The area of the folded napkin is 81 square inches.
What is square inches?Square inch is a unit of area, equal to the area of a square with sides of one inch.
A square with an area of 324 square inches can be folded in half to form a rectangle with half the area, or 162 square inches.
Folding the rectangle in half again will result in a smaller square with a side length equal to half the shorter side of the rectangle. The area of this smaller square is (1/2)^2 * 162 square inches = 81 square inches.
So, the area of the folded napkin is 81 square inches.
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If n(A) = 108, n(A ∪ B) = 160, and n(A ∩ B) = 43, find n(B).
The value of n(B) in the set is 23
How to determine the value of n(B)From the question, we have the following parameters that can be used in our computation:
n(A) = 108, n(A ∪ B) = 160, and n(A ∩ B) = 43,
The value of n(B) is calculated as
n(A u B) = n(A) + n(B) - n(A n B)
Substitute the known values in the above equation, so, we have the following representation
160 = 108 + n(B) - 43
This gives
n(B) = 160 + 43 - 180
Evaluate
n(B) = 23
Hence, the solution is 23
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Devaughn is 7 years older than Sydney. The sum of their ages is 87. What is Sydney's age?
Answer:
40
Step-by-step explanation:
Assign the variable x to Devaughn's age. If Devaughn is 7 years older than Sydney, then Sydney must be 7 years younger than him, so the expression x - 7 can represent Sydney's age.
The sum of their ages would be x + x - 7 or 2x - 7 which is also said to equal 87. Therefore, this can be written as an equation and be solved accordingly:
2x - 7 = 87
2x = 94
x = 47
Therefore, Devaughn is 47 and Sydney, who is 7 years younger, is 40.
Sydney's age is determined by setting up and solving a simple algebraic equation based on the information provided. The equation that represents this situation is S + (S + 7) = 87, which leads to the conclusion that Sydney is 40 years old.
Explanation:Devaughn is 7 years older than Sydney. Given that the sum of their ages is 87, we can represent this situation with algebra. Let's denote Sydney's age as S.
Considering Devaughn is 7 years older, we can represent his age as S + 7. Given that the sum of their ages is 87, we can write down this equation: S + (S + 7) = 87.
Solving this equation will help us find Sydney's age. First, simplify the left side: 2S + 7 = 87. Then, subtract 7 from both sides: 2S = 80. Finally, divide both sides by 2 to solve for S, yielding Sydney's age: S = 40.
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A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
120
86.4
Answer: C. 120!
Step-by-step explanation:
Okay so, first we need to find out our percentages of course.
I learned this trick that can help us with this question easily!
14% of 500 - 70 - Drama
14 * 5 = 70.
22% of 500 - 110 - Sports
22 * 5 = 110
20% of 500 - 100 - Reality
20 * 5 = 100
20% of 500 - 100 - Sci-fi
20 * 5 = 100
70 + 110 + 100 + 100 = 380
500 - 380 = 120
Therefore, documentaries is labeled as 24% of 500 or 120 out of 500.
Your welcome! ^^
please help me find domain and range
Answer:
D: ( - ∞, 5)
R: [- 3, ∞)
Step-by-step explanation:
The domain is the set of possible x values. The function has values from below five while not including 5(as shown by the open circle). Therefore the domain would be ( - ∞, 5). (Open brackets are non-inclusive while closed brackets are inclusive).
The range is the set of possible y values. The minimum of this graph seems to be at y = -3, and there is not a maximum as while the x values decrease, the y-values infinitely increase. Therefore, the range is [- 3, ∞)
10. Which of the following graphs would represent the solution set for y < 3/2 x – 4?
Solution set for y < 3/2 x – 4 is represented by Graph D.
What is inequality?In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal.
Given inequality,
y < 3/2x - 4
Since there is less than sign, the region should be shaded below dotted line.
Equation for the dotted line
y = 3/2x - 4
comparing it with Slope intercept equation,
y = mx + c
slope m = 3/2
y - intercept = - 4 unit.
Only graph D has the shaded part below dotted line.
Hence, Graph D represents y < 3/2 x – 4.
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Please use the law of sines to show me how to solve the triangle please. Thank you .
Angles in a triangle add to [tex]180^{\circ}[/tex].
[tex]\angle B=180^{\circ}-115.5^{\circ}-27.2^{\circ} \longrightarrow \boxed{\angle B=37.3^{\circ}}[/tex]
Using the Law of Sines:
[tex]\frac{AC}{\sin 37.3^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{AC=\frac{76\sin 37.3^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]
[tex]\frac{BC}{\sin 27.2^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{BC=\frac{76\sin 27.2^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]
sin(A) / a = sin(B) / b = sin(C) / c
where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.
