Answer:
y = [tex]\frac{6-2x}{4}[/tex]
Step-by-step explanation:
2x + 3y = 6 - y ( add y to both sides )
2x + 4y = 6 ( subtract 2x from both sides )
4y = 6 - 2x ( isolate y by diving both sides by 4 )
y = [tex]\frac{6-2x}{4}[/tex]
Chris deposits $6000 into an account that pays simple interest at a rate of 2% per year.
How much interest will he be paid in the first 3 years?
Answer:
$360
Step-by-step explanation:
You want the amount of simple interest earned by $6000 in 3 years at the rate of 2%.
InterestThe simple interest formula is ...
I = Prt
where P is the principal invested at rate r for t years.
Application$6000 invested at 2% for 3 years earns ...
I = $6000·0.02·3 = $360
Chris will be paid $360 in interest in the first 3 years.
Solve for y in this diagram. Justify your answer.
The value of y in the given diagram is 6cm.
What is triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.
Consider, the given triangle the two base angles are same.
So, the triangle is a isosceles triangle.
Since, when the base angles of an isosceles triangle are equal, the sides that face these angles are also equal.
Hence, the value of y in the given diagram is 6cm.
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Which of the fractions below is equivalent to
7/6 divided by 2/3?
4/7
7/4
7/9
9/7
The requried equivalent fraction is 7/4. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
here,
7/6 divided by 2/3
= 7/6 ÷ 2/3
= 7/6 × 3/2
= 7/4
Thus, the requried equivalent fraction is 7/4. Option B is correct.
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given the four digits 2, 4, 6, and 7, how many different positive two-digit integers can be formed using these digits if a digit can be repeated in an integer?
There are 12 different positive two digit integers can be formed using these digits if a digit can be repeated in an integer.
Integer:
An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). A negative number is the additive reciprocal of the corresponding positive number. In mathematics languages, sets of integers are often denoted by a bold Z or a bold {Z}.
Given the question :
The number of different positive two integer number can be obtained by:
P(4, 2) = 4P2
We know that:
[tex]^nP_r[/tex] = n! / (n - r)!
⁴P₂ = 4! / (4 - 2)!
⁴P₂ = 4! / 2!
⁴P₂ = (4 * 3 * 2 * 1) / ( 2 * 1)
⁴P₂ = 24 / 2
⁴P₂ = 12
Hence, 12 different positive two-digit integers can be formed using these digits if a digit may not be repeated in an integer.
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Question 6 of 10
What is the equation of a circle centered at the origin with radius 20?
OA. x³ + ³ = 400
OB. x³+y³ = 20
OC. x² + y² = 20
OD. x² + y² = 400
Answer:
x^2 + y^2 = 400
Step-by-step explanation:
the general equation of a circle is,
x^2 +y^2 = r^2
where x, y are the coordinates of the circle
r is the radius
Which of the following can be represented by the equation 3x = 24?(1 point)
Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
A survey was conducted to determine the favorite subject of seventh grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?
Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?
The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?
Answer:
The last answer is correct
Step-by-step explanation:
3x = 24 Divide both sides by 3
x = 8
A pair of shoes cost $8
19 points
Which relations represent a function?
The relation (10, 8), (7, 9), (9, 13), (8, 5) is representing a function. (option B)
What is a function?A function defines relations between input and output, where all input has a distinct output.
Given are the relations,
A) (14, 12), (10, 12), (-13, 7), (11, 15)
In this, two inputs 14 and 10 have same output 12, so it can not be a function.
B) (10, 8), (7, 9), (9, 13), (8,5)
In this, we can see, every input have distinct outputs, so it can be considered as a function.
Hence, (10, 8), (7, 9), (9, 13), (8,5) is a function.
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Solve for x them find the measure of the angle given...can someone please help me
The solution for the angle x in the figure is 130 degrees
How to determine the solution for x?From the question, we have the following parameters that can be used in our computation:
The transversal and the parallel line
By the theorem of vertical angles, we have the following equation
x = 5y
Also, we have the following equation
x = 2y - 78 --- by the theorem of corresponding angles
Substitute x = 2y - 78 in x = 5y
So, we have the following representation
5y = 2y - 78
Evaluate the like terms
3y = 78
Divide both sides by 3
y = 26
Substitute y = 26 in x = 5y
x = 5 * 26
Evaluate
x = 130
Hence, the value of x is 130
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STANDARD FORM MATHS HELP. POINTS
Answer:
1.64×10⁷ km16,400,000 km ("standard form" in the US)Step-by-step explanation:
You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:
c² = a² +b²
RQ² = PQ² +PR²
RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root
The distance between planets Q and R is 1.64×10⁷ km.
