In hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region
The hypothesis testing is defined as the process of collecting the data and using that as inference draw the calculation about the population parameter.
The reject region of the hypothesis testing is defined as the set of values for the test statistic for which the null hypothesis is rejected.
Therefore, the critical value is a number that establishes the boundary of the rejection region of the graph
Hence, in hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region
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What was the results of the Bonus March?.
Answer:
Step-by-step explanation:
The correct option is “C” protesters were driven out by force.
This is after President Hoover ordered an army regiment into the city to quash their protests. Under the leadership of General Douglas MacArthur, the army, rolled into Anacostia Flats forcing the Bonus Army to flee
Given m || n, find the value of x and y.
po
(2x+10)
(8x-20)°
m
n
The value of x and y is 19 and 132.
What is equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables. More than one variable may be present in a linear equation. An equation is said to be linear if the highest power of a variable is consistently 1. Another name for it is a one-degree equation.
Sol- as per the given question y= 8x -20
We have to add the equations
(2x+10)° + (8x-20)°= 180°
= (10x-10)° = 180°
= (10x)° = 190°
= X= 19
= Y = 8.19-20 = 132
Thus,
X = 19 and Y = 132.
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Given that
x
= 7.9 m and
θ
= 54°, work out AB rounded to 3 SF.
Answer:
6.39 m
Step-by-step explanation:
( for a right triangle such as this)
Sin (theta) = opp leg / hypotenuse = AB / x
sin (54) = AB / 7.9
7.9 * sin 54 = AB = 6.39 m
Use the figure below to answer the question.
Complete the statement: Angle GHI measures _____degrees
An angle GHI measures 28° degrees.
What is the angle sum property of a triangle?
The triangle's inner angles can be added up to 180°, according to the triangle's "angle sum property."
For example, in a triangle, ABC, the sum of angles A, B, and C will be 180°.
Given, ∡G = 62°
∡I = 90° and ∡ H = ?
From the angle sum property of a triangle,
∡G + ∡ H + ∡I = 180°
or, 62° + ∡ H + 90° = 180°
or, ∡ H + 152° = 180°
or, ∡ H = 180° - 152° = 28°
or, Angle GHI = 28°
Hence, the required value of Angle GHI is 28°.
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he length of the hypotenuse of a right triangle is hh , and the radius of the inscribed circle is rr. the ratio of the area of the circle to the area of the triangle is
Solution by e_power_pi_times_i
Since rs = A, where r is the inradius, s is the semiperimeter, and A is the area, we have that the ratio of the area of the circle to the area of the triangle is $\frac{\pi r^2}{rs} = \frac{\pi r}{s}$. Now we try to express s as h and r. Denote the points where the incircle meets the triangle as X,Y,Z, where O is the incenter, and denote AX = AY = z, BX = BZ = y, CY = CZ = x. Since XOZB is a square (tangents are perpendicular to radius), r = BX = BZ = y. The perimeter can be expressed as 2(x+y+z), so the semiperimeter is x+y+z. The hypotenuse is AY+CY = z+x. Thus we have s = x+y+z = (z+x)+y = h+r. The answer is (B) 3,14r/h+r
The ratio of the area of the circle to the area of triangle is πr : h+r.
We know that rs = A
where r is the radius , s is the semi perimeter and A is the area.
We have that the ratio of the area of the circle to the area of the triangle is
πr²/rs = πr/s.
Now we will express s as h and r. Denote the points where the in-circle meets the triangle as X,Y,Z where O is the in-center and denote
AX = AY = z, BX = BZ = y, CY = CZ = x.
Since XOZB is a square
Therefore r = BX = BZ = y.
The perimeter can be expressed as 2(x + y + x), so the semi perimeter is
x + y + z.
The hypotenuse is AY + CY = z + x.
Thus we have s = x + y + z
= (z + x) + y
s = h + r
Therefore the ratio of the area of circle to the area of the triangle will become πr : h+r.
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How do I do this x/12+1=x/3-x/4 and this is for solving linear equations.
Answer:
no solution
Step-by-step explanation:
You want to solve the equation x/12+1=x/3-x/4.
