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The number of stores in each level of the shopping mall are 56 stores.

An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let x represent the number of stores on each level.

A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:

(4 × x) = 226

4x = 226

Divide

x = 226 / 4

x = 56.5

There are about 56 stores per level.

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According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

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The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)

In this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:

cos 3x / (sin x · cos x)

Second, use trigonometric formulas:

cos (x + 2x) / (sin x · cos x)

(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)

cos 2x / sin x - sin 2x / cos x

csc x · cos 2x - sec x · sin 2x

The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.

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On solving the given problem, The value of the median of the distribution is closest to 5.

In order to visualize data, a histogram is used. The width and area of each rectangle in the histogram are proportional to the class interval and data frequency, respectively.

When a dataset is sorted in either ascending or descending order, the median is the value that appears in the middle of the dataset.

Ascending numbers are listed in the following order:

2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9

Median is -  5

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Factors over the complex numbers for the given expression y⁴ + 14y² + 49 is equal to [ ( y + i√7) (y - i√7 ) ]² .

As given in the question,

Given expression is :

y⁴ + 14y² + 49

Simplify the given expression to get the factors of it , we get ,

y⁴ + 14y² + 49

= y⁴ + 2 ( 7 )y² + ( 7 )²

= ( y² + 7 )²

Now convert the factors into complex numbers ,

= [ y² - (-1)(√7)²]²

We know that ( -1 ) = i²

= [ y² - ( i√7)² ]²

= [ ( y - i√7 )( y + i√7) ]²

Therefore, the complex numbers factors of the given expression is equal to [ ( y - i√7 )( y + i√7) ]².

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The number of miles Melissa travelled that night is approximately 667 miles.

Melissa is planning to rent out a limo for her friends and herself for prom.

Limousine rates charge a 450 flat rate plus an additional 30 cents for every mile travelled.

Melissa aid the limousines driver $200 for prom. The number of miles she travel can be calculated as follows;

using equation,

y = 450 + 0.3x

where

Therefore,

200 + 450 = 450 + 0.3x

650 = 450 + 0.3x

650 - 450 = 0.3x

200 = 0.3x

x = 200 / 0.3

x = 666.666666667

x = 667 miles

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The three points which correctly represents a solution to the given inequality are;

It follows from the task content that the points which are solutions to the given inequality bare to be determined.

Since the given inequality as in the task content is; y > 4 x - 3.

By evaluating the inequality at one x-value of x = 1.

We have ;

y > 4 ( 1 ) - 3

y > 4 - 3

y > 1.

Therefore, the possible values of y which are greater than 1 are; 2, 3, and 4.

On this note, it is correct to conclude that the points which are solutions to the given inequality are; ( 1, 2 ), ( 1, 3 ) and ( 1, 4 ).

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Answer:

-3x, where x is the number of yards lost on the first play.

Step-by-step explanation:

The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

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Answer: 6 and 3/8

Step-by-step explanation:

2 3/4 + 3 5/8=?

Find LCM of the 2 numbers

LCM is 8

Multiply 2 to 3/4 in 2 3/4

2 6/8 + 3 5/8

Add whole numbers

2 + 3 = 5

Add the fractions itself

6/8 + 5/8 = 11/8

11/8 = 1 3/8

Combine whole numbers and fractions

5 + 1 + 3/8

6 3/8

The value of angle Z= 39°, line XY= 21.9 and line XZ= 34.7

A right-angled triangle is a type of triangle which as one of it's sides equal to 90°. Since angle Y is 90°, then ∆ABC is a right-angled triangle

angle Z = 180-(90+51)

angle Z= 180- 141= 39°

using trigonometry ratio

tan51 = 27/XY

XY= 27/tan51

XY= 27/1.2

XY= 21.9

using Pythagoras theorem

XZ²= 21.9²+27²

XZ²= 1208.6

XZ= √1208.6

XZ= 34.7

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We can write the given statement as inequality as -

-(x/9) < 12

Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.

Reversal property : If (a > b) then (b < a) and  if (a < b) then (b > a).

Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).

The general equation of a straight line is y = mx + c

Other possible equations of lines are -

We have the following statement -

"the quotient of a number and three minus twelve is less than 12".

We can write the inequality as -

-(x/9) < 12

Therefore, we can write the given statement as inequality as -

-(x/9) < 12

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The probability that exactly one of the next four calls results in a reservation being made is 40.75%

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

A random call to their reservation phone line results in a reservation being made is 0.31

Now, we find

Exactly one call gets resevervation = 4 * (1-0.31)3(0.31)

= 0.4075 = 40.75%

Now we can simulate an experiment by using random numbers from 0 to 100,000 as probability values between 0 and 31,000 are p to reservation otherwise they don't.

