The missing step in the rational number proof is; Reason 2; Multiply to get a common denominator
How to prove Rational Numbers?
Let a/b and c/d be two rational numbers, where b and d are not zero and a, b, c and d are integers.
Step 1; a/b + c/d
Reason 1; Given
Step 2; a/b + c/d = ad/bd + cb/bd
Reason 2; Multiply to get a common denominator
Step 3; a/b + c/d = ad/bd + cb/bd = (ad + cb)/bd
Reason 3; Simplify
Since b and d cannot be zero, then bd cannot be zero. Also, since a, b, c, and d are integers, then bd, ad, bc and ad + bc are integers too. Thus, the fraction(ad + cb)/bd is a rational number.
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A store bought jeans at a cost of $40 a pair. Select all the statements that are true.
The true statements are,
⇒ If the price is marked up 25%, the selling price will be $50.
⇒ If the selling price is $70, the price is marked up 75%.
What is the Cost price?
Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a service.
Given that:-
A Store bought jeans at a cost of $40 a pair.
If the price is marked up 25%, the selling price will be $50
⇒ 40 x 25 / 100 = 10
Selling Price = $50
Hence, This is true statement.
And, If the selling price is $70, the price is marked up 75%.
P = 70 - 40 = $30
40 x 75 / 100 = $30
Hence, This statement is true.
Therefore, the true statements are;
⇒ If the price is marked up 25%, the selling price will be $50.
⇒ If the selling price is $70, the price is marked up 75%.
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The complete question is this,
A store bought jeans at a cost of $40 a pair. Select all the statements that are true.
A. If the price is marked up 20%, the selling price will be $60.
B. If the price is marked up 25%, the selling price will be $50.
C. If the selling price is $65, the price is marked up 50%.
D. If the selling price is $70, the price is marked up 75%.
7.
If twenty-one more than a fifth of a number is equal to two times the quantity of
three less than that number, what is the number?
Answer:
The number is 15.
Step-by-step explanation:
Let n be the number.
[tex] \frac{1}{5} n + 21 = 2(n - 3)[/tex]
[tex]n + 105 = 10(n - 3)[/tex]
[tex]n + 105 = 10n - 30[/tex]
[tex]9n = 135[/tex]
[tex]n = 15[/tex]
suppose that a function f has domain (-2,2) and range (-3,5). what is the domain of the function f(2x)?
The value of the domain for f(2x) is 2 * 4 to 2 * 18 or 8 to 36.
What is domain?The set of inputs that a function will accept is referred to as the domain of the function in mathematics. It is sometimes represented by the symbol dom(f), where f is the function.
The function f can be graphed in the Cartesian coordinate system in the specific case where X and Y are both subsets of R. In this instance, the graph's x-axis shows the domain as a projection of the function's graph there. It is a partial function in this instance, and the set of real numbers on which the formula may be evaluated to a real number is known as the natural domain or domain of definition of f.
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Suppose that people check their coats in a checkroom. if all claim checks are lost and the coats are randomly returned, what is the probability that all the people will get their own coats back?
The probability that all the people will get their own coats back is 1/7.
What is probability?Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a suggestion is valid. The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 shows difficulty of the occasion and 1 demonstrates sureness. The higher the likelihood of an occasion, the almost certain it is that the occasion will happen. A basic model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly plausible; the likelihood of "heads" rises to the likelihood of "tails"; and since no different results are conceivable, the likelihood of all things considered "heads" or "tails" is 1/2.
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the mathcounts international airport had 738,114 departures in 2001. if these were distributed uniformly throughout each 24-hour period, what is the mean number of seconds between each departure time? express your answer to the nearest whole number.
The MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.
For given question,
In 2001 there were 738,114 departures.
As we can see, 2001 was not a leap year.
So, the number of days in 2001 = 365
We find the number of departures per day in 2001.
738,114 / 365 = 2,022.23
So, approximately 2,022 departures per day.
Now we find the number of departures in an hour.
2,022 / 24 = 84.25
This means, approximately 84 departures per hour
We know that, 1 hour = 3,600 seconds
Now we find the mean number of seconds between departure time.
3,600 / 84 = 42.8
≈ 43 seconds
Therefore, the MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.
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Isabel's car gets 33.5 miles per gallon. Her gas tank
holds 15.25 gallons of gas. How many miles can Isabel
drive on a full tank of gas?
A 48.75 miles
B 487.5 miles
C 510.875 miles
D 5,108.75 miles
John chose D as the correct answer. How did he get
that answer?
