33. Solve the equation and check your solution: -2(x - 1) = 2 - 2x

Answer: The tip is 20% of the cost including tax. Thus .20 * X=3.50.Divide both sides of the equation by .20..20 divided into .20 = 1, so “X” = 1.And 3.50 divided by .20 = 17.50 So X = 17.50, cost of the meal plus the tax.The tax is .07, so we know that 100% of the meal cost PLUS 7% of the meal cost is 107% of the meal cost. That is 1.07 * Meal without tax = 17.50. Divide 17.50 by 1.07 and you get 16.355. Round up to 16.36.Is that right? Let’s see:7% tax on meal at 16.36 is 16.36 * .07 = 1.1452. Round up to 1.15.$1.15 + 16.36 = 17.51.And 20% (the tip) of 17.51 is .20 * 17.51 = 3.50Cost of the whole meal; food, tax and tip is 16.36+1.15+3.50 = 21.01. 

Step-by-step explanation: my big brain

The answer to the quadratic equation is x=1±√33/4.

In mathematics, a quadratic equation is one of degree 2, which means that its maximum exponent is 2. A quadratic has the formula y = ax2 + bx + c, where a, b, and c are all integers and a cannot be zero.

Use the quadratic formula to find the solutions.

−b±√b²−4(ac)/2a

Substitute the values a=2, b=−1, and c=−4 into the quadratic formula and solve for x.

1±√(−1)²−4⋅(2⋅−4)/2⋅2

Simplify.

Simplify the numerator

Raise −1 to the power of 2.

x=1±√1−4⋅2⋅−4/2⋅2

Multiply −4⋅2⋅−4.

Multiply −4 by 2.

x=1±√1−8⋅−4/2⋅2

Multiply −8 by −4.

x=1±√1+32/2⋅2

Add 1 and 32.

x=1±√33/2⋅2

Multiply 2 by 2.

x=1±√33/4

The result can be shown in multiple forms.

x=1±√33/4

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a) An approximate equation of the line of best fit for the data is,

⇒ y = 18/13 (x - 7)

b) The amount charged per hour by a dog sitter with 10 years of experience is, $54/13

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The scatter plot shows the number of years of experience, x , and the amount charged per hour, y , for each of 24 dog sitters in Texas.

Now, Add a line of best fit (see attached).

Here, The two points on the line are,

⇒  (7, 0) and (20, 18)

Thus, Use these points to find the slope of the line is,

⇒ m = (18 - 0) / (20 - 7)

⇒ m = 18 / 13

Use the found slope and one of the points in the point-slope form of the linear equation to find an equation for the line of best fit:

⇒ y - y₁ = m (x - x₁)

⇒ y - 0 = 18/13 (x - 7)

⇒ y = 18/13 (x - 7)

Substitute x = 10 we get;

⇒ y = 18/13 (x - 7)

⇒ y = 18/13 (10 - 7)

⇒ y = 18/13 × 3

⇒ y = $54/13

Thus, An approximate equation of the line of best fit for the data is,

⇒ y = 18/13 (x - 7)

b) The amount charged per hour by a dog sitter with 10 years of experience is, $54/13

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The value of the unknown is 628.57

Percent simply means "per hundred" and the symbol used to express percentage is %. One percent (or 1%) is one hundredth of the total or whole and is therefore calculated by dividing the total or whole number by 100. Example: 1% of 250 = (1 ÷ 100) x 250 = 2.5.

Represent the unknown by x

therefore;

35/100 × x = 220

multiply both sides by 100

35x = 22000

x = 22000/35

x = 628.57

therefore 35% of 628.57 is 220

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The number of questions on the math quiz, given the points per question and the total points, in the quiz, was 15 questions.

To find the number of questions in the quiz, you can use the formula :

= Number of total points in the quiz / Number of points per question

Number of total points in the quiz = 45 points

Number of points per question

The number of questions given in the quiz by Mr. Thurgood is:

= 45 / 3

= 15 questions

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The full question is:

Mr. Thurgood gave his students a math quiz last Friday. Each question on the quiz was worth 3 points, and the quiz was worth 45 points in all. How many questions were in the quiz?

