We see that under option B, you will make more money than under option A.
What is a percentage?
A relative value indicates the hundredth part of any quantity. One percent (symbolized 1%) is the hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
To compare the two options and determine which one will result in you making more money, we need to find the total amount of money you will make under each option.
Under option A, you will receive a $6,000 raise in year 1 and a 4% raise in year 2. Let's call your base salary S. After the first year, your salary will be S + $6,000. After the second year, your salary will be (S + $6,000) * 1.04 = S + $6,240.
Under option B, you will receive a 4% raise in year 1 and a $6,000 raise in year 2. After the first year, your salary will be S * 1.04 = S + $480. After the second year, your salary will be (S + $480) + $6,000 = S + $6,480.
Comparing the two options, we see that under option B, you will make more money than under option A. This is because option B includes a $6,000 raise in the second year, while option A includes a smaller 4% raise in the second year.
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Identify the correct base case for a proof by induction for the following statement.
1+3+5+. +(2n-1)=n^2
we prove the following step using proof by induction
What is proof by induction?
For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.
We are given a statement 1+3+5+. +(2n-1)=n^2
Now first let us prove the statement for n=1 where n is the number of terms
On the left hand side = 1
And on the right hand side = 1^2 = 1
Hence the statement is proved for n =1
Now let us prove the statement for n= k
Therefore we have 1+3+5+....+k=k^2
Now let us prove the statement for n= k+1
Hence we have
1+3+5+....+k+(k+1)=
k^1+k+1
= (k+1)^2
Hence proved
Therefore we prove the following step using proof by induction
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There are only blue weet, green weet and red weet in a box. The ratio of the number of blue weet to the number of green weet i 2:7. The ratio of the number of green weet to the number of red weet i 3:1. There are le than 140 weet in the box. What i the greatet poible number red weet in the box?
The greatest possible number of red sweets in the box is 28.
If the ratio between blue and red sweets is x, then the number of blue sweets equals 2x and the number of green sweets equals 7x. If the ratio between green and red sweets is y, then the number of green sweets equals 3y and the number of red sweets equals y. In this case, the number of green sweets must be the same.
7x = 3y
Additionally, 140 is the sum of all of them,
thus,
2x + 3y + y < 140
2x + 4y < 140
x + 2y < 70
x + 2 × 7x/3 < 70
3x + 14x < 210
17x < 210
x < 12.36
and x ought to be a whole number, therefore x = 12
, and the total number of sweets will equal 136.
y = 7 × 12/3 = 28
thus, The greatest possible number of red sweets in the box is 28.
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(complete question)
There are only blue sweets, green sweets, and red sweets in the box. The ratio of the number of blue sweets to the number of green sweets is 2:7 The ratio of the number of green sweets to the number of red sweets is 3:1 there are less than 140 sweets in the box. What is the greatest possible number of red sweets in the box? Your final answer must include, 'red sweets'.
function rule to find f(1)
By evaluating the function in x = 1, we will get:
f(1) = 4
How to find the value of f(1)?Here we have the following absolute value function:
f(x) = 11 - 7*|x|
We want to find f(1), this just means that we need to evaluate the function in x = 1.
That means that we need to replace the variable in the equation by the number 1, so let's do that:
f(1) = 11 - 7*|1|
Now we just simplify that, we will get:
f(1) = 11 - 7*|1|
= 11 - 7
= 4
f(1) = 4
That is the value we wanted to find.
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Why does the following equation have no solutions?
5-4x-7-10x=-8x-4-6x-10
The following equation's linear components have no solutions.
Because they contain the same variable term on one side of the equation but distinct constant values on the other, 5-4x-7-10x=-8x-4-6x-10.
What does linear equation mean?A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.
This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."
In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.
Given is an equation that reads 5-4x-7-10x=-8x-4-6x-10 and 14x-2=14x-14.
A linear equation has no solutions if both sides of the equation have different constant values but the same variable term.