__
Additional comment
The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.
You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.
Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.
Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)
The distance QR is :
[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]
[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]
Given f(x) = 6x − 8 and g(x) = −5x + 2, what is (f − g)(x)?
The expression which represents the composite function (f - g) (x) as required in the task content is; 11x - 10.
Which expression represents the composite function; (f - g) (x)?It follows from the task content that the expression which represents the composite function (f - g) (x) as required in the task content be determined.
Since the given functions are;
f(x) = 6x − 8 and g(x) = −5x + 2
The composite function; (f - g) (g) is equivalent to;
f (x) - g (x)
Therefore, we have;
(f - g) (x) = 6x - 8 - (-5x + 2)
(f - g) (x) = 6x + 5x - 8 -2
(f - g) (x) = 11x - 10.
On this note, the required expression which represents (f - g) (x) is; 11x - 10.
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Carson earns $113.75 for 7 hours of work. If he makes a constant hourly wage, which table represents the relationship between the number of hours he works and his total earnings?
The constant amount that Carson makes every hour is $16.25.
How to illustrate the relationship?It is important to note that this question has to do with a proportional relationship. Since Carson earns $113.75 for 7 hours of work and he makes a constant hourly wage.
The amount that he makes per hour will be:
= Amount / Number of hours
= $113.75 / 7
= $16.25
Therefore the constant amount he makes every hour is $16.25.
Note that the options weren't given but the question has been solved accordingly.
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PLEASE HELP!
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
The graphed two lines will have one solution.
Solutions of Pair of straight lines:Any line that isn't twisted or bent is said to be straight.
Intersecting Lines:Intersecting lines are two or more lines that have exactly one point in common. The point of junction is this central location that connects all of these lines.
A system of Intersecting Lines will have one unique solution
Parallel lines :Lines that are parallel to one another on a plane do not overlap or meet at any point. They are always parallel and equally spaced from one another.
A system of Parallel Lines will have no solution
Here we have
System of equations
Given that the two lines are not parallel line
As we can see that both lines meet at a point
So here we can conclude that both lines are Intersecting Lines
Therefore,
The graphed two lines will have one solution.
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HELPPPP FASTER MARK BRAINLIEST IF CORRECT
A college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
x > 0 and y > 0
0 < x ≤ 100 and 0 < y ≤ 400
0 < x ≤ 100 and y > 400
0 < x and y < 100
The constraints to represent the incoming students at the college is B. 0 < x ≤ 100 and 0 < y ≤ 400
How to illustrate the inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this situation, the college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students.
Let x = the number of out-of-state students and
y = the number in-state students.
The constraints is 0 < x ≤ 100 and 0 < y ≤ 400.The correct option is B.
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7. The variables xand yvary directly. When z= 12, y=4. Which of the following
equations represents this relationship?
Step-by-step explanation:
x varies directly as y
x=ky
12=4k
k=12/4
k=3
Can somebody tell me the answer worth 50 points!!!
Answer:
Two blue = 6
Step-by-step explanation:
Let r = red
Let b = blue
2r + r + b = 21
r - b = 3 Can we rewritten r = 3 + b Substitute 3 + b for r into the first equation
2r + r + b = 21
2(3 + b) + 3 + b + b = 21 Distribute the 2
6 + 2b + 3 + b + b = 21 Combine like terms
9 + 4b = 21 Subtract 9 from both sides
9 - 9 + 4b = 21 - 9
4b = 12 Divide both sides by 4
[tex]\frac{4b}{4}[/tex] = [tex]\frac{12}{4}[/tex]
b = 3
2 blues would equal 6.
Answer:
6
Step-by-step explanation:
Define the variables:
Let x = red pencilLet y = blue pencilFrom the given blackboard, create a system of equations from the first three equations:
[tex]\begin{cases}3x + y = 21\\\;\:x - y = 3\\2x + y = 15\end{cases}[/tex]
Add the first equation to the second equation to eliminate y:
[tex]\begin{array}{lrcccr}& 3x & + & y & = & 21\\+ & (x & - & y & = & 3\\\cline{2-6} &4x &&&=&24\end{array}[/tex]
Solve the equation for x:
[tex]\implies \dfrac{4x}{4}=\dfrac{24}{4}[/tex]
[tex]\implies x=6[/tex]
Substitute the found value of x into the second equation and solve for y:
[tex]\implies 6-y=3[/tex]
[tex]\implies y=3[/tex]
Therefore, the value of the red pencil is 6 and the value of the blue pencil is 3.
