Find the area of the rectangle.
The bottom one

Any pair of real numbers or algebraic expressions that are equivalent by the symbols ‘<’, ‘>’, ‘≤’ or ‘≥’ constitute an inequality.

A mathematical concept used to compare quantities is inequality. By highlighting the area that the inequality pertains to, we can graph the inequality on a number line.

Let's examine the number line graphing of inequality. Look at the illustration below, which shows the following disparities on a number line:

x ≥ 5, x > 5, x ≤ 5, and x < 5.

It should be noticed that if the inequality indicates that a certain number is included, we mark a filled circle on that specific number; nevertheless, if the inequality indicates that a certain number is excluded, we mark an empty circle on the number.

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The number of ways in which the prizes are allocated is 67,525.

Combinations are the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

Given that

Number of customers = 75

Number of prizes = 3

And, the value of the gift card = $10

Based on the above information,

The number of ways in which the prizes are allocated is shown below:

=⁷⁵C₃

=[tex]\frac{75!}{(3!*(75-3)!}[/tex]

After solving this the number of ways that came is 67,525

Hence, the number of ways in which the prizes are allocated is 67,525

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"Johann Sebastian Bach is the greatest of all the Baroque composers"

a proposition, The proposition is a meaningful statement. without any question,

Mathematical reasoning techniques are laid forth in the rules of mathematical logic. The father of logical reasoning was the Greek philosopher Aristotle. The theoretical foundation for many branches of mathematics, and hence computer science, is provided by logical reasoning. It is used in the design of computing devices, artificial intelligence, the definition of data structures for programming languages, and many other practical areas of computer science.

Statements to which the truth values "true" and "false" can be given are the focus of propositional logic. The objective is to evaluate these claims, either singly or collectively.

"Johann Sebastian Bach is the greatest of all the Baroque composers"

a proposition

The proposition is a meaningful statement. without any question,

in our case, Johann is the greatest composer, is truth statement,

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1. After 32 minutes the two pools will have the same amount of water.
2. 2,280 liters of water will be in each pool when they have the same amount.

Let's call the time in minutes when the two pools have the same amount of water "t". Getting into variables here.

At time t, the first pool will have 1272 + 31.5t liters of water, and the second pool will have 1600 + 21.25t liters of water.

For the two pools to have the same amount of water, we need:

1272 + 31.5t = 1600 + 21.25t

10.25t = 328

t = 32 minutes

I underlined all the answers if you don't want to read the entire thing, lol.

Question 1: So, 32 minutes after starting, the two pools will have the same amount of water.
Question 2: The amount of water in each pool will be:

1272 + 31.5 * 32 = 1600 + 21.25 * 32 = 1600 + 680 = 2,280 liters.

555

Step-by-step explanation:55

The minimum amount of glass used for the exterior  615340.84 m ²

We must calculate the lateral area which is given by:

A = (1/2) * pb * Ap

Where,

pb: perimeter of the base

Ap: Apotema

Calculating the apothem we have:

Ap = root ((646/2) ^ 2 + (350) ^ 2)

Ap = 476.27 feet

Calculating the perimeter of the base we have:

pb = 4 * (646)

pb = 2584 feet

Substituting values:

A = (1/2) * pb * Ap

A = (1/2) * (2584) * (476.27)

A = 615340.84 m ^ 2

The minimum amount of glass used for the exterior is:

A = 615340.84 m ²

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Correct question:

The luxor hotel in las vegas is a square base pyramid that is 646 feet wide at the base and 350 feet tall. if the outer walls of the hotel are covered in glass, what was the minimum amount of glass used for the exterior?

The confidence interval is (0.732, 0.318).

Total samples = E = 36

Number of outcomes  = 12

Calculating the probability

= 12/36

= 0.333

The probability that a population parameter would fall between a set of values for a specified percentage of the time is described by a confidence interval. Analysts typically employ confidence intervals that cover 95% or 99% of projected observations.

Value of z for 95% confidence interval = 1.96

Interval = p ± z ( p√ 1 - p/ E)

Taking positive sign

= 0.333 + 1.96 ( 0.333√ 1 - 0.333/ 36)

= 0.318

Taking negative sign

= 0.333 - 1.96 ( 0.333√ 1 - 0.333/ 36)

= 0.732

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Carrie has 1000 jellybeans in the box.

The volume of Carrie's box is 8 times larger than the volume of Bert's box because 2 x 2 x 2 = 8. Thus, Carrie's box can hold 8 times more jellybeans than Bert's box, which means it can hold approximately 8 x 125 = 1000 jellybeans.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Finding the volume of an object can help us to determine the amount required to fill that object, like the amount of water needed to fill a bottle, an aquarium or a water tank.

