Suppose you have two options from which to choose a pay raise for each of the next two years.

Option A: You received a $6,000 raise in year 1 and then 4% raise in year 2.
Option B: You receive a 4% raise for 1 year and then a $6,000 raise in year 2.

Which option will result in you making more money? Explain.

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]

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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Answer: B

Step-by-step explanation:

It says DE is 40 so B is incorrect.

Answer:

66.67

Step-by-step explanation:

(24*100)/36

Answer:

891 millas en 11 semanas.

Step-by-step explanation:

81* 11 es igual a 891.

:)

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.

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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By evaluating the function in x = 1, we will get:

f(1) = 4

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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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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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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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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The value of x is 5.

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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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

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.

The cost of the apples per pound is $1.8.

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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Answer:

Step-by-step explanation:

If a fair die is rolled 4 times, what is the probability, rounded to the nearest

Answer:

14. Original Price = $43.20

15. Original Price = $32.50

Answer:

47.46

Step-by-step explanation:

Answer: The answer is A. 47.46°.

Step-by-step explanation: Hope this helps.

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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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

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.

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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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%

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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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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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.

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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Answer: 28.57% mark up.

Step-by-step explanation:

If you subtract 25.57% from 84.00 you get 60.00

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'.

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.

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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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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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.

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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