Janice is at her favorite store checking out. She wants to buy a few shirts (s) that cost $14 each and a pair of jeans that cost $32. She wants to spend less than $88. How many shirts can she buy without going over her limit? Write an inequality to represent the scenario. Then, solve.

The simplified form of a rational equation [x + 1 / (x - 2)] / [x² / (x - 2) + 1] is equivalent to (x - 1) / (x + 2).

In this problem we need to determine the simplified form of a rational equation, whose form is:

R(x) = P(x) / Q(x)

Where:

The simplification process can be done by means of algebra properties. First, write the rational equation:

[x + 1 / (x - 2)] / [x² / (x - 2) + 1]

Second, expand the numerator and the denominator:

[(x² - 2 · x + 1) / (x - 2)] / [(x² + x - 2) / (x - 2)]

Third, simplify the fraction by algebra properties:

[(x² - 2 · x + 1) · (x - 2)] / [(x² + x - 2) · (x - 2)]

(x - 1)² / [(x + 2) · (x - 1)]

(x - 1) / (x + 2)

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Van 't Hoff's law, also known as the law of osmotic pressure, states that the magnitude of the osmotic pressure is directly proportional to the concentration of solute particles in a solution at a given temperature.

Van 't Hoff's law is an important concept in chemistry and thermodynamics. It explains the relationship between osmotic pressure and the concentration of solute particles in a solution. According to the law, the osmotic pressure of a solution is directly proportional to the number of solute particles in the solution, regardless of the type of solute. This means that if the concentration of solute particles in a solution increases, the osmotic pressure also increases, and vice versa. This law has numerous applications, particularly in the field of biology, where it is used to explain the movement of water and nutrients in and out of cells. For example, when a plant cell is placed in a hypertonic solution, water moves out of the cell, causing it to shrink. On the other hand, when a plant cell is placed in a hypotonic solution, water moves into the cell, causing it to expand. Understanding Van 't Hoff's law is therefore critical in many fields of science, particularly in biology, chemistry, and chemical engineering.

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The values of the given expressions are respectively,  -5.33, 5.33, -6,  -6,  6

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Here are the calculations for each expression:

1. (-8) x 2/3

  = (-8) x 2/3

  = -16/3

  = -5.33

2. (-8) x (-2/3)

   = (-8) x (-2/3)

   = 16/3

   = 5.33

3. -18/3 = -6

4. 18/(-3) = -6

5. (-18)/(-3) = 18/3

                 = 6

So, the values of each expression are -5.33..., 5.33..., -6, -6, and 6, respectively.

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Answer:

a= 77, b= 77, c= 103.

Step-by-step explanation:

a= 77 (vertically opposite)

b= a= 77 (corresponding angles)

c= 180-77

 = 103 (angles on a straight line)

Answer:

Step-by-step explanation:

A refrigerator is a cuboid, so W=3ft, L= 2.5ft, and H=6ft,

the volume of the refrigerator =W x L x H=3x2.5x6=45ft^3

The walls and other parts have 20ft^3 volume, so we have to minus them, so

volume left for food =45-20=25ft^3

Answer:

Step-by-step explanation:

Volume of the fridge = 3 × 2.5 × 6 = 45 ft³

then subtract the 20 ft³

45 - 20 = 25 ft³

Answer:

here are a total of 14 + 15 + 9 + 11 = 49 donuts.

The probability of selecting a maple donut is the number of maple donuts divided by the total number of donuts:

P(maple donut) = 14/49

So the probability of selecting a maple donut is 14/49, which can also be written as a fraction in simplest form: 2/7.

The area of the triangle is A = 10x¹⁰y³

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the area of the triangle be represented as A

Now , the base of the triangle is = 4x³y

Let the height of the triangle be = 5x⁷y²

And , The area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

Area of Triangle = ( 1/2 ) ( 4x³y ) ( 5x⁷y² )

On simplifying the equation , we get

Area of Triangle A = 10x¹⁰y³

Hence , the area of the triangle is A = 10x¹⁰y³

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The statement "a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its endpoints." is True because a line segment is defined as a part of a line that is bounded by two distinct end points and contains all the points on the line between those endpoints.