Isabel can drive 510.875 miles with a gas tank that holds 15.1 gallons of gas.
Given that, Isabel’s car gets 33.5 miles per gallon
Her gas tank holds 15.1 gallons of gas
To find the Number of miles can Isabel drive on a full tank of gas
Let "x" be the miles drive with 15.1 gallons of gas
From given,
1 gallon = 33.5 miles
15.25 gallon = x miles
This forms a proportion and we can solve the sum by cross multiplying
1 × x = 15.25 × 33.5
x = 510.875
Thus, Isabel can drive 510.875 miles on a full tank of gas
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3. Estimate √131 by finding what integers it falls
between. What integer is it closer to? Put all
three numbers on the number line to show
approximately where it would fall.
Answer:
this number falls between 11 and 12
Step-by-step explanation:
11 Squared is 121 and 12 squared is 144. 131 is between these numbers. It is closer to 11
Find X
3x + 16
5x-10
Mary, Tonya, Imani, and Luz were each painting identical-sized rooms. No one was able to finish in 1 day. The table shows the fraction of each room the girls painted.
Amount Painted
Which girl painted the most?
Imani painted the wall most
In mathematics, numbers can be classified into different types i.e. real numbers, natural numbers, integers, rational numbers, etc. This includes decimals. t is a standard form representing integers and non-integers.In algebra, a decimal is one type of number in which the whole and fractional parts are separated by a decimal point. The point between the integer and the fractional part is called the decimal point. For example, 34.5 is a decimal number.Decimal Numbers may be of different types, Recurring Decimal Numbers Non-Recurring Decimal Numbers Decimal Fraction
Mary painted 3/4 of the wall
3/4 = 0.75
Tonya painted 5/4 of the wall
5/7 = 0.71
Imani painted 11/13 of the wall
11/13 = 0.84
Luz painted 11/17 of the wall
11/17 = 0.64
Imani painted the wall most
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find an expression which represents the difference when (-5x 7) is subtracted from (9x 5)in simplest terms.
-14x + 2 is the expression which represents the difference when (-5x + 7) is subtracted from (9x + 5) in simplest terms, as obtained by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.
Now,
Given: Two expressions: (-5x + 7) and (9x + 5).
To find: Expression obtained when (-5x + 7) is subtracted from (9x + 5).
Finding:
By basic algebra, we can write:
=> ( -5x + 7) - (9x + 5) = ( -5x + 7) - 9x - 5
=> -5x - 9x + 7 - 5 = -14x + 2
Hence, -14x + 2 is the expression which represents the difference when (-5x + 7) is subtracted from (9x + 5) in simplest terms, as obtained by basic algebra.
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3x+5x-4y+9 pls help bro
Solution: 8x-4y+9
Step-by-step explanation:
Combine like terms
3x + 5x - 4y + 9
8x - 4y + 9
To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.
x-intercept(s): (−9/8,0)
y-intercept(s): (0,9/4)
Rewrite 120 + 400 using the GCF and factoring.
12(10 + 40)
20(10 + 2)
40(3 + 400)
40(3 + 10)
Pls help asap
What happens to you at the red circle on the graph?
the red point represents the moment when you return to your house, 8 time units after you originally left.
What happens to you at the red circle on the graph?
Let's assume that the graph represents the distance to your home as a function of time. (The x-axis represents time in time units and the y-axis represents the distance in distance units)
Then you can see how in the first 3 units of time you travel a certain distance from your home.
Then for the 3 next time units your position does not change, so you are in a fixed place.
In the next 3 time units you return to your house, here we reached the red point, which represents the moment when you return to your house, 8 time units after you originally left.
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GH has a midpoint at M(3, 6). Point G is at (2, 6). Find the coordinates of point H.
Write the coordinates as decimals or integers.
Thus coordiante of point H is(4,6)
The Midpoint Formula: The midpoint of two points,
(x1,y1) and (x2,y2) is the point
M=(x1+x2)/2 and (y1+y2)/2
(2+x2)/2=3
(6+y2)/2=6
solving above equation
x2=4
y2=6
Thus coordiante of point H is(4,6)
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a game where two players each throw two dice each. if any one die matches the other, you win a dollar. if there is no match, you lose a dollar. would you play this game or not and why?
Yes, I would play the game, because the probability of winning is 13/18.
Probability:
Probability refer the possible occurrence of any particular event.
