31.002 in expanded form

Answer:

12.5%

Step-by-step explanation:

12.5% of 120 is 15 so if you take 15 divided by 120 you would get 0.125 and turned into a percentage is the 12.5%

Yes. 66 is a real number. Every real number is either a rational number or a irrational number.

The Real numbers are defined as the numbers which have values that can be expressed as an infinite decimal expansion. It include integers, natural numbers. Real numbers can be positive and can be negative numbers. Real numbers can be a rational number or a irrational numbers. These two are the main groups of real numbers. Rational numbers can be written as the ratio of two integers. Irrational numbers cannot be written as the ratio of two integers. Irrational numbers are also the type of real numbers. The real numbers has the closure property, commutative property, the associative property and the distributive property.

To learn more about Real numbers please visit:

https://brainly.com/question/17201233

#SPJ4

The complete factor of the polynomial x² + 5x +6 is (x + 3)(x + 2).

You can factor it by using the factorization methods such as

Factor by grouping

Factor by grouping and completing the square

Factoring by using difference of squares

Factoring by using sum and difference of cubes

For example, you can factor it by using the difference of squares method:

x² + 5x +6 = (x² + 6x + 9) - (x +3)

We know x² + 6x + 9 = (x + 3)², So

x² + 5x +6 = (x + 3)² - (x + 3)

Taking (x + 3) common

x² + 5x +6 = (x + 3)(x + 3 - 1)

x² + 5x +6 = (x + 3)(x + 2)

So (x + 3)(x + 2) is complete factor.

--The question is not readable, answering to the question below--

"What is the complete factor of x² + 5x + 6?"

To know more on difference of squares method

https://brainly.com/question/21186386

#SPJ4

55/24 will be the simplified form of the expression 43/8 + 25/12 -31/6.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

given an expression 43/8 + 25/12 -31/6

Simplify given data

=> 43/8 + 25/12 -31/6

=> 5 + 3/8 + 2 + 1/12 - 5 - 1/6

=> 2 + 3/8 + 1/12 - 2/12

=> 2 + 3/8 -1/12

=> 2 + 9/24 -2/24

=> 2 + 7/24

=> 55/24

therefore, The simplified form of the given equation will be 55/24.

Learn more about fractions here:

https://brainly.com/question/10354322

#SPJ1

No, the existence of a limit at one point does not necessarily imply the existence of a limit at a nearby point.

The limit of a function at a certain point is determined by the behavior of the function in a neighborhood of that point, not just the behavior at that point. Two points that are close to each other can have different limits.

Therefore, the statement in the solution cannot be founded. The existence of the limit as x approaches a (f(x)) does not guarantee the existence of the limit as x approaches b (f(x))

Learn more about limits at point here: https://brainly.com/question/23343679

#SPJ1

Answer:

11

Step-by-step explanation:

the answer is 11 because of therom

The three conditions must be satisfied for a square to be in its simplest form, that is, first, No radicands other than 1 have perfect square factors. Secondly, there isn't a fraction in any radicand and finally, the fraction's denominator has no radicals.

A square root can be reduced to a simple form by first factoring it into primes, then finding the radical's index, and finally moving the group of numbers either inside or outside the radical.

The expressions both inside and outside the radical can then be made simpler by adding up all the numbers inside the radical.

The quotient property of square roots, which can be used to split radical expressions, is another beneficial property for simplifying radical expressions.

To learn more about square roots visit:

https://brainly.com/question/428672

#SPJ4

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Option A is correct.

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,
Given expression,
= 1/2x + 4

put x = 2
= 1/2 × 2 + 4
= 5

Now, another expression

= x + 6 - 1/2x - 2
Put x = 2

= 2 + 6 - 1/2 × 2 -2
= 5

Thus, both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Option A is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

The dimensions of the region bounded by the curve, y² = x, the lines,  x = 1 and x = 4, and the x-axis exists the dimensions ABCD

Thus area of ABCD = [tex]\int_1^4 \mathrm{ydx} \\[/tex]

[tex]& =\int_1^4 \sqrt{\mathrm{x}} \mathrm{dx} \\[/tex]

[tex]$& =\left[\frac{\mathrm{x}^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^4 \\[/tex]

[tex]$& =\frac{2}{3}\left[(4)^{\frac{3}{2}}-(1)^{\frac{3}{2}}\right][/tex]

simplifying,

[tex]$& =\frac{2}{3}[8-1] \\[/tex]

Then we get,

[tex]$& =\frac{14}{3} \text { units }[/tex]

To learn more about angle, refer to:

https://brainly.com/question/25716982

#SPJ4

Answer: 4x -30 > 25 would be your answer

Step-by-step explanation: I hope this helps!

