GEOMETRY The area of the base of a rectangular box measures 2x² + 4x-3 square units. The height of the box measures x units. Find a polynomial expression for the volume of the box.​

The answer to option D) is yes. The likelihood of choosing a carnation at random from vase K is higher than the likelihood of choosing one at random from vase J.

The possibility is determined on the range of potential outcomes. the estimated number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping the coin and receiving heads is 1 in 2. (a head or tail). We write P(heads) = 12 here.

Roughly simply, probability is the chance that everything will exist. When we wouldn't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes.

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Answer:

6,5

Step-by-step explanation:

The age of Lisa and Myra now is 35 years old and 5 years old, respectively.

To determine how old each person now, use algebraic expression and equation.

Let x = current age of Lisa

y = current age of Myra

If the sum of Lisa's age and Myra's age is 40, then we can express it as:

x + y = 40

x = 40 - y

If in 10 years, Lisa will be 3 times as old as Myra, then we can express it as:

x + 10 = 3(y + 10)

x + 10 = 3y + 30

x - 3y = 20

Substitute the equation for x into the 2nd equation and solve for y.

x - 3y = 20

(40 - y) - 3y = 20

40 - 4y = 20

4y = 20

y = 5

Substitute the value of y into the equation for x and solve.

x = 40 - y

x = 40 - 5

x = 35

Therefore, Lisa is 35 years old while Myra is 5 years old.

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Step-by-step explanation: To solve for e in this equation, you can start by isolating e on one side of the equation.

First, distribute the -2/5 on the left side of the equation:

-2/55 - 2/510e = e + 1/36e - 1/312

Now, you can combine like terms on both sides of the equation:

-2 - 4e = e + 2e - 4

Next, you can add e to both sides of the equation:

-2 - 3e = 2e - 4

Now you can add 3e to both sides of the equation:

-2 = 5e - 4

Now you can add 4 to both sides of the equation:

-6 = 5e

Finally, you can divide both sides of the equation by 5:

e = -6/5

So the value of e that satisfies the equation is -6/5.

The probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty = 0.493

Here, 21% of customers purchase extended warranty.

So, the probability p = 0.21

It takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty is nothing but none of the first three buy.

This means, we find probability P(X = 0) when n = 3.

Using Binomial distribution formula for probability,

P(X = 0) = ³C₀ (0.21)⁰ (1 - 0.21)⁽³ ⁻ ⁰⁾

P(X = 0) =  ³C₀ (0.21)⁰ (0.79)⁽³ ⁻ ⁰⁾

P(X = 0) = 0.493

Therefore, the required probability is 0.493

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The complete question is:

The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible

items are chosen at random one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who

purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independentWhich of the following is closest to the probability that X > 3;

that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?

There are 720  different slates of candidates possible.

Permutation:

The permutation is a statistical method that determines the number of possible arrangements. In permutation, the order of selection is important and replacements are not allowed.

Permutation can be divided into three different types:

The general formula of Permutations:

[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

n= total number of members.

r=number of members selected.

Here n=10 and r= 3

Now substitute the values in the above formula:

[tex]^nP_r=\frac{10!}{(10-3)!} \\\\^nP_r=\frac{10!}{7!}\\\\^nP_r= \frac{10*9*8*7!}{7!} \\\\^nP_r=10*9*8\\\\^nP_r=720[/tex]

Therefore, there are 720 different slates of candidates possible.

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The coordinates of the point shown after the transformation f(-2x) are given as follows:

(-4,-1).

The original coordinates of the the point in this problem are given as follows:

(2,-1).

Hence:

The transformation is given as follows:

f(-2x).

Meaning that the x-coordinate is multiplied by -2, hence the coordinates of the point shown after the transformation f(-2x) are given as follows:

(-4,-1).

(as 2 x -2 = -4).

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The perimeter of the rectangle with a length of 4 meters and a width of 150 centimeters is 11 meters.

A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The perimeter of a rectangle is expressed as;

Perimeter = 2( length + width )

Given the data in the question;

Plug the values into the above equation.

Perimeter = 2( length + width )

Perimeter = 2( 4 meters + 1.5 meters )

Perimeter = 2( 5.5 meters )

Perimeter = 11 meters

Therefore, the perimeter is 11 meters.

