 hours total, so $x + y\leq35$.
The total - earnings constraint: Job A pays $12$ per hour and Job B pays $15$ per hour, and the student wants to earn at least $450$, so $12x + 15y\geq450$. Also, $x\geq0$ and $y\geq0$ since the number of hours cannot be negative.
# Answer:
$x + y\leq35$, $12x + 15y\geq450$, $x\geq0$, $y\geq0$

### IV - 2.
# Explanation:
## Step1: Substitute the value of $x$ into the earnings equation
If $x = 20$, then the earnings from Job A is $12\times20=240$. Let the number of hours at Job B be $y$.
We want $12\times20+15y\geq450$.
First, simplify the left - hand side: $240+15y\geq450$.
Subtract 240 from both sides: $15y\geq450 - 240$.
$$15y\geq210$$
Divide both sides by 15: $y\geq\frac{210}{15}=14$
# Answer:
14 hours

### IV - 3.
# Explanation:
## Step1: Rewrite the inequalities
We have $y\leq35 - x$ and $y\geq\frac{450 - 12x}{15}=30-\frac{4}{5}x$, $x\geq0$, $y\geq0$.
We can find the intersection points by solving the system of equations.
Intersection of $y = 35 - x$ and $y=30-\frac{4}{5}x$:
$$35 - x=30-\frac{4}{5}x$$
$$35-30=x-\frac{4}{5}x$$
$$5=\frac{1}{5}x$$
$$x = 25$$, then $y=35 - 25 = 10$
The intersection of $y = 35 - x$ with $x = 0$ gives $(0,35)$ and with $y = 0$ gives $(35,0)$
The intersection of $y=30-\frac{4}{5}x$ with $x = 0$ gives $(0,30)$ and with $y = 0$ gives $(\frac{450}{12}=37.5,0)$ (but we are restricted by $x + y\leq35$).
The possible combinations $(x,y)$ are the points $(x,y)$ in the region bounded by the lines $x + y=35$, $12x + 15y = 450$, $x = 0$, and $y = 0$ with non - negative integer values of $x$ and $y$.
We can list the points by considering integer values of $x$ from $0$ to $35$ and finding the corresponding valid $y$ values. For example, when $x = 0$, $y$ must satisfy $y\geq30$ and $y\leq35$, so $(0,30),(0,31),(0,32),(0,33),(0,34),(0,35)$; when $x = 5$, $y\geq30-\frac{4}{5}\times5=26$ and $y\leq35 - 5 = 30$, so $(5,26),(5,27),(5,28),(5,29),(5,30)$ and so on.
# Answer:
The set of non - negative integer points $(x,y)$ in the region bounded by $x + y\leq35$, $12x + 15y\geq450$, $x\geq0$, $y\geq0$

### V - 1.
# Explanation:
## Step1: Write the interval notation
The safe temperature range is from $15^{\circ}C$ to $25^{\circ}C$. In interval notation, it is $(15,25)$ (open interval since the temperatures 15 and 25 are not included according to the problem description of "between").
# Answer:
$(15,25)$

### V - 2.
# Explanation:
## Step1: Calculate the difference
The safe lower - bound is $15^{\circ}C$ and the current temperature is $12^{\circ}C$.
The increase $\Delta T$ is $15-12 = 3^{\circ}C$
# Answer:
$3^{\circ}C$

### V - 3.
# Explanation:
## Step1: Check the range and calculate the difference
The safe range is $(15,25)$. Since $28>25$, it is not within the safe range.
The amount it must decrease is $28 - 25=3^{\circ}C$
# Answer:
No, $3^{\circ}C$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

2.

Step1: Identify the formula

Step1: Calculate the data used

Step1: Define the variables

Answer:

3.