50 POINTS

You are looking at starting a summer business mowing lawns to get started. You already need to purchase some items investing in your business. You already have a lawnmower, but below are the items you still need to purchase.

what is the total amount you plan to invest in your lawn mowing business? [__]

1. You just determined how much you are willing to invest to get your summer job started. Write an inequality to represent when you start making a profit if you charge $15 to mow one lawn.

2. at the end of the summer, you have mowed a total of 16 lawns right in equation that represents your total earnings. How much did you earn? [Show your work]

with investment costs taken into account, did you:
a. lose money
b. make money

50 POINTSYou Are Looking At Starting A Summer Business Mowing Lawns To Get Started. You Already Need

Answers

Answer 1

Regarding the situation described, it is found that:

The total amount invested is of $25.

1. You start making a profit when 15x - 25 > 0.

2. You earned $215 with this work.

With the investment, you made money (option b).

What is the total amount investment?

The investment was as follows:

Pack of 50 lawn bags for $10.Eye protecting glasses for $15.

Hence the total amount invested was of:

10 + 15 = $25.

What is the profit inequality?

The profit is given by revenue subtracted by costs.

In the context of this problem, the revenue and the cost functions are given as follows:

Revenue: R(x) = 15x (as you charge $15 to mow one lawn).Cost: C(x) = 25. (investment).

Hence the profit function is:

P(x) = R(x) - C(x)

P(x) = 15x - 25.

You start making a profit when:

P(x) > 0.

15x - 25 > 0.

The amount you earned mowing 16 lawns is of:

P(16) = 15(16) - 25 = $215.

(positive profit, hence you made money).

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Related Questions

7. The total cost of Mrs. Goodwin's donut purchase varies directly with the amount of donuts purchased. If
the total cost was $7.50 for 15 donuts, how many donuts can she purchase for $10.00?

Answers

The number of donuts that can be purchased for $10 is 20.

The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.

Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.

The price is directly proportional to the number of donuts purchased.

p ∝ n

We will remove the proportionality sign.

p = k*n

7.5 = k*15

k = 1/2

The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.

p = (1/2)n

10 = (1/2)n

n = 10*2

n = 20

Hence, the number of donuts that can be purchased for $10 is 20.

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find the median of the following: 14.8, 16.2, 4.8, 12.1, and 6.9. if needed, round your answer to the nearest tenth.

Answers

The mean will be the middle number or 12.1.

What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.

According to our question-

The median is the middle number  in the data set when the data set is written from least to greatest.

least to greatest 4.8, 6.9, 12.1, 14.8, 16.2

Hence, The mean will be the middle number or 12.1.

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Can anyone write the equation of the graph?

Answers

14x-3x^2
On the graph
This should answer your question
.0

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
32 kg to 56 kg

Answers

Answer:

4/7

Step-by-step explanation:

32:56

32÷2=16

56÷2=28

16:28

16÷2=8

28÷2=14

8:14

8÷2=4

14÷2=7

4:7

32:56 ~ 32/56

=4/7

help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The dive lasted approximately [tex] \boxed{\sf 2.76} [/tex] seconds.

Step-by-step explanation:

Given formula: h = 16t²

Where, t is time in seconds and h is the distance in feet traveled by a free-falling body or object.

According to the question,

Height of the cliff from which diver dives (h) = 122 feet.

By substituting the value of height in the formula we get:

[tex]\rm \implies 122 = 16 {t}^{2} \\ \\ \rm \implies {t}^{2} = \dfrac{122}{16} \\ \\\rm \implies {t}^{2} = 7.625 \\ \\ \rm \implies t = \sqrt{7.625} \\ \\ \rm \implies t = 2.76 \: seconds[/tex]

how many cubes are added

Answers

The number of centimeter cubes to be added to make the cuboid is; 30 cubes.

How to Interpret the elevation of objects?

From the given plan, side elevation and front elevation, we can see that the number of cubes needed to make the shape is 18 blocks.

From the front elevation, 12 blocks is required (4 * 3 blocks).

From the side elevation, 6 blocks are required which gives us a total of 18 blocks.

The number of blocks needed to make the given cuboid is;

Volume of cuboid = 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added = Volume cubes - Number of cubes from elevation

The number of cubes to be added = 48 cubes - 18 cubes

The number of cubes to be added = 30 cubes.

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In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?

Answers

Answer:

  27

Step-by-step explanation:

You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.

