The system of inequalities are
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) 14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
3) 8 hours babysitting, 7 hours dishwashing
Step-by-step explanation:
The given parameters are;
The amount per hour Janine makes from babysits = $14.50
The amount per hour Janine makes from dishwashing = $9.50
The minimum number of hours Janine can spend dishwashing = 7 hours
The maximum number of hours Janine can spend dishwashing = 10 hours
The maximum number of hours Janine can work each week = 7 hours
The minimum amount she wants to make each week = $140
Let x represent the number of hours Janine spends babysitting and let y represent the number of hours Janine spends dishwashing
1) From the question, we have;
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) Where
14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
Making, y, the subject of the formula of the above inequalities and plotting as functions is given as follows;
y ≥ 140/9.5 - (14.5/9.5)·x
y ≤ 15 - x
3) In order to earn as much money as possible given that the amount Janine earns from babysitting is more than the amount she earns from dishwashing, Janine should spend the least amount of time dishwashing, which is 7 hours, as given, and then spend the remaining 8 hours babysitting to receive $14.5 × 8 + $9.5×7 = $182.5
Answer:
Slope is defined as rise over run, which can be expressed as the difference of the y-coordinates divided by the difference of the x-coordinates. If we rise, we are moving vertically, or along the y-axis. If we run, we are moving horizontally, or along the x-axis.
The formula for the slope m of a line given two points (x1, y1) and (x2, y2) that lie on the line is:
m = (y2 - y1)/(x2 - x1)
m = (15 - 5)/(-6 - 4)
m= 10/-10
m = -1
Now, we can use the slope-intercept form of the equation of a line to obtain the equation of the line that satisfies the conditions outlined in the problem. Slope-intercept form is:
y = mx + b
Again, m represents the slope, while b stands for the y-intercept. We can use either point on the line to represent x and y. Let's choose the point (4, 5)
5 = -1(4) + b
5 = -4 + b
9 = b
The equation of the line is:
y = -x + 9
1. The growth rate equation has a general form of:
y = A (r)^t
The function is growth when r≥1, and it is a decay when
r<1. Therefore:
y=200(0.5)^2t -->
Decay
y=1/2(2.5)^t/6 -->
Growth
y=(0.65)^t/4 -->
Decay
2. We rewrite the given equation (1/3)^d−5 = 81
Take the log of both sides:
(d – 5) log(1/3) = log 81
d – 5 = log 81 / log(1/3)
d – 5 = - 4
Multiply both sides by negative 1:
- d + 5 = 4
So the answer is D
Answer:
8.64%
Step-by-step explanation:
Write it as a decimal
7/81 = 0.0864
0.0864 is the decimal representation for 7/81
For Percentage Conversion :
step 1 To represent 0.0864 in percentage, write 0.0864 as a fraction
Fraction = 0.0864/1
step 2 multiply 100 to both numerator & denominator
(0.0864 x 100)/(1 x 100) = 8.64/100
8.64% is the percentage representation for 7/81
Answer:
37/40
Step-by-step explanation:
