The equation be 38.67 + 13.6 then we get 52.27.
What is meant by decimal notation?A different way to represent a fractional value in mathematics is to use decimal notation. It denotes that base-10 fractional representation is being used. It is possible to change fractions into decimals and vice versa.
The same thing applies to decimals: they each represent a portion of a whole number. The distinction is in the notation used to write decimals vs fractions. By using decimal notation, we can graphically express how much of a whole number we are working with.
The decimal point must be moved till it is to the left of the first non-zero number in order to be written in scientific notation. The exponent is the amount of places the decimal point advances since each movement signifies a "power of 10".
Let the equation be 38.67 + 13.6 then we get 52.27.
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Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
4 jars
5 jars
10 jars
Answer: I'm pretty sure there was suppose to be a 4th option that is not included here, none of these are correct, Lorraine can fill 8 jars.
Step-by-step explanation: First, we need to convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then we divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
⚠️Please verify inthe comments if there was indeed a 4th option⚠️
Answer:
8
Step-by-step explanation:
convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
What do I put in the boxes?
What are types of solutions?
There are three main types of solutions found in mathematics for a given problem or equation: No solution, Unique solution, and Infinitely many solutions.
Solutions in mathematics are a set of values that can be assigned to the variables of an equation or a system of equations so that it holds true. In other words, it is a set of values that satisfies the equation or system of equations.
Types of solutions:
No solution: In this situation, there is no set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Unique solution: In this situation, there is only one set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Infinitely many solutions: In this situation, there are infinitely many sets of values that can be assigned to the variables of an equation or system of equations so that it holds true. This situation arises when the given equation is not independent.
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Think about how you can use a graph to help you out in someway in your daily life. what data from your life are you going to use? what kind of graph would you use to track this data? how will you use this graph to help you? explain.
The graph to represent this data is pie chart.
What is a Graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
The graph used to represent the data is shown in the figure;
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For every pound a company spends on advertising, it spends £0.24 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answer:
25:6
Step-by-step explanation:
1/0.24
100/24
50/12
25/6
Solve each triangle using the Law of Cosines.
As a farmer, suppose you want to fence off a rectangular field that borders a river. You wish to find out the dimensions of the field that occupies the largest area, if you have 1500 feet of fencing. Remember that a square maximizes area, so use a square in your work.
-Draw several diagrams to express the situation and calculate the area for each configuration, then estimate the dimension of largest possible field.
-Find the function that models the area in terms of one of its sides.
-Find the point that maximizes the function you found in the second bulleted item.
-Calculate the area of the field at the point you found in the third bulleted item, and then compare your results with the results in the first bulleted item.
According to the area of rectangle, the maximum area is given by a 300 × 500 ft rectangle that is being half of a square
The formula to calculate the area of square is written as
A = l x b
where l refers the length and b refers the breadth in rectangle.
Here we have know that if there were no river then the maximum area would be given by a square configuration since increasing the length and decreasing the width of a square by the same value t will decrease the area by a square with sides of length t.
Here we have to add the river on one side.
As we all know that we need to fence in a rectangle on one side of the river and then here we have imagine an identical rectangle on the other side of the river.
Then the maximum area is given when the two rectangles form a square that is when we have a rectangle twice as long as wide is written as
=> 1500 feet of fence then the rectangle has fenced sides written as 500feet and 300feet.
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a classroom of children has 11 boys and 18 girls in which five students are chosen to do presentations. what is the probability that at least four boys are chosen?
The total Number of ways to select five students out of 11 boys and 18 girls will be=104642
We have, total number of boys = 11, while the total number of girls = 18
Let us assume that,
X = total number of boys chosen
As it is given,
P(X>=4)=1
-P(X<=3)
Where, P(at most 3 boys are chosen) needs to be found out
As we know,
Here, the total number of ways to get at most 3 boys= Number of ways to get three boys and two girls + number of ways to get one boy and four girls + Number of ways to get two boys and three girls + Number of ways to get zero boys and five girls
Making the combination as per above arrangements:
We will get it as:
=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5
As we know,
The formula of combination is:
[tex]$${ }_n C_r=\frac{n !}{r !(n-r) !}$$[/tex]
[tex]${ }_n C_r=$[/tex] number of combinations
n= total number of objects in the set
r= number of choosing objects from the set
So, applying the concept of combination in the above,
=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5
[tex]= \frac{11!}{8! \times 3!} \times \frac{18!}{16! \times 2!}+\frac{11!}{9! \times 2!} \times \frac{18!}{15! \times 3!}+\frac{11!}{10! \times 1!} \times \frac{18!}{14! \times 4!}+\frac{11!}{11! \times 0!} \times \frac{18!}{13! \times 5!}[/tex]
[tex][\frac{11 \times 10\times9\times8! }{8!\times 6} \times \frac{18\times17\times16!}{16!\times2}]+[\frac{11\times10\times9!}{9!\times2} \times \frac{18\times17\times16\times15!}{15!\times6}]+[\frac{11\times10!}{10!} \times \frac{18\times17\times16\times15\times14!}{14!\times24}]+[\frac{1}{1} \times \frac{18\times17\times16\times15\times14\times13!}{13!\times120}][/tex]
[tex]=(165 \times153)+(55\times816)+(11\times3060)+(1\times856.8)[/tex]
=25245+44880+33660+856.8
=104641.8 = 104642 (approx)
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the probability of randomly picking out a paperback book from a bookshelf is 2 over 5. what are the odds in favor of choosing a paperback book? a.) 3:2 b.) 2:7 c.) 2:3 d.) 2:5
Therefore , selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.
What does the process of probability mean?Calculating the probability of an event happening or a declaration being true is the focus of the mathematical field of probability theory. A chance is just a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating the likelihood of an event occurring. Probability is a mathematical expression of the likelihood or probability that because an event will take place. The percentage ranges of 0% to 100% as well as the numerals 0 and 1 can be used to describe probabilities. the percentage of times an event occurs in a perfect collection of equally likely alternatives, out of all possible outcomes.
Here,
Given The likelihood of selecting a paperback book at random from either a bookshelf is 2/5, as stated.
In order to determine whether picking a paperback book is more likely to be strange,
So, using the information provided, we observe it.
that the odd favor of picking a paperback book is 2:1.
Option D is the proper choice.
Since selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.
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Answer:
2:3
Step-by-step explanation:
alberto sold half of his comic books. and then bought nineteen more. he now has 43. with how many did he start with
Answer:
48
Step-by-step explanation:
First you should subtract 43 and 19
then you get a answer 24
Multiply it by 2
you get 48
Answer:
no. of books =48 books
Step-by-step explanation:
lets say that he started with
x
books so,
(X÷2)-19=43
X÷2=24
X=48
two arithmetic sequences and both begin with and have common differences of absolute value , with sequence increasing and sequence decreasing. what is the absolute value of the difference between the st term of sequence and the st term of sequence ?
The difference between the 51st term of a and the 51st term of b is 1000.
the nth term of an arithmetic series is given by [tex]a_{n}= a_{0}+(n-1)*d[/tex]
where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference
Given that,
[tex]a_{0}=b_{0}=30[/tex]
Common difference of both series that have absolute value = 10
common difference of series a is 10 as this series is increasing
similarly, the common difference of series b is -10 as it is decreasing
Putting the values in the above equation we get:
[tex]a_{51}= a_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*10
=> 30 + 500 = 530
Thus, the value of [tex]a_{51}[/tex] is 530.
[tex]b_{51}= b_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*-10
=> 30 -500 = -470
Thus, the value of [tex]b_{51}[/tex] is -470.
so we have to find the value of [tex]a_{51}-b_{51}[/tex] which is 530 - (-470) =530 +470 =1000
Therefore, The difference between the 51st term of a and the 51st term of b is 1000.
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A coin-operated coffee vending machine dipene, on the average, 6 oz of coffee per cup. Can thi tatement be true of a vending machine that occaion
It is possible for this statement to be true for a vending machine that occasionally dispenses more or less than 6 oz of coffee per cup.
