1. Express 40 1/4% as a fraction (simplest form)



2. Express 65 5/8% as a fraction (simplest form)

A)

House 1 value is an exponential function.

House 2 value is a linear function.

B)

House 1:

f(x) = 253,980 x

House 2:

f(x) = 256,000 + 7000x

C)

House 1 will have the greatest value.

The significant difference in the value of either house after 45 years is $168844

The value of house 1 after 45 years:

f(45) = $739844

The value of the house 2 after 45 years:

f(45) = $571000

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

House 1:

The value of the hours is described by an exponential function.

There is an increase of 2% per year.

f(x) = 253,980 x [tex]1.02^x[/tex]

Where x is the number of years.

House 2:

The value of the hours is described by a linear function.

There is an increase of $7000 per year.

f(x) = 256,000 + 7000x

Where x is the number of years.

Now,

For x = 45,

f(45) = 253,980 x [tex]1.02^x[/tex]

f(45) = 253,980 x [tex]1.02^{45}[/tex]

f(45) = $739843.74

f(45) = $739844 ____(1)

f(x) = 256,000 + 7000x

f(45) = 256,000 + 7000 x 45

f(45) = 256,000 + 315000

f(45) = $571000 ______(2)

From (1) and (2),

House 1 will have the greatest value.

The significant difference in the value of either house after 45 years

= $739844 - $571000

= $168844

The value of house 1 after 45 years:

f(45) = $739844

The value of the house 2 after 45 years:

f(45) = $571000

Thus,

The Part  A, Part B, and Part C are given above.

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If the daily prices are $1.50 for children and $2.00 for adults , then the number of adults swam at public pool is 302  and number of children who swam at public pool is 258  .

let the number of children swam at swimming pool be = c ;

let the number of adults swam at swimming pool be = a ;

the total number of person who used the swimming pool is = 560 ;

the equation is ⇒ c + a = 560 ...equation(1) ;

the price for 1 child is $1.50 and price for 1 adult is = $2 ;

the total money collected can be written as :

= (price of children tickets)×(number of children that swam)+(price of adults tickets)×(number of adults that swam) ;

⇒ 1.5c + 2(560 - c) = 991  ;

⇒ 1.5c + 1120 - 2c = 991 ;

⇒ -0.5c = 991 - 1120  ;

⇒ -0.5c = -129 ;

⇒ c = 129/0.5 = 258 ;

So , adults (a) = 560 - 258 = 302 ;

Therefore , the number of adults are 302 and number of children are 258 .

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Solution of the given inequalities based on integer 'n' is given by :

a. Value of 'n' for 15n > 12n + 18 is n > 6.

b. All the possible integer value of 'n' for -2 <n + 3 ≤ 4 are -4, -3, -2, -1, 0.

a. Solution of the expression 15n > 12n + 18 is :

15n > 12n + 18

Subtract 12n from both the sides ,

⇒ 15n - 12n >  12n - 12n + 18

⇒ 3n > 18

Divide by 3 from both the sides,

⇒ 3n/3 > 18 /3

⇒ n > 6

b.  -2 <n + 3 ≤ 4

where 'n' is an integer

⇒ -2 -3 < n + 3 -3 ≤ 4 -3

⇒ -5 < n < 1

All the possible values of 'n' smallest to largest are:

-4, -3, -2, -1, 0.

Therefore, the answer of the questions based on integers 'n' are :

a. 15n > 12n + 18 ⇒ n > 6.

b. All possible integers of 'n' are -4, -3, -2, -1, 0.

The above question is incomplete , the complete question is:

a) Solve 15n > 12n + 18

b) n is an integer and -2 <n + 3 ≤ 4

Write down the possible values of n, from smallest to largest.

All values must be separated by commas. Eg. .... , .... , .....

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17 people were fans of the Chiefs or Royals but not Sporting KC.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. The basic operations of algebra include addition, subtraction, multiplication, and division, as well as the manipulation of exponents and roots.

