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What is the domain of the function?

To obtain a 40% alcohol solution from a 22% solution, you need to add 18% more alcohol.

100 ml of 22% alcohol solution contains 22 ml of pure alcohol and 78 ml of other ingredients.

Therefore, to obtain a 40% solution, you need 40 ml of pure alcohol in every 100 ml of solution.

So, 18 ml of pure alcohol should be added to 100 ml of 22% solution to obtain 40% solution.

Another way to calculate this is:

You can calculate the amount of pure alcohol you need to add by multiplying the initial volume of the solution (100ml) by the percentage increase in alcohol content (18%) .

100ml * 18% = 18ml

So you would need to add 18ml of pure alcohol to 100ml of 22% alcohol solution to obtain a 40% alcohol solution.

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Answer:



Step-by-step explanation:

Get a common denomenator, add the two fractions together and subtract the sum from 1 whole.

answer:B. 90 good luck I hope you pass

The answer is B which is 90

The additive inverse of 6 /- 13 is -6 /+ 13, which means that the two numbers have the same magnitude but opposite signs.

The additive inverse of a number is the number that needs to be added to the original number to get a result of zero. In other words, the additive inverse of a number is the opposite of the number in terms of sign. To find the additive inverse of 6 /- 13, we must multiply the negative sign of -13 by -1 to change it to a positive. This means that the additive inverse of 6 /- 13 is -6 /+ 13. This means that the two numbers have the same magnitude but opposite signs. To verify this, we can add the two numbers together. 6 /- 13 + -6 /+ 13 = 0. Therefore, the additive inverse of 6 /- 13 is -6 /+ 13.

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As per the given discount rate, the discount amount is $500 and the sale price is $2000

The term discount in math is defined as the process of equals the difference between the price paid for and it's par value.

Here we have given a department store has its mid year sale.

And here we have given that a knapsack originally priced at 2500 has a discount rate of 20%

Here let us consider that x be the discount, and then it can be calculated as,

=> discount amount = original price x 20%

Here we have to apply the values on the equation, then we get,

=> discount amount = 2500 x 20/100

=> discount amount = 500

Therefore, the sales price is calculated as,

=> Sales price = original price - discount price

=> sales price = 2500 - 500

=> sales price = 2000

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To meet, Armand and Jill will both travel for an equal length of time.

50t + 60t = 247.5 is the formula used to calculate the time, t, required for their meeting.

To meet Armand, Jill will travel 135 miles.

given that

Despite being 247.5 miles apart, Armand and Jill are heading in the same direction.

50 mph is the speed at which Armand is moving.

and Jill's vehicle is moving at a 60 mph pace.

Allow them to connect after t hours.

We understand that Distance=Speed*Time.

Armand traveled 50 miles, thus.

Jill traveled 60 t of distance.

Now that they are moving in that direction, do the following:

50t+60t=247.5--------------

(a)

1)To meet, Armand and Jill will both travel the same distance.

The value of 50t and 60t will differ for the same t, hence this statement is false.

2)Jill and Armand will both travel for an equal length of time to meet.

This is accurate because they will collide at the same time.

3)50t + 60t = 247.5 is the formula used to determine how long it will take for them to meet.

This statement is true.

4)They won't meet until 4.5 hours have passed.

We will calculate the value of t using equation (a) and determine if t=4.5 or not.

As 50t+60t=247.5

⇒ 110t=247.5

⇒ t=247.5/110=2.25

As a result, it will take 2.25 hours for them to finally meet.

Option 4 is therefore unsuitable.

5)To meet Armand, Jill will travel 135 miles.

Jill must travel 60 miles to meet Armand.

As t=2.25

60t = 60 x 2.25 = 135 miles.

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Answer:

2(3b+6) =78 : b=11

-2(6c-3) = -72 : c=6.5

Step-by-step explanation:

They are correct

Answer:

108

Step-by-step explanation:

x=2

12x+84

12(2)+84

24+84=108

The standard form of polynomial 2x³ + 8x² -23x +6.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

An expression that consists of exponents, constants, and variables that are concatenated using mathematical operations is referred to as a polynomial.

Given:

(x+6)(2x²-4x+1)

Multiplying the polynomial

= 2x³  -4x² + x + 12x² - 24x + 6

= 2x³ -4x² + 12x² + x -24x + 6

= 2x³ + 8x² -23x +6

Hence, the required polynomial is  2x³ + 8x² -23x +6.