Which is the equation of a line parallel to the line with the equation:
y = -3x + 5
PLEASE HELP
Answer:
5
Step-by-step explanation:
Write a set of 12 digits so the 5/12 of them are less than 3.
Answer:
Answer: 0, 1, 1, 2, 2, 4, 5, 6, 7, 0, 8, 9
Step-by-step explanation:
1. Start by writing five digits less than 3: 0, 1, 1, 2, 2
2. Then write four digits greater than 3: 4, 5, 6, 7
3. Finally, add three more digits of any value: 0, 8, 9
Match each expression in column A with an equivalent expression from column B
olumn A
1.
2.
3.
4,
-
-
-
3x-2x+0.5x
6(x+4)-2(x+5)
3(x+4)-2(x+4) +0.5(x+4)
20(2/5x+3/4y-1/2)
Column B
a. 1.5
b. 1.5%
c. 1/2 (16x+30y-20)
d. 2(2x+7)
20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A
what is expression ?It is necessary to multiply, distribute, add, or take in mathematics. The following is the way an expression is put next to each other: Number, expression, and logical operator The ingredients of a mathematical expression include numerals, variables, and equations (such as addition, subtraction, multiplication or division etc.) It is conceivable to contrast statements with phrases. An phrase, often known as an arithmetic operation, is any logical statement that abstract, numbers, and a mathematical operation between those. For instance, the word m in the formula given is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.
given
3x-2x+0.5x = 1/2 (16x+30y-20)
6(x+4)-2(x+5) = 1.5%
3(x+4)-2(x+4) +0.5(x+4) = 1.5
20(2/5x+3/4y-1/2) = 2(2x+7)
20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A .
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Find the numerical value of the log expression.
log a = 7 log b = 11 log c = 15
log
✓C5
a7b8
The given expression is a logarithm expression. The value of the log expression is -112.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is log (³√c⁵)/(a⁷b⁸).
The value of log a = 7, log b = 11, log c = 15
Applying the quotient formula log(a/b) = log a - log b in the given expression:
= log (³√c⁵) - log (a⁷b⁸)
Again applying the product formula log (ab) = log a + log b:
= log (³√c⁵) - log (a⁷) - log b⁸
Apply the power rule log (a^b) = b log a:
= (5/3) log c - 7log a - 8log b
Now putting the value of log a = 7, log b = 11, log c = 15:
= (5/3) × 15 - 7 × 7 - 8 × 11
= 5×5 - 49 - 88
= -112
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George and Adam painted the game room together. George painted of the room, and Adam painted 0.35 of the room.
What is the total percentage of the room painted by Adam and George?
O 50%
O 55%
O 60%
O 65%
If George painted 1/5 of the room and Adam painted 0.35 of the room then the total percentage of the room painted by Adam and George collectively is 55%.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.
The amount of room painted by George is = 1/5
The amount of room painted by George is = 0.35
Convert the fraction into percentage -
Percentage = 1/5 × 100
Percentage = 20%
Convert the decimal into percentage -
Percentage = 0.35 × 100
Percentage = 35%
The total percentage of room painted by George and Adam is -
Total % of room painted = % of room painted by George + % of room painted by Adam
Substitute the values into the equation -
Total % of room painted = 20 + 35
Total % of room painted = 55
Therefore, 55% of the room was painted.
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George and Adam painted the game room together. George painted 1/5 of the room, and Adam painted 0.35 of the room.
What is the total percentage of the room painted by Adam and George?
A parrot can fly 5 miles in one hour:
The parrot is 15 miles from its nest. If it hasn’t stopped flying, since it departed, how far from the nest was the parrot 30 minutes ago.
The parrot was 12.5 miles from its nest 30 minutes ago.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Average speed = distance/ time
Since the parrot can fly 5 miles in one hour,
So it can fly 5/2 = 2.5 miles in 30 minutes. (apply the division operation)
So 30 minutes ago, the parrot was 15 - 2.5 = 12.5 (apply the subtraction operation)miles from its nest.
Thus, the parrot was 12.5 miles from its nest.
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Solve the inequality for y.
<−6+−2y4
The value of the inequality is 1
What is inequality?In equality is a mathematical statement showing that two or more variables or quantities are not equal.
The given inequality is 6<2y+4
Making y the subject of the relation
6-4<2y
⇒2=2y
Making y the subject of the relation by dividing both sides by 2
therefore, y<1
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Which of the following statements about the polynomial function
F(x) = x³ + 2x² - 1 is true?