The term "on average" or "on the average" refers to the mean or expected value of a distribution. The vending machine may have some variations in the amount of coffee it dispenses, but on average it dispenses 6 oz of coffee per cup.
It is possible that the vending machine may dispense more or less than 6 oz of coffee per cup due to machine variations, incorrect calibration, or maintenance issues. However, as long as the mean or average amount of coffee dispensed over a certain period of time is 6 oz per cup, the statement is considered true.
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Based upon the input from Units 1 and 2, you have just received your next assignment that will contribute to your next decision. For the outdoor sporting goods client, based upon your prior decision on whether or not to expand to the next market or retain your current position, justify your decision further utilizing the chi-square distribution tool. One key criterion point: You do not have adequate data to formulate a full chi-square for the outdoor sporting goods client. However, you have sufficient data to initiate this process. You are charged to demonstrate the initial steps of a nonparametric test that are qualitative. Utilizing the null and alternative hypotheses, further present your justifications for your selection and what it means beyond the mere formulas. What is this going to tell the Board of Directors and contribute to the decision-making process? The following information may be helpful in understanding chi-square and hypothesis testing: Please review this helpful video. The presenter uses flipping a coin and rolling a die. These are examples and analogies used in the CTU resources. The following are assumptions that might make the assignment more helpful and make the responses more uniform: Continue to utilize the Big D scenario. Work under the assumption that the sample is based upon 2 different proposed product lines. Additionally, work under the assumption that the same demographics are utilized for each product.
My forecast is that you will either enter the next market or, more likely, keep your existing position. These are the theories we have.
Because we put our alternative hypothesis equal to what we wish to show, you should continue to hold the stance you already hold. The opposite hypothesis, or null hypothesis, is a claim that there is no difference. For instance,There is no discernible difference between the mean and sample population, according to the null hypothesis.Alternative Hypothesis H1: The mean and sample population differ significantly.Level of significance: A: If there is no difference in the sample as well as population means, there is a 5% chance that the null hypothesis will be rejected. In a non-parametric test, rankings are considered as a test statistic after being translated from the observed sample. We utilize the rankings to calculate the test statistic in non-parametric testing. The choice of accepting or the null hypothesis being rejected will be decided when the levels of liberty and crucial values have been defined. Chi square is used since there are only two choices to compare. As soon as we get our data, we can calculate the chi squared value x2 and determine the crucial values from table of freedom levels with 95% certainty.To know more about hypothesis visit:
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Marcus is making homemade barbecue sauce. The recipe calls for 3 cups of ketchup for every 1/2 of mustard. What is the rate in cups of ketchup per cup of mustard
The rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.
What are expression models?The expression model is defined as the model of the given situation in the form of an expression using variables and constants.
Here,
The recipe calls for 3 cups of ketchup for every 1/2 of mustard.
Now,
The rate in cups of ketchup per cup of mustard = ketchup/mustard
= 3 / [1/2]
= 3 × 2 = 6 / 1
Thus, the rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.
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your favorite restaurant has a promotion where you can win free food. you will roll 2 dice. the sum of the 2 dice will determine which prize you receive. 2-column table with 11 rows. column 1, outcome, entries 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. column 2, probability, entries startfraction 1 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 6 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 1 over 36 endfraction. which scenario uses the addition rule for mutually exclusive events? p(rolling a sum of 4) p(rolling a sum of 4 or rolling a sum of 5) p(rolling a sum of 12 or rolling a double 6) p(rolling a sum of 11 and rolling a sum of 12)
Answer: P(rolling a sum of 4 or rolling a sum of 5)
Step-by-step explanation: edge2023
The scenario that uses the addition rule for mutually exclusive events is:
p(rolling a sum of 4 or rolling a sum of 5) = p(rolling a sum of 4) + p(rolling a sum of 5)
This is because the events "rolling a sum of 4" and "rolling a sum of 5" are mutually exclusive, meaning that they cannot occur at the same time. Therefore, the probability of either event occurring is the sum of their individual probabilities.