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.........i need help past due
Answer:
The 3rd box and 4th box will be checked
Step-by-step explanation:
The ratio 9:7 for apples to oranges means for every 9 apples there will be 7 oranges. So, the 3rd box and 4th box will be checked.
HELP ASAP!! I will give Brainiest!
Angles X and Y are supplementary. Angle X measures 132.54°, and angle Y measures (m - 15)°. Find mzY
47.46°
62.46
85.08
117.54°
Answer:
47.46
Step-by-step explanation:
Answer: The answer is A. 47.46°.
Step-by-step explanation: Hope this helps.
Question
Which ordered pairs cause this relation NOT to be a function? Why?
{(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)}
Responses
A (0.5, 1), (3, 1); The same y-value has different x-values.(0.5, 1), (3, 1); The same y-value has different x-values.
B (3, 1) and (3, 2); The same x-value has different y-values.(3, 1) and (3, 2); The same x-value has different y-values.
C (3, 1) and (3, 2); The x-value in a function cannot be greater than the y-value.(3, 1) and (3, 2); The x-value in a function cannot be greater than the y-value.
D (0.5, 1) and (0, 0.5); A function cannot contain decimals.
Ordered pair (3, 1) and (3, 2) causes the relation to not be a function; The same x-value has different y-values.
How do you find out if a set of ordered pairs is a function or not?
For a set of ordered pairs to be a function, there must not be any two points that have the same first elements. This means that, the
x-coordinates must not repeat for any two given points.
According to the given question:
Given ordered pairs of a relation are
(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)
Domain set of the relation= {0, 0.5, 1, 3}
Co-Domain set of the relation = {0.5, 1, 2, 6}
Clearly the image of the x-coordinate 3 is not unique.
Hence, (3, 1) and (3, 2); The same x-value has different y-values.
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i need help with this
I would prefer to see the diagram labled on paper, including help, just bc typed out answers can be confusing to me
The height pf telephone pole is 55.2 ft.
What are similar triangles?
Similar triangles are triangles that have constant form, however their sizes could vary. All equal triangles, squares of any facet lengths area unit samples of similar objects. In alternative words, if 2 triangles area unit similar, then their corresponding angles area unit congruent and corresponding sides area unit in equal proportion.
Main body:
according to question :
height of wooden pole = 144 inches = 12 ft
(as 12 inches = 1 ft
therefore 144 inches = 12 ft)
distance between telephone pole and wooden pole = 45 ft
distance between pole and stake = 57.5 ft
distance between wooden pole and stake = 57.5 - 45 = 12.5 ft
we need to find height of telephone pole =?
as ΔABE are similar to ΔCDE , so
AB/BE = CD/CE
AB/57.5 = 12/12.5
AB = 12*57.5/12.5
AB = 55.2 ft
Hence , the height pf telephone pole is 55.2 ft.
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For Problems 14 and 15, find the original price given the total amount and
tip rate.
14. $51.84, 20%
15. $38.35, 18%
Answer:
14. Original Price = $43.20
15. Original Price = $32.50
helppppp pleaseeeeeeeeeeer
By using the property of congruency of triangles,
[tex]\angle[/tex]PSR = [tex]\angle[/tex]PSQ has been proved
What is congruency of triangles?
Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.
There are different axioms of congruency. They are
SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom
PS bisects [tex]\angle[/tex]QPR [Given]
PQ [tex]\cong[/tex] PR [Given]
[tex]\angle[/tex]QPS [tex]\cong \angle[/tex]RPS [PS bisects [tex]\angle[/tex]QPR]
PS [tex]\cong[/tex] PS [Reflexive property of congruence]
[tex]\Delta[/tex] PQS [tex]\cong \Delta[/tex] PRS [SAS axiom]
[tex]\angle[/tex]PSR = [tex]\angle[/tex]PSQ [Corrosponding parts of congruent triangles are congruent]
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theres 4 questions that i need help with asap. #geometry
please help.
After solving the equation we know ABCD is a parallelogram.
What is parallelogram?