Finally, substitute the found value of y into the last equation:
[tex]\implies 3 + 3 = \boxed{6}[/tex]
A student has two options to purchase a laptop.
Option 1: Pay $540 plus 15% sales tax now.
Option 2: Pay exactly $120 now and then $58 each month for 9 months.
What is the approximate percent increase in how much the student pays with Option 2 versus Option 1?
Responses
Approximate percent increase in how much the student pays with Optin 2 versus Option is 20%
How to find Percentage?$540 plus 15% sales tax now.=$515
Pay exactly $120 now and then $58 each month for 9 months=$642
There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any topic are calculated in terms of percentages in academics. Ram, for instance, scored 78% in his final exam. This percentage is determined using Ram's overall grade point average (GPA) across all disciplines. We must apply a different formula, like the one shown below, to determine the percentage of a number.X Equals P% of NumberIf we don't use the percent sign, we must write the calculations above as P/100 * Number = X.To learn more about Percentage refer to:
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help me plsssss
i put the image below
if u can see it
help asap
Answer:
q= 1.09
Step-by-step explanation:
the works there its a little messy tho
drag and drop the quantity on the right column with a number from the left column
Answer: 27, 65, 29, 77, 37
Step-by-step explanation:
The number of diagonals of an [tex]n[/tex]-gon is [tex]\frac{n(n-3)}{2}[/tex].
The number of apothems of an [tex]n[/tex]-gon is [tex]n[/tex].
Answer:
Step-by-step explanation:
Bob ran for president of the chess club, and he received 48 votes. There were 64 members in the club. What percentage of the club members voted for Bob?
75% percentage of the club members voted for Bob.
What is meant by percentage?The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages. 10%, a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.
Given,
The number of votes received by Bob=48 votes
Total number of members in the club=64
Then,
(48/64)×100
=75%
Therefore, 75% percentage of the club members voted for Bob.
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From a hot-air balloon, Justin measures a 34° angle of depression to a landmark
that's 1424 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
960.50 feet
Step-by-step explanation:
You want to know the height of a balloon if it is 1424 feet horizontally from a landmark at an angle of depression of 34°.
TangentThe geometry of the problem can be modeled as a right triangle with a base angle of 34°, the adjacent leg 1424 feet, and the opposite leg being the height of the balloon. The tangent relation tells us ...
Tan = Opposite/Adjacent
Opposite = Adjacent·Tan
height = (1424 feet)·tan(34°) ≈ 960.50 feet
The balloon's vertical distance from the ground is 960.50 feet.
__
Additional comment
If the angle is measured to the nearest degree, then the height of the balloon is somewhere between 943 feet and 979 feet. The only purpose served by reporting the distance to the nearest 0.01 foot is to see if you can use your calculator correctly.
To make that precision for the height meaningful, the angle would need to be measured with an error less than 0.00014°, about 1/2 arc-second. This is better resolution than the best surveying instruments offer, by a factor of about 30.
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Write the equation for a line that passes through the given points Write the equation in slope- intercept form
. (6,-4), (6,5)
The equation of the line, in slope-intercept form, that passes through the given points, (6,-4) and (6,5) is: x = 6.
How to Write the Equation of a Vertical Line?An vertical line can be written in slope-intercept form as x = a, because the line has no y-intercept and the change in x values in the slope formula is equal to zero.
The value of a in the equation is the point on the x-axis where the vertical line intercept, irrespective of the change in y-values up the line.
Given the line goes through the points, (6, -4) and (6, 5), it means the line is a horizontal line because they both have the same x-value, 6.
Therefore, the value of a is 6. The equation of the line would be x = 6.
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Emma grew 6 plants with 3 seed packets. How many seed packets does Emma need to have a total of 16 plants in her backyard? Solve using unit rates.
Emma needs 8 seed packets to grow 16 plants.
What is unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Finding the value of a single unit using the unitary technique, then extrapolating from this value.
Given that,
Emma grew 6 plants with 3 seed packets.
To grow 6 plants Emma needs 3 seed packets.