Reason: The 90 degree angle means we have a right angle, and it leads to a right triangle. The triangle is also scalene since all three angles are different (it means all side lengths are different).

The solutions of the quadratic equation are:

[tex]x = 1/2 \pm \sqrt{2}[/tex]

Here we want to solve the quadratic equation:

(2x - 1)^2 = 8

To use the quadratic formula, we need to expand this.

(4x^2 - 4x + 1) = 8

4x^2 - 4x + 1 - 8 = 0

4x^2 - 4x - 7 = 0

Remember that for a quadratic equation:

a*x^2 + b*x + c = 0

The quadratic formula is:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Then in this case the solutions are:

[tex]x = \frac{4 \pm \sqrt{(-4)^2 - 4*4*(-7)} }{2*4} \\\\x = \frac{4 \pm \sqrt{128} }{8}\\\\x = 1/2 \pm \sqrt{128/64} \\\\x = 1/2 \pm \sqrt{2}[/tex]

These are the solutions.

Learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

The measure of the base of the triangle is 10 millimetres

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

Area of the triangle = 80 square millimetres

Height of the triangle = 16 millimetres

Using the above as a guide, we have the following:

The base of the triangle = 2 * Area/Height

Substitute the known values in the above equation, so, we have the following representation

The base of the triangle = 2 * 80/16

Evaluate

The base of the triangle = 10

Hence, the base is 10 millimetres

Read more about triangles at

https://brainly.com/question/2437195

#SPJ1

Complete question

The area of the triangle is 80 square millimeters and the height of the triangle is 16 millimetres.

Calculate the length of the base

The absolute value function is increasing on [0,∞) and decreasing on (−∞,0].

There are a few ways to describe what is meant by the absolute value |x| of a real number x. You may have been taught that |x| is the distance from the real number x to the 0 on the number. So, for example, |5| = 5 and | − 5| = 5, since each is 5 units from 0 on the number line.

Another way to define absolute value is by the equation |x| = √x2. Using this definition, we have

|5| = √(5)² = √25 = 5 and | − 5| = √(−5)² = √25 = 5. The long and short of both of these procedures is that |x| takes negative real numbers and assigns them to their positive counterparts while it leaves positive numbers alone.

To know more about absolute value function, here

https://brainly.com/question/10664936

#SPJ4

-2x-33=x
simplify by adding 2x on both sides

-33=3x

divide by 3 on both sides

x=-11

The estimate of the no. of people to vote varies by 25% from the actual no. of voters turned out.

Finding the per cent variation of estimated votes from the actual turnout

The no. of people estimated to vote in the election = 7000

The actual no. of people who voted = 5600

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

∴ The per cent by which the estimate vary from the actual turnout is given by,

= [{7000 – 5600}/ {5600}]×100

= [1400/5600]×100

= 0.25×100

= 25%  

Therefore, the 25% of the estimate vary from the actual amount.

For more such questions on percentage

https://brainly.com/question/29306119

#SPJ4

Answer:

2nd is the correct answer

The side that will be in palce of Questionmark by Similarity of Triangle is WZ.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Since Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Properties:

Similar equivalent side ratios exist.

Triangle WZX and WXY:

Angle WZX = angle WXY= 90 degrees

Angle WXY is a common angle .

So triangle WZX and WXY are similar (AAA similarity)

So, the ratio of sides are equal.

Therefore,

WY / WX = WX / WZ

The side that will be in place of WZ

To learn more about Similarity of Triangle refer to :

brainly.com/question/24333831

#SPJ2

Answer:

To find the amount of money after 10 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt)

Where:

A = the amount of money after 10 years

P = the initial investment (24000 birr)

r = the interest rate (4%)

n = the number of times the interest is compounded per year

t = the number of years

In this case, since the interest is compounded annually, n = 1.