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Answer:

t=2

Step-by-step explanation:

t>o and t² - 4 = 0

[tex]t^2=4[/tex]

[tex]t=\sqrt{4}[/tex]

[tex]t=+2/-2[/tex]

As t>0

Therefore, t=+2

Thus, if t>o and t² - 4 = 0, the value of t=+2

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The experimental probability that you are elected president and your friend is elected treasurer is obtained as follows:

Number of desired outcomes/50.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes for this problem is given as follows:

50.

As the number of randomly generated numbers is of 50.

The number of desired outcomes is the amount of the 50 numbers that have either 1 or 2 in the tens place, and also either 1 or 2 in the units place.

Hence the probability is given by the following fraction:

Number of desired outcomes/50.

The problem is incomplete and could not be found in any search engine, hence the answer was given in general terms.

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Answer:

-152

Step-by-step explanation:

Given that h(t) = 161-4t and g(t) = 3-2t,

g(-1) = 3-2(-1) = 3+2 = 5

h(1) = 161-4(1) = 161-4 = 157

Therefore, g(-1)-h(1) = 5 - 157 = -152

So the value of g(-1)-h(1) is -152

The second derivative test for a multivariable function is generally in a positive definite quadratic form.

In mathematics, the second partial derivative test is a method in multivariable calculus which used to determine if a critical point of a function is a local minimum, maximum or saddle point.

A partial derivative of a multivariable function is a derivative with regard to one variable with other variables adhered constant. It is used to describe the concepts of gradient, divergence, and curl in terms of partial derivatives.

The second derivative of a function is directly the derivative of the function's derivative. Let's consider, as an example, the function f(x) = x^3 + 2x^2.

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The minimum value is 0.5 and the maximum value is 3.5.

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Our Pythagorean triplets will be (3,4,5) and (6,8,10).

So what is the Pythagorean triplet?

The square of the greatest number in a Pythagorean triplet equals the sum of the squares of the other two numbers.

The greatest side in a right-angled triangle is called the hypotenuse.

So, in our first triplet (3,4,5) the greatest side is 5. So, hypotenuse = 5.

=  [tex]hypotenuse^{2}[/tex] = [tex]5^{2}[/tex] = 25.

Now, [tex]3^{2}[/tex] + [tex]4^{2}[/tex] = 9 + 16 = 25.

So, [tex]5^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex].

Thus (3,4,5) is a Pythagorean triplet.

In the second case (6,8,10) hypotenuse = 10.

= [tex]hypotenuse^{2}[/tex] = [tex]10^{2}[/tex].

Now, [tex]6^{2}[/tex] + [tex]8^{2}[/tex] = 36 + 64 = 100.

So, [tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]8^{2}[/tex].

Thus (6,8,10) is a Pythagorean triplet.

In the Third case (8,10,12) Hypotenuse = 12.

= [tex]hypotenuse^{2}[/tex] = [tex]12^{2}[/tex] = 144.

Now, [tex]8^{2}[/tex] + [tex]10^{2}[/tex] = 64 + 100 = 164.

So, [tex]12^{2}[/tex] [tex]\neq[/tex] [tex]8^{2}[/tex] + [tex]10^{2}[/tex].

Thus (8,10,12) is not a Pythagorean Triplet.

Therefore our two results (3,4,5) and (6,8,10) are Pythagorean triplets.

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A conversion of this equation in point-slope form into standard form is y = x/2 + 1.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

y - 3 = -1/2(x + 4)

Making y the subject of formula in the above equation, we have the following:

y = x/2 - 2 + 3

y = x/2 + 1

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12b+12p can be written as (9b + 9p) + (3b + 3p) to show the fruit for Nathan's kebabs and Linda's kebabs separately.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

Given,

Each kebab needs the same number of blueberries, b, and the same number of pineapple pieces, p.

Total number of kebabs = 12

Fruits needed to make them = 12b + 12p

Fruits needed to make 3 kebabs by Linda = 3b+3p

If Linda makes 3 kebabs

then Nathan would make 12 -3 = 9 kebabs

Fruits needed make 9 kebabs by Nathan = 9b + 9p

thus, to show the fruit for Nathan's kebabs and Linda's kebabs separately, 12b + 12p can be written as

12b + 12p

= 9b + 3b + 9p + 3p

Grouping,

= (9b + 9p) + (3b + 3p)

Hence, (9b + 9p) + (3b + 3p) is the rewritten form of 12b+12p so that it shows the fruit for Nathan's kebabs and Linda's kebabs separately.

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Margie worked for 47 hours.

The given table is about the times recorded on the timesheet for the week.

We have to calculate the total time she worked for.

From 7:05 to 3:58

If 7:05 is a.m. then 3:58 will be 15:58 pm.