A line segment is a part of a line that has two endpoints and connects them. It is the shortest distance between two points and has a definite length, but no width or height. A line segment can be part of a straight line or a curved line.

A line segment is a section of a line that is defined by two distinct end points and includes every point on the line between them. It is the basic building block of geometry and can be used to measure distances, angles, and shapes.

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Answer: 8521.8 ÷ 8 = 1065.225

Step-by-step explanation: This is extremely simple all you require is a calculator with which you can plug in the variables

71 degrees Fahrenheit is equal to approximately 21.7 degrees Celsius using the conversion method formula.

To convert Fahrenheit to Celsius, you can use the following formula:

Celsius = (Fahrenheit - 32) x 5/9

Plugging in 71 degrees Fahrenheit, we get:

Celsius = (71 - 32) x 5/9

Celsius = 39 x 5/9

Celsius = 195/9

Celsius ≈ 21.7

Therefore, 71 degrees Fahrenheit is approximately 21.7 degrees Celsius.

The Celsius scale is also known as the centigrade scale, because it is divided into 100 degrees between the freezing and boiling points of water at standard atmospheric pressure.

On the Fahrenheit scale, there are 180 degrees between the freezing and boiling points of water. Therefore, each degree on the Fahrenheit scale is equivalent to 5/9 of a degree on the Celsius scale.

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The probability that the country is in the south Asia region is 7/87

The probability is a mathematical concept that tells us how likely an event is to occur.

The probability that a country is in South Asia given that it has high business startup costs is represented as P(A|B). This is calculated as follows:

P(A|B) = P(A and B) / P(B)

Where P(B) is the probability that a country has high business startup costs and can be calculated as:

P(B) = B / Total number of countries

And P(A and B) is the probability that a country is in South Asia and has high business startup costs, which can be calculated as:

P(A and B) = A / Total number of countries

So, substituting the values, total high startup cost is 87 and and, South Asia start up cost is 7, Then, the probability that the country is in the south Asia region is

=> 7/87

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Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.

The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.

The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.

Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.

Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.

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The centroid of this triangle is located at the point (6, 3).

The centroid of a triangle is the point where the three medians of a triangle intersect. Medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side.

The centroid is the "center of mass" or the "balance point" of the triangle. In other words, if the triangle were made of a solid material and suspended by a string attached to the centroid, it would balance.

To find the coordinates of the centroid of a triangle, we will use the following formula:

G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

Where G is the centroid, and (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the triangle's vertices.

So for the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0), we have:

G = (2 + 6 + 10)/3, (5 + 5 + 0)/3

G = (18/3, 10/3)

G = (6, 3.333...), which we can round to (6, 3)

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Using the law of tangents, the angle of the person’s eyes to the top of the building is approximately 36.87 degrees.

Angle  isc figure that can be described as the amount of rotation between two straight line not planes and angles is measured in degree with the full circle being 360°.

This can be calculated by setting up the following equation:

tan(angle) = 80 ft / (200 ft - 4 ft)

Solving for the angle, we get:

angle = tan-1(80 ft / 196 ft)

angle = tan-1(0.408163265)

angle = 36.87 degrees (to the nearest hundredth of a degree).

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Answer:

Step-by-step explanation:

Prim's algorithm is a greedy algorithm used to find the minimum spanning tree (MST) of a connected, undirected graph. It works by growing the tree one vertex at a time, always adding the vertex with the lowest weight edge that connects it to the growing tree. The algorithm starts with an arbitrary vertex, adds it to the tree, and then repeats the following steps until all vertices are in the tree:

Find the vertex that is not in the tree but has the minimum weight edge connecting it to the tree.

Add the vertex to the tree and mark it as visited.

Update the minimum weight edges connecting the vertices that are not yet in the tree to the growing tree.

This process continues until all vertices are in the tree, and the final result is the minimum spanning tree. The visualization of Prim's algorithm for minimum spanning tree can be represented graphically by showing the growth of the tree one vertex at a time, and highlighting the edges that are added to the tree in each step. The animation can be used to show how the algorithm is making decisions based on the weights of the edges and how it is gradually building the minimum spanning tree.

