Answer:
random variable
Step-by-step explanation:
Random variable also known as stochastic variables are variables that are used in statistics and probability, The value of a random variable must be determined by chance which remain uncertain and depends on the outcome of a random process or experiment.
Unlike algebra, when random variable is introduced into a mathematical model, it is represented by capital letter and it has a single numerical value.
James buys a 3 books from the bookstore for $39.99. He has a coupon for 25% off the original price. He is charged 8.5% sales tax. What is the total cost of his purchase?
Answer:
Step-by-step explanation:
The cost of the three books that James bought from the bookstore.
He has a coupon for 25% off the original price. This means that the amount by which the original price was reduced would be
25/100 × 39.99 = 0.25 × 39.99 = $9.8325
The cost of the books would be
39.99 - 9.8325 = $30.1575
He is charged 8.5% sales tax. This means that the amount paid for tax would be
8.5/100 × 30.1575 = 0.085 × 30.1575 = $2.56
the total cost of his purchase would be
2.56 + 30.1575 = $32.7175
Answer:
$32.7175
Step-by-step explanation:
Let x be a positive number such that the distance between x and -3.8 on a number line is exactly two times the distance between x and 1.7. What is the value of x? Express your answer as a decimal to the nearest tenth.
Answer:
0.4
Step-by-step explanation:
Equation is
x-(-3.8)=2(x-1.7)
solving for x,
x+3.8=2x-3.4
x=0.4
Final answer:
The value of x is found by setting up an equation based on the distances provided and considering two separate cases for the absolute value. After solving the equation, the positive value of x is determined to be 7.2.
Explanation:
To solve for the value of x in this problem, we need to set up an equation based on the information given about the distances on a number line. The distance between x and -3.8 is twice the distance between x and 1.7. This translates to the following equation:
|x - (-3.8)| = 2|x - 1.7|
We then solve this equation step-by-step:
First, simplify the equation:Therefore, the value of x to the nearest tenth is 7.2.
While our weight is typically displayed without decimal places (e.g., 165 lbs), it can be displayed with great decimal precision. Limited only by the precision we place on it, the variable of weight is ______.
Answer:
Continuous observation
Step-by-step explanation:
Generally, the weight of any person is displaced in whole numbers without the inclusion of decimal numbers. The decimal numbers are mostly rounded up to the whole number. Based on the argument made in the given problem, the type of weight variable for this type of analysis is known as continuous observation.
Determine whether the underlined number describes a population parameter or a sample statistic. Explain your reasoning. Modifying Sixty minus five with underline of the 97 passengers aboard an airship survived an explosion.
Answer:
Step-by-step explanation:
Match the units with the rotational quantity angular displacement angular velocity angular acceleration tangential acceleration tangential velocity radius a. meters per second b. meters per second-squared c. radians per second-squared d. radians e. radians per second f. meters.
Answer:
Below.
Step-by-step explanation:
a = tangential velocity
b = tangential acceleration
c = Angular acceleration
d = angular displacement
e = Angular velocity
f = radius.
A pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. Is the perimeter of the pentagon greater than 26 centimeters?(1) The area of the circle is 16π square centimeters.
(2) The length of each diagonal of the pentagon is less than 8 centimeters.
Answer:
Step-by-step explanation:
Check the attachment for solution
600 units of electricity and 100 units of gas were used for a total cost of $388. Next month, 400 units of electricity and 150 units of gas were used for a total cost of $277. Find the cost per unit of gas.
Answer:
Cost per Electricity Unit= $0.61
Cost per Gas Unit= $0.22
Step-by-step explanation:
Suppose,
Cost per Electricity Unit: e
Cost per Gas Unit: g
for the first month condition, equation would be
[tex]600*e+100*g=388...........................................(i)[/tex]
and for the next month condition, equation would be like
[tex]400*e+150*g=277...........................................(ii)[/tex]
By solving both linear equations simultaneously, we get
e=0.61 and g=0.22
The demand d for a companys product cost x is predicted by the function d(x) = 500-2x. The price p in dollars that the company can charge for the product is given by p(x)=x+5
The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function.
Explanation:The subject of this question is Mathematics. The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function:
p(x) = x + 5 = d(x) + 5 = (500 - 2x) + 5 = 505 - 2x
So the price can be represented by the equation p(x) = 505 - 2x.