The probability that a randomly selected woman does not have red/green colorblindness is 0.98 (98%).

The probability of not having red/green colorblindness is the inverse of the probability of having colorblindness. The probability of having red/green colorblindness is given as 0.92%. To calculate the probability of not having red/green colorblindness, subtract the probability of having colorblindness from 1. 1 - 0.92 = 0.08. This means that the probability of not having red/green colorblindness is 0.08, or 8%. To convert this to a percentage, multiply by 100. 0.08 x 100 = 8%. The probability of not having red/green colorblindness is 8%. This can also be written as 0.98 (98%).

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The solution of the inequality is x < 5

Inequalities are defined as unequal comparison between two expressions, numbers or equations on the basis of their sizes on the number line.

From the information given, we have that;

-8<4(8-2x)

expand the bracket

-8 < 32 - 8x

collect like terms

-8 - 32 < -8x

subtract the like terms

-40 < - 8x

Make 'x' the subject of formula, we have to divide both sides by the coefficient of x, we get;

-40/-8 < -8x/-8

Divide the values

x < 5

Hence, the value is x < 5

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Answer:

2900

Step-by-step explanation:

16/25+24/30+3/4

=25*30*4=2900

Domain and range of the composite function (gof)(x) formed by given f(x) and g(x) is equal to all positive real numbers and y > 6 , y ∈R  respectively.

Function f(x ) is :

f(x) = e^x

Function g(x) is :

g(x) = x + 6

To find the range of composite function (gof)(x) simplify the function .

(gof)(x)

= g ( f(x))

Substitute f(x) = e^x we get

= g ( e^x )

Replace x by e^x in g(x) we get,

= e^x + 6

Domain of the composite function is given by all the value based on e^x that is all positive real numbers.

Range is translated by 6.

y > 6 , y∈ R ( positive real numbers)

Therefore, the domain and range of  composite function (gof)(x) is all positive real numbers and y > 6 , y∈ R ( positive real numbers) respectively.

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The inequality of the statement is x <= 5

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

The data plan on your family's cell phone costs more if your family uses more than 5 GB in a month

Represent the data plan with x

This means that the inequality is

x <= 5

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(−5, 2) is point lie on a line that passes through the origin with a slope of −2/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the points lie on a line that passes through the origin with a slope of −2/5

The line passes through (0, 0) and (x, y) form a slope of -2/5

-2/5=y/x

So y is 2 and x is 5.

Hence, (−5, 2) is points lie on a line that passes through the origin with a slope of −2/5

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Answer: IS easy you only need to put your answer that you got when you multiply the numbers:)

Step-by-step explanation:

The height, in inches, of the entertainment center is 32 inches while other dimensions are 16 inches.

The volume of the unit will be the product of length, depth and height. Now the depth will be 2x. Based on this, performing the calculation to find the value of x.

Volume = length × depth × height

8192 = x × x × 2x

Performing multiplication on Right Hand Side of the equation

8192 = 2x³

Rewriting the equation according to x

x³ = 8192/2

Performing division on Right Hand Side of the equation

x³ = 4096

Taking cube root on Right Hand Side of the equation

x = [tex] \sqrt[3]{4096} [/tex]

x = 16 inches

Height = 2×16

Performing multiplication on Right Hand Side of the equation

Height = 32 inches

Thus, length and depth are 16 inches and height is 32 inches.

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The most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C 12, 4), D(5,2) is A. parallelogram.

The most precise name for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C (8, 8), D (8,5) is A. kite

Since the lengths of all sides are equal and the opposite sides are parallel, because the slopes of two parallel lines are equal. Therefore, ABCD is a parallelogram because opposite sides are parallel and congruent.

Also, since, the two disjoint pairs of consecutive sides are congruent as AB=DA and BC=CD. Thus, by definition of kite, that Two disjoint pairs of consecutive sides are congruent, the given quadrilateral is a kite.