The probability of rolling a sum of 4 is 3/36, and the probability of rolling a sum of 5 is 4/36. The addition rule states that the probability of rolling a sum of 4 or 5 is the sum of their individual probabilities: 3/36 + 4/36 = 7/36
The other scenarios do not use the addition rule for mutually exclusive events:
p(rolling a sum of 4) is a single event and does not involve a second event.
p(rolling a sum of 12 or rolling a double 6) although the two events are mutually exclusive, it's not the sum of their individual probabilities.
p(rolling a sum of 11 and rolling a sum of 12) these events are not mutually exclusive, they can happen at the same time, so it's not the sum of their individual probabilities.
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Determine the probability of tossing two heads in a row by:
Listing all possible outcomes ((H,T), (H,H) and so on) and circling the desired outcome.
Calculating desired outcome
--—----------------
Total number of outcomes
Answer:
4
Step-by-step explanation:
(H,H) (T,T)(T,H)(H,T)
the length of a rectangle is 4 inches shorter than its width. the perimeter of the rectangle is 80 inches. what are the length and width of the rectangle?
If length of a rectangle is 4 inches shorter than its width and perimeter of rectangle is 80 inches , then the length of rectangle is 18 in and width of rectangle is 22 in .
The Perimeter of rectangle can be calculated by using formula : [tex]2(l+w)[/tex] ;
let the width of rectangle be = w ,
it is given that the length is 4 inches shorter than width , that means ;
the width of rectangle is ⇒ [tex]w-4[/tex] ;
So , the perimeter becomes ⇒ [tex]80=2(l+w)[/tex]
⇒ [tex]80=2(w-4+w)[/tex]
⇒ [tex]40=2w-4[/tex] ;
⇒ [tex]2w=44[/tex] ;
⇒ [tex]w=22[/tex] ;
and substituting [tex]w=22[/tex] , we get [tex]l=22-4 = 18[/tex] in
Therefore , the length of rectangle is 18 in and width is 22 in .
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Last summer, there were 888 houses for sale in Neil's town. The other 37 houses in the town were not for sale. What percentage of the houses in Neil's town were for sale last summer?
Answer:
96% of the houses were up for sale.
Step-by-step explanation:
Total number of houses
888 = 37 = 925
888 / 925 = .96
You change a decimal into a percent by multiplying by 100%
.96 x 100% = 96%
jake sold 28 tickets to the school fair, and jeanne sold 21 tickets. what is the ratio,in simplest form
The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne in the simplest form, will be 4:3
The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 28:21.
To simplify this ratio, we can divide both numbers by their greatest common factor (GCF). The GCF of 28 and 21 is 7.
So, the simplified ratio is 28/7: 21/7 = 4:3
So the ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 4:3 in simplest form.
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The Total number of cherries on a plate, in a cup, and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?
Circle O shown below has a radius of 30 inches. To the nearest tenth of an inch,
determine the length of the arc, x, subtended by an angle of 1.8 radians.
30 inches
0=1.8 rad
Answer:
To the nearest tenth of an inch, the length of the arc is 54.0 inches
Step-by-step explanation:
To determine the length of the arc, x, we need to use the formula for arc length, which is:
arc length = radius * angle (in radians)
Therefore,
arc length = 30 inches * 1.8 radians = 54 inches
find an equation of the tangent line to the given curve at the specified point. y = e^x /x , at the point (1, e)
An equation of the tangent line to the given curve at the specified point will be y = e(x - 1) + e.
Given the equation y = e^x /x and the point (1, e), the goal is to find an equation of the tangent line at this point.
To do this, we need to find the derivative of the equation at the point (1, e). Taking the derivative with respect to x gives us:
y' = (e^x * (1 - 1/x) - e^x/x^2) / x^2
Since we are looking for the derivative at the point (1, e), we can plug in x = 1 to get the derivative at this point:
y' = (e - e/1) / 1^2
y' = e
Therefore, the equation of the tangent line at the point (1, e) is y = e(x - 1) + e.
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The input and output values of a function f (x) are shown in the table.
X
-4
-3
-2
-1
0
f (x)
2
1
0
1
2
If g (x) = 2f (x), then which table shows the input and output values of g (x)?
The table which shows the input and output values of g (x) is,
f (x) g(x)
2 4
1 2
0 0
1 2
2 4
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The input and output values of a function f (x) are shown in the table.