A. F(x) has 1 relative minimum and 0 relative maximums
x →∞, F(x) →-∞
B. as,
x →-∞, F(x) →-∞
x → ∞, F(X) → ∞
C. as
x → -∞, F(X) →-∞
D. F(x) has 0 relative minimums and 1 relative maximum
The end behavior of the polynomial is:
x → ∞, F(X) → ∞
x → -∞, F(X) →-∞
Then the correct option is C.
Which statements are true about the polynomial?Here we have the polynomial:
F(x) = x³ + 2x² - 1
And we want to see which ones of the given statements are true. At the end of the answer you can see the graph of the function so you can know how it behaves.
There we can see that there is one relative maximum and one relative minimum, and that the end behavior is:
x → ∞, F(X) → ∞
x → -∞, F(X) →-∞
Then the only correct option is C.
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make six Simplified algebraic expressions with step by step
The step-by-step process of making simplified algebraic expressions are shown below
How to make six simplified algebraic expressions?Below are six simplified algebraic expressions with step by step solutions:
1. Simplify: 2x + 3x
Step 1: Combine like terms: 2x + 3x = 5x
Step 2: Simplified expression: 5x
2. Simplify: 7x - 4x
Step 1: Combine like terms: 7x - 4x = 3x
Step 2: Simplified expression: 3x
3. Simplify: 5y + 2y + 3y
Step 1: Combine like terms: 5y + 2y + 3y = 10y
Step 2: Simplified expression: 10y
4. Simplify: 8z - 6z
Step 1: Combine like terms: 8z - 6z = 2z
Step 2: Simplified expression: 2z
5. Simplify: 4a + 6a - 3a
Step 1: Combine like terms: 4a + 6a - 3a = 7a
Step 2: Simplified expression: 7a
6. Simplify: 9b - 7b + 5b
Step 1: Combine like terms: 9b - 7b + 5b = 7b
Step 2: Simplified expression: 7b
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You own Company X. When you started the company, you initially invested $12,000.
You also borrowed $12,000 through a five-year (long-term) loan, of which you have
paid back $2,018. You have retained $1,291 in earnings to be reinvested in the
company, and you decided to put $1,000 of it aside for a long-term investment. The
company owns land and a building worth $8,878 and equipment worth $4,230. As of
today, the company has $8,250 in cash, $1,225 in inventory, and is due to receive
accounts worth $675. However, the company owes its suppliers $485 and has a
$500 loan to pay off in the next six months.
You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.
What does "company" mean?Businesses, a noun in plural. a group of people who are connected or who have joined together. a guest or guests: We're having people over for dinner. a collection of individuals together for social purposes. association, camaraderie, and fellowship She is a lot of joy to be around.
The Old French word "compagnie," which was first used in the Salic code and meaning "one who eats bread with you," is where the English word "company" originates. To describe a "society, friendship, closeness, or body of troops," it was first used in 1150.
You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.
Total Amount to be when start the company is $12000 + $12000
= $24000
Out of which company owns land and a building worth $8,878 and equipment worth $4,230 and have retained $1,291 in earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term investment.
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An ice cream shop sells ice cream cones, c, and
milkshakes, m. Each ice cream cone costs $1.50
and each milkshake costs $2.00. Donna has $19.00
to spend on ice cream cones and milkshakes. If
she must buy 5 ice cream cones, which inequality
could be used to determine the maximum number
of milkshakes she can buy?
A. 1.50(5) + 2.00m 2 19.00
B. 1.50(5) + 2.00m ≤ 19.00
C. 1.50c +2.00(5) ≥ 19.00
D. 1.50c +2.00(5) ≤ 19.00
Answer:B. 1.50(5) + 2.00m ≤ 19.00
Step-by-step explanation:This inequality can be used to determine the maximum number of milkshakes that Donna can buy with her $19.00. The expression on the left side of the inequality represents the total cost of her purchase and the expression on the right side of the inequality represents the amount of money she has to spend. Since she must buy 5 ice cream cones, that is represented by the 1.50(5) term. The 2.00m term represents the cost of the milkshakes she can buy, with m representing the number of milkshakes. The inequality states that the total cost of her purchase must be less than or equal to the amount of money she has to spend, so the maximum number of milkshakes she can buy can be determined by rearranging the expression.
If Donna buys 5 ice cream cones, that adds up to, £10.00.
She is then left with £9.00.
9 divided by 1.50 = 6.
She is able to buy 6 milkshakes with the money she has left. However, she is now left with no money.