106$ money will be in the account after one year if the initial amount is $100.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

we have

Money in particular savings accounts increases by about 6% after a year.

we know that

The simple interest formula is equal to

A = P(1 +rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is the Number of Time Periods

Part 1) How much money will be in the account after one year if the initial amount is $100

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 100(1 +0.06)

A = 106$

Part 2) How much money will be in the account after one year if the initial amount is $50

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 50(1 +0.06)

A = 53$

Part 3) How much money will be in the account after one year if the initial amount is $200

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 200(1 +0.06)

A = 212$

Part 4) How much money will be in the account after one year if the initial amount is $125

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 125(1 +0.06)

A = 132.5$

Part 5) How much money will be in the account after one year if the initial amount is $x

in this problem we have

P = 100

r =6%

t = x year

substitute in the formula above

A = 100(1 + 0.06x)

A = 6x +100

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The value of the missing part of triangle DFC which is FD would be = 12.

Triangle ACD is congruent to triangle DFC

ED/AD = BC/AC

where;

ED = 9

AD = 15

BC= 12

AC=?

Make AC the subject of formula;

AC= 12×15/9

AC= 180/9

AC = 20

Using the adjacent values of the new and original sides of the triangle to calculate the scale factor.

That is ;

AD is congruent to FC = 15 = 9

But Scale factor = Dimension of the new shape ÷ Dimension of the original shape

Scale factor = 15/9= 1.67

To calculate FD using the scale factor;

1.67= 20/FD

FD= 20/1.67

FD= 12 (approximately)

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By proportion formulas and Pythagorean theorem, the length of side FD is approximately equal to 26.571.

Herein we find a geometric system formed by two similar right triangles (ΔABE, ΔACD) and a third distinct right triangle (ΔCDF). Two triangles are similar when both have congruent interior angles and sides that are not congruent though proportional.

Then, the system of similar triangles can be defined by following proportion formula:

AB / AE = AC / AD

x / 6 = (x + 12) / 15

15 · x = 6 · (x + 12)

15 · x = 6 · x + 72

9 · x = 72

x = 8

AB = 8

Now we determine the length of side CD by Pythagorean theorem:

CD = √(AC² - AD²)

CD = √[(x + 12)² + 15²]

CD = √(20² + 15²)

CD = 25

And the side FD is finally found by Pythagorean theorem:

FD = √(CD² + CF²)

FD = √(25² + 9²)

FD = √706

FD ≈ 26.571

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There are 24 children in the group.

To divide something into equal groups or to determine how many equal groups there are, use the division procedure. When equal groups are combined to find a total in multiplication, division is the opposite process.

If 6 pizzas were shared among 8 groups of children, each group would receive 6/8 = 3/4 of a pizza.

If each child got 3/8 of a pizza, then in a group of children each group would have 8 * 3/8 = 3 children.

Therefore, in total, there were 8 * 3 = 24 children.

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The conversion factor between kilometers per hour and miles per hour is 1.609344. Therefore, to convert from kmh to mph, we need to divide the speed in kmh by this conversion factor. 80kmh is equivalent to approximately 49.71 mph.

To find the speed in mph, we can use the following formula:

mph = kmh / 1.609344

Plugging in the given speed of 80kmh, we get:

mph = 80kmh / 1.609344

mph = 49.70969538

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The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

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Answer:B.Sample space

Step-by-step explanation:

The cost of each pineapple juice bottle at Store A is $0.90 more than at Store B.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The rate of the pineapple juice bottle at store A is given as,

Rate = $7.32 / 3

Rate = $2.44 per bottle

From the graph, the two points are (10, $15.40) and (20, $30.80). Then the rate is given as,

Rate = ($30.80 - $15.40) / (20 - 10)

Rate = $1.54

The difference between the rates is given as,

⇒ $2.44 - $1.54

⇒ $0.90

The cost of each pineapple juice bottle at Store A is $0.90 more than at Store B.

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The complete question is attached below.