SolutionThere are a couple of ways you can solve this. If you're intimidated by the fractions, you can get rid of them by multiplying the equation by a common denominator. In this case, multiplying by 12 gives ...
x +12 = 4x -3x . . . . . . original equation multiplied by 12
x +12 = x . . . . . . . . . . simplified
12 = 0 . . . . . . . . . . . . subtract x from both sides
This equation is plainly false. No value of x will make it be true.
The given equation has NO SOLUTION.
Alternate solutionYou can do the arithmetic with the coefficients as they are:
x/12 +1 = x(1/3 -1/4)
x/12 +1 = x/12
1 = 0 . . . . . . . . . . subtract x/12; false
The equation has NO SOLUTION.
__
Additional comment
It is a good idea to become comfortable doing arithmetic with numbers however you find them: integers, fractions, mixed numbers, decimals, percents, scientific notation.
A decent calculator can help, if you need it. Modern graphing calculators are fully capable of working with mixed numbers, fractions, percents, and scientific notation. Any spreadsheet can do this, too.
There are very good inexpensive or free apps for phone and tablet that provide all the capability of a good graphing calculator.
What are the 4 ways to solve a system?.
Answer:
I know 3
substitution and elimation method and graphing (sorry i was never taught a fourth method ):
hopes this helps please mark brainliest
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
Using the definition of divisibility, 2p is the greatest common factor.
In the given question we have to factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
The given polynomial is 2p^3+6p.
Now taking 2p common from both terms
=2(p^2+3)
By the definition of divisibility, we get
2p | 2p^3 and 2p|6p, 2| 2p^3 and 2|6p also p|2p^3 and p|6p.
So, 2,p and 2p are common factors of 2p^3 and 6p.
Hence, 2p is the greatest common factor.
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The right answer is:
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
2p^3+6p
Write the following as a number: minus one thousand, eight hundred and five point nine six.
The final number is a decimal number which is equal to -1805.96.
It is given to us that the set of expression is given by -
minus one thousand, eight hundred and five point nine six.
We have to write the given expression as a number.
According to the given information we see that there is a "point" word in the expression. This implies that the final number will be a decimal number.
So, from the given information, we can represent the number as -
-1805.96
Thus, the final number is a decimal number which is equal to -1805.96.
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The masts for the Millennium Dome were held up during construction by wire ropes as shown in the diagram. A is 106 m above the ground, C is vertically below A, the gradient of AB is 1 and CD is 53 m. a Find the gradient of AD. b Find the length of BD.
a)The gradient of AD will be 2.
b)The length of BD. will be 159 m.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.
It is given that, A is 106 m above the ground, C is vertically below A, the gradient of AB is 1 and CD is 53 m.
Suppose the length BC is x
Gradient of AB = 1
AB/BC=1
106/x=1
x=106
BC=106 m
CD = 53 m
The gradient of AD is,
m = BC/CD
m=106/53
m=2
b)
The length of BD is found as,
BD=BC+CD
BD=106+53
BD=159 m
Thus, the gradient of AD will be 2 and the length of BD. will be 159 m.
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William bought a photocopier and supplies for $162. 50, which will allow him to make copies for $0. 12 each. A photocopy store charges $0. 21 for each copy. How many copies must william make before his total cost is less than getting copies made at the photocopy store?.
William must make 1806 copies before his total cost is less than the photocopy store.
Let William made x copies from his home photocopier.
Now total cost of x copies = 0.12 x + 162.5
Total cost of x copies from the store = 0.21 x
Now his cost needs to be lower, so we form an inequality to solve this problem.
0.12x + 162.5 < 0.21x
or, 0.12x - 0.21x < -162.5
or, -0.09x < -162.5
or, x > 1805.56
Hence the minimum value of x will be 1806.
Therefore we can say that he needs to make at least 1806 copies.
The two sides of a mathematical equation having an inequality must be equal. In inequality, we compare several values in contrast to equations. The equal sign can be substituted with the less than (or less than as well as equal to), larger above (or greater to), or is not equal to signs.
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What does 5 less than N mean?.
5 less than N means we subtract 5 to the given variable N. So the expression will be N - 5.