A parallelogram is a two-dimensional shape with four straight sides. All of the sides are equal in length and the opposite sides are parallel. Additionally, opposite angles are also equal. The shape is called a parallelogram because parallel lines are present on either side. Parallelograms can come in many different forms, such as rectangles and rhombuses. The properties of a parallelogram include the fact that the diagonal line that divides the parallelogram into two halves bisects the angles. Additionally, the cross product of the two diagonals is equal to the area of the parallelogram. Parallelograms are used in a variety of areas, including architecture, engineering, and mathematics. Depending on the application, parallelograms can be used to construct a variety of shapes, such as circles and ellipses.
Given: A (2,5), B (7,6), C (6,2), D (1,1)
AB ⇒ A (2,5), B (7,6) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(-5+1)^{2}+(-6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(-4)^2+(-8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
CD ⇒ C (6,2), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7-3)^{2}+(6+2)^{2} }[/tex]
⇒ [tex]\sqrt{(4)^2+(8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
BC = B (7,6), C (6,2) ⇒ [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(3+5)^{2}+(-2+6)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
AD ⇒ A (2,5), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7+1)^{2}+(6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
As, AB = CD = BC = AD all sides are equal.
Hence proved, ABCD is a parallelogram.
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What is an equation of the line that passes through the point (6,1)(6,1) and is parallel to the line x+3y=15x+3y=15?
The equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15 is 3y+x=9.
What is an equation of a line?The general equation of a straight line is given by the expression
y = mx + c, where m is the gradient and y = c is the point at which the line intersects the y-axis.
Given,
The line is parallel to the line x + 3y = 15 and passes through the point (6,1).
The procedures listed below can be used to find the equation of the line that runs parallel to the line x + 3y = 15 and passes through the point (6,1).
Step 1 - Keep in mind that two parallel lines have equal slopes.
Step 2: As a result, the line's slope across point (6,1) is -1/3.
Step 3: Accordingly, the equation of a line passing through the point (6,1) and being parallel to the line (x + 3y = 15) may be found using the one-point slope form of a line.
The one-point slope form is shown below in Step 4:
y-y₁=m(x-x₁)
Step 5: In the equation above, substitute the values of the known terms.
y-1=-(1/3)(x-6)
3y - 3 = -x + 6
3y +x = 9
Therefore, the equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15 is 3y+x=9.
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6th Grade Mathematics Inequalities
Answer:
[tex]n < 91[/tex]
Step-by-step explanation:
Move all terms not containing n to the right side of the inequality.
Add 5 to both sides of the inequality.
[tex]\frac{n}{13} < -12+5[/tex]
Add −12 and 5.
[tex]\frac{n}{13} < -7[/tex]
Multiply both sides by 13.
[tex]\frac{n}{13} *13 < -7*13[/tex]
Simplify the left side by canceling the common factor of 13.
[tex]n < -7*13[/tex]
Simplify the right side by multiplying −7 by 13.
[tex]n < 91[/tex]
We often use functions to model or represent situations and relationships. These
representations can be as equations, graphs, tables, or even verbal descriptions.
What does it mean to "represent" something? In what other situations have you heard
that term used, and how was its meaning in those situations similar to its usage in
algebra? please help
Answer:
Step-by-step explanation:
If a fair die is rolled 4 times, what is the probability, rounded to the nearest
The number of beads in a jar is 50 to the nearest ten.
(a) What is the minimum possible number of beads in the jar?
(b) What is the maximum possible number of beads in the iar?
PLS ANSWERRRRRSSSSSSS. I GIVE BRAINLIESTTT
Answer:
x = 5.4
Step-by-step explanation:
[tex]\frac{7.2}{4}[/tex] = [tex]\frac{x}{3}[/tex] Cross multiple and solve for x
4x = (7.2 x3)
4x = 21.6 Divide both sides by 4
x = 5.4
Answer:
x = 5.4
Step-by-step explanation:
[tex]\frac{x}{7.2} =\frac{3}{4}[/tex]
[tex]x=\frac{(7.2)(3)}{4} =\frac{21.6}{4} =5.4[/tex]
Hope this helps
Mr. Brown' hotel bill i $140. He leave 12% of the hotel bill a a tip for the houekeeping ervice. How much i Mr. Brown leaving a a tip?