Have given ,

26 people were fans of the Kansas City Chiefs

36 people were fans of the Kansas City Royals

18 people were fans of both the Chiefs and the Royals

13 people were fans of the Chiefs and Sporting KC

20 people were fans of the Royals and Sporting KC

6 people were fans of none of the teams

The principle of inclusion and exclusion says that the number of people who are fans of the Chiefs or the Royals but not Sporting KC is:

(26 + 36) - (18 + 13 + 20) + 6 = 62 - 51 + 6 = 17

So, 17 people were fans of the Chiefs or Royals but not Sporting KC.

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When solving absolute value inequalities involving the greater than symbol (>) or greater than or equal to symbol (≥), we have to consider two cases absolute value expression greater than the constant and less than the constant.

The absolute value expression is greater than the constant:

|x| > c or |x| ≥ c

In this case, we can split the solution set into two parts: x < -c and x > c. The solution is all real numbers less than -c and all real numbers greater than c.

The absolute value expression is less than the constant:

|x| < c or |x| ≤ c

In this case, we can split the solution set into two parts: -c < x < c. The solution is all real numbers between -c and c, excluding -c and c.

For example, consider the inequality |x| > 2. The solution is x < -2 or x > 2, so the solution set is {x | x < -2 or x > 2}.

--The question is incomplete, answering to the question below--

"When solving inequalities that involve absolute value, there are two cases to consider for inequalities involving >. Explain"

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The histogram's smallest and greatest ranges, 0 to 4.9 and 45 to 49.9, respectively, represent the percentage of residents in each state and the District of Columbia who identify as Hispanic or Latino.

The histogram's smallest and greatest ranges, 0 to 4.9 and 45 to 49.9, respectively, represent the percentage of residents in each state and the District of Columbia who identify as Hispanic or Latino.

Percentage refers to quantifying anything per 100, as the word indicates.You can get the percentage, for instance, by dividing your score by 100.

Given: The histogram summarizes the proportion of persons who identify as Hispanic or Latino in each state and the District of Columbia,

The x-axis displays the population's frequency, while the y-axis displays the population's Hispanic or Latino proportion.

Consider the graph to determine the narrowest range possible,

The smallest possible range = 0 - 4.9

Calculate the broadest range feasible while keeping in mind the graph,

The largest possible range = 45 - 49.9

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Answer: x=6, y=-6

Step-by-step explanation:

-4x + -2y = -12 (a)

4x + 8y = -24 (b)

(a)+(b)= -4x+4x+8y+(-2y)=-12+(-24)

                                 6y= -36

                                   y=-6

put y=-6 into formula (a)

-4x+12=-12

-4x= -24

x=6

Answer:

I'm doing this to complete one of the steps. good luck my friend

Step-by-step explanation:

The sum of money that can be divided between two parts = Rs 200

Adding three times the smaller part to half of the larger part then its will always be less than Rs 200

Let The smaller part = Rs S

The larger part = Rs L

The sum of parts = Rs 200

Larger + Smaller = Rs 200

L+S=200---------------(1)

And, Adding three times the smaller part to half of the larger part then the result will always be less than Rs 200

(3S+1/2× L)-200 = 0

3S+ L/2=200                    

6S+L=400 --------(2)

Solving eq 1 and eq 2

(6S+L)-(L+S)=400 - 200

(6S-S )+(L-L )=200

5S+0=200

S = 200/4

∴Smaller = S=Rs40

Now, Plug the value of S into eq 1

L+S = Rs 200

L+40 = Rs 200

L = 200 - 40

L = Rs 160

Larger = L= Rs160

Hence, the larger part is Rs 160 and the smaller part is Rs 40      

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When the figure is dilated by a scale factor of 3, the original coordinates of P are (1,2).

A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. The study of algebraic equations on graphs is known as coordinate geometry. Plotting points, lines, and curves on an x and y axis is an example of coordinate geometry. Make corrections.

