Sum and Product of Rational and Irrational Numbers

Answer:

Equation in terms of k about the average age is:

(2k + 61) / 5 = 17

After solving the equation, k = 12 years

Step-by-step explanation:

Age of Roxanne = k years

Age of the sister = (k + 8) years

Age of brothers = 21, 18 and 14 years

Total number of siblings = 5

Average age of siblings = [k + (k + 8) + 21 + 18 + 14] / 5

or, 17 = [2k + 61] / 5

or, 85 = 2k + 61

or, 24 = 2k

or, 12 = k

So, k = 12 years

electricity consumed:28 units

charge upto 20 units : 20 * Rs 3 : Rs 60

charge from (21 to 28) : 8 * Rs 6.50 : 52

total charge including service charge : Rs 60 + Rs 52 + Rs 50 : Rs 162

The statement that is not consistent with the display of the graphs of the z-distribution and of the z-distribution is given as follows:

The critical value for the t-distribution with this degrees of freedom will be less than 0.68.

The graph shows two curves, given as follows:

The z-distribution curve is more centered around the mean, meaning that most it's sample means will be closer to the mean than for the t-distribution.

Along the tails, the t-distribution curve is higher, meaning that it has a higher percentage of sample means around the tails and a higher critical value.

The critical value of 0.68 is for values one standard deviation for the mean for the z-distribution, while for the t-distribution it is higher, hence it is the false statement.

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The CD be worth in 5 years is

We would use the following formula to calculate compound interest:

A = P(1 + r / n) nt

Where

A is the CD's total value after t years.

The interest rate is represented by r.

The periodic interval at which it was compounded is represented by n.

P stands for the principal, or the amount of the CD purchase.

Considering the data provided,

P = 1500

r = 6% = 6/100 = 0.06

Since it was compounded 12 times in a year, n = 12.

The phrase changes.

A = 1500(1+0.06/12)^12 × t

A = 1500(1+0.005)^12t

A = 1500(1.005)^12t

1) If t is five years,

A = 1500(1.005)^12 × 5

A = $2023.3

2) If t equals ten years,

A = 1500(1.005)^12 × 10

A = $2729.1

3) If t equals 486 months, then 486/12 is 40.5 years.

A = 1500(1.005)^12 × 40.5

A = $16935

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If ∠2=10x+7 and one angle is 67 degrees then value of x is 6.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that the triangle has two equal sides which makes the triangle as isosceles.

In an isosceles triangle the two sides will be always equal and the angles will be also equal.

One angle of the triangle is 67 degrees

We need to find the ∠2.

As we know that the equal sides make equal angles.

∠2=67 degrees

and from given ∠2=10x+7

Now equation 67 with the 10x+7 to find the value of x.

So 67=10x+7

subtract 7 from both sides

67-7=10x+7-7

60=10x

Divide both sides by 10

x=60/10

x=6

Hence, the value of x is 6.

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Answer:

is there a pitcher with it

Step-by-step explanation:

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The maximum number of individuals who can visit the amusement park is 4.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question

The number of persons who can visit the theme park will be determined by the inequality that can be used to compute x and the information provided in the question:

8 + 23(x) ≤ 100

8 + 23x ≤ 100

23x ≤ 100 - 8

23x ≤ 92

x ≤ 92/23

x ≤ 4

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The measure of an interior angle (in degrees) of an [tex]n[/tex]-sided regular polygon is [tex]\frac{180(n-2)}{n}[/tex].

[tex]n=45 \implies \frac{180(n-2)}{n}=\boxed{172^{\circ}}[/tex]

The degree measure of one angle of a 45-sided regular polygon is 172°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, the polygon has 45 sides.

To find the measure of an interior angle of a regular polygon,

we make use of the formula for each angle = (n - 2) × 180 / n.

The formula calculated is only valid in cases of regular-sided polygons.

n =  45 substituting the value of n to the formula.

(n - 2) × 180 / n

= 180 ( 45-2) / 45

= 180 x 43 / 45

= 7740 / 45

= 172°

Therefore, the measure of one angle is 172°.

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The ratio of the number of men to women to adults is 5 : 3 : 4 and the number of women is 360

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

Men : Women = 5 : 3

Children : Adults = 1 : 2

This means that

Children : Men : Women  = 1 : 2(Men : Women)

So, we have the following representation

Children : Men : Women  = 1 : 2(5/8 : 3/8)

Open the brackets

Children : Men : Women  = 1 : 5/4 : 3/4

Multiply through by 4

Children : Men : Women  = 4 : 5 : 3

Rewrite the ratio as

Men : Women : Children 5 : 3 : 4

Here, we have

People = 1440

Recall that

Men : Women : Children 5 : 3 : 4

So, we have

Women = 3/(5 +3 + 4) * 1440

Evaluate the sum

Women = 3/12 * 1440

Evaluate the products

Women = 360

Hence, the number of women is 360

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Answer:

width is 2.75 and $6.60

Step-by-step explanation:

first divided by 132 by 12 which gives you 11 then divided 11 by 4 and you get 2.75.