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The account balance on April 1st is $102.33. On April 15th a payment of $25.00 is made. On April 25th a purchase of $11.27 is made. What is the finance charge if the annual rate is 22%? What is the new account balance?
Answer:
Finance Charge = $1.42
New Account Balance = $90.02
Step-by-step explanation:
APR (Annual Percentage Rate) = 22%
Periodic Rate = 1.83% (APR/12)
Beginning Balance = $102.33
Payment made on 15th day = $25.00
Purchase made on 25th day = $11.27
Finance Charge = (Beginning Balance - Payment made on 15th day) x Periodic Rate
Finance Charge = ($102.33 - $25.00) x 0.0183
Finance Charge = $77.33 x 0.0183
Finance Charge = $1.42
New Account Balance = Beginning Balance - Payment made on 15th day + Purchase made on 25th day + Finance Charge
New Account Balance = $102.33 - $25.00 + $11.27 + $1.42
New Account Balance = $90.02
The finance charge is approximately $1.67, and the new account balance after accounting for the payment and purchase is $90.27.
We start with the account balance on April 1st, which is $102.33. On April 15th, a payment of $25.00 is made, and on April 25th, a purchase of $11.27 is made.
1: Calculate the Average Daily Balance
From April 1st to April 14th (14 days): $102.33From April 15th to April 24th (10 days): $102.33 - $25.00 = $77.33From April 25th to April 30th (6 days): $77.33 + $11.27 = $88.60Average Daily Balance = ( (14 * 102.33) + (10 * 77.33) + (6 * 88.60) ) / 30 = $91.22
2: Calculate the Finance Charge
Given the annual interest rate of 22%, we first find the monthly rate: 22% / 12 = 1.833%.
Then we calculate the finance charge:
Finance Charge = Average Daily Balance * Monthly Rate
Finance Charge = $91.22 * 0.01833 ≈ $1.67
3: Calculate New Account Balance
New Balance = Previous Balance - Payment + Purchase + Finance Charge
New Balance = $102.33 - $25.00 + $11.27 + $1.67 = $90.27
The new account balance is $90.27.
Lizette's math test grades are 70, 72, and 68. If she scores 100 on her next test, what will happen to the RANGE of her scores? A) It will double. B) It will stay the same. C) It will increase 6 times. D) It will increase 8 times.
Answer D.It will increase 8 times.
Step-by-step explanation:
Answer: It will increase 8 times
Step-by-step explanation:
Range simply means the smallest number subtracted from the biggest number. Initially, the scores were 70, 72 and 68 then making the range 68-72 = 4. Now a new score is added which is 100 and it is obviously the biggest number now. So we subtract 68 from 100 that is ; 100-68= 32. This new range is 8 times more than the former. That is, 32/4 = 8.
The talent show committe sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $5 each. Id the total receipts were $1740, how many of each type of ticket was sold?
Answer:445 student tickets were sold.
75 adult tickets were sold.
Step-by-step explanation:
Let x represent the number of student tickets that were sold in the talent show.
Let y represent the number of adult tickets that were sold in the talent show.
The talent show committee sold a total of 530 tickets in advance. This means that
x + y = 530
Student tickets cost $3 each and the adult tickets cost $5 each. The total receipts were $1740. This means that
3x + 5y = 1740 - - - - - - - - - - - - 1
Substituting x = 530 - y into equation 1, it becomes
3(530 - y) + 5y = 1740
1590 - 3y + 5y = 1740
- 3y + 5y = 1740 - 1590
2y = 150
y = 150/2 = 75
x = 530 - y = 530 - 75
x = 455
.
Mattie is making a collar for her dog. She needs to buy some chain,a clasp, and a name tag. She wants the chain to be 40 centimeters long. One meter of chain costs $9.75. The clasp is $1.29 and the name tag is$3.43. How much will it cost to make a collar?
Answer:the total cost of the collar is $5.11
Step-by-step explanation:
To make a collar for her dog, she needs to buy some chain,a clasp, and a name tag.
The length of the chain that she wants to buy is 40 centimeters.
1000 centimeters = 1 meter
40 centimeters = 40/1000 = 0.04 meters.