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The variance of 'x'  for the continuous distribution over the interval 40 to 44 is approximately b) 1.333

The variance of a continuous uniform distribution over the interval [a, b] is:

Calculate the variance using the formula:

                                       Var(x) = (b-a)^2/12

where [a, b] is the interval over which the continuous uniform distribution is defined

But putting a= 40 and b = 44, calculate the variance by putting them in the above formula

So, Var(x) = (44-40)^2/12

     Var(x) = 4^2/12

     Var(x) = 16/12

     Var(x) = 4/3

     Var(x) = 1.333

Therefore, the variance of 'x' for the continuous distribution over the interval 40 to 44 is approximately b) 1.333

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The simplified monomials are:

Let's simplify each monomials we have.

3a³b² - 5a³b² = -2a³b² --> both exponents are already equal

5xy - 2x²y + 2xy = 7xy - 2x²y

                           = xy (7 - 2x)

-6w : -2w = 3

a⁴ . a³ = a⁽⁴⁺³⁾

          = a⁷

(-x⁵)² = - x ⁽⁵ˣ²⁾

        = - x¹⁰

k⁹ / k⁵ = k⁽⁹⁻⁵⁾

          = k⁴

-5x³ . (-3x⁴) = 15x⁷

(-2x²y)² . (-3xy³) = (4x⁴y²) . (-3xy³)

                          = -12x⁵y⁵

2a⁻⁵b⁶ . 5a²b² = 10 a⁻³b⁸

                       = 10b⁸ / a³

(-4y⁴)² = 16y⁸

(a²bc³)⁴ . (b²c)³ = (a⁸b⁴c¹²) . (b⁶c³)

                        = a⁸b¹⁰c¹⁵

(6cd⁻¹)⁻³ = 1 / (6cd⁻¹)³

              = (d/6c)³

              = d³ / 216c³

(4a)⁻³ . a⁻⁴ = 1/(4a)³ . (1/a⁴)

                 = 1/64a³ . 1/a⁴

                 = 1/64a⁷

(3xy)² . (-4x³y²)³ = (9x²y²) . (-64x⁹y⁶)

                          = -576x¹¹y⁸

(4a⁻¹b⁵c⁻³)³ = (4b⁵ / ac³)³

                  = 64b¹⁵ / a³c⁹

9d⁸/3d¹⁰ = 3/d²

6a⁵b² / 4ab³ = 3a⁴/ 2b

32x³y²z⁵ / -8xyz² = -4x²yz³

(2y⁵)⁴ / 10y¹⁵ = 16y²⁰ / 10y¹⁵

                    = 8y⁵ / 5

(3x⁵y³ / x³y⁶)⁴ = (3x²/y³)⁴

                      = 81x⁸ / y¹²

(-6a⁵b)² - 8a³b = 36a¹⁰b² - 8a³b

12a⁷b                     12a⁷b

                        = 3a⁵b - 8a⁵b

                       = -5a⁵b

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If we throw uniformly at random a point on segment [0,1], then its expected position is 1/2.  the expected positions 1/3 and 2/3 of two random points on segment [0,1] are [0,1/3],[1/3,2/3]and[2/3,1]

In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen. Given the interval is [0,1]

Then it's expected position is 1/2

So [0,1/2] and[1/2,1]

Now we get the two expected positions

I. E three intervals

So (1-0)/3

=1/3

So 1/3 and 2/3 are expected positions

They are [0,1/3],[1/3,2/3]and[2/3,1]

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The area of the rhombus is 54 sq. units

Area of the trapizium is 115 sq. units.

A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

A parallelogram's general characteristics are as follows:

In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.

The area of a rhombus = ½ x (product of the lengths of the diagonals)

= ½ *18*6 = 54 sq. units

Area of the trapizium = ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

=½ *(17 + 29) * 5 = 115 sq. units.

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Answer:

40:60:80

Step-by-step explanation:

1. add the ratio first 2+3+4 =9, then divide the amount by the total number of parts

2. multiply the quotient by each part (20×2, 20×3 and 20×4)

The simplified form of the expression is  [tex]2^{-3}[/tex].

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is,

=> [tex]\frac{2^5\times 2^2}{2^7 \times 2^3}[/tex]

We know that [tex]a^x\times a^y = a^{x+y}[/tex] then

=> [tex]\frac{2^{5+2}}{2^{7+3}}[/tex]

=> [tex]\frac{2^7}{2^{10}}[/tex]

Now [tex]\frac{a^x}{a^y}=a^{x-y}[/tex] then

=> [tex]2^{7-10}[/tex]

=> [tex]2^{-3}[/tex]

Hence the simplified form of the expression is  [tex]2^{-3}[/tex].

