The company could have mowed more than 54 lawns.
How to Solve linear inequality?Let the number of lawns mowed be x.
Then the total earning of landscaper is 30x.
The total amount given to the employees in a week is 210*7=$1470.
Then the profit of landscaper would be 30x-1470 which is greater than $150.
30x-1470 > 150
30x > 1620
x > 54
Therefore, possible numbers of lawns the company could have mowed are greater than 54 lawns.
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Between 61 and 80 lawns could have been mowed by the business in a week in order to turn a profit of more than $150. So options (d) and (e) are correct.
To determine the possible numbers of lawns the company could have mowed, we need to calculate the profit for a 7-day week and compare it with the given condition that the profit exceeds $150.
Step 1: Determine daily and weekly expenses
The daily salary expense is $210.
For 7 days, the total salary expense is:
[tex]\[ 210 \times 7 = 1470 \text{ dollars} \][/tex]
Step 2: Calculate profit per lawn
The company earns $30 for each lawn mowed.
Let ( n ) be the number of lawns mowed in a week.
Step 3: Calculate total earnings from mowing lawns
Total earnings for ( n ) lawns is:
[tex]\[ 30n \text{ dollars} \][/tex]
Step 4: Determine the profit
Profit is total earnings minus total expenses:
[tex]\[ \text{Profit} = 30n - 1470 \][/tex]
Step 5: Apply the condition that profit is more than $150
The inequality to solve is:
[tex]\[ 30n - 1470 > 150 \][/tex]
Step 6: Solve the inequality
Add 1470 to both sides:
[tex]\[ 30n > 1620 \][/tex]
Divide both sides by 30:
[tex]\[ n > 54 \][/tex]
Step 7: Identify the possible number of lawns mowed
The number of lawns must be greater than 54.
From the given options (12, 37, 54, 61, 80), the possible numbers are:
[tex]\[ 61 \text{ and } 80 \][/tex]
Thus, the two possible numbers of lawns the company could have mowed to make a profit of more than $150 in a week are 61 and 80.
Complete Question:
A landscaper earns $30 for each lawn her company mows, but she pays $210 per day in salary to her employees. If her company made more than $150 profit from mowing lawns in a 7-day week, what are the possible numbers of lawns the company could have mowed? Select two options. 12
37
54
61
80
10x+2y=10 in slope intercept form
Choose the equation below that represents the line that passes through the point (2, 4) and has a slope of 3.
Answer
y - 4 = 3(x - 2)
y + 2 = 3(x + 4)
y + 4 = 3(x + 2)
y - 2 = 3(x - 4)
...?
The correct equation for the line that passes through the point (2, 4) with a slope of 3 is 'y - 4 = 3(x - 2)' using the point-slope form of a linear equation.
The equation that represents the line passing through the point (2, 4) with a slope of 3 is y - 4 = 3(x - 2). To find the equation of a line given a point and a slope, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.
Since the line must pass through (2, 4) and the slope (m) is 3, we plug these values into the point-slope form to get the correct equation.
y is directly proportional to x^2. It is known that y=10 for a particular value of x. Find the value of y when the value of x is halved
...?
If y is directly proportional to x^2, when x is halved, y becomes 0.25 times its original value. Given the original value of y is 10, when x is halved, the new y is 2.5.
Explanation:When we say that y is directly proportional to x^2, it means there exists a constant of proportionality (let's call this 'k') such that the equation y = k*(x^2) always holds. From the problem, we know that y=10 for a certain x, let's square this x sometimes referred as x2 (we could say [tex]x2 = (x^1.5)^2).[/tex]
If x is halved, the new x which we can call [tex]x1 = 0.5*x2[/tex], then substitute x1 in the equation of direct proportion we get [tex]y1 = k*(0.5 *2)^2 = y*0.25[/tex], this is because (0.5)^2 is 0.25. So, the new y when x is halved (y1) will be 0.25 as much as the original y. Therefore, if your initial y was 10, your new y would be y1 = 10*0.25 which equals 2.5.
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Simplify i³⁸. [i=√(-1)]
The 38th power, [tex]i^{38[/tex] simplifies to -1.
To simplify [tex]\( i^{38 \),[/tex] you can start by recognizing the pattern that powers of i repeat every four terms. This means that [tex]\( i^{4\),[/tex] equals 1, [tex]\( i^{8 \),[/tex] also equals 1, and so on. Therefore, [tex]\( i^{38 \),[/tex]can be simplified as follows:
[tex]\[ i^{38} = i^{4 \cdot 9 + 2} \][/tex]
Since [tex]\( i^4 \)[/tex] is equal to 1, we have:
[tex]\[ i^{38} = (i^4)^9 \cdot i^2 = 1^9 \cdot (-1) = -1 \][/tex]
So,[tex]\( i^{38} \)[/tex] simplifies to -1.