One meter of chain costs $9.75. Therefore, 0.04 meters of chain would cost
0.04 × 9.75 = $0.39
The clasp is $1.29 and the name tag is $3.43. Therefore, the total cost of the collar would be
0.39 + 1.29 + 3.43 = $5.11
find the area of a triangle with a base of 18 in. and a height of 6 in. Use the formula for area of a triangle
Area =
[tex] \frac{1}{2} 6h[/tex]
Answer:
The area is 54
Step-by-step explanation:
6x18 = 108
108 x 1/2 = 54
Answer:
area 51
Step-by-stareaep explanation:
Olga purchases a rectangular mirror (the shaded region) that fits exactly inside a frame. The outer perimeter of the frame measures 60 cm by 80 cm. The width of each side of the frame is 10 cm. What is the area of the mirror?
Answer:
2,400cm^2
Step-by-step explanation:
This is quite an interesting question.
Now, we know the frame measures 60 by 80. We also know that the thickness of the frame is 10cm in length. Hence from the side of the mirror to the other side of the frame is 10cm.
We have the 10cm on each side of the frame. Making a total of 40cm and 20cm each allowance on the length and breadth of the mirror. The length and breadth of the mirror is thus 40cm by 60cm.
The area of a rectangle is L * B
The area of the mirror is 40 * 60 = 2,400cm^2
The fact that the width of each side of the frame is 10 cm means that each side of the mirror is 20 cm smaller than the corresponding side of the frame. Therefore, the mirror measures 40 cm by 60 cm, with an area of 2400.
A car drives 40 miles on local roads at 20 mph, and 180 miles on the highway at 60 mph, what is the average speed of the entire trip?
(A) 36 mph
(B) 40 mph
(C) 44 mph
(D) 52 mph
(E) 58 mph
Answer: C) 44 mph
Step-by-step explanation:
We know that [tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]
Given : A car drives 40 miles on local roads at 20 mph.
i.e. Time taken : [tex]t_1=\dfrac{40}{20}=2\ hour[/tex]
Also, it drives 180 miles on the highway at 60 mph.
i.e. Time taken : [tex]t_2=\dfrac{180}{60}=3\ hour[/tex]
We know that the formula for Average speed is given by :-
[tex]A.V.=\dfrac{\text{Total distance}}{\text{Total Time}}[/tex]
So the average speed of the entire trip will be :-
[tex]\dfrac{40+180}{t_1+t_2}\\\\\\=\dfrac{220}{2+3}=\dfrac{220}{5}\\\\=44[/tex]
Hence, the average speed of the entire trip is 44 mph.
Therefore , the correct answer is C) 44 mph.
Which equation represents the function graphed on the coordinate plane? g(x) = |x + 4| – 2 g(x) = |x – 4| – 2 g(x) = |x – 2| – 4 g(x) = |x – 2| + 4. Which equation represents the function graphed on the coordinate plane?
g(x) = |x + 4| – 2
g(x) = |x – 4| – 2
g(x) = |x – 2| – 4
g(x) = |x – 2| + 4
On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 2).
Answer:
[tex]g(x)=|x+4|-2[/tex]
Step-by-step explanation:
All the absolute value functions given in the option are of the form:
[tex]g(x)=|x-h|+k[/tex], where (h,k) is the vertex
From your description the absolute value graph has vertex at (-4,-2)
Hence h=-4 and k=-2.
We substitute to get:
[tex]g(x)=|x--4|+-2[/tex]
We simplify to get:
[tex]g(x)=|x+4|-2[/tex]
The following is a histogram showing the distribution per year of the commutative property damage caused by tornadoes, over the period 1950 to 1999, in each of the 50 states and Puerto Rico. The data are in millions of dollars, and the class intervals are 0 to < 10, 10 to < 20, and so forth.
The histogram depicts the year-by-year damage in millions of dollars caused by tornadoes from 1950 to 1999. It uses class intervals to display the frequency of damage costs, where each bar represents a specific cost range.
Explanation:In the given question, we discuss a histogram that represents the commutative property damage caused by tornadoes from 1950 to 1999 across the 50 US states and Puerto Rico. The histogram's class intervals are set from 0 to < 10, 10 to < 20, and so forth, and the data are in millions of dollars. A histogram is a type of graphical representation used in statistics to display the distribution of data. Each bar in a histogram represents the tabulated frequency at each interval. In this case, the frequency is the year count in which the commutative property damage caused by tornadoes falls within a specific monetary range.