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Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]

Product of an Equation:

In mathematics, a product is a number or quantity obtained by multiplying two or more numbers. Example: 4 × 7 = 28, where the number 28 is said to be the product of 4 and 7. Another example: 6 times 4 is 24, so 6 multiplied by 4 is 24. The product of two positive numbers is a positive number, as if the product of two negative numbers is also positive (e.g., -6 × -4 = 24).

Now,

(A) We need to find the product of two given expressions.

[tex]\frac{1}{2x} -\frac{1}{4}[/tex] ×  [tex]5x^{2} -2x +6[/tex]

To multiply two given expressions, first multiply the first term in the first parenthesis by the entire expression in the second term, then do the same for the second term in the first parentheses.

[tex]\frac{1}{2x} -\frac{1}{4}[/tex] × [tex]5x^{2} -2x +6[/tex]

⇒ [tex]\frac{1}{2x} * [5x^{2} -2x +6] - \frac{1}{4} * [5x^2 - 2x +6][/tex]

⇒ [[tex]\frac{1}{2x} * 5x^2[/tex] - [tex]\frac{1}{2x} *2x[/tex] + [tex]\frac{1}{2x}* 6[/tex] ] - [ [tex]\frac{1}{4} * 5x^2 + \frac{1}{4} * 2x - \frac{1}{4}*6[/tex]]

Now, simplify the equation:

[tex]\frac{5x}{2} -1 + \frac{3}{x} - \frac{5x^2}{4} +\frac{x}{2} +\frac{3}{2}[/tex]

Rearranging the equation:

[tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]

Thus, the product of the two expressions is [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex].

(B) To compare the two expressions we will find the value of the two given expressions,

[tex]\frac{1}{2x} -\frac{1}{4} * 5x^{2} -2x +6[/tex] = [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]

For the value of:

[tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]

simplifying the equation:

    [tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]

⇒ [tex][\frac{1}{4x} * (5x^{2} -2x +6)] - [\frac{1}{2} * (5x^{2} -2x +6)][/tex]

⇒ [tex]-\frac{5x^2}{2} + \frac{9x}{4} + 3.5 +\frac{3}{2x}[/tex]

As you can see, the result of the product of the two expressions is different.

Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]

Complete Question:

What is the product of 1/2x-1/4 & 5x^2-2x+6? Write your answer in standard form.

(A) show your work.

(B) is the product of 1/2x-1/4 & 5x^2-2x+6 equal to the product of 1/4x-1/2 & 5x^2-2x+6? Explain your answer

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As a result, f(-2) has a value of -1 by simply substituting the value of x in the function. as Each function is given a domain and a codomain, often known as a scope.

Math deals with numbers with their variants, formulae and adjacent tissues, structures and associated locations, and areas where they might be found. The term "function" refers to the connection between a series of inputs, of which each has a corresponding output. A function is a connection between the inputs and outputs where each input result in a single, unique output. A domain as well as a codomain, or scope, are allocated to each function. Functions are generally symbolized by the letter f. (x). The input is an x. On functions, another functions, many-to-one functions, within operations, and on functions are the four main types of functions that are available.

given

f(x)=2(x)+3=5

= f(-2) = 2(-2) + 3 = 5

= -4 + 3

= -1

As a result, f(-2) has a value of -1 by simply substituting the value of x in the function. as Each function is given a domain and a codomain, often known as a scope.

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Answer:

Trinomial

Step-by-step explanation:

A trinomial is an algebraic expression with three, unlike terms.

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When computing the area of a circle, the mathematical constant pi () is required. Pi is the circumference-to-diameter ratio of a circle and is approximately equal to 3.14159.

The area of a circle is calculated by multiplying pi by the radius squared (r2). To estimate the area of a circle, utilize pi in the calculation since it is a vital aspect of the relationship between the circumference and diameter of a circle.