Dubble Check: to chock multiply 12 x 4 x 2.75 which gives you 132.

Cost: Multiply 132 times 5 and you get 660 then place a decimal point between 6 and 6 to get $6.60

The pros and cons regarding the methods of the polynomial include:

Graphing the related system eliminates the need to rewrite the equation in order to set it equal to 0. It is simpler because you can graph each side of the equation separately.

It can be difficult to locate the system's intersection point at times. You may need to zoom in or learn how to resize the window. Using the related function allows you to find the points by focusing on the x-axis.

A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations such as addition, subtraction, multiplication, and division.

The formula is ax² + bx + c = 0, where a and b are coefficients, c is a constant, and the polynomial degree is 2. A trinomial equation is a polynomial with three variable terms. It is also known as a cubic equation. To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.

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Step-by-step explanation:

in a fraction as exponent the numerator defines the pure exponent of the base, and the denominator gives the degree of root of the base.

so, this is

[tex] \sqrt[5]{y^{3} } [/tex]

Answer:

[tex] \sqrt[5]{ {y}^{3} } [/tex]

Step-by-step explanation:

When converting an expression with a fractional exponent to its radical form, the base number goes inside the radical(which means it becomes the radicand) along with the numerator(which remains an exponent). Whereas the denominator of the exponent becomes the index, or what dictates whether the radical is a square root, cube root, etc.

EX:

[tex] {y}^{ \frac{a}{m} } = \sqrt[m]{ {y}^{a} } [/tex]

For the given equation, 1/x + 2/x+10 = 1/3,

1)The least common denominator is x+10. Option c is correct.

2)The equation will have 2 valid solutions. Option a is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is,

1/x + 2/x+10 = 1/3

[tex]\frac{1}{x}+\frac{2}{x+10}=\frac{1}{3}[/tex]

Cross-multiply the given equation,

[tex]3\left(x+10\right)+6x=x\left(x+10\right)[/tex]

The obtained value of x after simplifying the equation is,

[tex]\\\ x=5,\:x=-6[/tex]

Thus, for the given equation, 1/x + 2/x+10 = 1/3, the least common denominator is x+10. Option c is correct and the equation will have 2 valid solutions. Option a is correct.

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Answer: x= 2

Step-by-step explanation:

X+3/2(-1/2x+5/3)+2=3x-1

= x - 3/4x + 15/6 +2 = 3x -1

= 1/4x + 15/6 + 2 = 3x -1

= 1/4x + 27/6 = 3x -1

= 1/4x + 33/6 = 3x

= 33/6 = 11/4 x

= x = 2

The value of x is 18 if ∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that:

∠C and ​ ∠D ​ are vertical angles.

5x-7 = 8x-55

Subtract 5x from both sides:

-7 = 3x -55

Add 55 to both sides:

3x = 48

x = 48 /3

x = 16

Thus, the value of x is 18 if ∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?

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To solve this expression, we need to use the rules of order of operations, which dictate the order in which mathematical operations should be performed. The order of operations is typically abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Using the order of operations, we can solve the expression as follows:

64 - (-2)⁵ ÷ 2³ + (-1)³ · (0.5)²

= 64 - (-2)⁵ ÷ 8 + (-1)³ · 0.25

= 64 - (-32) ÷ 8 + (-1)³ · 0.25

= 64 + 32 + (-1)³ · 0.25

= 96 + (-1)³ · 0.25

= 96 + (-1) · 0.25

= 96 - 0.25

= 95.75

Therefore, the final result of the expression is 95.75

Answer:

#4 is one, and #5 is two.

Step-by-step explanation:

Therefore the given function is a polynomial function consisting of the constant 0 and the leading term 1.

A polynomial function is a function in an equation that only employs non-negative integer powers or only positive integer exponents of a variable, such as in a quadratic equation, cubic equation, etc. For instance, the polynomial 2x+5 has an exponent of 1.

Here,

Exponents are positive integers for the polynomial function given.

The positive integer 2x has an exponent of 1.

[tex]x^{5}[/tex], where is a positive integer with exponent 5, and.

Real numbers like 5 and 1 are among the coefficients in the function.

Consequently, a polynomial describes the function.

Having a degree of 5, it is a polynomial.

A polynomial is written in standard form by beginning with the term with the highest exponent and writing the remaining terms in descending order of terms with lower exponents.

Standard form for the polynomial is f(x)=2x+ [tex]x^{5}[/tex].

consisting of the constant 0 and the leading term 1.

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The equivalent fraction for 12/16 will be A. 3/4, 24/32

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

It should be noted that equivalent fraction for 12/16 will be found by reduction to lowest term. This will be:

12/16 = 3/4

Also multiply the numerator and denominator by 8 will give 24/32. In conclusion, the correct option is A.