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Answer:

No, it would not fit because one cup is 8 ounces and if you times 8 and 13 it 104 so it would not fit they would need another container.

Step-by-step explanation:

hope it helps

take upper base = 12

take upper base = 12right side= 20

take upper base = 12right side= 20apply pythagorus

take upper base = 12right side= 20apply pythagorus .

take upper base = 12right side= 20apply pythagorus .= 13

now semi circle= 2 pi r/2 = pi × (11/2)

add all

12 +20+13× 5.5pi

Answer:

64.27cm

Step-by-step explanation:

Total perimeter =

semicircle +  Length of rectangle +  Breadth of rectangle and triangle +

hypotenuse of Triangle

semicircle = pi x r     (r = radius)

= 3.14 x 11/2

= 17.27 cm   -----------------(1)

Length of rectangle = 12cm  (Given) ----------------------(2)

Base (rectangle and triangle) = 20cm (Given) --------------------(3)

Hypotenuse = Root of (20-11)^2 + 12^2

= Root of  9^2 + 12^2

= Root of 81 + 144

= Root of 225

= 15cm ---------------------------(4)

By adding (1), (2), (3) and (4) we get

= 17.27 + 12 + 20 + 15

= 64.27cm

The solution to the inequality equation given above would be = X ≥ 3

An Inequality equation is defined as the type of equation that is used to show the relationship between two variables that are not equal using the following symbols such as < or >.

The equation given are as follows:

= 8x−14≤10

Bring the like terms together;

= 8x ≤ 10+14

= 8x ≤ 24

= X ≥ 24/8

= X ≥ 3

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The solution to the inequality equation is expressed as; x ≤ 3

Equations and inequalities are considered to be both mathematical sentences that are formed by relating two expressions to each other. In an equation, the two expressions are considered as equal which is shown by the symbol =. Meanwhile in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

The equation we are to solve is; 8x − 14 ≤ 10

Add 14 to both sides to get;

8x ≤ 24

Divide both sides by 8 to get;

x ≤ 3

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1) The proof that ΔFEH ≅ΔFGH is given as follows:

ΔFH bisects ∠EFG (Given)

∠FEH ≅ ∠ FGH.

FH = HF (Given)

∠EFH ≅ ∠FHG (Angle Bisector Theorem)

Thus, ΔFEH ≅ΔFGH  (Angle  - Side - Angle Theorem)

2) The proof that ΔPQR ≅ ΔTSR is:

∠RPQ ≅ ∠RTS - Given

R is the midpoint of QS - Given the Definition of Midpoint

QR ≅ RS -  Definition of Midpoint

∠PRQ ≅ ∠SRT Vertical Angles

Thus: ΔPQR ≅ ΔTSR - Angle - Angle - Side Theorem.

3) the proof that ΔABC ≅ Δ DCB is given as follows:
ΔABC and ΔDCB are Right Angled Triangles

AB ≅ DC - Given

BC ≅CB - Reflective Properties; thus

ΔABC ≅ ΔDCB - Hypothenus Leg Theorem.

According to the hypotenuse-leg (HL) theorem, if the hypotenuse and a leg of a right triangle are both congruent with the corresponding hypotenuse and leg of another right triangle, the triangles are congruent. According to the HL theorem, these triangles are congruent.

There is one exception to this rule: when the angles are straight angles. Using words: The triangles are congruent if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle.

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Answer:

Step-by-step explanation:

Based on the numerical data, we can estimate that 26 more labor hours will be necessary to satisfy the labor hours required without overtime.

The Fair Labor Standards Act, enacted by the federal government, places a cap on the number of hours per week (40 hours) that businesses may demand their employees to perform in exchange for regular pay. Employers were now required to give employees who put in more than 40 hours of work additional compensation in the form of overtime pay.

Hence,

Overtime pay is usually 1.5 times the employee's regular hourly wage.

So, if an employee is paid $15 per hour, their overtime rate is $22.50 per hour ($15 multiplied by 1.5).

If another employee is paid $25 per hour, overtime is $37.50 per hour ($25 x 1.5).

It would require 26 more labor hours will be necessary to satisfy the labor hours required without overtime.