Complete question is:
Simplify i³⁸. [i=√(-1)]
Robert makes $3.50 per hour working at a convenience store. If he gets a bonus of $25 of this week how many hours must he work to make at least $165?
1. Solve for Y 1/2y+4x=z
Select all ratios equivalent to 5:15.
2:60, 20:9, 7:21, 1:3
Using CPCTC, name the congruent parts of ΔABC & ΔQRS that are not labeled as congruent in the diagram.
A. AB=QR,BC=RS,
B.AC=QS,
C.AC=QS,BC=RS,
D. AB=QR,BC=RS,
Answer: A. AB=QR,BC=RS
Step-by-step explanation:
The congruence property of congruence triangle CPCTC says that the corresponding parts of congruent triangles are congruent.
From the given figure, we have
[tex]\angle{A}\cong\angle{Q}\\\angle{C}\cong\angle{S}[/tex]
[tex]\overline{AC}=\overline{QS}[/tex]
The other congruent parts in the triangle.
[tex]\overlien{AB}\cong\overlien{QR}[/tex] [∵ AB corresponds QR]
[tex]\\\\\overlien{BC}\cong\overlien{RS}[/tex] [∵BC corresponds RS]
If f(x) and f^-1(x) are inverse functions of each other and f(x)=2x+5, what is f^-1(8)
Answer:
[tex]\text{The value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]
Step-by-step explanation:
Given the function
[tex]f(x)=2x+5[/tex]
[tex]\text{we have to find the value of }f^{-1}(8)[/tex]
First we have to find the inverse
Step 1: Put f(x)=y, the equation becomes
[tex]y=2x+5[/tex]
Step 2: Replace x to y and y to x, we get
[tex]x=2y+5[/tex]
Step 3: Solve for y and then replace it with [tex]f^{-1}x[/tex]
[tex]x-5=2y[/tex]
[tex]y=\frac{x-5}{2}[/tex]
[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Now substitute x=8, we get
[tex]f^{-1}(8)=\frac{8-5}{2}=\frac{3}{2}[/tex]
[tex]\text{hence, the value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]
You buy 40 of your favorite songs from a Web site that charges $0.97 for each song. What is the cost of 40 songs?
If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the least education?
a. accountant
b. architect
c. pharmacist
d. surveyor
Answer:
D
Step-by-step explanation:
The horizontal axis of the graph is Salary.
Given there is a positive correlation between salary and education, means that as if education increase, salary increase OR if education decrease, salary decrease, and vice versa.
Out of the 4 choices, they wanted to know the one that requires LEAST education. So we will look at the bar that has LEAST salary.
Looking at the graph and bars, out of the 4 choices, Surveyor has the LEAST SALARY, so SURVEYOR would require LEAST EDUCATION. Answer choice D is right.
The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}.[/tex] Option (d) is correct.
Further Explanation:
Given:
The options are as follows,
(a). Accountant
(b). Architect
(c). Pharmacist
(d). Surveyor
Explanation:
Correlation is a relationship between the two events. The change in one will affect the in change of another one.
There are two type correlations.
A positive correlation mean that if one increases the second event will also increase and if one decreases the second event will also decreases.
A negative correlation mean that if one increases the second event will also decrease and if one decreases the second event will also increase.
There is a positive correlation between salary and education.
The least salary in the given option is of surveyor and has least education.
The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}[/tex]. Option (d) is correct.
Learn more:
Learn more about normal distribution https://brainly.com/question/12698949 Learn more about standard normal distribution https://brainly.com/question/13006989 Learn more about confidence interval of meanhttps://brainly.com/question/12986589
Answer details:
Grade: High School
Subject: Statistics
Chapter: Correlation
Keywords: correlation, salary, education, positive correlation, based, careers, least education, accountant, architect, pharmacist, surveyor, negative correlation, average salaries, personal trainer,
Solve: 3x-3y=3
y=-5x-17
The simultaneous equations 3x-3y=3 and y=-5x-17 can be solved using substitution, resulting in the solution x = -8/3 and y = -11/3.
To solve the simultaneous equations 3x-3y=3 and y=-5x-17, we can use substitution or elimination. Substitution is straightforward since we already have y expressed in terms of x in the second equation. We can substitute y=-5x-17 into the first equation:
3x - 3(-5x - 17) = 33x + 15x + 51 = 318x = -48x = -48 / 18x = -8/3Now, plug x back into y=-5x-17 to find y:
y = -5(-8/3) - 17y = 40/3 - 17y = 40/3 - 51/3y = -11/3The solution to the system of equations is x = -8/3 and y = -11/3.