The answer would be B.1.50(5) +2.00m≤19.00
PS: please put me as brainiest it would really help, or if you are not able to do so, for any reason, please answer one of my questions thankyou :)
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Solve the following system of equations algebraically. Be sure to show each step of your work.
y = 2x² - 5x+9
y = 2x² + 5x - 1
The solution of system of equations x is 1 and value of y is 6.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of equations are y = 2x² - 5x+9 and y = 2x² + 5x - 1
Subtract both the equations
y-y=2x² - 5x+9 -2x² - 5x +1
0=-10x+10
10x=10
Divide both sides by 10
x=1
Now plug in x value in any of the equation.
y=2(1)² - 5(1)+9
y=2-5+9=6
Hence, the solution of system of equations x is 1 and value of y is 6.
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Select the correct answer. Consider functions f and g. The picture shows a one-to-one function diagram. x has values of 1, 2, 3, and 4, and g of x has values of 0, 1, 4, and 9. Every x value has a relation in g of x values. What is the value of ? A. B. C. D.
The value of the function f(g(4)) is C) 4.
The diagram shows that f(1) = 0, f(2) = 1, f(3) = 4, and f(4) = 9. Therefore, the value of f(g(4)) is equal to f(9) = 4.
The other options are incorrect. Option A is incorrect because f(0) is not defined. Option B is incorrect because f(4) is not equal to 0. Option D is incorrect because f(1) is not equal to 9.
Here is the solution in steps:
The diagram shows that f(1) = 0, f(2) = 1, f(3) = 4, and f(4) = 9.
Therefore, the value of f(g(4)) is equal to f(9) = 4.
The other options are incorrect. Option A is incorrect because f(0) is not defined. Option B is incorrect because f(4) is not equal to 0. Option D is incorrect because f(1) is not equal to 9.
Therefore, the answer is C. 4.
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Complete the equation so that it has infinitely many solutions.
5(6b-3)-3b =___
b____
The given equation would be, 5(6b-3) - 3b = 0 and b can take infinite number of values to make the equation true.
What equation system has an infinite number of solutions ?
The prerequisite for a situation in which an equation has an endless number of solutions is that the right and left sides of the equation are equal.
The equation is already complete and has infinitely many solutions.
The unknown variable is b, and there are an infinite number of values that b can take to make the equation true.
5(6b-3) - 3b = 0
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PLEASE HELP ME I WILL GIVE YOU 5 STAR RATING A THANKS AND BRAINLIEST RATINGGGGG
The set of pairs for which x and y vary inversely is given as follows:
{(-1, -2/7), (4, 1/14), (6, 1/21)}
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
For an inverse relation, the relation is modeled as follows:
y = k/x.
Meaning that when x increases, y decreases at a constant rate.
The constant is then given as follows:
k = yx.
Hence the third relation is then the relation for which x and y vary inversely, as:
k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.
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In a class full of men and women,
2
9
of the class are women. What is the ratio of men to women in its simplest form?
The answer is 9:2 or 2:9. It depends if there is 9 women and 2 men or 2 women and 9 men.
Mark me branliest. :D
Can someone help me it would mean alot
Due to length restrictions, we kindly invite to read the explanation for further details on how to go across the maze with linear functions.
How to go across the maze
In this problem we find a maze formed by representations of linear functions on Cartesian plane, of which we must determine the slope of each line until finish is reached. This can be done by understanding the following instructions based on results from secant line formula:
Slope of line 1 is undefined.Slope of line 2 is less than - 1.Slope of line 3 is equal to 1. Slope of line 4 is more than 1 and less than 0.Slope of line 5 is equal to 0.Slope of line 6 is more than 0 and less than 1. Slope of line 7 is equal to 1.Slope of line 8 is more than 1.The procedure to go across the maze is shown below:
Start at square A.Select choice "- 1 / 3".Go to square B.Select "Undefined".Go to square E.Select "2".Go to square F.Select "- 1 / 2".Go to square C.Select "2".Go to square B.FAIL
Start at square I.Select choice "2".Go to square J.Select choice "0".Go to square K.Select choice "- 1".Finish.SUCCESS
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Bradley’s new puppy, Rufus, weighed 8.6 pounds at his first visit to the veterinarian. At his second visit, Rufus weighed 14.2 pounds. Let p be the number of pounds Rufus gained between visits. Write and solve an equation to find p.
Answer:
5.2
Step-by-step explanation:
8.6 Pounds + P = 14.2 Pounds
-8.6 Pounds -8.6 Pounds
P = 5.2
Rufus gained 5.6 pounds between his first and second visits to the veterinarian.