What is Algebra ?Algebra shows the numbers by alphabets in a equation including mathematical operations. In algebra we used alphabet which shows a variable unknown quantity, unknown variables which helps in changing a mathematical statement into an equation.
In the given question a mathematical statement is given and we have to change the mathematical equation into an algebraic expression by using the information.
What does 5 less than N means ?The statement 5 less than N means 5 is being subtracted from N. The mathematical expression for 5 less than N is equal to N - 5.
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Write an equation dor thi math problemfAt one tore a trophy cot $12. 50. Engraving cot $0. 40 per letter. At another tore, the ame trophy cot $14. 75. Engraving cot $0. 25
The equation we get from the given information that is one award that cost $12.50 was torn. Each letter costs $0.40 to engrave is 2.25x - 0.15y=0.
Given that,
We have to compose an equation for this math issue. One award that cost $12.50 was torn. Each letter costs $0.40 to engrave. The identical trophy cost $14. 75 at another location. Cost of engraving: $0.25
We know that,
Let us take the,
Trophy cot as x and engraving cot as y
We can write as
12.5x+ 0.4y= 14.75x+ 0.25y
12.5x- 14.75x+ 0.4y -0.25y=0
-2.25x + 0.15y=0
2.25x - 0.15y=0
Therefore, The equation we get from the given information that is one award that cost $12.50 was torn. Each letter costs $0.40 to engrave is 2.25x - 0.15y=0.
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a recent article posted to the journal of nutritional science surveyed dog owners to ask about their dog walking habits in order to find out whether the dogs were getting enough exercise. of course, the necessary amount of exercise varies by breed; results were categorized according to breed. read (or glance through) the article below; the study design and results sections are the most relevant.
The correct answer will be, An observational study of dog owners logged into the Channel 4 website
What is Sampling?
If the data are distributed normally, a z test can be used to determine whether the means of two populations are different from one another. This calls for the determination of the value of the z test statistic, along with the setups of the null hypothesis and alternative hypothesis. The decision-making standard is based on the z critical value for Sampling . The z critical value used during hypothesis testing divides the distribution graph into acceptance and rejection zones. The test statistic must fall inside the rejection region in order for the null hypothesis to be rejected; otherwise, it cannot.
a recent article posted to the journal of nutritional science surveyed dog owners to ask about their dog walking habits in order to find out whether the dogs were getting enough exercise.
Using a sample and normally distributed data in this case
Hence, we can say An observational study of dog owners logged into the Channel 4 website
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Nerida Kyle is thinking of buying a car to avoid taking Lyft to work. She is using the cost-benefit principle to evaluate this decision and is calculating the costs and benefits to owning the car over the next year. She's gathered the following information to help her make her decision: The car costs $15,000 to purchase, but she can resell it after a year of use for $13,500. She thinks gas will cost her about $1,200 for the year. The annual insurance premium for her car is $800. Maintenance and repairs will cost about $300 for the year. Using Lyft to get to work would cost her $4,000 for the year. The cost of the car for the year is:
The cost of the car for the year is $3800 for Nerida Kyle and it will cost less than lyft.
The cost of the car for the year will be calculated based on the amount she will spend in total on the car. The formula to be used is -
Total cost = Cost price of the car - Selling price
Cost price of car will be sum of all the expenses, calculated as follows -
Cost price of the car = 15000 + 1200 + 800 + 300
Performing addition on Right and Side of the equation
Cost price of the car = $17,300
Total cost for the year = 17,300 - 13,500
Performing subtraction on Right and Side of the equation
Total cost for the year = $3,800
Hence, Nerida Kyle will spend $3,800 on car which is better than lift.
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use a quadratic equation to find two real numbers with a sum of 31 and a product of 210. two real numbers with a sum of 31 and a product of 210 are and
Answer:
The numbers are 10 and 21.
Step-by-step explanation:
x + y = 31
xy = 210
x = 31 - y
(31 - y)y = 210
31y - y² = 210
y² - 31y + 210 = 0
(y - 21)(y - 10) = 0
y - 21 = 0 or y - 10 = 0
y = 21 or y = 10
The two real numbers are 10 and 21.
What is a quadratic equation?Quadratic Equations are algebraic expressions of degree 2 in one variable and are of the form ax² + bx + c = 0.
