On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
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Type the correct answer in the box. Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of the circle measured in inches is modeled by the function , where s is time in seconds. The area of the spill when seconds is square inches.
The area of the oil spill is 2.924π square inches.
What is the radius of the circle?
Any line segment connecting a circle's center to its perimeter is considered a circle's or sphere's radius, and in more recent usage, their length is also considered. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."
Here, we have
The radius of the circle of oil spread is modeled by the function r = ∛s where s = time in seconds.
The area of the oil spill A = πr²
= π(∛s)²
So, we need to find the area of the oil spill when s = 5.
So, A = π(∛s)²
A = π(∛5)²
A = π(1.7099)²
A = 2.924π square inches.
Hence, the area of the oil spill is 2.924π square inches.
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A school is selling cookies as a fundraiser. Each box contains 10 cookies. Each student can sell 17 boxes of cookies. How many cookies can 11 students sell
11 students could sell 1870 cookies.
Explain about the expressions?A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.
Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.
An expression is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in certain ways. Language phrases can comprise actions on their own, but they do not make up complete sentences.
= 10 X 17
= 170 X 11
= 1870
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What is the nature of roots of quadratic equation x^2 =- 2x 1?
The nature of roots of quadratic equation x² = -2x + 1 is real and distinct.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
x² = -2x + 1
transform it into the standard form:
x² + 2x - 1 = 0
Calculate the discriminant:
D = 2² - 4 (-1) = 8
Since D > 0, the roots are two distinct real roots.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation x² = -2x + 1?
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H)
how many five- card hands are possible that contain at least three kings?
==========================================================
Explanation:
We'll break things up into cases. The phrasing "at least 3" means "3 or more".
We either will have 3 kings or 4 kings.
----------------------------------------------
Case A) There are exactly 3 kings.
Use the nCr combination formula. There are n = 4 kings total and we select r = 3 of them. That gives 4C3 = 4 ways to pick the 3 kings.
Put another way: there are 4 ways to leave a certain king out of the hand.
Then we have 52-4 = 48 cards that aren't a king, and we need to fill the remaining r = 2 slots. Through the nCr formula, you should find that 48C2 = 1128
To recap, we found
4 ways to pick the three kings1128 ways to pick the other two cards that aren't kingsThat gives 4*1128 = 4512 ways to have case A happen.
----------------------------------------------
Case B) There are exactly 4 kings
4C4 = 1, so there's only one way to select all the kings. The order doesn't matter. Then we have 48 cards to pick from for the fifth slot.
Overall there are 1*48 = 48 ways to have case B play out.
----------------------------------------------
There were 4512 ways to have case A happen, and 48 ways to have case B happen.
These cases are mutually exclusive to allow us to simply add the counts:
4512+48 = 4560
This is why the final answer is 4560
The histogram shows the ages of passengers riding in a tour van. How many passengers are under 45 years of age? Enter your answer as a number, like this: 42
Answer:
12
Step-by-step explanation:
3 + 4 + 5 = 12
fraction bigger than 2 out of 5 and smaller than 2 out of 3. When i divided numerator by denominator , it will be 0.533.
The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3, 1/5 is a fraction.
We have,
Let the fraction be a/b.
2/5 < a/b < 2/3
Now,
a/b
= (2/3 + 2/5) / 2
= (10 + 6) / 30
= 16/30
= 8/15
= 0.533
Thus,
The fraction is 8/15.
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What is the number of terms in the expansion of 2x 3y 2 )( 2x 3y 2 2?
The number of terms in the expansion of [tex](2x^3y^2)(2x^2y^3)[/tex] is 12.
When expanding the product of two polynomials, the number of terms in the expansion is equal to the product of the number of terms in each polynomial. In this case, the first polynomial has 1 term (2x^3y^2) and the second polynomial has 1 term (2x^2y^3), so the number of terms in the expansion will be 1*1=1.
