The sum of the digits of a two-digit number is 10. When the digits are reversed, the new number is 36 more than the original number. Find the original.

The Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.

The Basic Counting Principle is a technique used in mathematics, more especially in probability theory and combinatorics, to determine how many combinations of options, items, or outcomes are possible. The Rule of Multiplication, the Product Rule, the Multiplication Rule, and the Basic Counting Rule are some of its alternate names.

It has a connection to the Sum Rule, often known as the Rule of Sum, which is a fundamental counting method used to calculate probabilities.

According to the Basic Counting Principle, if a decision or event has a potential result or set of options, and a different decision or event has b possible outcomes or choices, then the sum of all the unique combinations of outcomes for the two is ab.

Using the fundamental counting principle, if an event occurs in m ways and another event occurs in n ways then the total occurrence is given as (m)(n).

Given that,

m = 3 for choosing between sizes.

n = 3 for distilled, filtered, or spring water.

Thus, the total number of occurrence is given as:

T = (3) (3) = 9

Hence, the Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.

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We write the decimal as a fraction with the decimal value as the numerator and a power of 10 as the denominator, we get 1.1 as a fraction is 11/10.

To convert a decimal to a fraction, we write the decimal as a fraction with the decimal value as the numerator and a power of 10 as the denominator.

For 1.1, we can write it as:

1.1 = 11/10

Therefore, 1.1 as a fraction is 11/10.

Decimal numbers are a way to represent numbers that are not whole numbers or integers. A decimal number consists of two parts: a whole number part and a fractional part, separated by a decimal point. To convert a decimal number to a fraction, we need to write the decimal as a fraction with the decimal value as the numerator and a power of 10 as the denominator.

In the case of 1.1, we can write it as a fraction with a numerator of 11 (the decimal value) and a denominator of 10 (the power of 10 that corresponds to the first decimal place). We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. So the final fraction is 11/10.

Converting decimals to fractions is a useful skill in many areas of math, science, and engineering. It allows us to represent numbers in different ways and to perform calculations that involve fractions and decimals. Knowing how to convert between these two types of numbers can also help us understand the relationship between them and how they are used in real-world applications.

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Completely factorize the polynomial using any methods that are appropriate, then look for shared factors and the polynomial's roots. Next, double-check your work to confirm accuracy.

Follow these steps to determine a polynomial's factorization:

Completely factor the polynomial using any relevant techniques, including grouping, utilizing the difference of squares or cubes, or using the quadratic formula.

By multiplying them all together, you can verify that each factor is accurate. The final figure must match the initial polynomial.

Look for shared factors among the polynomial factors. If the polynomial has common components, remove them from the equation and rewrite it as the product of the common factors and the other factors.

The polynomial's roots can be verified by setting each factor to zero and calculating the variable. The roots ought to correspond to the original polynomial.

Verify your work a second time to make sure all relevant elements have been identified and taken into consideration.

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Answer:

[tex]y-8=3(x+2)[/tex]

Step-by-step explanation:

The equation of the line with slope [tex]m[/tex] passing through [tex](x_1, y_1)[/tex] in point-slope form is [tex]y-y_1=m(x-x_1)[/tex].

According to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.

What is an equation?

A formula known as an equation uses the equals sign (=) to express how two expressions are equal. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have left hand side equal to right hand side in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as an expression.

Given,

The cost of renting a video game = $3.50

The total cost of rentals for the month  = $31.50

The equation given is:

    3.5x = 31.5

The term 3.5x in the equation represents the total cost of a month when the number of video games rented is x.

In this case x = 31.5/3.5 = 9

Therefore, according to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.

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The airline fees was $41 each

The over the weight limit of the bag is 3 pounds

Number pounds of Natalie's bag = x

Airline 1:

29 + 4x

Airline 2:

23 + 6x

Equate airlines 1 and 2

29 + 4x = 23 + 6x

collect like terms

29 - 23 = 6x - 4x

6 = 2x

divide both sides by 2

x = 6/2

x = 3 pounds

Hence,

Airline 1:

29 + 4x

= 29 + 4(3)

= 29 + 12

= $41

Airline 2:

23 + 6x

= 23 + 6(3)

= 23 + 18

= $41

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Answer: 4cos(pi/6x)+3

Step-by-step explanation:

Answer:10[tex]\sqrt{7}[/tex]

Step-by-step explanation:

The friend that had the least portion of action games would be = Thomas with 20 action games in total.

The number of action games that Thomas has = 5

The number of sports video games for every action game = 6

Therefore the total number of sports game he has = 5×6 = 30.

The number of action games that Franklin has = 9

The number of sports video games for every action game = 6

Therefore the total number of sports game he has = 9×6 = 54.

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Answer:

Step-by-step explanation:

reflict means to put the point in the other way but in the same point.

The limit as x approaches -2 is equal to 0. The correct option is B.

The limit of the function f(x) = x² - 4 / x + 2 as x approaches 2 is equal to 0. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:-

The limit of the function f(x) = x² - 4 / x + 2 as x approaches -2 is equal to 4. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:

f(-2) = (-2)² - 4 / -2 + 2 = 4 - 4 / 0 = 0

So, the limit as x approaches -2 is equal to 0.