By subtraction of these timings we can get the number of hours she has worked.

15:58 - 07:05 = 8:53 (8 hours 53 minutes)

From 7:30 a.m. to 17:01 pm

17:01 - 07:30 = 9:31 (9 hours 31 minutes)

From 8:01 a.m. to 17:32 pm

17:32 - 08:01 = 09:31 ( 9 hours 31 minutes)

From 07:22 a.m. to 16:46 pm

16:46 - 07:22 = 09:24 (9 hours 24 minutes)

From 6:55 am to 16:31 pm

16:31 - 06:55 = 9:36 (9 hours 36 minutes)

Therefore, total time she worked = 8:53 + 9:31 + 9:31 + 9:24 + 9:36 = 44:175 (44 hours 175 minutes)

Now we will convert minutes to hours

175 minutes = 2 hours 55 minutes

So total working hours = 44 hours + 2 hours 55 minutes = 46 hours 55 minutes ≈ 47 hours

Therefore, Margie worked for 47 hours.

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The coordinate A , B and C will be A(2,2), B(2,6) and C(10,2)

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

In order to make it simple to identify the points, a cartesian plane divides the plane space into two dimensions. The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axes of the coordinate plane. The origin is the place where these coordinate axes connect, and they split the plane into four quadrants (0, 0). Additionally, each point in the coordinate plane is denoted by the coordinates (x, y), where x represents the point's location in relation to the x-axis and y represents its position in relation to the y-axis.

Since it is factored by 2

The coordinate A , B and C will be

A (1*2, 1*2) = A(2,2)

B(2,6) and C(10,2)

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The quotient of 3 8 and 2 3 is equal to 4. This can be determined by dividing 3 8 by 2 3 and simplifying the fractions. The result is 4.

To determine the quotient of 3 8 and 2 3, begin by dividing 3 8 by 2 3. This can be done by multiplying the numerator (3) and denominator (8) of 3 8 by the reciprocal of 2 3, which is 3 2. Doing this yields 9 16. Now, reduce the fraction by dividing both the numerator and denominator by the greatest common factor (GCF) of 9 and 16, which is 3. The result is 3 5. Finally, convert the fraction to a whole number by dividing the numerator (3) by the denominator (5). The result is 4. Therefore, the quotient of 3 8 and 2 3 is 4.

3 8 ÷ 2 3 = (3 × 3 2) ÷ (8 × 3 2) = 9 16 ÷ 9 2 = 9 16 ÷ 3 = 3 5 = 3 ÷ 5 = 4

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The product is the answer to a multiplication problem.

You can obtain the result by repeatedly adding the whole number of groups in the problem. This is known as repeated addition. We are aware that multiplication is the term used to describe repeated addition. On a number line, we start at 0 and go steadily to the right side of the number line to multiply integers. Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division. In arithmetic, multiply refers to continuously adding sets of the same size. In mathematics, multiplying the numbers yields the product of two or more integers.

The multiplication of two integers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.

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Yes, the given statement that prime number is infinite is true.

As given in the question,

Let us consider there are finite prime numbers.

The finite prime numbers be P₁ , P₂, P₃ , ......., Pₙ

Now let us consider there exist a number which represents the product of all the given numbers

P =  P₁ × P₂ × P₃ × .......× Pₙ

To make P as a prime number add 1 to it.

P = P₁ × P₂ × P₃ × .......× Pₙ + 1

It represents that P is the next prime numbers to the given 'n' prime number.

This implies that

Out supposition is wrong.

Therefore, there exist infinite number of prime numbers.

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Answer:

Step-by-step explanation:

area of trapezoid = 1/2 (a + b) h

where 'a' and 'b' are parallel sides.

and 'h' is height.

                 area     = 1/2 (9 + b) 18.9

                  226.8 = 1/2 (9 + b) 18.9

                   226.8 × 2 = (9 + b) 18.9

                     453.6 = (9 + b) 18.9

                     453.6 ÷ 18.9 = (9 + b)

                        24 = (9 + b)

                          b = 15 millimeters

On solving the provided question, we can say that in this circle the radius is [tex]7\pi /6[/tex] area = [tex]\pi r^2[/tex] =3.14*7/6*2/6*3.14*3.4 = 13.0365822222 = 12 units sq.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in this circle the radius is [tex]7\pi /6[/tex]

area = [tex]\pi r^2[/tex] =3.14*7/6*2/6*3.14*3.4 = 13.0365822222 = 12 units sq.

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The total volume of the tank is 400π + 78.72 cubic metres. To the nearest cubic meter, it is approximately 400π + 79 cubic metres.