X f (x)
-4 2
-3 1
-2 0
-1 1
0 2
Here, We have;
⇒ g (x) = 2f (x),
Hence, The table which shows the input and output values of g (x) is,
f (x) g(x)
2 2×2 = 4
1 1×2 = 2
0 0×2 = 0
1 2×1 = 2
2 2×2 = 4
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A man is 38 years old, and his daughter is 14 years old. How many years will it be before the man's age is just twice the age of his daughter?
This is an algebraic word problem and it evaluated to be 10 years time before the age of the man will be twice the age of the daughter.
Algebraic word problemIn algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.
We shall represent the number of years it will be before the age of the man will be twice the age of the daughter with the letter x so that;
38 + x = 2(14 + x) {open bracket}
38 + x = 28 + 2x
38 - 28 = 2x - x {collect like terms}
10 = x
also x = 10.
Therefore, the agebraic word problem have a solution of 10 years before the age of the man will be twice the age of the daughter.
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A company models its net income, in thousands of dollars, with the function f(x) = 9x2 – 54x – 144, where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?
The quantity of units that the company needs to sell in order for the net income to equal $0 would be = 8.
How to calculate the quantity of units using quadratic equations?The net income of the company in thousands of dollars is represented with the function;
f(x) = 9x2 – 54x – 144,
It can be simplified as follows:
f(x) = 9(x² - 6x - 16)
Then:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, hence:
x + 2 = 0 -> x = -2.
x - 8 = 0 -> x = 8.
The positive value and not a negative shows that there are amount of products sold which should be = 8.
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Is 1 a factor of all number?
1 is a factor of every whole number. Every whole number can be evenly divided by 1, so 1 is a factor of every whole number.
1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.
1 is the greatest factor of itself and the smallest factor of any other number.
There are some properties of factors one:
Every whole number is the product of 1 and itself so, each number is a factor of itself.
Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.
Every number other than 1 has at least two factors, namely the number itself and 1.
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4x+9=101 what is the value of x
Answer: x = 23
Step-by-step explanation:
Move all terms that don't contain
x
to the right side and solve.
Hope this helps :)
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 7 0-9 3 10 9 ; 2=lambda = 7, 10 0 0 10
The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).
what is matrix ?Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array. In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.
given
Eigen values ( λ )
| A - λI | = 0
= ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0
= λ = 7 , 11 , 11
eigen vector for λ = 7
( A - IB ) X = 0
= Let y = 1 , n1 = ( -1 1 0 )
eigen vector for λ = 11
( A - λI ) X = 0
n2 = ( 0 1 0 ) let n3= ( -2 0 1 )
D = ( 7 0 0 , 0 11 0 , 0 0 11 )
The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).
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Write a method that takes two circles, and returns the sum of the areas of the circles. This method must be named areaSum() and it must have two Circle parameters. This method must return a double. For example suppose two Circle objects were initialized as shown:
The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double.
Circle c1 = new Circle(5);
Circle c2 = new Circle(7);
[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]
1. Create a public static method named areaSum that takes two Circle objects as parameters.
2. The method should return a double.
3. Inside the method, use the getArea() method of the Circle class to get the area of both circles.
4. Return the sum of the areas of both circles.
5. The method should look like this:
[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]
The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double. The method uses the getArea() method of the Circle class to get the area of both circles and returns the sum of the areas.
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12 in ,10 in 8 in what type of triangle is
The type of triangle that is given by the dimensions, is a Scalene triangle.
What are types of triangles ?A scalene triangle has sides that are all measured differently. In such a triangle, no side will be the same length as any other side. Every interior angle in a scalene triangle is also unique.
The lengths of two of the three sides in an isosceles triangle are equal. The angles that are opposite the equal sides are therefore equal. An isosceles triangle, in other words, has two equal sides and two equal angles.
Each side of an equilateral triangle has an equal length. Each internal angle in this scenario will be 60 degrees in length. An equilateral triangle is often referred to as an equiangular triangle since its angles are equal.
The dimensions here are not the same which means that all the sides are not equal and so this is a scalene triangle.
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