Here,

scale factor=3

dilated point=(3,6)

original coordinates=(3/3,6/3)

=(1,2)

The original coordinates of P are (1,2) when figure is dilated by a scale factor of 3.

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The charge to play two games is $19 and the charge to play six games is $49.

The question states the expression to calculate the charge. The expression has a variable x, which indicates the number of games. Thus, keeping the value of x in the formula to find the charge.

Calculating a part -

t = 7.5 × 2 + 4

Performing multiplication on Right Hand Side of the equation

t = 15 + 4

Performing addition on Right Hand Side of the equation

t = 19

Thus, the charge to play two games is $19.

Calculating b part -

t = 7.5 × 6 + 4

Performing multiplication on Right Hand Side of the equation

t = 45 + 4

Performing addition on Right Hand Side of the equation

t = 49

Thus, the charge to play six games is $49.

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Answer:

The correc answer is Option A.

Answer:

x = 80

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Note that x is being divided by 4. To isolate x, do the opposite. Multiply 4 to both sides of the equation:

[tex]\frac{x}{4} = 20\\(\frac{x}{4} ) * 4 = (20) * 4\\x = 20 * 4\\x = 80[/tex]

x = 80 is your answer.

~

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The percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

[tex]$$\begin{aligned}& \mu=\$ 35,000 \\& \sigma=\$ 8,000\end{aligned}$$[/tex]

we need to calculate probability for

[tex]& P(24000 < x < 46,000)\\ \\& =P\left(\frac{24000-35,000}{8,000} < \frac{x-\mu}{\sigma} < \frac{46,000-35,000}{8000}\right)\\ \\& =P(-1.37 < z < 1.315) \\\\& =P(z < 1.37)-P(z < -1.37)[/tex]

[tex]& =0.9147-0.0853[/tex]          [tex]=0.9162-0.0838 \\[/tex]

[tex]& =0.8294[/tex]    [tex]=0.8324 \\[/tex]

[tex]& =82.94 \% \\[/tex]    [tex]& =83.09[/tex]

Therefore, the percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.

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The measure of FD = 16.001 units

Consider following diagram.

We can observe that ΔABE and ΔACD are similar triangles.

By definition of similar triangle the sides of ΔABE and ΔACD must be in proportion.

AB/AC = AE/AD

Let us assume that AB = x

x/(x + 12) = 6/15

15x = 6(x + 12)

15x = 6x + 72

9x = 72

x = 8

So, AB = 8 units

And AC = 12 + 8

       AC = 20 units

Consider right triangle ΔACD

Here, AC = 20, AD = 15

Using Pythagoras theorem,

AC² = AD² + CD²

CD = [tex]\sqrt{AC^2 - AD^2}[/tex]

CD = [tex]\sqrt{20^2 - 15^2}[/tex]

CD = 13.23 units

For right triangle CDF,

Using Pythagoras theorem,

FD² = CD² + CF²

FD² = 13.23² + 9²

FD = 16.001

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An  inequality represents the situation is: t < 3

The correct answer is an option (a) t < 3

We know that an inequality is a mathematical statement that represents the inequalities between two algebraic expressions with two variables .

It is an unequal relation between two algebraic expressions.

The symbols used between the expression:

less than ‘<’,

greater than ‘>’,

less than or equal to ‘≤’

greater than equal to ‘≥’,

Let t represents the distance between Tori's house and the school.

Tori lives less than 3 miles from the school.

This means, the distance t is less than 3 miles

so, we get an inequality t < 3

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The formula for a cube's volume is L * W * H.But because it is a cube, its length, breadth, and height are all equal and correspond to one of the cube's edges. The answer is 2.7 equals 3 centimeters.

The formula for a cube's volume is L * W * H.But because it is a cube, its length, breadth, and height are all equal and correspond to one of the cube's edges.Finding the cube root of the volume will allow you to determine the length of a cube's edge.