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The numbers required in the word problem are

Let's call the numbers x and y

From the first equation, we have:

2x + y = 18

From the second equation, we have:

3x - y = 7

Solving simultaneously by substitution method

3x - y = 7

3x = 7 + y

x = (7 + y)/3

substitute this expression for x into the first equation:

2x + y = 18

2((7 + y)/3) + y = 18

14/3 + 3y/3 = 18

14/3 = 18 - 3y/3

14/3 = 18 - y

collecting like terms

y = 18 - 14/3

y = 18 - 4 2/3

y = 13 1/3

substituting to solve for y

x = (7 + y)/3

x = (7 + 13 1/3)/3

x = 10 4/3/3

x = 3 4/3

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The opposite sides of FGHJ are parallel.

A quadrilateral is a four-sided polygon, having four edges and four corners.

FGHJ is a quadrilateral.

From the figure we can observe that opposite sides are equal which means the quadrilateral is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

The line segment FG≅JH

GH≅FJ

The sides are congruent and parallel.

Hence, the opposite sides of FGHJ are parallel.

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Answer:

Step-by-step explanation:

x=12wb+rb

probability of rb=5/11

12+11=23

5/23

rb=5/23

Answer:

In a box-and-whisker plot, the box represents the middle 50% of the data, with the median value marked by a vertical line inside the box. The "whiskers" extend from the box to the minimum and maximum values in the data set that are not considered outliers. Outliers are marked by individual points outside the whiskers.

To determine the percentage of data values that are greater than a given value, we need to look at the box-and-whisker plot to see where that value falls in the data set. If the value is outside the box, we know that at least 50% of the data values are either greater or less than that value, depending on whether the value is greater or less than the median. If the value is inside the box, we know that exactly 50% of the data values are greater and 50% are less than that value.

In the case of the value 72, we cannot determine the percentage of data values that are greater than it without knowing where it falls in the box-and-whisker plot. If it falls outside the box, we only know that at least 50% of the data values are greater than it. If it falls inside the box, we only know that exactly 50% of the data values are greater than it.

Step-by-step explanation:

Answer: Hello! I'm JK!.....

[tex]\frac{13}{75}[/tex]

Step-by-step explanation:

The range of the data is from 10 to 85.

[tex]\frac{85-72}{85-10}[/tex]  = [tex]\frac{13}{75}[/tex]

So your answer is [tex]\frac{13}{75}[/tex]

I really hope this helps you.  XoXoGoldenMaknae<3

The area of the shape is given as 24.52 cm2

We have two triangles and 1 rectangle

we have to find the area of the triangles first and then solve for the area of the rectangle.

The area of a triangle = 1/2bh

for first triangle

area = 1/2 * 2.7 * 3

= 4.05

for second triangle

height = 6.8 - 2.7

= 4.1

area = 1/2 * 3.4 * 4.1

= 6.97

For the rectangle

area = l * w

= 2.7 * 5 = 13.5

The area = 13. 5 + 6.97 + 4.05

= 24.52 cm2

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The extraneous values of the rational function are given as follows:

x = 7 and x = -3.

The extraneous values of a function are the values of x that are outside the function's domain.

In this problem, we have a rational function, hence the extraneous values are the values that make the denominators zero, as follows:

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Using a system of equations, Company A charges 25 + 0.06x more than Company B.

A system of equations involves two or more equations whose solutions are found concurrently or at the same time.

A system of equations is also known as simultaneous equations.

                                   Company A     Company B    Difference

Fixed charge                  $75.50             $50.50        $25 ($75.50 - $50.50)

Variable charge per mile $0.16               $0.10         $0.06 ($0.16 - $0.10)

Let the number of miles covered = x

The total cost of Company A (Equation 1) = 75.50 + 0.16

The total cost of Company B (Equation 2) = 50.50 + 0.1

The difference in total cost for x miles      = 25 + 0.06w

Thus, for each mile of travel that the family rents the car, Company A will charge more than Company B by exactly 25 + 0.06w.

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Answer:

36°

Step-by-step explanation:

2x+3x=5x

5x=180°

x=180°:5=36°

The area of the figure nearest hundredth will be 84.13 square feet.

The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The figure is the combination of the rectangle and the semicircle. Then the area of the figure is the addition of the rectangle and the semicircle. Then we have

A = L x W + (π / 8) D²

A = 14 x 5 + (3.14/ 8) (14 - 4 - 4)²

A = 70 + 0.3925 x 36

A = 70 + 14.13

A = 84.13 square feet

The area of the figure nearest hundredth will be 84.13 square feet.

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The missing diagram is given below.

The statement that best describes Jace's work is D. Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.

The concept that will be used here is word problem solution , then we need to interprete it then perform the neccessary simplification. . We were told that  the  sentence as an equation is 56 is 14 more than a number.

14+ = 56

then we can represent the number as X

then input into the equation as:

14+X = 56

x=56-14

=42

Therefore, option D is correct.

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complete question:

Jace wrote a sentence as an equation.

56 is 14 more than a number.

14+ = 56

Which statement best describes Jace's work?