Applying unitary method:
To grow 1 plants Emma needs 3/6 seed packets.
To grow 16plants Emma needs (3 × 16)/6 seed packets.
= 8 seed packets.
The unitary method is used to unite rate.
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The volume of a right cylinder is found by the formula V equals pi r squared h. Two cylinders both have a height of 10 centimeters. One has a volume of 2009.6 cubic centimeters. The other has a volume of 196.25 cubic centimeters. What is the radius of each cylinder? (Use 3.14 as an approximation of pi.)
The radii of the cylinders found using the formular for the volume of a cylinder, and the 2009.6 cubic centimeter and 196.25 cubic centimeter volumes of the cylinders, indicates;
The radius of the 2009.6 cm³ cylinder is 8 centimeters
The radius of the 196.25 cm³ cylinder is 2.5 centimeters
What is a cylinder?A cylinder is a solid that has three dimensions, consisting of two circular, parallel bases that enclose a curved pipe like surface in between.
The volume of one cylinder = 2009.6 cubic centimeters
The volume of the other cylinder = 196.25 cubic centimeters
The height of each cylinder, h = 10 centimeters
The formula for finding the volume of a cylinder is; V = π·r²·h
Where;
r = The radius of the cylinder
h = The height of the cylinder
The formula for finding the volume of a cylinder indicates;
r² = V/(π·h)
r = √(V/(π·h))
The radius of the cylinder of volume 2009.6 cubic centimeters, r₁ is therefore;
r = √(2009.6/(3.14 × 10) = 8
The radius of the 2009.6 cubic centimeters volume cylinder is r₁ = 8 cm
The radius, of the 196.25 cubic centimeters cylinder, r₂, is therefore;
r₂ = √(196.25/(3.14×10)) = 2.5
The radius of the 196.25 cubic centimeter volume cylinder, r₂ = 2.5 cm
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Find the perimeter of the triangle XYZ with verticles X (1, 3) , Y(-4, -1) and Z(4, -1). Round your answer to two decimal places
Answer:
The perimeter is approximately 6.40.
Step-by-step explanation:
To find the perimeter of a triangle with vertices X (1, 3), Y (-4, -1), and Z (4, -1), we can first find the distance between each pair of points using the distance formula.The distance between points X and Y is:
$d(X,Y) = \sqrt{((1 - (-4))^2 + (3 - (-1))^2)} = \sqrt{25 + 16} = \sqrt{41}$
The distance between points Y and Z is:$d(Y,Z) =
\sqrt{((-4 - 4)^2 + ((-1) - (-1))^2)} = \sqrt{0 + 0} = 0$
The distance between points X and Z is:
$d(X,Z) = \sqrt{((1 - 4)^2 + (3 - (-1))^2)} = \sqrt{9 + 16} = \sqrt{25}$
We can then find the perimeter of the triangle by adding up the lengths of the sides. In this case, the perimeter is $d(X,Y) + d(Y,Z) + d(X,Z) = \sqrt{41} + 0 + \sqrt{25} = \sqrt{41} + \sqrt{25} = 6.40\ldots$.
Rounded to two decimal places, the perimeter is approximately 6.40.
Interpret parts of the algebraic expression to describe the real-world scenario.
The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released.
By how much is the value of the comic increasing per year?
How much was the initial value of the comic?
The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released. is
(a) [tex]0.2$[/tex]
(b) [tex]1.5$[/tex]
[tex]0.2 y+1.5 \longleftarrow \text { initial value }[/tex]
[tex]when $y$ increase one. the value increase $\$ 0.2$[/tex]
Travelling to movies and television programmes. An element of a comic book being in a popular film or television programme is a major factor in its value rising. Characters' comic book appearances have become far more valuable as they are integrated into the Marvel Cinematic Universe.
Marvel's first comic book just sold for $1.26m. Movies have contributed to the enduring popularity of superheroes, bringing in new audiences. The printed comic is still big business, worth over $1bn in North America alone.
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Solve for x. 2.5x + 1.5
please show steps and how you got answer
The value of x and y at which function P = 3x+2y becomes maximum are
(9,0), data from given graph.
What is the graph?
Graph is the pictorial representation of given data.
Graph is defined as to create a diagram that shows a relationship between two or more things. An example of graph is to create a series of bars on graphing paper.
The four most common are
1. Probably line graphs,
2. Bar graphs and histograms,
3. Pie charts, and
4. Cartesian graphs
To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.