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The required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
3 1/2+(-7 1/5) = 3+(-7) + 2/5 + (-1/5)
7/2 - 34/5 = -4 + 2/5 + -1/5
-33/10 =  -4 + 1/5
-33/10 ≠ -19/5

Thus, the required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.

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Fewer than 15% of coins were quarters. Exactly 80% of the coins were nickels, dimes, and quarters. Nickels, dimes, and quarters account for 95% of the total number of coins.

Quarters are coins that are used in many countries as a form of currency. Quarters are generally made of metal and are round in shape. They are typically smaller than other coins, such as dimes and nickels, and have a value of 25 cents (or one-fourth of a dollar). Quarters are often used in everyday transactions, such as buying candy or a newspaper, or to pay for parking. In the United States, there are five different designs of quarters in circulation, each representing a different state or territory.

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The sum of the expressions 2x/5 + 5/8 + x/5 - 1/4 is option b) 3x/8 + 3/8

Here we have 2x/5 + 5/8 + x/5 - 1/4

Now since we have constants as well as variables here, to add these up, we will add the constants and variables separately.

The constants are the ones with just numbers, while the variables are those terms that have the term x with them.

Hence adding up the constants will give us

5/8 - 1/4

The LCM of denominators 8, and 4 is 8

Hence, we get

5/8 - 2/8

= 3/8

Now adding the variable gives us

2x/5 + x/5

= 3x/5

Hence the sum is

3x/5 + 3/8

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Complete Question

2x/5 + 5/8 + x/5 - 1/4

a) 3x/5 + 1/8

b) 3x/5 + 3/8

c) 3x/5 + 5/8

d) 3x/5 + 7/8

It is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.

The expression

(2/5 * 5/8) + (1/5 * x - 1/4)

can be simplified as follows:

2/5 * 5/8 = 1/8

1/5 * x - 1/4 = (1/5 - 1/4) x = -3/20 x

So the expression becomes

1/8 + (-3/20 x) = (1/8 - 3/20 x).

This is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.

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The value of the 7 in the one's place is 1/1000 times the value of the 7 in the thousand places.

According to the question,

The number is 7,567.23.

Place value in Maths describes the position or place of a digit in a number. Each digit has a place in the number.

The difference in place value in one's place and thousand places is 1000.

The 7 in the thousands place is 1000 times the value of the 7 in the one's place.

So, The value of the 7 in the one's place is 1/1000 times the value of the 7 in the thousand places.

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The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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The relationship between tan A and tan B is: tan A * tan B = 1

From the question, we have the following parameters that can be used in our computation:

angle A + angle B = 90 deg

When angle A + angle B = 90 degrees,

The two angles are complementary, meaning they add up to 90 degrees.

In this case, the relationship between tan A and tan B is:

tan A * tan B = 1

This is known as the tangent addition formula.

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I found the answer with the ruluer it's 11.3

It all depends on how you want your hamburger. If you're serving it as a main dish, 300 hamburger patties (each around 4 ounces) should be plenty to feed 300 people. If you utilize hamburger meat as a topping or filler in a meal, you'll need a different amount.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. The four basic arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic mean is a number calculated by dividing the sum of a set's elements by the number of values in the set.

Here,

It all depends on how you want to eat the hamburger. If you're serving it as a main course, 300 hamburger patties, each weighing around 4 ounces, should plenty to satisfy 300 people. It will need a different quantity of hamburger meat if you use it as a topping or filler in a dish.

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Complete question:

How much hamburger will it take to make 300 three oz patties with a 20% shrinkage?

The percentage of American women that have shoe sizes that are at least 11.1 is; 0.0015

Empirical Rule

We are given;

Mean; x' = 8.04

Standard deviation; σ = 1.53

Using the empirical rule, we can have the data either 1, 2, or 3 standard deviations from the mean.

Thus;

At 1 standard deviation from the mean, we have;

8.04 ± 1(1.53)

⇒ (6.52, 8.56)

At 2 standard deviations from the mean, we have;

8.04 ± 2(1.53)

⇒ (5, 11.08)

At 3 standard deviations from the mean, we have;

8.04 ± 3(1.52)

⇒ (3.48, 12.6)

We can see that the one with at least 12,6 is 3 standard deviations from the mean which from the empirical rule is 99.7%

Thus;

percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%

P(x ≥ 12.6) = 0.15% = 0.0015

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Answer: B, C, A.

Step-by-step explanation: positive, not negative