Setup

Let t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...

  t +(t +5) = 2t+5

The value of the number is ...

  10t +(t+5) = 11t +5

The value is 3 times the sum of digits, so we have ...

  11t +5 = 3(2t +5)

Solution

  11t +5 = 6t +15

  5t = 10 . . . . . . . . . . subtract (6t+5)

  t = 2

  (t+5) = 7

The number is 27.

A sample of size 50 from a normal distribution has sample mean 5 and sample variance 20. Find 96% confidence intervals for the variance and standard deviation of the distribution.

Answers

The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.

A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.

n = 50 makes up the sample size.

Furthermore, the sample variance is s² = 20

The following is the formula for both the variance confidence interval:

σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]

Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.

The 90% confidence interval's lower bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)

= 32.54

The 90% confidence interval's upper bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)

= 96.86

Consequently, the confidence level for the distribution's variance is (96.86, 32.54).

Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).

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The perimeter of this triangle is not more than 30 cm. 2n+3 cm, 2n+2 cm, n cm
a. Write an inequality to show this.
b. Solve the inequality.
c. What are the largest possible lengths of the sides?

Answers

The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30

The solution to the inequality is n ≤ 5 The largest possible lengths of the sides is 13 cm

Inequality to represent the perimeter of a triangle

Perimeter of the triangle = not more than 30 cmSide a = (2n + 3)cmSide b = (2n + 2) cmSide c = n cm

Side a + side b + side c ≤ perimeter of the triangle

(2n + 3) + (2n + 2) + n ≤ 30

open parenthesis

2n + 3 + 2n + 2 + n ≤ 30

5n + 5 ≤ 30

substract 5 from both sides

5n ≤ 30 - 5

5n ≤ 25

divide both sides by 5

n ≤ 25/5

n ≤ 5 cm

The largest possible lengths of the sides is:

Side a = (2n + 3)cm

= 2(5) + 3

= 10 + 3

= 13 cm

Side b = (2n + 2) cm

= 2(5) + 2

= 10 + 2

= 12 cm

Side c = n cm

= 5 cm

So therefore, the largest possible length of the triangle is 13 cm

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Determine the smallest integer value of x in the solution of the following inequality.
-4x - 1 ≤ 13

Answers

Answer:

-3.5

Step-by-step explanation:

-4x-1+1≤ 13+1

-4x/-4 ≤ 14/-4

x≤ -3.5

a data analyst creates a scatterplot. the analyst wants to put a text label on the plot to call out specific data points. what function does the analyst use?

Answers

The analyst should use the alpha aesthetic. The alpha aesthetic makes some points on a plot more transparent than others to call out specific data points.

What is scatterplot?

A set of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of correlation, if any, between the values of observed quantities or phenomena, scatter plots are crucial in statistics (called variables). In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.

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Which of these strategies would eliminate a variable in the system of equations?


2x + 8y = -3


3x + 6y = -4


A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.


B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.



C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations

Answers

Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.

Rewriting the equation -

2x + 8y = -3 : Equation 1

3x + 6y = -4 : Equation 2

Multiplying equation 1 with and equation 2 with -2.

6x + 24y = -9 : Equation 3

-6x - 12y = 24 : Equation 4

Adding the equation 3 and equation 4. This will eliminate the variable x.

12y = 15

y = 5/4

So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.

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A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same
amount of time it flew 300 miles against the wind. Find the speed of the wind.

Answers

The speed of the wind is 50 mile per hour  .

In the question ,

it is given that

the speed of the plane is [tex]=[/tex] 200 miles per hour .

let the speed of the wind is = "w"

So ,the speed of the plane with wind is [tex]=[/tex] 200 + w

and the speed of the plane against  wind is [tex]=[/tex] 200 - w

we know that , distance [tex]=[/tex] speed × time

the plane flew "500 miles" with wind ,

which means ,

500 [tex]=[/tex] (200 + w) × t      .....(1)

and the plane flew 300 miles against the wind ,

which means ,

300 [tex]=[/tex] (200 - w) × t       ......(2)

adding both the equations ,

we get

800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)

800 = t × 400

t = 2

Substituting  , t = 2 in 500 [tex]=[/tex] (200 + w) × t      

we get

500 = (200 + w) × 2

500/2 = 200 + w

250 = 200 + w

w = 250 - 200

w = 50

Therefore , The speed of the wind is 50 mile per hour  .