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Figure FGHJ is shown below.
Figure F G H J has 4 sides. Sides F J and G H are congruent and parallel, and sides G F and H J are congruent and parallel. Angles G and J are 130 degrees.
Which names accurately describe figure FGHJ? Select two options.
parallelogram
quadrilateral
rectangle
rhombus
trapezoid
Answer:
parallelogramquadrilateralStep-by-step explanation:
The figure has 4 sides, so is a quadrilateral. Opposite sides are parallel, so the figure is a parallelogram.
Angles are not 90°, so the figure is not a rectangle. Sides are not all the same length, so the figure is not a rhombus. Because the figure has two pairs of parallel sides (not just one pair), it is not a trapezoid.
Answer:
a and b on edge
Step-by-step explanation:
The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for one feature at the Center is $5 for children, $7 for students, and $9 for adults. The attendance for the Sunday matinee is given by the matrixChildren - Students - AdultsCinema I - 225 - 110 - 70Cinema II - 95 - 160 - 225Cinema III - 280 - 65 - 110Cinema IV - 0 - 240 - 225a. Write a column vector B representing the admission prices.b. Compute AB, the column vector showing the gross receipts for each theater.c. Find the total revenue collected at the Cinema Center for admission that Sunday afternoon.
Answer:
a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]
b) Matrix AB = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]
c) $12,695
Step-by-step explanation:
Matrix A = [tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex]
a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]
Gross Receipt = AB
[tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex] . [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex] = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]
c) Total revenue is the sum of receipts from 4 cinemas given in part b
Hence,
Total revenue = $2525 + $3620 + $2845 + $3705 = $12,695
Graph f(x)= square root of 9
Attached is a graph of the function [tex]f(x)=\sqrt{9}[/tex]
Jerome solved the equation 1 3 x + 5 6 = 1 as shown. 1. Subtraction property of equality: 1 3 x + 5 6 − 5 6 = 1 1 − 5 6 2. LCD: 1 3 x = 1 6 − 5 6 3. Multiply by the reciprocal: ( 3 1 ) 1 3 x = −4 6 ( 3 1 ) 4. Solve and simplify: x = −12 6 = −2 Analyze Jerome's steps. In which step did he make an error?
Answer:
In step 2, the LCD was not used correctly to make equivalent fractions.
Step-by-step explanation:
Answer:
In step 2, the LCD was not used correctly to make equivalent fractions.
Step-by-step explanation:
A bag of baby carrots and a container of hummus dip contain a total of 650 calories. For a snack, Rosarita ate of the bag of carrots and of the container of hummus. Her snack contained a total of 260 calories. If x represents the total number of calories in the bag of carrots and y represents the total number of calories in the container of hummus, what is one of the equations for this scenario? X+y=650 x+y=260
Answer:
[tex]x + y = 650[/tex]
Step-by-step explanation:
We are given the following in the question:
Total calories in a bag of carrot and a container of hummus dip = 650
Rosarita's snack:
Some of the bag of carrots and some of the container of hummus.
Total calories in Rosarita's snack = 260
Let x represents the total number of calories in the bag of carrots and y represents the total number of calories in the container of hummus.
Then, we can write the following equation to represent total number of calories in both a bag of carrot and a container of hummus dip:
[tex]x + y = 650[/tex]
Since Rosarita did not eat the whole bag of carrot and the whole container of hummus and also x and y are the total calories in whole bag of carrot and container of hummus respectively.
Answer:
x+y=650
Step-by-step explanation:
its right on edge 8th grade math
A library contains 2000 books. There are 3 times as man non fiction books. Write and solve a systems of equations to determine the number of nonfiction and fiction books.
Answer:
The number of fiction books is 500 and non fiction books is 1500.
Step-by-step explanation:
Given:
Total book library contains = 2000.
There are 3 times as many non fiction books as fiction books.
Now, to determine the number of non fiction books and fiction books.
Let the fiction books be [tex]x.[/tex]
And the non fiction books be [tex]3x.[/tex]
Total books = 2000.