In simpler terms, a quadratic equation is be defined as a polynomial equation of degree 2.
Given that, there are two real numbers with a sum of 31 and a product of 210.
We need to find their values using the concept of quadratic equation,
So, according to the question,
x + y = 31 (eq 1)
xy = 210 (eq 2)
x = 31 - y
(31 - y) y = 210
31y - y² = 210
y² - 31y + 210 = 0
(y - 21) (y - 10) = 0
y - 21 = 0 or y - 10 = 0
y = 21 or y = 10
Hence, the two real numbers are 10 and 21.
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Tony is putting money into a checking account. Let represent the total amount of money in the account (in dollars). Let represent the number of Tony has been adding money. Suppose that and are related by the equation . Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the starting amount of money in the account? s What is the change per in the amount of money in the account?
Weekly change: 40
Initial investment: 450
Given that,
Tony is transferring funds to his checking account. Let y signify the overall balance of the account's funds (in dollars). Let x be the quantity Bill has been adding money for in weeks. Assume that 40x+450=y represents the equation between x and y.
Given that x is the number of weeks Bill added money, this indicates that he was depositing $40 into the account every week.
Because x denotes the number of weeks he was contributing money and x is by 40, not 450, the initial amount was 450.
Therefore, Weekly change: 40 and Initial investment: 450
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in order to test if the mean from population a is greater than the mean from population b what kind of t-test would you use?
According to the given statement the option B and C are correct:
b) unpaired t-test
c) one-sample t-test
Briefing:We will apply an unpaired test in this situation because both populations are independent and unrelated to one another, making it impossible to pair the data from the two populations.
Consider the statement, "The mean from population A is bigger than the mean from population B," for example. This suggests that we'll utilize a single-tailed, unpaired test. Therefore, option d and b may be the best pairing.
What exactly is a one-sample t-test?To ascertain whether an unknown population mean differs from a given value, the one-sample t-test is a statistical hypothesis test.
What distinguishes a t-test with one sample from one with two samples?The t-value is calculated using your sample data from the two groups and the 2-sample t-test. The procedure is quite comparable to the 1-sample t-test, and the signal-to-noise ratio can still be compared. The 2-sample t-test necessitates independent groups for every sample, unlike the paired t-test.
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The complete question you are looking for is:
In order to test if the mean from Population A is greater than the mean from Population B what kind of t-test would you use? (can be any combination of answers)
a) two-tailed t-test
b) unpaired t-test
c) one-sample t-test
d) one-tailed t-test
e) paired t-test
can someone explain how to do this with the answer pls
Answer:
x = 23
Step-by-step explanation:
The sum of two interior angles is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation based on this information to find the value of x:
2x + 3 + 51 = 100 add like terms
2x + 54 = 100 subtract 54 from both sides
2x = 46 divide both sides by 2
x = 23
is 3 an element of the set {1,2,3}
Answer:
yes
Step-by-step explanation:
3 is inside the brackets
a school counselor wants to compare the effectiveness of an online sat preparation program with an in-person sat preparation class. for an experiment, the counselor recruits 30 students who have already taken the sat once. the response variable will be the improvement in sat score. select all true statements. the completely randomized design is preferred the completely randomized design is better because it eliminates bias by considering all students to be equal at the start of the experiment. the matched pair design is preferred students who did not score well the first time they took the exam may benefit greatly from the class. by matching students by initial score, we can account for the variability in improvement that is introduced by the variability in student ability, making it easier to determine which program is more effective. students who scored well on the exam initially may not have much room for improvement even if the treatments are effective.
The correct statements for comparing the effectiveness of the SAT preparation program are the 3rd, 4th, 5th, 6th statements.
The statements in order are
The completely randomized design is preferredThe completely randomized design is better because it eliminates bias by considering all students to be equal at the start of the experimentThe matched pair design is preferredStudents who did not score well the first time they took the exam may benefit greatly from the classBy matching students by initial score, we can account for the variability in improvement that is introduced by the variability in student ability, making it easier to determine which program is more effectiveStudents who scored well on the exam initially may not have much room for improvement even if the treatments are effectiveSince, school counselor want to compare effectiveness of SAT preparation program with response variable will be the improvement in SAT score.