In linear equation,$308 is Mr. Brown leaving a a tip .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The amount of hotel bill= $140
He leaves 12% of the hotel bill as a tip for the housekeeping service.
Thus, the amount of tip= 12% of hotel bill
=12% of $140
= 12/100 * 140
= 12 * 14
= 168
Therefore, the total amount Mr. Chin pays, including tip =$140+$168 =$308
Hence, Mr. Chin pays $308, including tip
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When you multiply a three digit number by a two digit number what i the greatet number of digit the product can have
On multiplying a three digit number by a two digit number the greatest number of digit the product can have is 5 digits.
Let , the two numbers be 788 and 12
on multiplying,
788 * 12
=9456
Again,
let the numbers be 999 and 99
999 * 99
=98901
Therefore, it is clear that the maximum number of digits in the product will have is 5 digits.
Repeated addition is the process of multiplication. The calculation of the product of two numbers can be done in a number of ways. Here, you can see what is meant when a number is multiplied by a two-digit number .
Find out how to multiply a number by a two-digit number in the sections below. The three different approaches used to determine the multiplication are shown in detail.
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Help its for a competency
Answer:
y = -3x + 10
Step-by-step explanation:
Do you want the equation of the line?
y = mx + b
the b is where the line intersects the y axis. That is at 10. The slope is down 3 and right 1. That would be -3
A shopper wants to ensure he has enough cash to purchase a $390 grandfather clock, so he
asks a clerk what the total will be with the sales tax included. The clerk tells him the total will
be $429. What is the sales tax percentage?
Write your answer using a percent sign (%).
Answer: The sales tax percentage is 10%
Step-by-step explanation:
we find the price by take 429 - 390 = $39
Then we take 39 divided by 390 then timed a 100 = 10%
Wyatt wants to buy pears and apples to make a fruit tart. Pears cost $3.50 per pound and apples cost $3 per pound. How many pounds of fruit does he buy if he buys 3 pounds of pears and 2 pounds of apples? How many pounds of fruit does he buy if he buys x pounds of pears and y pounds of apples?
The pounds of fruit he buy if he buys 3 pounds of pears and 2 pounds of apples is $16.75.
In case he buys x pounds of pears and y pounds of apples, then he will have ($3.50x + $3.25y) number of fruits.
How can this be calculated?The concept that will be used is the concept of addition.
We were told that the Pears cost $3.50 per pound and apples cost $3 per pound from the question.
We can get the total pounds of fruits bought by multiplying the pounds of apples with cost per pound and then add it to the multiplication of the pounds of blueberries and cost per pound which can e expressed as:
($3.50 x 2) =$ 7
+ (3.25 x 3) = $9.75
Then add together as
($ 7 + $9.75 )= $16.75
Then if if he buys x pounds of pears and y pounds of apples, the number of pounds friuyt he buys will be
$3.50x + $3.25y
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Manuel bought 9 pounds of apples.
He has eaten 34 of a pound so far and has $15 worth of apples left. Write and solve an equation to find the cost of the apples per pound to the nearest dollar. How much did the apples cost per pound?
The cost of the apples per pound is $1.8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 42x = 10 is an equation.
From the question, We were given
9 pounds of apples.
Amount of apples eaten = 3/4 of a pound
This means,
1 pound - 3/4 pound = 1/4 pound left
Now,
The pounds of apples left:
= 8 + 1/4
= 33/4 pounds
33/4 pounds = $15
Multiply 4/33 on both sides.
1 pound = 4/33 x $15
1 pound = $1.8
Thus,
The cost of the apples per pound is $1.8.
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the hour property of the datetime structure stores the hour as an integer between 1 and 24. question 47 options: true false
False. The hour property of the datetime structure stores the hour as an integer between 0 and 23.