Hence, the probability that exactly one of the next four calls results in a reservation being made is 40.75%

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The perimeter of the new enlarged garden whose side length lengthened by factor of 8 is equal to 576ft.

As given in the question,

Shape of the garden is right triangle

Let 'x' , 'y' , and 'z' represents the three sides of the triangle shape garden.

Perimeter of the garden = 72 ft

⇒ x + y + z = 72 ft  __(1)

Now, length of the each sides of the new garden is lengthened by factor of 8.

Sides of the new garden are '8x' , '8y' , and '8z'

Perimeter of the new garden = 8x + 8y + 8z

⇒ Perimeter of the new garden = 8 ( x + y + z )

⇒ Perimeter of the new garden = 8 (72)

⇒ Perimeter of the new garden =  576 ft

Therefore, perimeter of the new garden is equal to 576ft.

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Answer: 122 12/46 OR 122 R 12 OR 1252.69565

Step-by-step explanation:

Answer: It is A

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

First, divide 7.30 by 73 to find how much 1 text message costs. We get 0.1. Next, divide 10.20 by 0.1, which gives us the final answer of 102.

Answer:

99 text messages

Step-by-step explanation:

        $7.50 = 73

           ÷73    ÷73

         ---------------------

amount to  =   $0.102739726

send one text

0.102739726x = $10.20

÷0.102739726    ÷0.102739726

-------------------------------------------------

x ≈ 99.28

I hope this helps!

Answer:

272 bison

Step-by-step explanation:

y(5)=240[tex](1+0.025)^{5}[/tex]

y(5) = 271. 5 bison ≈272 bison

The pair of lines given are parallel to each other.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following pair of lines -

y = 5x + 12

y = 5x - 1.3

Since the slope of lines are same, both of these lines are parallel to each other.

Therefore, the pair of lines given are parallel to each other.

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Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

Answer:

103

Step-by-step explanation:

angle 1 and angle 5 are the same as each other.

South direction was she facing.

What does the word "direction" mean?

Direction can refer to the way something moves, the way you must go to get somewhere, the way something is beginning to take shape, or the direction you are facing.

                                  When you turn right rather than left, that is an illustration of direction.

Which forms of direction are there?

There are only four genuine directions north, south, east, and west. Northeast, Southeast, Southwest, and Northwest are the directions on the compass that are located midway between these cardinal points.            

                                                 These transitional locations are referred to as intermediate directions. Maps and globes only display east-west and north-south lines.

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The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here, perimeter =2(x-2+5)

= 2(x+3)

= 2x+6 units

Area of a rectangle =length × width

= (x-2) × 5

= 5x-10 square units

Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

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1) 16.7% probability of rolling 10+.

2) 50% probability an odd number is rolled.

3) 7 is the most likely total result.

These are all the possible outcomes:

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes

1) what is the probability of rolling 10+?

There are 6 possible outcomes in which 10+ is rolled:

(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).

So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.

2) what is the probability of rolling an odd number?

There are 18 possible outcomes in which an odd number is rolled.

So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.

3) what is the total that is most likely to result?

There are 6 outcomes in which 7 is rolled.

So 7 is the most likely total result.

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The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.

A geometry translation is an isometric transformation, meaning that the original figure and the image are congruent.

Given that, WXY is the image of RST after a translation 3 units up.

As we know in translation, both figures are congruent so, we have,

WX = RS

XY = ST

WY = RT

And

∠ R = ∠ W

∠ S = ∠ X

∠ T = ∠ Y

Hence, The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.

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Answer:

[tex]x=1.45[/tex]

Step-by-step explanation:

[tex]2\left(x-4 \frac{1}{2} \right)=-6.1 \\ \\ 2\left(x-\frac{9}{2} \right)=-6.1 \\ \\ 2x-9=-6.1 \\ \\ 2x=2.9 \\ \\ x=1.45[/tex]

Answer:

Website A is cheaper by 29 cents

Step-by-step explanation:

A

49.95 + 4.39 = 54.34

B

47.68 + 6.95 = 54.63

54.63 - 54.34 = 0.29

Answer:

the difference is 0.29 cents

website A is cheaper

Step-by-step explanation:

(47.68 + 6.95) - (49.95 + 4.39)

54.63 - 54.34 = 0.29

Answer:

-12x + 2

Step-by-step explanation:

-6+8 = 2

-3x - 9x = -12x

-12x + 2

Answer:

Step-by-step explanation:

-12x+14 i believe

The reduced form of the fraction would be 2.8/2.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

Given that a/b is a fraction and when it is divided by 100 it will result in 0.014.

So we can write,

            [tex]\frac{\frac{a}{b} }{100}=0.014\\\\ \frac{a}{b}=0.014*100\\\\\frac{a}{b}=1.4\\[/tex]

Now 1.4 can be written as

       a/b = 2.8/2

Hence, the reduced form of the fraction would be 2.8/2.

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