Note: (5,4) is not a vertex.
(0,8) :
P = 3*0 + 2*8
= 16
(5,4):
P = 3*5 + 2*4
= 23
(9,0):
P = 3*9 + 2*0
= 27.
So, the maximum value = 27 at (9,0).
So, the x value = 9 and
the y value = 0.
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3. Students at Polk Middle School are given a fitness test. The results of their tests are shown in the table. Use the table to answer questions a-c. a. Find the time it takes each student to run . Evian:_ Toby:_ Jillian:_ b. Which student is running at the fastest rate? Expl c. Jillian is trying out for the cross country team. To make the team, she must run in less than . Will Jillian make the team? Explain.
The time for each of them to cover 1 mile is; Evian = 10 min, Toby = 9 min and Jillian = 12 min. The fastest is Toby and No, Jillian can't make the team.
What is unit rate?A unit rate means a rate for one of something.
Given that, Students at Polk Middle School are given a fitness test.
The fitness test result is;
Evian can run [tex]1\frac{1}{2}[/tex] miles in 15 minutes, Toby can run 2/3 miles in 6 minutes and Jillian can run 3/4 miles in 9 minutes
a) The rate of running in 1 mile = (total miles covered)/(total time taken)
Evian =
3/2 miles in 15 minutes
1 mile = 15x2/3
1 mile = 10 minutes
Toby =
2/3 mile in 6 minutes
1 mile = 6x3/2
1 mile = 9 minutes
Jillian =
3/4 miles in 9 minutes
1 mile = 9x4/3
1 mile = 12 minutes.
b) Since, Toby is covering 1 mile in the least minutes in comparison with other two, therefore Toby is fastest among them.
c) Jillian's rate = 1 mile in 12 minutes
Speed = 1/9 miles per minute
Therefore, she will cover 7/2 miles in = 12x7/2 = 42 minutes
That means, she can't make the team.
Hence, the answers are a) Evian = 10 min, b) Toby = 9 min and Jillian = 12 min, the fastest one is Toby and Jillian can't make the team.
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PLEASE HELP!!!!
Write the quadratic equation whose graph has x-intercepts of -11 and 3 and passes through the point (1, 192)
A: y=8x^2+64x−264
B: y=8x^2−64x−264
C: y=−8x^2+64x+264
D: y=−8x^2−64x+264
The quadratic equation with the given x-intercepts and that passes through the point (1, 192) is the one in option D.
y = -8x^2 -64x + 264
What is the quadratic equation?If a quadratic equation has x-intercepts x₁ and x₂ and a leading coefficient a, we can write the quadratic equation as:
y = a*(x - x₁)*(x - x₂)
Here we know that the x-intercepts are -11 and 3, replacing that in the equation above we will get:
y = a*(x + 11)*(x - 3)
We also know that the line passes through the point (1, 192), replacing the values in the quadratic equation we will get:
192 = a*(1 + 11)*(1 - 3)
192 = a*12*-2
192 = -24*a
192/-24 = a
-8 = a
So the quadratic equation is:
y = -8*(x + 11)*(x - 3)
Expanding this, we will get:
y = -8x^2 -64x + 264
So the correct option is D.
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Indigo goes out to lunch. The bill, before tax and tip, was $10.85. A sales tax of 3%
was added on. Indigo tipped 18% on the amount after the sales tax was added. The
total cost of the meal plus tip and tax was more than the cost of the bill by what
percent? Round to the nearest whole number.
The total cost of the meal plus tip and tax was more than 122% of the cost of the bill.
What is percent?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
Indigo goes out to lunch.
The bill, before tax and tip, was $10.85.
A sales tax of 3% was added on.
Indigo tipped 18% on the amount after the sales tax was added.
The amount after adding sales tax is,
$10.85 x 3% = 0.3255
⇒ $10.85 + 0.3255 = $11.1755
Now to find the amount after tipped 18% on the amount after the sales tax was added.
$11.1755 x 18% = 2.01159
⇒ $11.1755 + 2.01159 = $13.18709
Hence, the amount after tipped 18% on the amount after the sales tax was added is $13.18709.
Let x be the percent of more than the cost of the bill of $13.18709.
⇒
[tex]\frac{10.85(x)}{100} = 13.18709\\ x = \frac{100 (13.18709)}{10.85}\\ x = 121.54[/tex]
Hence, the total cost of the meal plus tip and tax was more than 122% of the cost of the bill.
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