So,

A = 24000(1 + 0.04)^(1*10)

A = 24000(1.04)^10

A = 24000(1.46) = 24000*1.46 =35,040 birr

So, after 10 years the total amount of money will be 35,040 birr.

Answer:

p = 73.21 pounds of strawberries

Step-by-step explanation:

M + 10 = 5.6p - 96

314 + 10 = 5.6p - 96

314 +96 = 410

410 = 5.6p

410/5.6 = p

73.2142857143 = p

p = 73.2142857143

Answer:

75 pounds

Step-by-step explanation:

Replace M in the equation with 314

314 + 10 = 5.6p - 96

324 = 5.6p - 96

5.6p = 324 + 96

5.6p = 420

Divide both sides by 5.6

p = 75

We are aware that x+y=15 (the total number of mugs he buys).The man then purchased 5 large cups and 10 mini mugs .

Let x represent how many little cups he buys.

Let y represent how many large mugs he purchases.

We are aware that x+y=15 (the total number of mugs he buys)

We are also aware of the mugs' costs.

The total price (69) can therefore be deduced to equal 3.50x + 6.80y.

To find x, use the first equation.

x = 15 - y

You can now enter that x-value into the other equation.

69 = 3.50(15 - y ) + 6.80y

Solve for y now.

69 = 52.5 -3.50y + 6.80y

69= 52.5 + 3.3y

16.5 = 3.3y\sy = 5

So, we are aware that the man purchased 5 huge cups.

You can re-insert the y value into x+y=15.

x+5=15\sx+10

The man then purchased 5 large cups and 10 mini mugs!

To learn more about mugs' costs refer

https://brainly.com/question/17449859

#SPJ1

Answer:

Step-by-step explanation:25

Parallelogram II and IV have the same area.

A parallelogram with the same base and height has the same area, regardless of shape. The product of base and height is equal. 

The following is a list of the characteristics of a parallelogram:

Learn more about parallelogram at https://brainly.com/question/13795683

#SPJ1

In class 9, matter is typically defined as anything that has mass and takes up space. Matter can be found in different forms and states, such as solid, liquid, and gas.

The study of matter in class 9 typically includes the following topics:

Properties of matter: Students learn about the different physical and chemical properties of matter, such as density, melting point, boiling point, and solubility.

States of matter: Students learn about the three states of matter (solid, liquid, and gas) and how they are different from each other in terms of properties such as shape, volume, and compressibility.

Changes of state: Students learn about how matter can change from one state to another, such as melting, freezing, boiling, and condensation.

Mixtures and solutions: Students learn about the different types of mixtures, such as homogeneous and heterogeneous mixtures, and solutions, such as true solutions, colloidal solutions, and suspensions.

Particles of matter: Students learn about the nature of matter and how matter is made up of tiny particles called atoms and molecules. They also learn about the arrangement of these particles in solids, liquids, and gases.

Physical and chemical changes: Students learn about the differences between physical and chemical changes in matter and examples of each.

To know more on matter

https://brainly.com/question/29783877

#SPJ4

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

Know more about multiplication principle here:https://brainly.com/question/10275154

#SPJ1

Answer:

x=5000 I think

Step-by-step explanation:

1800-1600=200$ difference between choices

this difference equals a 4% commission on the amount of furniture she sells during the month

If the amount of sales is x$, then a 4% commission on the amount is 0.04x$

so 0.04x=200

x=200%2F0.04

x=5000$ amount of sales for that two choices will be equal

(a)1+2×3×4×5 is equal to 121 which shows it is square integer.

(b)1+3×4×5×6 is equal to 361 that shows it is square integer and 1+4×5×6×7 is equal to 841 that shows it is square integer.

(c)n(n+3) is equal to n²+3n and second expression would be a+2.

(d)The expression in the term of a is a²+2a+1

•Integers are any number, including positive, negative, and zero. The Latin root of the word "integer" means "whole" or "intact." Therefore, integers do not contain decimals or fractions.