Jace is not correct. The phrase more than suggests using the symbol > and Jace did not use that symbol.

Jace is not correct. He was correct to use addition, but the equation should be 56+ p = 14

Jace is not correct. The first number in the sentence is 56, so the equation should start with 56.

Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.

The equation of the nth term is 4 + n.

The 75th term is 79.

It is a sequence where the difference between each consecutive term is the same.

Example:

5, 7, 9, 11, 13 is an arithmetic sequence.

We have,

5, 6, 7, 8, ,,,,,a(75),,,,,,,,

This is an arithmetic sequence.

a = 5

d = 1

Now,

The nth term of arithmetic is a + (n - 1)d.

So,

= 5 + (n - 1)1

= 5 + n - 1

= 4 + n

The nth term is 4 + n.

The 75th term.

i,e

For n = 75,

= 4 + n

= 4 + 75

= 79

Thus,

The equation of the nth term is 4 + n.

The 75th term is 79.

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[tex]\log _6 \sqrt[3]{6} \quad[/tex]=0.3 i.e 1/3

[tex]\log _2 64[/tex] =6

[tex]-3 \log _5 25 \quad[/tex]=-6

[tex]\log _2 \sqrt[4]{8} \quad[/tex] = 0.75

[tex]\log _3 \frac{1}{81}[/tex]=-4

Generally, A logarithm is a mathematical function that determines the power to which a given number (called the base) must be raised to obtain a certain value. In other words, a logarithm is the inverse operation of exponentiation.

For example, if we take the base 2 and the value 8, the logarithm of 8 to the base 2 (written as log2 8) is 3, because 2 raised to the power of 3 (i.e., 2^3) equals 8.

Logarithms are widely used in many fields of science, engineering, and mathematics, particularly in areas where large numbers or very small numbers are involved. They are also used in data analysis, signal processing, and many other applications.

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Answer:

Values of x are ±4 and ±5

Step-by-step explanation:

Let y = [tex]x^{2}[/tex]

Which means: [tex]y^{2} = x^{4}[/tex]

Therefore:

A quadratic equation is formed:

[tex]y^{2} - 41y + 400 = 0[/tex]

The above quadratic equation can be simplified either by The Double Bubble Method or using the quadratic formula

Double Bubble Method:

[tex]y^{2} - 41y + 400 = 0[/tex]

The pair of factors of 400 that add together to give 41 are 25 and 16. Use these two factors to rewritre -41y:

[tex]y^{2} - 25y - 16y + 400 = 0[/tex]

Then do Factorization by grouping (i.e group the terms with common factors before factorizing):

[tex]y(y -25) - 16(y - 25) = 0[/tex]

[tex](y - 25)(y - 16) = 0[/tex]

The product of two expressions is zero, which means either of the two expressions is equal to Zero:

Either: [tex]y - 25 = 0[/tex]

Substituting [tex]y = x^{2}[/tex]:

          = [tex]x^{2} - 25 = 0[/tex]

         = [tex]x^{2} = 25[/tex]

         = [tex]\sqrt{x^{2}} = \sqrt{25}[/tex]

         ∴ x = ±5

 Or: [tex]y - 16 = 0[/tex]

Substituting [tex]y = x^{2}[/tex]

     [tex]= x^{2} - 16 = 0[/tex]

     [tex]= x^{2} = 16[/tex]

     [tex]= \sqrt{x^{2}} = \sqrt{16}[/tex]

    ∴ x = ±4

∴Values of x are ±4 and ±5

Answer:

Step-by-step explanation:

The factors of 96 are the integers that divide evenly into 96. To find the factors of 96, you can divide 96 by integers starting from 1 and increasing until you reach 96.

The factors of 96 are:

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

These are all the integers that divide evenly into 96.

Answer:

10.305

Step-by-step explanation:

Since the fish was share evenly amongst the 3 dolphins, and each one got 6, the equation will be:

f = d x n

where

f represents the fish

d represents the dolphin

n represents the number of fish each got.

Let's assume that the number of fish in the bucket before Colleen feeds the dolphins is "f". To find out how many fish there were in the bucket, you can use the following equation:

f = 3 * 6

where 3 is the number of dolphins and 6 is the number of fish each dolphin gets. Solving for "f", you get:

f = 3 * 6

f = 18

So there were 18 fish in the bucket before Colleen fed the dolphins.

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Answer: Choose Option D (look at the image for the solution and make sure to give me brainliest)

Step-by-step explanation:

There are two quadratic functions as A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.

The quadratic function is defined as a function containing the highest power of a variable is two.

A. 2b(b - 7) + b = 0 is a quadratic function because it can be simplified to the form of ax² + bx + c = 0 where a, b, and c are constants and x is the variable. In this case, a = 2, b = -13, and c = 0.

B. (4a + 2)(2a - 1) + 1 = 0 is also a quadratic function because it can be simplified to the form of ax² + bx + c = 0. In this case, a = 8, b = -2, and c = 1.

C. 2y + 2(3y - 5) = 0 is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.

D. 8 - 5x = 4(3x - 1) is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.

Thus, the correct answer would be options A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.

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