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Can someone help me with this aleks question

Answers

For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.

As given in the question,

Two triangles ΔTRS and ΔQRP,

It is given that :

Line segment SR ≅ Line segment PR

Line segment SP bisects Line segment TQ

⇒ line segment TR ≅ line segment RQ

∠TRS ≅ ∠PRQ ( by vertically opposite angle )

By Side angle side theorem we have ,

ΔTRS ≅ ΔPRQ

Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.

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students and courses have ....... relationship: a. one to one b. one to many c. many to many d. none. mcq answer

Answers

The students and courses have one to many relationship.

A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.

In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.

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You have 7,160 grams of a radioactive kind of bismuth. How much will be left after 10 days if
its half-life is 5 days?
grams

Answers

The solution is 1790 grams

The amount of bismuth left after 10 days if the half life is 5 days will be

1790 grams

What is half-life of an element?

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

Let the half life of the element be represented as t½

The value of t½ = 5 days

Now , the initial amount of bismuth N₀ = 7160 grams

The number of days t = 10 days

The amount of bismuth left after 10 days = N( t )

Now , the value of N( t ) is given by the formula ,

N( t ) = N₀ ( 1/2 )^ t/ t½

Substituting the values in the equation , we get

N( t ) = 7160 ( 1/2 )^10/5

N( t ) = 7160 ( 1/2 )²

N( t ) = 7160 / 4

N( t ) = 1790 grams

Therefore , the value of N( t ) is 1790 grams

Hence , the amount of bismuth left is 1790 grams

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Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!

Answers

The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

In this question we have been given an expression.

We need to identify the property that is used to multiply two binomials.

(3x+5)(2x+7)=2x(3x+5)+7(3x+5)

Consider two binomials,

(3x+5)(2x+7)

= (2x+7)(3x+5)                     ...............(commutative property)

= 2x(3x+5)+7(3x+5)            ................(distributive property)

Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

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Solve for X please help

Answers

Answer:

17

Step-by-step explanation:

4x-10=58(alternate interior angles)

4x=68

x=17

PLEASE HELP 69 POINTS

Triangle A has vertices (−2, 1), (1, 1), and (1, 0).

Which triangle is similar to triangle A?

Responses

Triangle Y with vertices (−4, 3), (2, 3), and (2, 2)

Triangle W with vertices (−4, 2), (2, 2), and (2, 0)

Triangle X with vertices (−2, 2), (1, 2), and (1, 0)


Triangle Z with vertices (−4, −1), (2, −1), and (2, −2)

Answers

The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to

Triangle W with vertices (−4, 2), (2, 2), and (2, 0)

What are similar triangles?

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.

Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)

The difference is a scale factor of 2

(−2, 1) * 2 =  (−4, 2)

(1, 1) * 2 = (2, 2)

(1, 0) * 2 = (2, 0)

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Add/Subtract Rational Numbers :


Add ; -1/2 + 2/3 (Simplify)

Evaluate ; -1/8 - (-5/6) (Simplify)

Answers

1. answer is 1/6
2. 17/24

Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7

Answers

The addition of the decimals given as 3.8 and 2.7 will be 6.5.

What are decimals?

Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.

In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:

= 3.8 + 2.7

= 6.5

Therefore, the value is 6.5.

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Please help

The equation y = -8/3x + 40 represents an alternative speed slide the city of Geocove is thinking of constructing in their waterpark. The graph of this equation is shown. Suppose that a rider travels downward 8 feet on this slide. What is the value of their horizontal change?

6 feet
2.7 feet
8 feet
3 feet

Answers

The value of their horizontal change is 2.7 feet

How to determine the value of their horizontal change?

The equation of the function is given as

y = -8/3x + 40

From the question, the distance travelled by the rider is given as

Distance = 8 feet downward

This means that

Horizontal change = slope

A linear equation is represented as

y = mx + c

Where

Slope = m

By comparing y = mx + c and y = -8/3x + 40, we have

Slope = m = 8/3

This gives

Horizontal change = 8/3

Evaluate

Horizontal change = 2.7

Hence, the horizontal change is 2.7 feet

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Given: AD
Prove: DE
A
D
BC and ZBCD ZADC
CE
C
Intro
B
Correct! Assemble the next
statement.
Angles Segments Triangles Statements Reasons
SAS
CPCTC
reflexive property
Statements
✓1. AD BC
✓ 2. ZDEA and CEB are
vertical angles
3. ZBCD
ZADC
vertical angles theorem
Reasons
1. given
2. def. of vertical angles
3. given

Answers

Triangle ADC and ΔBDC are congruent.     then DE ≅ CE

         

What do you mean by congruent?