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Carrie has 1000 jellybeans in the box.

The volume of Carrie's box is 8 times larger than the volume of Bert's box because 2 x 2 x 2 = 8. Thus, Carrie's box can hold 8 times more jellybeans than Bert's box, which means it can hold approximately 8 x 125 = 1000 jellybeans.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Finding the volume of an object can help us to determine the amount required to fill that object, like the amount of water needed to fill a bottle, an aquarium or a water tank.

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Answer:

unlikely

Step-by-step explanation:

25% of the cookies are chocolate chip, so the other 75% would be oatmeal raisin and sugar cookies. 0.25 is equal to 25%, so it is unlikely you will get a chocolate chip cookie.

The simplification of the expression are :

a. 1/-5z

b. -5b/3c

c. 2a/9x

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

A. To simply 2xy/-10xyz

we divide through by 2xy which is the common factor

= 1/-5z

B. -15ab/9ac

we divide through by 3a, which is the common factor

= -5b/3c

C. -6ac/-27cx

we divide through by -3c, which is the common factor

= 2a/9x

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The function f is increasing for x > 3/2.

To determine the values of x for which the function f is increasing, we need to find the critical points of f, which are the values of x where the function changes from increasing to decreasing or vice versa.

The first step is to find the derivative of f:

f'(x) = (2x - 3)e-x

Next, we need to find the critical points by setting f'(x) = 0 and solving for x:

(2x - 3)e-x = 0

2x - 3 = 0

x = 3/2

This is the only critical point of f. To determine the behavior of f near this critical point, we need to find the second derivative of f:

f''(x) = (2 - 3e-x)

For x < 3/2, f''(x) < 0, which means f is concave down and f'(x) is decreasing. This means that f is decreasing for x < 3/2.

For x > 3/2, f''(x) > 0, which means f is concave up and f'(x) is increasing. This means that f is increasing for x > 3/2.

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The perimeter of square ABCD is 8 [tex]\sqrt{13}[/tex]  units.

Coordinates of the vertices are A(-2, 1), B(2, 7), C(8, 3) and D(4, -3)

A square's perimeter is equal to the sum of its four sides or the product of four and one of its sides.

Therefore, the square's perimeter is equal to a + b + c + d.

4 × any of the sides because the sides of a square are equal to one another.

Since ABCD is a square:

Perimeter of a square = 4 × (length of a side)

=4 × AB

Formula to calculate the distance between two points [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] is, [tex]$\mathrm{d}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex]

Therefore, distance between two points A(-2, 1) and B(2, 7) will be,

AB = [tex]\sqrt{(2+2)^2+(7-1)^2} \\[/tex]

AB = [tex]\sqrt{4^2+6^2} \\[/tex]

AB = [tex]\sqrt{52} \\[/tex]

AB = 2[tex]\sqrt{13}[/tex]

Hence the perimeter of square ABCD can be calculated as 4 × AB

Now Perimeter of a square ABCD = 4 × 2[tex]\sqrt{13}[/tex]

= 8 [tex]\sqrt{13}[/tex]  units

Therefore the answer is 8 [tex]\sqrt{13}[/tex]  units

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Square ABCD has vertices at A(−2,1), B(2,7), C(8,3), and D(4,−3). How many units is the perimeter of square ABCD?

The slope of the line that passes through points (2, 8) and (-3, 14) is -1.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Given:

The coordinates of point = (2, 8) and (-3, 14),

Calculate the slope of the line from the formula given below,

m = (y₂ - y₁) / (x₂ - x₁)

Here m is the slope.

Substitute the values,

m = (13 - 8) / (-3 - 2)

m = −1

Therefore, the slope of the line that passes through points (2, 8) and (-3, 14) is -1.

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Limit, (4 + b)² - 8², Algebraically Determining Limits, h approaches 0, Expansion Formula for Square, Lim [(4 + b + h)² - 8² = (4 + b)² - 64.

To algebraically determine the limit, we can use the definition of a limit.

The limit of (4 + b)²-8² as h approaches 0 is equal to the limit of (4 + b + h)² - 8² as h approaches 0 minus (4 + b)² - 8².

Using the expansion formula for a square, we can write:

(4 + b + h)² - 8² = (4 + b)² + 2(4 + b)h + h² - 64

Now, taking the limit as h approaches 0:

lim [(4 + b + h)² - 8²] = lim [ (4 + b)² + 2(4 + b)h + h² - 64 ] = (4 + b)² - 64

So,

lim (4 + b)² - 8² as h approaches 0 = lim [(4 + b + h)² - 8²] - (4 + b)² + 64 = lim [(4 + b + h)² - 8²]

Hence,

lim (4 + b)² - 8² as h approaches 0 = lim [(4 + b + h)² - 8² = (4 + b)² - 64.