A polynomial function is one in which the variable's non-negative integer powers or positive integer exponents are the only parts of the equation. Examples of polynomial functions include quadratic, cubic, and other equations. An example of a polynomial with an exponent of 1 is 2x+5.
However, the expression provided is not a polynomial, it is a number.
[tex]2x^3y^2 * 2x^2y^3 = 4x^5y^5[/tex]
It is just one term.
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1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given few inequalities and some operations are performed on them
For first inequality:
=> 4 < 7
Multiply both sides by 3, then by 2, then by 4, then by 9
=> 4 *3 * 2 * 4 * 9 < 7 *3 * 2 * 4 * 9
=> 864 < 1512
there is no change in the inequality sign and it is still true.
For the second inequality:
=>11 > -2
Add 3 to both sides, then add 3, then add (-4)
=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)
=> 13 > 0
there is no change in the inequality sign and it is still true.
For the third inequality:
=> -2 ≤ -2
Subtract 6 from both sides, then 8, and then 2
=> -2 -6 -8 -2 ≤ -2 -6 -8 -2
=> -18 ≤ -18
there is no change in the inequality sign and it is still true.
For the fourth inequality:
=> -4 < 8
Divide both sides by -4
=> -4 / -4 < 8 / -4
Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign
=> 1 > -2
Divide both sides by -2
=> -1/2 < 1
there are two times a change in the inequality sign and it is still true.
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Which variation is represented by this situation:
Lisa and Maria are at a convention. There is enough food at the convention to feed 300 attendees for 4 days. If 400 people attend the convention, how long will the food last?
If 400 people attend the convention,
the food will last for 3 days.
What is inverse proportion?Two quantities a and b are said to be in inverse proportion if an increase in quantity a, there will be a decrease in quantity b, and vice-versa. In other words, the product of their corresponding values should remain constant. Sometimes, it is also known as inverse variation.
That is, if ab = k, then a and b are said to vary inversely. In this case, if b1, b2 are the values of b corresponding to the values a1, a2 of a, respectively then a1 b1 = a2 b2 or a1/a2 = b2 /b1
Given,
Food for 300 people will Last for 4 days.
Attending people = 400
Let the food for 400 will last for x days.
According to the question,
300 × 4 = 400 × x
x = 300 × 4 /400
x = 3
Hence, the food will last 3 days,
if 400 people attend the convention.
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Find the sum of the interior angles of a nonagon.
A. 140°
B. 1,620°
C. 1,260°
D. 1,450°
The sum of the interior angles of a nonagon (a 9-sided polygon) is 1,450°.
1. The interior angles of a polygon can be calculated by subtracting 2 from the number of sides, then multiplying the result by 180°.
2. For a nonagon (a 9-sided polygon), the calculation is
(9-2) × 180° = 1,450°.
The sum of the interior angles of any polygon can be calculated using the formula
(n-2) × 180°,
where n is the number of sides of the polygon. This formula works because the sum of the interior angles of any polygon is always equal to (n-2) times the measure of a single interior angle. For a nonagon, a 9-sided polygon, the calculation is
(9-2) × 180° = 1,450°.
This means that the sum of the interior angles of a nonagon is 1,450°.
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How do I solve for the fourth line
Answer:
y = -8/3x + 73/4
Step-by-step explanation:
A line perpendicular to the 3rd equation has a slope that is the negative inverse of the other line. It also has the same y-intercept (b) because it is forming a square.
Therefore, the equation of the 4th line is:
y = -8/3x + 73/4
Jean Junction is selling jeans at 15% off the regular price the regular price is $25 per pair what is the discount amount
Answer:
15% off means take $3.75 off the regular price
Step-by-step explanation:
$25(0.15) = $3.75
$25 - $3.75 = $21.75 sale price
Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
Answer:
Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
Step-by-step explanation:
Which bag of potatoes is the better deal?
Answer:
5 kg.