Answer:

3v + 14w + 13

Step-by-step explanation:

The expression can be simplified as follows:

(3v + 8w + 19) + (6w - 6)

Combining like terms, we have:

(8w + 6w) and (19 - 6)

3v + 14w + 13

So the simplified expression is equal to 3v + 14w + 13.

Answer:13

Step-by-step explanation:

y=2x+7
x=3

2*3+7=13?

The solution is, the value of w is 13.

Here, we have,

We are given that the point (3,w) lies on the line y = 2x + 7.

This means that if we substitute x = 3 into the equation y = 2x + 7,

we will get the value of y at x = 3, which is equal to w.

so, we get,

Substituting x = 3 into the equation y = 2x + 7, we have:

y = 2(3) + 7

y = 6 + 7

y = 13

So, after simplification we get, w = 13

Therefore, the value of w is 13.

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The dimensions of the original mat are 27 inches by 21 inches.

A closed figure bounded by four sides in which opposite sides are equal is known as rectangle.

The area of rectangle is calculated by the given formula,

A = length x breadth

Length and width  of the rectangle can be found from the following expression after solving for x. The expression is given by :

outside area - inside area = 184 square inches

{(2·x - 3)·(x + 8)} - {(2·x - 7)·(x + 4)} = 184  (On substitute length and width expressions. Each area is the product of length and width.)

⇒{( 2·x² + 16·x - 3x - 24)} - {(2·x² +  8x  -7x -28) }= 184

⇒(2·x² + 13x - 24) - ( 2·x² + x -28) = 184

⇒ 12·x + 4 = 184 .................(On simplifying the expression)

⇒ 12·x = 180

⇒ x = 15

Then the original length of the mat is given by substituting value of x in outside length expression :

2·x - 3 = 2·15 - 3 = 30 - 3 = 27 inches

and the original width of the mat is given by :

x + 6 = 15 + 6 = 21 inches

Hence, the overall dimensions of the original mat are 27 inches by 21 inches.

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The cost of each battery would be Battery 1 = $195, Battery 2 = $80 and Battery 3 = $65.

Battery 1 (most expensive).= 3(X)

Battery 2 ( third battery) = 15+ X

Battery 3 (least expensive) = X

The total cost of the whole battery = $340

That is;

$340 = 3x + 15+ X + X

340 = 5x + 15

5x = 340 - 15

5x = 325

X = 325/5

X = $65

Therefore the cost of each battery;

Battery 1 = 3× 65 = $195

Battery 2 = 15 + 65 = $80

Battery 3 = $65

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Answer:

length = 21 in , width = 14 in

Step-by-step explanation:

the ratio of length : width = 3 : 2 = 3x : 2x ( x is a multiplier )

the area (A) of a rectangle is calculated as

A = length × width

given A = 194 , then

3x × 2x = 194

6x² = 194 ( divide both sides by 6 )

x² = 49 ( take square root of both sides )

x = [tex]\sqrt{49}[/tex] = 7

then

length = 3x = 3 × 7 = 21 in

width = 2x = 2 × 7 = 14 in

The perimeter of the given triangle in mixed fraction form is 4 1/2 ft.

A triangle is a closed, 2-dimensional shape with three straight sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. There are many types of triangles, including equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), scalene triangles (no sides or angles are equal), right triangles (one angle is a right angle, or 90), and obtuse triangles (one angle is greater than 90). Triangles are used in many areas of mathematics, science, and engineering.

Here,

The perimeter of the triangle:

=2 1/8+5/6+1 3/4

First, we need to convert all the mixed numbers into improper fractions:

2 1/8 = 17/8

5/6 = 10/16 = 15/24

1 3/4 = 7/4

Now we can add the three fractions:

17/8 + 15/24 + 7/4

To add these fractions, we need to find a common denominator. The smallest number that all three denominators divide into is 24. So we can rewrite the fractions with 24 as the denominator:

17/8 = 51/24

15/24 (already in the correct form)

7/4 = 42/24

Now we can add the numerators:

51/24 + 15/24 + 42/24 = 108/24

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 12:

108/24 = (9 × 12)/(2 × 2 × 2 × 3) = 9/2

=4 1/2 ft

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