Now, to get the number of non fiction books and fiction books we put an equation:
[tex]3x+x=2000.[/tex]
[tex]4x=2000.[/tex]
Dividing both sides by 4 we get:
[tex]x=500.[/tex]
Fiction books = 500.
Non fiction books = [tex]3x=3\times 500=1500.[/tex]
Therefore, the number of fiction books is 500 and non fiction books is 1500.
To solve for the number of nonfiction and fiction books in the library, set up a system of equations and solve them to find there are 500 fiction books and 1500 nonfiction books.
Explanation:To determine the number of nonfiction and fiction books in the library, we can use a system of equations. Let's denote the number of fiction books as F and the number of nonfiction books as NF. According to the problem, the total number of books in the library is 2000, and there are 3 times as many nonfiction books as there are fiction books.
Our two equations will be:
F + NF = 2000 (Total number of books)
NF = 3F (3 times as many nonfiction books)
To solve these equations:
Substitute the second equation into the first one:
F + 3F = 2000
4F = 2000
Divide both sides by 4 to find F:
F = 2000 / 4
F = 500
There are 500 fiction books. Now we can find the number of nonfiction books by multiplying 500 by 3:
NF = 3 * 500 = 1500
So, the library has 500 fiction books and 1500 nonfiction books.
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Bonds from the city of Tavel Gorge worth $1,000 each are selling at 110.611. If Sean wishes to purchase three such bonds, how much can he expect to pay? a. $3,000.00.b. $3,331.83.c. $3,318.33.d. $331.83.
The bonds are being sold at 110.611% of their face value, so each bond costs roughly $1,106.11. Therefore, to purchase three bonds, Sean would need to pay roughly $3,318.33.
Explanation:When the question states that the bonds are 'selling at 110.611', it means that each bond is sold at 110.611% of its face value, which is $1,000. So to find the price of one bond you would multiply $1,000 by 1.10611 (110.611%), which equals roughly $1,106.11. Thus, if Sean wishes to purchase three bonds, you would simply multiply the price of one bond by three: $1,106.11 times 3 equals $3,318.33. So, Sean should expect to pay approximately $3,318.33 if he wants to purchase three bonds from the city of Tavel Gorge.
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Answer:
The bonds are being sold at 110.611% of their face value, so each bond costs roughly $1,106.11. Therefore, to purchase three bonds, Sean would need to pay roughly $3,318.33.
Step-by-step explanation:
Which of the following represent Exponential Decay? Choose all that apply.
Answer:
y = (7/8)x
Step-by-step explanation:
Exponential decay is represented when the number used is less than 1. 7/8 is the only choice that is less than 1.
y = (7/8)ˣ is an exponential decay because b = 7/8 < 1.
Exponential functionAn exponential decay is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier which is less than 1.
From the question y = (7/8)ˣ is an exponential decay because b = 7/8 < 1.
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A 76.00 pound flask of mercury costs $162.50. The density of mercury is 13.534g/cm 3.
A. Find the price of one cubic inch of mercury by calculating intermediate values.
B. What is the price of one pound of mercury?
C. What is the price of one gram of mercury?
D. What is the price of one cubic centimeter of mercury?
E. What is the price of one cubic inch of mercury?
Answer:
a) 1805.55$
b) 2.14$
c)0.005$
d)0.064$
e)1805.55$
Step-by-step explanation:
Density of mercury is 844.9 lb/ft3.
a) 76 pound flask of mercury is 76/844.9=0.09 ft^3. 0.09 ft^3 mercury cost 162.5$, then 1 ft^3 mercury is
[tex]p=(162.5/0.09)=1805.55[/tex]
1805.55$
b) One pound of mercury is 2.14$
[tex]p=162.5/76=2.14[/tex]
c)76 pound equals 34473 grams. It makes:
[tex]p=162.5/34473=0.005[/tex]
0.005$ is the price of one gram mercury.
d)Total amount of mercury is 34473 grams. Then total volume of mercury is:
[tex]V=34473/13.534=2547.14[/tex]
2547.14 cm3. And the unit price is:
[tex]p=162.5/2547.14=0.064[/tex]
e) 1805.55$. It is found already.
Find x.
- show details and examples to show your answer.