Step-by-step explanation:
2 kg for $0.96 is more expensive than 5 kg for $1.95
Identify the place value of the underlined digit.
1) 0.9838.47
3) 145.58
4) 0.005
5) 31.0643
The place value of the following underlined digit are as follows:
0.983 = hundredths.8.47 = hundredths.145.58 = tens.0.005 = tenths.31.0643 = unit.What is a place value?In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.In this scenario, the underlined digit 8 in "0.983" has a place value of hundredths because it is located 2 places after the decimal point. Additionally, the underlined digit 4 in "145.58" has a place value of tens because it is located 2 places before the decimal point.
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Complete Question:
Identify the place value of the underlined digit.
1) 0.983
2) 8.47
3) 145.58
4) 0.005
5) 31.0643
Use the given confidence interval to find the margin of error and the sample mean
(12.7, 19.5)
The margin of error and the sample mean of the confidence interval are given as follows:
Margin of error: 3.4.Sample mean: 16.1.How to obtain the margin of error and the sample mean of the confidence interval?The confidence interval is defined as follows:
(12.7, 19.5).
The definition of a confidence interval is that it is obtained as the sample mean plus/minus the margin of error.
Hence the sample mean is calculated as the mean of the bounds of the interval, hence:
(12.7 + 19.5)/2 = 16.1.
The margin of error is calculated as the absolute value of the difference of each bound from the sample mean, hence:
|19.5 - 16.1| = |12.7 - 16.1| = 3.4.
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Hello can someone help me with this please
Answer:
Below
Step-by-step explanation:
x - 6 = 12 add 6 to both sides of the equation
x - 6 + 6 = 12 + 6 simplify
x = 18
3x-1 = 11 add 1 to both sides of the equation
3x -1 + 1 = 11 + 1
3x = 12 now divide both sides by 3
3x/3 = 12 / 3 simplify
x = 4
What's the value of the following game: You roll a 100 sided die with sides 1-100. You can either take this number of dollars, or pay $1 to roll again. You can keep on paying $1 to roll for as long as you like.
You roll a 100 sided die with sides 1-100. The optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
Can a die have 100 sides?The 100-sided die Lou Zocchi created is known by the trademark "Zocchihedron," and it made its debut in 1985. It assumes the appearance of a ball with 100 flattened planes, unlike other polyhedran dice. It is also known as "Zocchi's Golfball."
optimal strategy is to stop and take dollar if roll > x, and to pay $1 and continue when roll <= x (as applicable to all/any turn/roll). We need to find x in order to maximize E.
Assuming optimal expected value to be E, once you cast the first roll, there are two possible scenario:
1) we get roll value > x with probability (100-x)/100, and decide to take that amount, expected winning = (x+1+100)/2 (that amount varies uniformly from x+1 to 100 in this case, take the average)
2) we get roll value <= x with probability x/100 and decide to continue, with future expected winning again = E and 1$ loss in fee. Total expected winning in this scenario = E-1
[math]E=\frac{(100-x)}{100}\times\frac{ (x+1+100)}{2}[/math][math] + \frac{x}{100}\times(E-1)[/math]
[math]E = \frac{(100-x)(101+x) - 2x}{200 - 2x}[/math]
maximizing E w.r.t. x,
dE/dx = 0
2x^2 - 400x + 19600 = 0
x = ( 400+/- sqrt(160000-4*2*19600) ) / 4
Since, 1<= x <= 100, therefore x = ( 400+ sqrt(160000-4*2*19600) ) / 4
x = 85.85786
We just have to calculate E(x=85) and E(x=86) and compare.
E((x=86) = 87.35 and E(x=85) = 87.33
so optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
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Solve for x.