What has the sum of 20 but the difference is 8?
Parallelogram ABCD is dilated to form parallelogram EFGH. Side BC is proportional to side CD.
What corresponding side is proportional to segment FG?
What does the equal sign with an arrow mean?
The recipe calls for 1 egg, which makes 8 slices of pumpkin pie. how many eggs would be needed to make 56 slices of pumpkin pie ?
To find the number of eggs needed for 56 slices of pumpkin pie when the recipe calls for 1 egg for 8 slices, simply set up a proportion and solve. In this case, you would need 7 eggs for 56 slices of pie.
To determine how many eggs are needed to make 56 slices of pumpkin pie, we use a proportion. Given that 1 egg makes 8 slices of pie, we set up the proportion as follows:
1 egg / 8 slices = x eggs / 56 slicesSolving for x, which represents the number of eggs needed for 56 slices, we get that x = 7 eggs.
Write three ratios equal to 7/35? A 1/7, 2/14, 3/21 B 5/7, 10/7, 15/7 C 7/35, 7/40, 7/45 D 1/5, 2/10, 3/15 I think it is C or D.
Answer:
[tex]\frac{1}{5} ;\frac{2}{10} ;\frac{3}{15}[/tex]
Step-by-step explanation:
To find the three ratios we only have to find the most simple ratio of [tex]\frac{7}{35}[/tex], and then find the other ratios that are equal to it.
So, [tex]\frac{7}{35} = \frac{1}{5}[/tex]
Also, [tex]\frac{1}{5} =\frac{2}{10}[/tex], by multiplying by two each part of the fraction.
Similarly, [tex]\frac{3}{15} = \frac{1}{5}[/tex], by multiplying by three.
Therefore, comparing all these ratios, all are the same, they are equal to [tex]\frac{1}{5}[/tex]. So, the option that correctly has these choices is D.
denise bought 5.2 pounds of rice for $5.29. using the unit rate, how much would 2 pounds of rice cost?
Eight people, female and male, were surveyed about their choice of car color, green or blue. The table shows the choices they made.
Which two-way table correctly compares the categorical data?
Person Gender
(male or female) Car color
(green or blue)
1 female green
2 female green
3 female blue
4 male blue
5 male green
6 female blue
7 male blue
8 male blue
A.
Green Blue
Female 4 5
Male 4 3
B.
Green Blue
Female 2 1
Male 2 3
C.
Green Blue
Female 4 4
Male 3 1
D.
Green Blue
Female 2 2
Male 1 3
The correct two-way table for comparing the car color choices of eight surveyed individuals by gender is Option D, which shows 2 females choosing green and 2 blue, while 1 male chose green and 3 chose blue.
The question is about analyzing a two-way table that compares categorical data: gender and car color preferences. To find the correct table, we need to tally the choices made by each person based on the information given and compare it to the options provided in the answer choices. By counting the number of times each gender chose each color, we can determine the accurate representation of the data.
For females, 2 chose green and 2 chose blue.
For males, 1 chose green and 3 chose blue.
Given this information, the correct two-way table that compares the categorical data is:
Option D.
Green Blue
Female 2 2
Male 1 3
This table correctly captures the car color preferences by gender among the eight people surveyed.
The price of a pair of shoes is $52. The price is 15% lower than last week. What was the price of the shoes last week? Round your answer to the nearest cent. Enter your answer in the box. $
The original price of the shoes can be found by dividing the current price, $52, by 0.85, which yields an original price of approximately $61.18.
The current price of a pair of shoes is $52, which is 15% lower than it was last week. To find the original price, you can set up an equation where the original price minus 15% of the original price equals the current price of $52.
Let x represent the original price. The equation is then x - 0.15x = $52. Simplify this to 0.85x = $52. Divide both sides by 0.85 to solve for x.
x = $52 / 0.85
x = $61.18
Therefore, the price of the shoes last week was approximately $61.18.
7 × 30 = 7 × ___ tens
7 × 30 = 7 × 3 tens.
To solve 7 × 30 in terms of tens, we first observe that 30 can be written as 3 tens since 30 equals 3 × 10.
Therefore:
7 × 30 can be rewritten as 7 × (3 × 10), which simplifies to 7 × 3 tens.
So, 7 × 30 = 7 × 3 tens.
A new game is being constructed where the game board is going to have 8 rows with 10 spaces in each row. What is the smallest game board that can be made?
Answer: There can be made 40 smallest game boards.
Step-by-step explanation:
Since we have given that
Number of rows = 8
Number of spaces in each row = 10
we need to find the smallest game board that can be made.
As we know that For Smallest we always find "L.C.M" because L.C.M. stands for least common multiple.