A cube's edge measures 3 centimeters in length and has a volume of 27 cubic centimeters.

Six square faces make up the three-dimensional shape of a cube.

It has 12 edges and 8 vertices.

Volume of a cube is equal to the length of an edge3

In order to calculate the length of an edge, the cube root of the cube's volume must be known if the cube's volume is given.

Find the cube root of 27 to get the length of an edge.

2.7 equals 3 centimeters

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The points that lie on the y-axis of the graph have a x-coordinate of zero.

Hence the format of the point is of:

(0,y).

The general format of an ordered pair is given as follows:

(x,y).

For the x-coordinate, we have that:

On the y-axis, the point does not move horizontally, just vertically, hence the points that lie on the y-axis of the graph have a x-coordinate of zero, and the format of the point is given as follows:

(0,y).

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The values of y are 0, 3 and 7/4 respectively. The solution has been obtained by using the substitution method.

What is substitution method?

The substitution approach is one of the algebraic methods for resolving simultaneous linear equations. It entails swapping any variable to change its value from one equation to another. By doing this, two linear equations are merged into one straightforward equation with one variable.

We are given a rule which is that y= x-1/4

Various values of x are given

So, in order to find the values of y, we will use the substitution method.

When x=1/4, then

⇒y=1/4-1/4

⇒y=0

When x=13/4, then

⇒y=13/4-1/4

⇒y=12/4

⇒y=3

When x=2, then

⇒y=2-1/4

⇒y=8/4-1/4

⇒y=7/4

Hence, the values of y are 0, 3 and 7/4 respectively.

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The complete question has been attached below

The old box of cereal contained 24.5 ounces.

Take 30% of the original box of cereal.

To find 30% of a number, multiply the number by 0.3.

35 ounces x 0.3 = 10.5 ounces

Subtract 10.5 ounces from 35 ounces.

35 ounces - 10.5 ounces = 24.5 ounces

Answer: The old box of cereal contained 24.5 ounces.

When you take a single number and multiply it by several, you are multiplying. A 5 multiplied by a 4 results in 20 (5 + 5 + 5 + 5). We multiplied the number five by four times. Due to this, multiplication is occasionally referred to as "times."

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The difference between the number of expected outcomes and the number of actual outcomes is 1/30.

What is the difference?

The expected outcome of flipping heads and rolling a number less than 3 = probability of flipping a head x probability of rolling a number less than 3

Probability of flipping a head = number of sides that are heads / total number of sides = 1/2

Probability of rolling a number less than 3 = number of sides that are less than 3 / total number of sides = 2/6 = 1/3

The expected outcome = 1/2 x 1/3 = 1 /6

The difference =

[tex]\frac{1}{6} - \frac{2}{15}[/tex]

[tex]\frac{15 - 12}{90}[/tex] = [tex]\frac{3}{90}[/tex] = [tex]\frac{1}{30}[/tex]

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The negation of the following statements are a. R: Ron did not go to school. b. S: A triangle does not have 3 sides. c. T: x ≠ 9 d. U: 20 is not a multiple of 3.

It's vital to know the opposite of a particular mathematical statement from time to time in mathematics. This practice is known as "negating" a claim. Remember that if a claim is true, then the negation must be false.

The negation of the following statements is:

a. R: Ron did not go to school.

b. S: A triangle does not have 3 sides.

c. T: x ≠ 9

d. U: 20 is not a multiple of 3.

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The complete proof of the parallel lines k and l is:

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two lines are parallel

Then go ahead to use the angle theorems and transitive properties to complete the proof

So, the complete proof is:

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Yes, it is possible that you have to travel a greater distance to reach point b than to reach point a.

A straight line is a geometric concept that refers to a line that extends indefinitely in two directions without any curvature. It is the shortest distance between two points in Euclidean space and it is represented by an equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

As both destinations, A and B are measured as the crow flies, or in a straight line, and you are able to travel only in straight lines along the main directions (north, south, east, and west), it is possible that the path to point B includes more turns or obstacles, such as buildings or rivers, that require you to travel further in order to reach the destination.