To support varied needs, three different property types are available:
1. Date — A day of the Gregorian calendar, without reference to a time zone or locale. The unit is a whole day, such as July 23, 2006.
2. Time of Day — A time of day, without reference to a time zone or locale. The unit is seconds, such as 15 seconds after 1:25 P.M.
3. Date Time — A date and time, stored internally to the millisecond if available, in a known time zone. For example 15.452 seconds after midnight on July 23, 2006 in London, U. K.
When presented with a DateTime value, a corresponding date and a time-of-day (in a specified time zone) can be determined.
However, the converse is not usually true: when starting with a Date and a TimeofDay value, multiple differing but "correct" DateTime values can be constructed, depending on assumptions about time zone, Daylight Savings Time, and other considerations. For example, when the date is January 1 in London, it can be December 31 in New York.
Thus, the given statement is false.
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What percent is 24 out of 36
Answer:
66.67
Step-by-step explanation:
(24*100)/36
Which of the following statements is INCORRECT?
A. FE = 58
B. DE = 58
C. x = 8
D. DF = 40
Answer: B
Step-by-step explanation:
It says DE is 40 so B is incorrect.
It costs chevy $20,000,000 to develop and market a new model of cars. The company sells each car for $25,000. If chevy wants to make a profit of more than $5,000,000, write an inequalty that represents this.(Inequality is this question i need help on)
The inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.
Given that, it costs chevy $20,000,000 to develop and market a new model of cars.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Let the number of cars sold be x.
So, selling price of cars is $25,000x
Profit =Selling price-Cost price
⇒ 25,000x-20,000,000≤5,000,000
Solve the inequality
Add 20,000,000 on both the sides of an inequality, we get
25,000x≤25,000,000
⇒ x≤25,000,000/25,000
⇒ x≤1000
Therefore, the inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.
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Leyla anda en bicicleta 81 millas cada semana, cuantas millas anda en 11 semanas
Answer:
891 millas en 11 semanas.
Step-by-step explanation:
81* 11 es igual a 891.
:)
Find the value of x.
The value of x is 5.
What is a polygon?A polygon is a flat object whose sides are made up of lines. It is a two-dimensional form called a polygon. The sides of regular polygons are all the same length.
Given the polygon and its exterior angle measures.
The sum of the measures of the exterior angles of a polygon is 360°, therefore, it follows:
(10x + 43)° + 66° + (12x + 39)° + (7x + 15)° + 52° = 360°
29x + 215° = 360°
29x = 360° - 215°
29x = 145°
x = 5
Hence, the value of x is 5.
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The sports store bought a baseball bat for $60 and sold it for $84. What percentage is the markup? 15 POINTS!!! WILL VOTE BRAINLIEST
Answer: 28.57% mark up.
Step-by-step explanation:
If you subtract 25.57% from 84.00 you get 60.00
It takes 3 days for Sonia to prepare the walls and paint her room. her friend Jennifer wants to help her on the job. If Jennifer does the same job entirely her own, she needs 5 days to complete it. How many days does it take if both Sonia and Jennifer work together on the job
The number of days it would take if both Sonia and Jennifer work together on the job is 1 7/8 or 1.875 days.
How long would it take them working together?Let the amount of time (in days) that it would take both Sonia and Jennifer working together to paint Sonia's room be t. Additionally, the amount of work done by both Sonia and Jennifer to paint her room in 1 day is given by:
The amount of work done by Sonia in 1 day is 1/x or 1/3.
The amount of work done by Jennifer in 1 day is 1/y or 1/5.
Therefore, the amount of work done by both Sonia and Jennifer working together to paint Sonia's room in 1 day is given by this mathematical expression:
Combined work done = 1/x + 1/y
Combined work done = 1/3 + 1/5
Combined work done = 8/15
Next, we would calculate the combined time as follows:
8/15 × t = 1
Combined time, t = 15/8
Combined time, t = 1 7/8 or 1.875 days.
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