So, L.C.M. of 8 and 10 = 40
Hence, there can be made 40 smallest game boards.
At which angle will the hexagon rotate onto itself?
Answer:
The correct answer is: 60°
Step-by-step explanation:
Rotational symmetry is a type of symmetry, in which an object returns back to its original shape after rotation at an angle of 360°/n about a fixed point.
A hexagon is a regular polygon that has six edges and vertices. It has six internal angles, 120° each.
Since there are 6 equal edges, therefore, the hexagon will rotate onto itself after every rotation at an angle of: 360°/n = 360°/6 = 60°
2/3 of a circle is what percent of a circle
At a local University 54.3% of incoming first-year students have computers. If 3 students are selected at random, find the following probability. A) At least one has a computer
B) None have computers
The lines p and q intersect at point O. What is the value of x?
X =
Answer:
The value of x is 16 .
Step-by-step explanation:
Definition of vertically opposite angles
Two lines crosses angles opposite to each other are called vertically opposite angle .
Thus
(2x + 13)° = (3x-3)°
(Vertically opposite angles )
2x + 13 = 3x-3
2x - 3x = -3-13
-x = -16
x = 16
Therefore the value of x is 16 .
what is 475.53 minus 67.37
GRAPHING EXPONENTIAL FUNCTIONS
1. If (-1, y) lies on the graph of y = 3^x+1, then y =
a) 0
b) 1/3
c) 1
2. If (x, 1/100) lies on the graph of y = 10^x, then x =
a) 2
b) -1/2
c) -2
3. If (-1, y) lies on the graph of y = 2^2x, then y =
a) -4
b) 1/4
c) 1
4. What is the relationship between the graphs of y = 2^x and y = 2^-x?
a) reflections over the x-axis
b) reflections over the y-axis
c) reflections over y = x
5. If (3, y) lies on the graph of y = -(2x), then y =
a) 1/8
b) -6
c) -8
6. Which of the following equations is not exponential?
a) y = 1x
b) y = (1/2)x
c) y = -2x
7. If (-2, y) lies on the graph of y = 4^x, then y =
a) -16
b) 1/16
c) 16
8. If (-3, y) lies on the graph of y = 3^-x, then y =
a) -27
b) 1/27
c) 27
9. If (-3, y) lies on the graph of y = 3^x, then y =
a) 1/27
b) -1
c) -27
10. If (-3, y) lies on the graph of y = (1/2)^x, then y =
a) 8
b) 1/8
c) -8
The detailed answer provides the solutions to a series of questions involving finding specific values for y given x in various exponential equations, as well as recognizing the relationship between graphs of exponential functions and identifying which equations are not exponential.
1. If (-1, y) lies on the graph of y = 3ˣ+1, then y equals the value of the function when x is -1. Therefore, y = 3⁻¹ + 1 which simplifies to y = 1/3 + 1 = 4/3, which is not one of the provided options.
2. If (x, 1/100) lies on the graph of y = 10ˣ, then we need to find the value of x such that 10ˣ equals 1/100. 10ˣ = 1/100 is equivalent to 10ˣ = 10⁻², so x = -2.
3. If (-1, y) lies on the graph of y = 2²ˣ, we substitute x with -1. Then y = 2²*⁻¹ = 2⁻² = 1/4.
4. The relationship between the graphs of y = 2ˣ and y = 2⁻ˣ is that they are reflections over the y-axis. When x is replaced by -x in the function, the resulting graph is a reflection over the y-axis.
5. If (3, y) lies on the graph of y = -(2ˣ), then y is the negative value of 2 raised to the power of 3, which is -8. So, y = -8.
6. Among the given equations, y = -2ˣ is not exponential because it lacks the variable as an exponent. So, y = -2ˣ is not exponential.
7. If (-2, y) lies on the graph of y = 4ˣ, then y = 4⁻² = 1/16.
8. If (-3, y) lies on the graph of y = 3⁻ˣ, then y = 3⁻⁽⁻³⁾ = 3³ = 27.
9. If (-3, y) lies on the graph of y = 3ˣ, then y = 3⁻³ = 1/27.
10. If (-3, y) lies on the graph of y = (1/2)ˣ, then y = (1/2)⁻³ = 2³ = 8.
Which of the following expressions is this one equivalent to?
(x^4+2x^3-x-2)÷(x^3-1)
A. 2x-5- (3/x^3-1)
B. x^2+x+1
C. x+2
D. x^2+3x+2
...?
Answer: x+2. The answer is C.
Step-by-step explanation:
Solve the equation sin theta = 0.3 to the nearest tenth. Use the restrictions 90degrees < theta < 180degrees.
A)
θ=107.5
B)
θ=162.5
C)
θ=197.5
D)
θ=17.5