We have,
To find the number of pounds Rufus gained between visits, we need to subtract his initial weight from his weight at the second visit.
Therefore, we have:
pounds gained = weight at second visit - weight at the first visit
p = 14.2 - 8.6
p = 5.6
Therefore,
Rufus gained 5.6 pounds between his first and second visits to the veterinarian.
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Top 15 highest paid professions on average
A) Medical
B) Education
C) Real Estate & Investment
D) Fortune 500 executives & board of directors
Answer:
b, education
Sana makatulong
The unemployment compensation is calculated by finding the total of the quarterly wages of two consecutive quarters and dividing by 26. The weekly employment is 60% of that amount. In the quarter of January, February, and March, Roger made a total of $12,950.80. In the quarter of April,May, and June, he made a total of $12,250.10. Find Roger’s weekly unemployment amount.
Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.
Define percentage.In mathematics, a percentage is any amount that can be stated as a proportion of 100. Also occasionally used are the abbreviations "pct.," "pct," or "pc." But the "%" mark is usually used to indicate it. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. A number should be preceded by the percent sign (%) to denote it is a percent.
Here,
Given :
A weekly unemployment amount is calculated using the following three components:
1. Determine the quarterly wage total (consecutive)
2. Multiply the sum by 26.
3.Multiplying by the rate of unemployment
Calculate the total of a quarterly salaries first:
=> (12950.80 + 12250.10) / 26
=> 25,200.9/26
=> 969.26 * 40 %
=> 387.704
Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.
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make linear Equation Application
for this pie recipe using any of
these numbers:
6 table spoons unsalted butter
2 table spoons sugar
1 Cup heavy cream
8 ounces of Semi Sweet chocolate
3 large eggs
1 table spoon vanilla extract
2 cups mini marshmallows
The proportional relationship modeling the number of eggs needed to make x pies is given as follows:
y = 3x.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Variable x: number of pies.Variable y: number of large eggs.3 large eggs, hence the constant of the proportional relationship is given as follows:
k = 3.
Then the equation of the proportional relationship is given as follows:
y = 3x.
Which is a linear function with a slope of 3 and an intercept of zero.
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Each side of the base of a square pyramid measures 10 inches. The height of each lateral face of the pyramid is also 10 inches.
What is the surface area of the pyramid?
Enter your answer in the box.
in²
The surface area of the pyramid is 300 square inches.
What is the surface area of the pyramid?The surface area of a square pyramid can be calculated by:
Adding the area of the base (a square)To the sum of the areas of the lateral faces (four triangular faces).The area of the square base is
10 inches * 10 inches = 100 square inches.
Based on the given parameters:
The area of each triangular face is:
(10 inches * 10 inches) / 2 = 50 square inches.
So, the total surface area of the pyramid is:
100 square inches + 4 * 50 square inches = 300 square inches.
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Murthy has a rectangular wooden box whose length is 7m and breath is 5m. He want to cover the top surface of it with a nice cloth. The cost of the cloth is 50 per sq.m.
The cost of the cloth to cover the top surface of the box is 1,750.
What are rectangles?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Given the rectangular wooden box,
length = 7 m
breadth = 5 m
the top surface of the box is in the shape of a rectangle, to cover the surface with cloth we need to calculate the area of the surface to find the total cloth needed to cover,
area of rectangle = l*b
l = length, b = breadth
A = 7*5
A = 35 m²
area of the cloth needed is 35 m²
cost of 1 square meter = 50
cost for 35 m² cloth = 50*35
cost for 35 m² cloth = 1,750
Hence the required cost is 1,750.
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Question
Which statement best describes a graph of paired points that form a proportional relationship?
Responses
A straight line cannot be drawn through all of the the points, but the line passes through the origin.
A straight line cannot be drawn through all of the the points, but the line passes through the origin.
A straight line can be drawn through all the points, and the line passes through the origin.
A straight line can be drawn through all the points, and the line passes through the origin.
A straight line can be drawn through all the points, but the line does not pass through the origin.
A straight line can be drawn through all the points, but the line does not pass through the origin.
A straight line cannot be drawn through all of the the points, and the line does not pass through the origin.
A straight line cannot be drawn through all of the the points, and the line does not pass through the origin.
A straight line can be drawn through all the points, and the line passes through the origin. Option C
What is a proportional relationship?We know that a relationship is proportional when we can be able to find an association between the variables. It is either the variables are increasing or that the variables are decreasing.
here, we have,
Thus, we would notice that if there is an association between the variables then the graph would be a straight line graph and the graph would have to pass through the origin.
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