That's why it is possible that you have to travel a greater distance to reach point B than to reach point A.

Therefore Yes, it is possible that you have to travel a greater distance to reach point b than to reach point a.

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(a) [tex]\frac{x}{x^2 + x + 3}[/tex] will be a continuous function in interval (- ∞ ,  ∞), (b)   [tex]\frac{x + 7}{\sqrt{x} }[/tex] will be a continuous function in interval (0,  ∞), and (c) [tex]x\sqrt{x + 6}[/tex] will be a continuous function in interval [-6,  ∞).

(a)  [tex]\frac{x}{x^2 + x + 3}[/tex]

x² + x + 3 will never be zero.

so it will be a continuous function all the time or in the interval (- ∞ ,  ∞).

(b)  [tex]\frac{x + 7}{\sqrt{x} }[/tex]

in this function x cannot be negative or zero.

so the function will be a continuous function for x >0

or in the interval (0,  ∞)

(c)  [tex]x\sqrt{x + 6}[/tex]

for this function, the value of  (x + 6) cannot be a negative value.

or x + 6 >=0 or x >= -6

so the function will be continuous in the interval [-6,  ∞)

Therefore, (a) [tex]\frac{x}{x^2 + x + 3}[/tex] will be a continuous function in interval (- ∞ ,  ∞), (b)   [tex]\frac{x + 7}{\sqrt{x} }[/tex] will be a continuous function in interval (0,  ∞), and (c) [tex]x\sqrt{x + 6}[/tex] will be a continuous function in interval [-6,  ∞).

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The complete question is:

describe the interval(s) on which the function is continuous. (enter your answer using interval notation.)

(a)  [tex]\frac{x}{x^2 + x + 3}[/tex]

(b)  [tex]\frac{x + 7}{\sqrt{x} }[/tex]

(c)  [tex]x\sqrt{x + 6}[/tex]

Answer: x = 3

Step-by-step explanation:

Set the two equal to each other.

-5 (2x+1) = -35

-5 x 2x = -10x , -5 x 1 = -5

-10x -5 = -35

Add 5 to both sides.

-10x = -30

Divide both sides by -10.

x = 3

Answer:

RT = 17.9

RS = 9.7

m<T = 33°

Step-by-step explanation:

sin R = opp/hyp

sin R = ST/RT

sin 57° = 15/RT

RT = 15/sin 57°

RT = 17.9

cos R = adj/hyp

cos R = RS/RT

cos 57° = RS/17.88544939

RS = 17.88544939 × cos 57°

RS = 9.7

m<R + m<S + m<T = 180°

57° + 90° + m<T = 180°

m<T = 33°

The region is function determining the total sales and the number of boxes covered to make the desired sale. The inequality representing the function is f(b) ≤ 3.75b + 25.

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 values and determine whether they are less than or higher than.

a. The region represents the function determining the total sales and the number of boxes covered in order to make the desired sale.

b. The inequality that represents the area under the graph up until the point of intersection is given by:

f(b) ≤ 3.75b + 25

The less than equal to sign is used, as the area used lies below the curve.

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Answer:

7/20

Step-by-step explanation:

Answer:

The shaded area is equal to [tex]\frac{7}{20}[/tex]

Step-by-step explanation:

The full circle has a value of 1.

We know that 1/4 and 2/5 of the circle are not shaded and we are asked for the shaded area.

We can use 1-(1/4)-(2/5) to find the shaded area.

1-1/4=3/4

3/4-2/5=15/20-8/20=7/20

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After divide, the value of quotient is 23.4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 159.12 divided by 6.8

Now, We can divide the numbers as;

⇒ 159.12 divided by 6.8

⇒ 159.12 ÷ 6.8

⇒ 23.4

Thus, The value of quotient = 23.4

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