It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.

Given,

        AD ≅ BC

      ∠BCD ≅ ∠ADC

In triangle ADC and ΔBDC

                    AD ≅ BC    ( GIVEN )

      ∠BCD ≅ ∠ADC          ( GIVEN )

             DC = DC             ( Common line)

so  triangle ADC and ΔBDC are congruent.

             then DE ≅ CE

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Simplify negative 1 and 2 over 3 minus 9 and 2 over 5.

11 and 1 over 15
negative 10 and 4 over 8
negative 16 over 15
negative 166 over 15

Answers

The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).

What is the simplified form of the expression?

It follows from the task content that the simplified form of the given expression is to be determined.

Since the given expression is; -1 ⅔ - 9 ⅖.

First, the mixed numbers as in the task content must be converted to fractions so that we have;

- 1 ⅔ = -5/3 and

9 ⅖ = 47/5

Therefore, the required evaluation is; -5/3 - 47/5

= -25/15 - 141/15

= (-25 - 141) / 15

= -166/15

Therefore, the required simplified form of the expression is; negative 166 over 15.

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Solve for a side in right triangles

Really need help with this one!!

Answers

The value of side AC is AC = 3.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

The given triangle  ΔABC is a right angled triangle.

So, to find the side AC we can use the cosine ratio,

[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]

AC ≈ 3.

Hence, the length of side AC is 3.

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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

Answers

The equations that can be used to solve for y, the length of the room

y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0

How do we obtain the relevant equations that can be used for the problem?

First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:

Area of a rectangle = Length × Width

Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:

y( y - 5) = 750

When this equation is fully expressed, we will get the following equations:

y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0

Therefore, options, B, C, and E are correct.

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what is the sum of the exponents of the prime factors of the square root of the largestperfect square that divides 12! ?

Answers

8 is the  sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!

We are asked the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!.

As, the largest perfect square that divides 12! is

2^10 * 3^4 *5^2 = 2073600.

Now, the square root of the number 2073600 is,

1440

Now, we have to find the prime factorization of 1440

1440 = 2×2×2×2×2×3×3×5

Now, in the prime factorization of 1440

the exponent of 2 is 5, exponent of 3 is 2 and the exponent of 5 is 1.

So, the sum of the exponents of the prime factors be 5+2+1 = 8

Hence, 8 is the  sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!

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avoiding an accident when driving can depend on reaction time. that time, measured from the moment a driver sees the danger until he/she gets his/her foot on the brake pedal, is normally distributed with a mean of 1.5 seconds and a standard deviation of 0.18 seconds. what is the interquartile range of the reaction times? report your answer to at least the nearest hundredth of a second (i.e. with at least two digits after the decimal point).

Answers

The interquartile range of the reaction times is 0.528 or 52.80%

A normal model is represented as (μ, σ). Therefore for (1.5, 0.18), the mean (μ) = 1.5 and the standard deviation (σ) = 0.18

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

The z score shows by how many standard deviations the raw score is above or below the mean. It is given as:

The interquartile range is x = 1.45 and x = 1.75

For x = 1.45

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z=(1.45-1.5)/0.18

 = -0.28

For x = 1.75

Z=(1.75-1.5)/0.18

 = -1.39

From the normal distribution table,

P(1.45 < x < 1.75) = P(-0.28 < z < 1.39)

                            = P(z < 1.39) - P(z< - 0.28)

                            = 0.9177 - 0.3897

                           = 0.528

                          = 52.8%

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2x-84=108
x=?

please help ​

Answers

Answer:

X=

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−84=108x

Step 1: Subtract 108x from both sides.

2x−84−108x=108x−108x

−106x−84=0

Step 2: Add 84 to both sides.

−106x−84+84=0+84

−106x=84

Step 3: Divide both sides by -106.

−106x

−106

=

84/−106x=−42/53

NEED HELP FINDING THE EQUATION!!! THXXXX

Answers

Answer:

See below

Step-by-step explanation:

Horizontal lines have ZERO slope

Vertical lines have 'undefined' slope

for this example  x = 1/2    includes the point and has undiefined slope

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