Given,
A game where two players each throw two dice each. if any one die matches the other, you win a dollar. if there is no match, you lose a dollar.
Here we need to find whether we able to play this one or not.
To find that one, first, we have to identify the winning scenarios,
Let us consider five winning scenarios. Lets represent the dice outcomes as A, B, C, and D, where your dice are A and B and the other player's are C and D. The five scenarios are:
1) A = B
2) A = C
3) A = D
4) B = C
5) B = D
We know that the total possible outcomes is 6^4. We can go through each scenario and count the possible outcomes. We must be careful to avoid overcounting.
Based on this,
The probability that none match is
=> 6*5*4*3/6^4
=> 360 / 1296
=> 5 / 18
So, probability of winning is,
=> 1 - 5/18
=> 13/18.
So, based on the probability the chance of winning is high. So, we can play it.
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measure the length of a ordinary sheet of 8x11 paper in metric units (if you do not have a metric measuring device, you can measure in us units and use a free online conversion tool to change to metric units). what is the area of the sheet of paper in correct metric units?
The area of the sheet of paper in correct metric units is 602.6c[tex]m^{2}[/tex].
What is an area?A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).
Calculations:
The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.
Area of sheet of paper=length*width
=27.9*21.6
=602.6 c[tex]m^{2}[/tex]
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Select the correct answer.
Which statement corrects the error, or errors, in this definition?
In a dilation, each point in the preimage and its corresponding point in the image are at equal distances from a given line. Also, the line segment
joining two such points is perpendicular to the given line.
OA. A dilation is when an object moves in a circular arc around a point.
OB. A dilation proportionally stretches or compresses an object based on a given scale factor..
OC. A dilation moves points a specified distance along a line parallel to a specified line.
O D.
The definition is correct.
Answer:
A dilation proportionally stretches or compresses an object based on a given scale factor.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
what is the approximate value of this square root? 162‾‾‾‾√ enter your answer, rounded to the nearest tenth, in the box.
The square root of 162 to the nearest tenth is 12.7, estimated using the prime factorization method.
What is the square root of a number?
The square root of a number x is given by y, such that (y)2 = x. It is denoted by the symbol, ' √ '. For example, the square root of 4 is 2 and the square root of 169 is 13, etc.
Calculation of the square root of 162
We are given the number 162
Let us apply the prime factorization method to find the square root of 162
The prime factors of 162 are 2 × 81
The prime factors of 162 in pairs are 2 × (3 × 3) × (3 × 3)
Now, the square root of 162 is given by:
√162 = √ (2 × (3 × 3)2)
= 3 × 3 × √2
= 9 × √2
= 9 × 1.414
= 12.726
Hence, the square root of 162 up to the tenth place is 12.7.
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12. Classify the statement below as a descriptive or inferential statistic and explain why.
Because of the SG distance learners, Robin expects to serve 12% less meals this year than last year.
The given statement is a descriptive statistic.
What is descriptive statistics?Descriptive statistics are relatively short informational coefficients that summarize a given data set, which can be a representation of the entire population or a sample of a population. Descriptive statistics are divided into measurements of central tendency and measures of variability (spread). Descriptive statistics are used to describe or summarize the data in meaningful and useful ways. It would be useful to know, for example, that each of the participants in with us example wore blue shoes. Even so, it'd be useful to know how evenly distributed their anxiety ratings were.So, the statement "Robin expects to serve 12% fewer meals this year than last year" is a descriptive statistic.
Therefore, the given statement is a descriptive statistic.
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Without computing, determine which
number is greater, [(-4)415 or -[(4¹2)³].
Explain your reasoning.
Since a negative number's exponent is always positive, [(-4)⁴]⁵ will always be greater than -[(4¹²)³].
What is number system?
The Number System covers any of the several sets of symbols and usage guidelines for indicating numbers, which are used to indicate how many items are present in a particular group. Thus, the Roman numeral I, the Greek letter alpha, the first letter used as a numeral, the Hebrew letter aleph, or the modern number 1, which is nothing more than Hindu-Arabic in origin, can all be used to express the idea of "oneness."
A mathematical representation of the numbers in a given set is called a number system.
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State which metric unit you would probably use to measure item.
Mass of a beach ball
The basic unit of mass of the ball in the metric system is the gram.
What is mass?The base units of length (distance), capacity (volume), and weight (mass) in the metric system are the meter, liter, and gram, respectively. We utilize units that are derived from metric units to measure smaller or greater quantities.