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The change in the scale factor is 4/5.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

12 / 15

12 ÷ 3 = 4

15 ÷ 3 = 5

4/5

Answer key: The change of scale means that 1 inch represented 4 feet, but now 1 inch represents 5 feet.

1 inch represents 4 feet which factors 12 feet.

4 cannot factor 15 feet.

5 can factor 15 feet.

1 inch would represent 5 feet then.

15 ÷ 5 = 3 inches

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The perimeter of the triangle would be 18.1 yards.

What is Pythagorean theorem ?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between the three sides of a right triangle in Euclidean geometry. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.

Given the information in the problem, we can use the Pythagorean theorem to find the length of the other leg, a:

      [tex]c^2 = a^2 + b^2\\\\7.5^2 = a^2 + 5.4^2\\\\56.25 = a^2 + 29.16\\\\56.25 - 29.16 = a^2\\\\27.09 = a^2\\\\a = \sqrt{27.09} \\\\a = 5.2\ yards[/tex]

The perimeter of the triangle is the sum of the lengths of all its sides:

Perimeter = a + b + c

Perimeter = 5.2 + 5.4 + 7.5

Perimeter = 18.1 yards (rounded to the nearest tenth)

Therefore, The perimeter of the triangle would be 18.1 yards.

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Variance is a useful tool for gaining a deeper understanding of a dataset beyond just the mean.

Variance is a measure of how far the individual values in a set of data are from the average value.

The variance is calculated by first finding the difference between each value in the dataset and the mean, squaring these differences, and then averaging the squared differences.

The result is a non-negative number that indicates how far, on average, each value deviates from the mean. If the variance is small, it means that most of the values are close to the mean, while a large variance indicates that the values are widely spread out.

One important use of variance is in statistical inference, where it is used to make predictions about a population based on a sample of data. Variance also plays a role in hypothesis testing, where it is used to determine whether the differences between two sets of data are statistically significant.

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By solving linear equation, it can be calculated that x = 60 , y = 70 is one possible solution of the linear equation.

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by <, >, ≤, ≥

A one degree inequation is known as linear inequation.

Let the number of tacos sold be $x and the number of burrito sold be $y

He only has enough supplies to make 130 tacos or burritos.

x + y ≤ 130 ... (1)

He sells each taco for $4.25 and each burrito for $8.50.

Isaac must sell a minimum of $850 worth of tacos and burritos each day.

4.25x + 8.5y ≥ 850

x + 2y ≥ 200 ... (2)

The inequalities has been solved graphically as;

One possible solution is x = 60, y = 70

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The cumulative frequency is the running total of the frequency; each value in the cumulative frequency column is the sum of the previous and current frequency values.

From the data on the number of children, the following can be calculated:

Table of Frequency:

No. of Children | Frequency 0 | 1 2 | 2 3 | 2 4 | 2 5 | 1

Table of Relative Frequency:

Children | Frequency | Relative Frequency 0 | 1 | 1/9 2 | 2 | 2/9 3 | 2 | 2/9 4 | 2 | 2/9 5 | 1 | 1/9

Table of Cumulative Frequency:

Child Count | Frequency | Cumulative Frequency

0 | 1 | 1 \s2 | 2 | 3 \s3 | 2 | 5 \s4 | 2 | 7 \s5 | 1 | 8

Because the cumulative frequency is the frequency's running total, each value in the cumulative frequency column is the sum of the previous and current values in the frequency column.

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By using the truth table The correct options are (a) The row where both p and q are true, but r is false and (c) The row where p, q and r are all false.

Given, (p ^ r) -> ~(q v p)

Creating truth table:

=> p ^ r will return true if both the values of p and r are true else will return false.

=> q v p will return true if at least one of the values of q or p is true else will return false.

=>~(q v p) will return true if the truth value of q v p is false else will return false.

=>(p ^ r) -> ~(q v p) will return false if truth value of p ^ r is true and truth value of ~(q v p) is false else will return true.

p    q    r      (p ^ r)     (q v p)         ~(q v p)     (p ^ r) -> ~(q v p)

F    F    F         F            F                   T                   T

F    F    T         F            F                   T                   T

F    T    F         F            T                    F                  T

F    T    T         F            T                    F                  T

T    F    F         F            T                    F                  T

T    F    T         T            T                    F                  F

T    T    F         F            T                    F                  T

T    T    T         T            T                    F                  F

=> Option (a) is correct because according to the row number 7 where p = q = T and r = F, the result = T

=> Option (b) is wrong because according to row number 6, where p = q = T and q = F, the result = F

=>Option (c) is correct because according to row number 1, where p = q = r = F the result = T

=>Option (d) is wrong because according to the row number 8 where p = q = r = T the result = F

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The Shipping Company Cost, y=$(5.75+0.31x) is a linear function that determines the cost of shipping based on weight.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

A shipping company charges a $5.75 handling fee in addition to $0.31 per pound to ship a package.