What is the volume of a cylinder?

The volume of a cylinder is the amount of space inside the cylinder. It can be calculated by multiplying the area of the base by the height of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base of the cylinder and h is the height.

The tank is shown as a cylinder with a rectangular prism on top. To find the volume of water the tank can hold, we will need to find the volume of the cylinder and the rectangular prism separately, and then add them together.

The cylinder has a radius of 5 metres and a height of 8 metres. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. So the volume of the cylinder is V = π(5²)(8) = 400π cubic metres.

The rectangular prism has a length of 4.2 metres, a width of 2.2 metres and a height of 8 metres. The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width and h is the height. So the volume of the rectangular prism is V = (4.2)(2.2)(8) = 78.72 cubic metres.

So the total volume of the tank is 400π + 78.72 cubic metres. To the nearest cubic meter, it is approximately 400π + 79 cubic metres.

Please note that since π is an irrational number, the value of 400π is not an exact value, but an approximation.

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x and y​ are not proportional and the value of the card in 2011​ is $33.14.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Given that, when he retired in 2000 his card was worth ​$7.73. The value has increased by ​$2.31 each year since then.

Let the value of the card y in dollars and the number of years x the player has been in retirement.

Now equation is y=7.73+2.31x

When x=1

y=$10.04

When x=2

y=7.73+2.31(2)

y=$12.35

When x and y are proportional

1/10.04 ≠2/12.35

Now, the value of the card in 2011​

y=7.73+2.31(11)

y=$33.14

Hence, x and y​ are not proportional and the value of the card in 2011​ is $33.14.

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Answer:

the radius is 8.5

Step-by-step explanation:

54 divided by pie/3.14 = 17 (plus decimals)

17 Divide by 2 = 8.5

In mathematics, there are several types of inequalities that are commonly studied, including linear inequalities, quadratic inequalities, absolute value inequalities, rational inequalities, logarithmic inequalities and trigonometric inequalities.

Linear inequalities: These are inequalities involving a linear function and a single variable. They can be represented in the form of "ax + b > c" or "ax + b < c" where a, b, and c are constants, and x is the variable.

Quadratic inequalities: These are inequalities involving a quadratic function and a single variable. They can be represented in the form of "ax^2 + bx + c > 0" or "ax^2 + bx + c < 0" where a, b, and c are constants, and x is the variable.

Absolute value inequalities: These are inequalities involving the absolute value of a variable or expression. They can be represented in the form of "|x| > a" or "|x| < a" where x is the variable and a is a constant.

Rational inequalities: These are inequalities involving a rational function (a function with a fraction) and a single variable. They can be represented in the form of "f(x) = (ax+b)/(cx+d) > 0" or "f(x) = (ax+b)/(cx+d) < 0" where a, b, c, d are constants, and x is the variable.

Logarithmic inequalities: These are inequalities involving logarithmic functions and a single variable. They can be represented in the form of "loga(x) > b" or "loga(x) < b" where a and b are constants, and x is the variable.

Trigonometric inequalities: These inequalities involve trigonometric functions such as sine, cosine, and tangent. These inequalities can be used to describe the range of possible values for an angle or a real-valued function.

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MN, RS, and NP in this triangle are, respectively, 410, 400, and 320 when MN = 5x + 10.

Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometrical forms. Triangle ABC is the term used to describe a triangle containing the vertices A, B, and C.A triangle is a polygon because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.

given

as AMNP-ARST

the x = 80

so MN = 5 * 80 + 10

= 410

RS = 6* 80 - 8

= 400

MN, RS, and NP in this triangle are, respectively, 410, 400, and 320 when MN = 5x + 10.

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To solve the expression 4e + d + 12 - 2e for given values of d and e, we need to substitute the given values in place of the variables in the expression and then perform the calculations.

Given that d = 6 and e = 2

So, the expression becomes:

4(2) + 6 + 12 - 2(2)

Now we can perform the calculation:

8 + 6 + 12 - 4 = 10 + 12 = 22

Therefore, the value of the expression 4e + d + 12 - 2e when d = 6 and e = 2 is 22.

Answer:

[tex] \sf \: d + 2e + 12 = 22 [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 4e + d + 12 - 2e

Now we have to use,

→ d = 6

→ e = 2

Let's simplify the expression,

→ 4e + d + 12 - 2e

→ d + 4e - 2e + 12

→ (d) + (4 - 2)e + (12)

→ d + (2)e + 12

→ d + 2e + 12

→ 6 + 2(2) + 12

→ 6 + 4 + 12

→ 10 + 12 = 22

Therefore, the answer is 22.