2x = 25-3x
Simplify your answer as much as possible.
x
=
3 0.8
X
Ś
[tex]2x = 25-3x[/tex]
Simplify:
[tex]2x=-3x+25[/tex]
Add 3x to both sides:
[tex]2x+3x=-3x+25+3x[/tex]
[tex]5x=25[/tex]
Divide both sides by 5:
[tex]\dfrac{5x}{5} =\dfrac{25}{5}[/tex]
[tex]\fbox{x = 5}[/tex]
Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. • The equation that relates Runner #2’s distance (in miles) with time (in minutes) is `t=8. 5d`. Find the slope/rate of ch
If the equation that relates the Runner 2’s distance (in miles) with time (in minutes) is [tex]t=8.5d[/tex] then the slope/rate of change of Runner 2 is 8.5 minutes for 1 mile .
The three runners are training for the marathon ,
The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is ⇒ [tex]t=8.5d[/tex] ,
to cover the distance of 2 miles Runner2 will take [tex]t= 8.5 \times 2[/tex] minutes ;
So , [tex]t=17[/tex] minutes ;
the first point will be (2,17) .
and to cover the distance of 4 miles the runner 2 will take [tex]t= 8.5 \times 4[/tex]
So , [tex]t=34[/tex] minutes ;
the second point will be (4,34) .
we have to find the rate of change/slope of runner 2 ,
that can be written as : [tex]Slope = \frac{34-17}{4-2}[/tex]
On simplifying ,
we get ;
[tex]Slope = \frac{17}{2}[/tex] ;
So , [tex]Slope = 8.5[/tex].
Therefore , the rate of change of Runner 2 is 8.5 .
The given question is incomplete , the complete question is
Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is "t = 8.5d". Find the slope/rate of change of Runner 2 ?
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The area of the triangle is no more than 30 square inches. Right and solve inequality that represents a.
(HELP ASAP!)
The answer is a ≤ 30.
An inequality is a mathematical expression that compares two values or expressions using an inequality operator. In this case, the inequality would be a ≤ 30. This means that the area of the triangle must be less than or equal to 30 square inches.
This can be solved by finding the area of the triangle. To do this, we need to know the lengths of the sides of the triangle. Suppose we have sides p, q, and r. Then the area of the triangle can be found using the formula:
a = 1/2 × b × h
where q is the base of the triangle and r is the height. To ensure that the area of the triangle is no more than 30 square inches, the inequality must be satisfied. That is, 1/2 × b × h ≤ 30. This inequality can be rewritten in terms of the side lengths by substituting 1/2 × q × r for h. This gives us a ≤ 30.
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Cheese pizza was preferred by 40 students pepperoni pizza was preferred by 28 based on the results how many of the 340 students can be expected to prefer cheese pizza?
The number of students expected to prefer cheese pizza from the 340 students is 200 stduents.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Cheese pizza = 40 students
Pepperoni pizza = 28
The ratio of cheese and Pepperoni pizzas.
= 40:28
= 10:7
Now,
Cheese pizza = 10x
Pepperoni pizza = 7x
The number of expected students who prefer cheese pizza.
= (10x)/(17x) x 340
= 10/17 x 340
= 10 x 20
= 200
Thus,
The number of expected students preferring cheese pizza is 200.
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ind the Average Rate of Change of the table below for the interval 0 < x < 4
The average rate of change is equivalent to 2.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the table as shown below -
[x] : 0 1 2 3 4
[y] : -2 -3 1 3 6
The rate of change in the interval 0 < x < 4 is -
AROC = (6 + 2)/(4 - 0)
AROC = 8/4
AROC = 2
Therefore, the average rate of change is equivalent to 2.
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What is the degree of the polynomial √ 3?
The degree of the polynomial √3 is 1.
What is polynomial?Polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponents of variables. Polynomials are often used to solve problems in algebra, geometry, calculus and other branches of mathematics.
A polynomial is an expression made up of variables, constants, and exponents.
A polynomial is said to have a degree when the highest degree of any of its terms is known.
The degree of a polynomial is determined by the highest exponent of a given term. In the case of √3, the exponent is 1, making the degree 1.