Using X for the weight in pounds and for the cost of shipping in dollars

Let the number of pounds being shipped=x

Shipping Company charges $5.75 plus an additional $0.31 per pound to ship a package.

Shipping Company Cost =  $5.75 + ($0.31 X Number of Pounds)

Shipping Company Cost,  y=$(5.75+0.31x)

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The answer to the question is: 10 books left in stock.The equation that used to solve this problem is 7 + 10 = x - 17.

This question can be solved by using an equation. The equation that used to solve this problem is 7 + 10 = x - 17. This equation can be solved by first multiplying both sides by 2. This will give us 2x17 = x. Then, subtract 17 from both sides, which gives us x = 119 - 17. Finally, subtract 7 from both sides to get 10 = x - 17. Therefore, the answer to the question is 10 books left in stock.

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The range of the graph is -4 ≤ y ≤ 2.

Option C is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

A coordinate plane with a segment going from the point (-3, 2) to (0, 1) and another segment going from the point (0, 1) to (5, -4).

This means,

(-3, 2) to (5, -4)

The range of the graph is the y-coordinate.

So,

-4 to 2

This can be written as,

-4 ≤ y ≤ 2

Thus,

The range is -4 ≤ y ≤ 2.

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Answer:

guys i have no idea

Step-by-step explanation:

The volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, a hemisphere fits snugly inside a cylinder with a radius of 8 cm. A cone fits snugly inside the same hemisphere.

Since, all of them are tightly packed in one another therefore, radius of all them will be equal,

And, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.

r = radius of cylinder = 8 cm and

h = height of cylinder = radius of hemisphere = 8 cm

We know that,

Volume of a cylinder = π × radius² × height

Volume of a cone = 1/3 × π × radius² × height

Therefore,

a) The volume of cylinder =

π × 8² × 8 = 512π cm³  

b) The volume of cone =

1/3 × π × 8² × 8 = 170.6π cm³  

c) Volume of the hemisphere = (512π + 170.6π) / 2

= 341.3π cm³  

Hence, the volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.

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The function rule for the statement "The output is seven more than one-third of the input" can be written as: y = 1/3x + 7

The pattern represented in the input/output table must be represented by the function rule when it is written from the data in the table. Start by searching for a pattern between the input and output numbers. The output numbers' values are quite similar to the input number multiplied by three.

Let x be the input, and y be the output.

As we have the statement as:

The output is seven more than one-third of the input

So, we can write the function as:

y = 1/3x + 7

This represents the relationship between the input and the output,

where the output is seven more than one-third of the input.

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Z is a vector space over F with the operations(v1, w1)+(v2, w2)=(v1 + v2, w1 + w2) and c(v1, w1)=(cv1, cw1) is proved.

A vector is a mathematical object that can be added and multiplied by a number, also known as a scalar.

In this case, we have two vector spaces, V and W, which are sets of vectors that can be added and scaled in a certain way, with the scalars taken from a field F.

=> (v1, w1)+(v2, w2)=(v1 + v2, w1 + w2)

We then define a new set, Z, which consists of ordered pairs of vectors, one from V and one from W. With the operations of adding two vectors element-wise and scaling a vector by a scalar, we can show that Z is also a vector space over F.

=> c(v1, w1)=(cv1, cw1).

To do this, we need to verify that Z satisfies the properties of a vector space, such as closure under addition and scalar multiplication, associativity and commutativity of addition, the existence of an additive identity and inverse, and distributivity of scalar multiplication over vector addition.

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Answer:

The answer could be x * 33 + 30.

Step-by-step explanation:

In this expression, the parentheses indicate that 14 and 19 are to be added together first, which equals 33. The expression x * 33 means that 33 is being multiplied by x. Finally, 30 is being added to this product. So both expressions represent the same mathematical operation.

Here's how to check our answer:

First, we simplify the expression inside the parentheses:

x(33) + 30

Next, we multiply x and 33:

x * 33 + 30

Finally, we add 30 to the product of x and 33:

x * 33 + 30

So, the expression x * 33 + 30 is equivalent to the expression x(14 + 19) + 30.

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x(14+19)+ 30 =

     33   +  30

33x+30