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1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :

What is rational coefficients?

A coefficient is a number that is placed in front of a variable. A variable and a rational number are preceded by a rational coefficient, which may be an integer, decimal, or fraction.

(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32

1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisfices the given conditions. The leading coefficient here is 1, we call this a monic polynomial.

2. There may be something missing in the question here

3. We can use the factoring techniques to find the roots :

x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :

(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)

We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :

Y = (x-5)(x²+9)

This is the maximum we can do on R, but on C the set of complex we can still factor again.

x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9

Δ < 0, Δ = - 36

Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i

Y = (x-5)(x-3i)(x+3i)

So the solution is S = {5, 3i, -3i} the three roots of the function.

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Based on the Pythagorean theorem, the set of side of lengths that will form a right triangle are:

2, √5, 3

2, 2, √8

Based on the Pythagorean theorem, any set of side lengths that will form a right triangle would have the following relationship:

b² = a² + c², where b is the longest side or the hypotenuse of the right triangle and "b and c" are the lengths of the legs of the triangle.

For side lengths, 4, 8, and 12, we have:

12² = 4² + 8²

144 = 16 + 64

144 = 80 [not true, cannot form a right triangle]

For side lengths, 2, √5, 3, we have:

3² = (√5)² + 2²

9 = 5 + 4 [true, this set will form a right triangle]

For side lengths, 2, 2, √8, we have:

(√8)² = 2² + 2²

8 = 4 + 4

8 = 8 [true, this set will form a right triangle]

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The number of shirts Samuel can fold in 2 minutes is 12

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

Number of Shirts 3 6 ?

Time (minutes) 0.25 0.50 2

Represent the missing value with x

So, we have the following representation

Number of Shirts 3 6 x

Time (minutes) 0.25 0.50 2

From the above table of values, we have the following equation

6 : x = 0.5 : 2

Multiply the second ratio by 12

So, we have

6 : x = 6 : 12

By comparison, we have

x = 12

Hence, the number of shirts is 12

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The aggregate sum of perusing time for seven days as a blended number and an ill-advised part will be 1 ¹/₂ hour.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

An educator gives understudies free understanding 1/2 time for 1 hour, three times each week.

The aggregate sum of perusing time for seven days as a blended number and an ill-advised division is given as,

⇒ 1/2 x 3

Simplify the expression, then we have

⇒ 1/2 x 3

⇒ 3/2

⇒ 1 ¹/₂ hours

The aggregate sum of perusing time for seven days as a blended number and an ill-advised part will be 1 ¹/₂ hour.

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The slant height of the cone is 12.6 units

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

h= 12

diameter = d = 8

so, radius, r = d/2 = 8/2 = 4

Formula for slant height , l is:

l = √(h² + r²) = √(12² + 4² )

 = √(144 + 16) = √160 = 12.649 ≈ 12.6 units

The slant height of the cone is 12.6 units

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Answer:

Answer:

Step-by-step explanation:

[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Given numbers :

[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Let's convert percent and fraction into like decimals.

[tex]\frac{4}{9}\ = 0.444[/tex]

We know that to convert percentage into decimals, we need to divide it by 100, we get

[tex]40.5 = \frac{40.5}{100} = 0.405[/tex]

[tex]\frac{11}{25} = 0.400[/tex]

Now , placing the above decimal numbers in order  from least to greatest

[tex]0.400, 0.405, 0.440, 0.444[/tex]

[tex]=0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

a) The monthly repayment amount is $466.67.

b) The total interest paid on loan is $21,000.

Interests on student loans are computed using the simple interest system, instead of compound interest.

The total interest payable is a function of the outstanding balance (principal amount plus accumulated interest) during the non-payment period, the interest rate, and the number of years of payment.

Unsubsidized Loans plus Accumulated Interest = $35,000

Interest rate (APR) = 6%

Repayment period = 120 months (10 years x 12)

Interest on the student loan = $21,000 ($35,000 x 6% x 10)

Total amount to repay for 10 years = $56,000

Monthly repayment = $466.67 ($56,000 ÷ 120)

Thus, the monthly repayment will be $466.67, which is determined by adding the total interest for 10 years to the outstanding balance and dividing the result by 120 months.

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The predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

The given results of regression:

y = –0.693x + 28.802

The formula for regression equation is:

y = ax + b

So, given that:

a = –0.693

b = 28.802

r2 = 0.571536

r = 0.756

Back to the given results of regression:

y = –0.693x + 28.802

In this case, y represents the number of sit-ups a person can do, and x represents the hours of TV watched per day.

Thus, the predicted number of sit-ups for a person who watches x = 6 hours of TV is:

y = –0.693x + 28.802

y = –0.693 * 6 + 28.802

y = –4.158 + 28.802

y = 24.644

Hence, the predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

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