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The depth of water in a tank oscillates sinusoidally once every
8 hours. If the smallest depth is 6. 6 feet and the largest
depth is 9. 4 feet, find a possible formula for the depth in terms
of time t in hours. Assume that at t=0 the water level is at
the average of the depth and is rising.
.
The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.
Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D
where, A --> amplitude
B--> period in form of pi
C--> phase or horizontal shift
D --> vertical shift
We have, the depth of water in a tank oscillates sinusoidally.
The smallest depth of water in tank = 6.6 feet
The largest depth of water in tank = 9.4 feet
We have to determine the formula of depth of water in tank as a function of time in hours .
For sinusoidal function,
Amplitude , A = average depth
= ( largest depth + smallest depth)/2
= (6.6 + 9.4)/2
= 16.0/2 = 8
Now, The period of 8 hours so, B = 2π/8
=> B = 45° = π/4
Also, upward shift , D is 9.4 - 6.6 = 2.8
Horizontal shift, C = 0
So, required function is D = 2.8 + 8 sin(π t/4) .
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Kyle puts all of his craft beads into a bag. Exactly 1/3 of the beads are blue and 5/16 are red. What is the unit rate of blue beads to red beads in Kyle's bag?
The unit rate of blue beads to red beads in Kyle's bag is 1(1/15).
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Blue beads = 1/3
Red beads = 5/16
The unit rate of blue beads to red beads.
= 1/3 ÷ 5/16
= 1/3 x 16/5
= 16/15
= (16/15) / 1
= 1(1/15) / 1
Thus,
The unit rate is 1(1/15).
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find four consecutive odd integers such that 4 times the sum of the first and third is 4 larger than 4 times the fourth
The four consecutive odd integers = 15, 17, 19, 21
What are integers ?Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers.
All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.
According to our question-
First digit: x
Second digit: x + 2
Three-digit number Equals x + 4
Fourth digit: x + 6
The difference between the opposite of the third and the first two sums up to 55.
x + x + 6 = -(x + 4) + 55
x + x+6 = (-x - 4) + 55
2x + 6 = -x + 51
assemble similar terms
2x + x = 51 - 6
3x = 45
x = 15
Therefore,
First digit: x = 15
Second digit: 15 + 2 + x = 17
Third number: 15 + 4 + 4 = 19
Fourth digit: x+6 = 15+6 = 21
The four odd numbers in a row equal 15, 17, 19, and 21.
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24,000 at 5 5% for 5 years
Answer:660,000
Step-by-step explanation:
principle= 24,000
rate=5.5%
time = 5years
simple interest= P×R×T
. =24000×5.5×5
. = 660,000
a form of reasoning called is the process of forming general ideas and rules based on your experiences and observation
A form of reasoning called induction is the process of forming general ideas and rules based on your experiences and observations.
What is the Induction?The process of welcoming newly hired employees and assisting them in adjusting to their new positions and working surroundings is known as induction. Beginning a new work can be stressful, so new hires require assistance adjusting to their new environment.
The action or process of inducting someone to a position or organization.
We have given that,
A form of reasoning called is the process of forming general ideas and rules based on your experiences and observations.
As a result, the process of formulating general hypotheses and rules based on your observations and experiences is known as induction.
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5 mop and 7 broom cot a total of $855. 0. A mop cot $15. 00 more than a broom. Find the cot of:
a) 1 mop
b) 1 broom
pleae how working
the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
What is the system of equations?
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.
To find the cost of a mop and a broom, we can set up a system of equations using the information given:
Let x be the cost of a broom
Let y be the cost of a mop (which is $15 more than a broom)
From the problem, we know that:
y = x + 15 (since a mop costs $15 more than a broom)
5x + 7y = 855 (since 5 mops and 7 brooms cost a total of $855)
We can substitute the first equation into the second equation:
5x + 7(x + 15) = 855
5x + 7x + 105 = 855
12x = 750
x = 62.5
Hence, the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
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