We can consider this as a improvement assessment, so that the initial abilities of each student will be different. With this we can see the improvement from student with bad initial score, and for the student that has a good score in initial exam they barely to have improvement.
For example student A have initial score 600 and student B have initial score 1300 after preparation program student A have final score 1200 and student B have final score 1350. In the example, we can see 200% improvement from student A and only 4% improvement from student B.
Also, with matching pair design that based on variable, we can see the variability in improvement making it easier to know the effectiveness of SAT preparation program than the randomized design.
Thus, the correct statements is the 3rd, 4th, 5th, 6th statements.
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Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them. Give a probability model for this chance process.
Probability model for this chance process is:
P(X=2) = [tex]6_C_2*(1/6)^2*(1-1/6)6-2[/tex]
Given:
Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.
Using binomial distribution:
We are given that there are 6 grand children and 2 of them are needed to picked.
Let number of grandchildren to be choose is X.
Every children has equal chance to get selected, therefore Probability for everyone is 1/6.
P(X) = Bino(6,1/6)
P(X) = [tex]6_C_X*(1/6)^X*(1-1/6)^{6-X}[/tex]
P(X=2) = [tex]6_C_2*(1/6)^2*(1-1/6)^{6-2[/tex]
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What is the common multiple of 14 and 28?.
The common multiple of 14 and 28 is 28.
Common multiple:
A common multiple is defined as a whole number, a shared multiple of each set of numbers. The multiples common to two or more numbers are called the common multiples of those numbers.
Here we have to find the common multiple of 14 and 28.
Data given:
Two numbers = 14 and 28
We can also write these numbers as:
14 = 2 × 7
28 = 2² × 7
The common multiple of these numbers is 2² × 7
Therefore the common multiple of these numbers is 28.
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What are the 3 linear functions?.
Answer:
point-slope form, standard form, and slope-intercept form
Step-by-step explanation:
The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.
Here is an image with each form
How much is two third?.
The two third can be written as 2/3 which in decimal means 0.6667 and when expressed as a percentage it is 66.67%
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
The two third can be written as 2/3. It basically means 2 parts of 3 total parts. Here the numerator is 2 and demominator is 3.
It can be written in decimal as 2/3 = 0.666
This is an irrational fraction when converetd into decimal system, it becomes a recurring decimal.
The equivalent fraction of 2/3 is 4/6 or 20/30 etc
Therefore, The two third can be written as 2/3 which in decimal means 0.6667 and when expressed as a percentage it is 66.67%
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a study done on a marriage counseling course showed that the proportion of couples for which the communication program can prevent divorce is . suppose we have strong reason to believe the proportion is less than , and we carry out a hypothesis test. state the null hypothesis and the alternative hypothesis that we would use for this test.
The null hypothesis we get H₀: P≥ 77% and H₁: P< 77% when According to a study on a marriage counselling course, 77% of couples can avoid divorce.
Given that,
According to a study on a marriage counselling course, 77% of couples can avoid divorce with the help of a communication programme. Suppose we do a hypothesis test because we have good reason to assume the proportion is lower than 77%.
We have to describe the alternative hypothesis H₁ and the null hypothesis H₀ that we would employ in this test.
We know that,
According to the task we can say that,
From the definition we can say,
H₀: P≥ 77%
H₁: P< 77%
Therefore, the null hypothesis we get H₀: P≥ 77% and H₁: P< 77% when According to a study on a marriage counselling course, 77% of couples can avoid divorce.
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the shopping times of 64 randomly selected customers at a local supermarket were recorded. the average and variance of the 64 shopping times were 33 minutes and 256, respectively. compute a 90% confidence interval for the true population mean
The shopping times were recorded for 64 randomly selected customers from a local supermarket. The average and variance of the 64 shopping times were 33 minutes and 256, respectively.
Estimate the true average shopping time per customer, with a confidence coefficient of 1- = 0.90.
x-bar = 33 min
ME = 1.645 = 3.29
90% CI: 33-3.29 < u < 33+3.29
Population Means – You can use this calculator to find the confidence interval for your sample mean if you are estimating the mean of a population trait (e.g., the mean blood pressure of a group of patients).