Mass is a physical body's total amount of matter. Inertia, or the body's resistance to acceleration when a net force is applied, is also measured by this term. The strength of an object's gravitational pull to other bodies is also influenced by its mass.
Therefore, the basic unit of mass of the ball in the metric system is the gram.
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Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
How much interest will Rich accrue during the 4.5-year non-payment period?
Rich has to pay an interest of $1525.10 during the 4.5 year non payment period.
In the question
it is given that the Amount of loan taken by Rich = $7900
non payment time period = 4.5years
Interest charged during the non payment time = 4.29%
Interest charge for the first year = 4.29% of 7900
= 0.0429 * 7900 ...(as 4.29% = 0.0429)
= 338.91
So , the interest charge for first non payment year = $338.91
to find the interest for 4.5 years , multiply the first year interest by 4.5.
So the interest charge for 4.5 years = 4.5*338.91
=1525.095
≅1525.10
Therefore , Rich has to pay an interest of $1525.10 during the 4.5 year non payment period.
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the sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term
Answer:
A=10. D=_3
Step-by-step explanation:
Start from 10 and make minus 3 every time
Lawana is making cone-shaped hats 4 inches in diameter, 6.5 inches tall, with a slant height of 6.8 inches for party favors. Find each measure to the nearest tenth.
a. the volume of candy that will fill each cone
Given hats are forming a conical shape and the volume of the cone will be 27.28 inches³.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Given that,
4 inches in diameter, 6.5 inches tall, slant height of 6.8 inches
So,
D = 4 inches
Now radius r = D/2
r = 4/2 = 2 inches.
Height h = 6.5 inches.
The volume of the conical bar is given as ;
(1/3)πr²h
So,
Volume = (1/3)π(2)²6.5
Volume = 27.28 inches³
Hence "The volume of the given conical-shaped hat will be 27.28 inches³".
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a restaurant offers three desserts, and exactly twice as many appetizers as main courses. a dinner consists of an appetizer, a main course, and a dessert. what is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003? (a) 4 (b) 5 (c) 6 (d) 7 (e) 8
8 is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003.
What are Integers in Math?
An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043Let m be the number of main courses the restaurant serves, so 2m is the number of appetizers.
Then the number of dinner combinations is 2m * m * 3=6m².
Since the customer wants to eat a different dinner in all $365$ days of 2003, we must have
6m² ≥ 365
m² ≥ 60.83
Also, year 2003 is not a leap year, because 2003 divided by 4 does not equal an integer. The smallest integer value that satisfies this is E = 8.
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PLEASE HELP!!!
We want to find the median of the following set of scores:
26, 9, 15, 5, 5, 27, 23, 12
Answer: 13.5
Step-by-step explanation:
First arrange the scores in order:
5, 5, 9, 12, 15, 23, 26, 27
**remove 1st and last number in the set of scores every time**
Median of 5, 5, 9, 12, 15, 23, 26, 27=
Median of 5, 9, 12, 15, 23, 26=
Median of 9, 12, 15, 23=
Median of 12, 15 =
**Take mean of remaining two numbers**
(12+15)/2=
27/2=13.5
9.66 x 0.46 estimated
Answer:
10
Step-by-step explanation:
so just round to the ones below or above 5
Simplify this expression-
-6(2 + x)
Answer:
-12 -6x
Step-by-step explanation:
I did this by distributing
-6 x 2 = -12
-6 x x= -6x
-12 -6x is your final answer
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
The sum of three consecutive even integers is 48. Find the value of the middle of the
three.
Answer:
16
Step-by-step explanation:
You want the middle of three consecutive even integers that have a sum of 48.
Consecutive even integersWe can let x represent the middle of the three integers. Then the other two are (x -2) and (x +2), and their sum is ...
(x -2) +x +(x +2) = 48
3x = 48 . . . . . simplify
x = 16 . . . . . . divide by 3
The middle integer of the three is 16.
__
Additional comment
As we see here, the average of the three integers is their sum divided by their number: 48/3 = 16. The middle of an odd number of consecutive integers will be equal to their average value. Hence, the middle integer must be 16.
David requires at least $250 to hold his birthday party. If David can save $43 by the end of each month, how many months will he need to save to be able to afford his birthday party?
a. Write an inequality that describes this situation.
b. Solve the inequality. Show all your work.
c. Write your answer in a complete sentence.
Answer: 250/43
Step-by-step explanation
Answer:
he would need seven weeks, i believe.