Answer: 17.3
Step-by-step explanation:
Since it is a right angled triangle , we will use the application of SOHCAHTOA in solving it ,which means
sine Ф = opposite / hypotenuse
cosine Ф = adjacent / hypotenuse
Tangent Ф = opposite / adjacent
Ф stands for the given angle.
From the diagram , the given angle is 25 ,this means that
opposite = x
hypotenuse = 41
This means that we will use sine Ф = opposite / hypotenuse to find the value of x.
Therefore:
sin 25 = x/41
x = 41 sin 25
x = 41 x 0.4226
x = 17.3273
x ≈ 17.3
Construct a dotplot for the following data. 4.85 4.94 5.12 5.14 4.80 4.99 5.19 4.94 4.85 5.12 5.04 4.96 5.28 5.05 4.83 5.27 5.12 5.19 4.89 5.15 5.04 5.17 5.24 5.04 4.91 5.26
Answer:
x frequency
4.8 1
4.83 1
4.85 2
4.89 1
4.91 1
4.94 2
4.96 1
4.99 1
5.04 3
5.05 1
5.12 3
5.14 1
5.15 1
5.17 1
5.19 2
5.24 1
5.26 1
5.27 1
5.28 1
find the dot plot as attached below
Step-by-step explanation:
Construct a dotplot for the following data. 4.85 4.94 5.12 5.14 4.80 4.99 5.19 4.94 4.85 5.12 5.04 4.96 5.28 5.05 4.83 5.27 5.12 5.19 4.89 5.15 5.04 5.17 5.24 5.04 4.91 5.26
Rearranging the data into frequency table
x frequency
4.8 1
4.83 1
4.85 2
4.89 1
4.91 1
4.94 2
4.96 1
4.99 1
5.04 3
5.05 1
5.12 3
5.14 1
5.15 1
5.17 1
5.19 2
5.24 1
5.26 1
5.27 1
5.28 1
HELP! Given a pyramid l = w = 9.0 mm and V = 324.0 cubic mm , find h in mm
Answer:
The answer to your question is height = 12 mm
Step-by-step explanation:
Data
l = w = 9 mm
V = 324 mm³
h = ?
Formula
V = [tex]\frac{Ab x h}{3}[/tex]
Solve for h
3V = Ab h
3V / Ab = h or h = 3V / Ab
Find the area of the base
Ab = l x w
= 9 x 9
= 81 mm²
Substitution
h = [tex]\frac{3(324)}{81}[/tex]
Simplification
h = [tex]\frac{972}{81}[/tex]
Result
h = 12 mm
Caleb made $105 mowing lawns and walking dogs, charging the rates shown. If he mowed half as many lawns as dogs walked, how many lawns did he now and how many dogs did he walk?
Question is Incomplete;Complete question is given below;
Caleb made $105 mowing lawns and walking dogs, charging the rates shown. If he mowed half as many lawns as dogs walked, how many lawns did he mow and how many dogs did he walk? $7.50 for walking dogs and $20 for mowing lawns
Answer:
Caleb mowed 3 lawns and walked 10 dogs.
Step-by-step explanation:
Let the number of dogs he walked be 'd'.
Let number of lawn he mowed be 'l'.
Given:
If he mowed half as many lawns as dogs walked
So we can say that;
[tex]l=\frac{1}{2}d=0.5d \ \ \ \ equation\ 1[/tex]
Now given:
Cost for mowing each lawn = $20
Cost for walking each dog = $7.50
Total amount made = $105
Now we can say that;
Total amount made is equal to Cost for mowing each lawn multiplied by number of lawn he mowed and Cost walking each dog multiplied by number of lawn he mowed.
framing in equation form we get;
[tex]20l+7.5d=105 \ \ \ \ \ equation \ 2[/tex]
Substituting equation 1 in equation 2 we get;
[tex]20(0.5d)+7.5d=105[/tex]
Applying distributive property we get;
[tex]10d+7.5d=105\\\\17.5d=105[/tex]
Dividing both side by 17.5 we get;
[tex]\frac{17.5d}{17.5}=\frac{105}{17.5}\\\\d= 6[/tex]
Substituting the value of 'd' in equation 1 we get;
[tex]l=0.5d=0.5\times6=3[/tex]
Hence Caleb mowed 3 lawns and walked 10 dogs.