The estimate is your "best guess" at the unknown mean, and the confidence interval displays how reliable the estimate is. You may determine a range of values within which the population mean is expected to fall using the confidence interval.
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The 90% confidence interval is ( 992.053088, 1119.946912 ).
Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ. The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.
As per the question,
Number of customers ( n ) = 64mean ( μ ) = 33 minutesStandard deviation ( σ ) = 256 minutes⇒ degree of freedom ( df ) = n - 1
= 64 - 1
df = 63
⇒ α = 0.05
⇒ t = 1.998341 ( Calculated using excel functions )
At 90% confidence, the confidence interval is
( μ - t ) ( s / √n ) ≤ x ≤ ( μ + t ) ( s / √n )
( 33 - 1.998341 ) ( 256 / √64 ) ≤ x ≤ ( 33 + 1.998341 ) ( 256 / √64 )
( 31.001659 ) ( 256 / 8 ) ≤ x ≤ ( 34.998341 ) ( 256 / 8 )
( 31.001659 ) ( 32 ) ≤ x ≤ ( 34.998341 ) ( 32 )
992.053088 ≤ x ≤ 1119.946912
Therefore, ( 992.053088 ≤ x ≤ 1119.946912 ) is the 90% confidence interval for the true population mean.
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a pollster is going to sample a number of voters in a large city and construct a 90% confidence interval for the proportion who support the incumbent candidate for mayor. find a sample size so that the margin of error will be no larger than 0.05. be sure to round up to the next whole number.
Value of n for confidence interval 90% is 66.
What is confidence interval?
A confidence interval, in statistics, refers to the chance that a population parameter can fall between a collection of values for a particular proportion of times.
Main body:
Finding Sample Size for Estimating a Population Proportion:
n = [tex]\frac{z}{M}^{2} }[/tex]p(1-p)
M = is the margin of error
p = is an estimated value of the proportion
We want to construct a 90% confidence interval for with a margin of error equal to 5%.
Because there is no estimate of the proportion given, we use p = 0.50 for a conservative estimate.
For a 90% confidence interval, z = 0.816
n = (0.816/0.05)^2 *0.5(1-0.5)
n = 266.3424*0.5*0.5
n = 66 approximately
Hence value of n = 66 .
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Is cube short for cubicle?.
In short form we can write the word Cubicle as a word, Cube. However, both the words can be used for different purposes or having different interpretation.
Given, a word Cubicle
we have to write the given word in short form.
now to write any word in short form, we have to make its length or abbreviate the word.
As, the word is Cubicle.
Then, the word Cubicle can be written in as Cube in short form.
However, both the words can be used for different purposes or having different interpretation. Such as, Cube is used for a Particular shape or figure in Geometry i.e. the 3-D shape of the cube. Whereas, Cubicle is used for the small small cabins of the employees in the corporate offices.
Hence, the word Cubicle can be written in as Cube in short form, but may be with different meaning.
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if the length of one side of a square is increased by 1 inch and that of another side is diminished by 2 inches, a rectangle is formed whose area is 180 inches. find the length of a side of the square
The length of the square is 9 inches when a rectangle with a surface area of 180 inches is created by lengthening one side of a square by 1 inches and shortening another by 2 inches.
Given that,
A rectangle with a surface area of 180 inches is created by lengthening one side of a square by 1 inches and shortening another by 2 inches.
We have to find the square's side length should be determined.
We know that,
Let us take the length of the square as x.
So,
The length of one side of a square is increased by 1 inch means
x+1
The length of other side of the square is diminished by 2 inch to form a rectangle means
2x
The area of the rectangle is length × breath.
180=(x+1)(2x)
2x²+2x-180=0
x²+x-90=0
x²+10x-9x-90=0
x(x+10)-9(x+10)=0
(x+10)(x-9)=0
We get,
x+10=0 ⇒ x=-10
x-9=0 ⇒ x=9
The length can not be negative so x=9
Therefore, The length of the square is 9 inches when a rectangle with a surface area of 180 inches is created by lengthening one side of a square by 1 inches and shortening another by 2 inches.
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