•Consequently, both negative and positive whole numbers can be added to create a set of integers.

•An integer, which includes both positive and negative integers, including zero, is a number without a decimal or fractional component. Z stands for an assortment of integers that includes the following.

•If a number is smaller than zero, it is said to be negative. For instance, 1, 2, 3, etc. Zero is defined as not having a positive or negative value. The sum is a whole number.

To learn more about Integer visit:

brainly.com/question/15276410

#SPJ1

Answer:7.5

Step-by-step explanation:

The median is the middle value of a set of observations when they are arranged in ascending order. Since the observations are already arranged in ascending order and there are 7 observations, the median will be the fourth value.

Given that the median is 32, we know that the fourth value is 32. The observations are:

13, x, 26, 32, 39, 41, 50

So x + 3x + 2 = 32

4x + 2 = 32

4x = 30

x = 7.5

The value of x is 7.5.

The multiplicative inverse of 3/7 will be 7/3. Thus, correct option is B).

The word "inverse" refers to something that has an opposite impact. A number's multiplicative inverse is a number that, when multiplied by the inputted number, produces the result 1, or 1. It is the reciprocal of an integer, as defined by the multiplicative inverse.

1/N or N-1 is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. To put it another way, it is a technique for dividing a number by itself to produce identity 1.

To learn more about multiplicative inverse: https://brainly.com/question/21973802

#SPJ4

Note that the correct question is:

What is the multiplicative inverse of 3/7 ?

A) - 3/7

B) 7/3

C) - 7/3

D) 1

The value for 1 mol Na is 23 gm/mol and 1 mol Br_2 is 160 gm/mol, so the volume will be different.

What is mole?

The mole idea is a useful way to indicate how much of a substance there is. Any measurement can be divided into two components: the magnitude in numbers and the units in which the magnitude is expressed.

Even one gram of a pure element is known to have an enormous number of atoms when working with particles at the atomic (or molecular) level. The mole idea is frequently applied in this situation. The unit of measurement that receives the most attention is the "mole," which is a count of a sizable number of particles.

The molar mass for 1 mole of solid sodium (Na) = 23 gm/mol

The molar mass for 1 mole of liquid bromine (Br) = 79.90 gm/mol

The molar mass for 1 mole of liquid bromine (Br_2) = 160 gm/mol

The molar mass of both the substances in 1 mol quantity is different.

The volume of both the elements will be different.

The molar mass of any element does not corresponds with the mole value.

Therefore, there is different in volumes.

To learn more about mole from the given link

https://brainly.com/question/15356425

#SPJ1

When a=9 and c=3, A varies as b and c together. If a=40, b-2, and c=5, B. [tex]40x^{2}[/tex] - 2 x + 5 = 0 and [tex]9x^{2} +3 = 0[/tex] are the quadratic equations.

When a=9 and c=3, A varies as b and c together. If a=40, b-2, and c=5, B. [tex]40x^{2}[/tex] - 2 x + 5 =0 and [tex]9x^{2} +3 =0[/tex] are the quadratic equations.

Domain of [tex]$40 x^2-2 x+5:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Range of [tex]$40 x^2-2 x+5:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq \frac{199}{40} \\ \text { Interval Notation: } & {\left[\frac{199}{40}, \infty\right)}\end{array}\right]$[/tex]

Axis points of interception [tex]$40 x^2-2 x+5: \quad$[/tex] Y Intercepts: (0,5)

Vertex of [tex]$40 x^2-2 x+5: \quad$[/tex] minimum [tex]$\left(\frac{1}{40}, \frac{199}{40}\right)$[/tex]

Factor [tex]$9 x^2+3: \quad 3\left(3 x^2+1\right)$[/tex]

[tex]$$9 x^2+3$$[/tex]

Replace 9 with 3 - 3.

Put 3 in as 3 - 1.

[tex]$$=3 \cdot 3 x^2+3 \cdot 1$$[/tex]

Exclude common word 3

[tex]$$=3\left(3 x^2+1\right)$$[/tex]

To learn more about quadratic equation refer to :

https://brainly.com/question/1214333

#SPJ1