Pi is not required when determining the area of a square, rectangle, or cube since the formulas for these shapes are different.

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The question is -

The mathematical constant pi is needed when calculating the area of a _.

a. circle

b. square

c. rectangle

d. cube

Answer:

1.769 pounds

Step-by-step explanation:

36.269 - 34.5 = 1.769

The measure of the angle X is equal to 38.7° to the nearest tenth using the trigonometric ratio of tangent of X.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

For the tangent of X equal, we can make x the subject by finding the tan inverse of opposite divided by the adjacent side as follows:

tan X = 8/10 {opposite/adjacent}

X = tan⁻¹(0.8)

X = 38.6598

Therefore, the measure of the angle X is equal to 38.7° to the nearest tenth using the trigonometric ratio of tangent of X.

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When x = 6, the value of y is:

y = -5x

y = -5(6)

y = -30

Therefore, when x = 6, y is equal to -30.

Answer:

-30

Step-by-step explanation:

given,

y = -5x

x = 6

Now,

y = -5x

or, y = -5(6)

therefore, y = -30

Answer:

  (c)  x = 18/5

Step-by-step explanation:

You want the solution to -(-2 -5x) +(-2) = 18.

Eliminating parentheses, we have ...

  2 +5x -2 = 18

  5x = 18 . . . . . . . simplify

  x = 18/5 . . . . . . divide by 5

Answer:

91.63%

Step-by-step explanation:

The annual interest rate is 1.2% if Stanley invests £7500 for 4 years in a savings account.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for compound interest:

[tex]A = P (1 + r/n)^(^n^t^)[/tex]

where A = the final amount, P = the principal (initial investment), r = the annual interest rate (as a decimal), n = the number of times the interest is compounded per year and t = the time in years

We know that P = £7500, t = 4 years, and A = £7866.53.

Let n is 1

Plugging in the values we know, we get:

£7866.53 = £7500 (1 + r/1)⁴

Simplifying the equation:

(1 + r)⁴ = 1.04887

Taking the fourth root of both sides:

1 + r = 1.012

Subtracting 1 from both sides:

r = 0.012 or 1.2%

Therefore, the annual interest rate is 1.2%.

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Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. The expected value of his or her total winnings for the four spins is $800.

Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again.

We have to determine the expected value of his or her total winnings for the four spins.

Total winning depends on the fourth term.

Outcome              Skunk        100        200        500

Probability              1/4            1/4          1/4          1/4

Total Winning          0             900       1000       1300

Expected Total Winning = 1/4 (0 + 900 + 1000 + 1300)

Expected Total Winning = 1/4 × 3200

Expected Total Winning = 800

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The complete question is:

Contestants on a game show spin a wheel like the one shown in the figure above. Each of the four outcomes on this wheel is equally likely and outcomes are independent from one spin to the next.

The contestant spins the wheel.

If the result is a skunk, no money is won and the contestant's turn is finished.

If the result is a number, the corresponding amount in dollars is won.

The contestant can then stop with those winnings or can choose to spin again, and his or her turn continues.

If the contestant spins again and the result is a skunk, all of the money earned on that turn is lost and the turn ends.

The contestant may continue adding to his or her winnings until he or she chooses to stop or until a spin results in a skunk.

Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. What is the expected value of his or her total winnings for the four spins?

False. The given statement is not a valid proof of the theorem because it is circular.

The proof starts with the assumption that there exists an integer k such that n < k < n^2 and then uses this assumption to conclude that the theorem is true. However, this does not actually prove the existence of k, it simply restates the theorem. A valid proof would need to start with some other set of premises and use logical deduction to arrive at the conclusion that such a k exists. The given statement is not sufficient to establish the truth of the theorem.

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$612.50.

Step-by-step explanation:

Answer:

8.2%

Step-by-step explanation:

To find the sales tax percentage, we need to determine how much of the total price was due to sales tax. To do this, we can subtract the price of the cupboard from the total price:

$92.82 - $85.78 = $7.04

So the sales tax was $7.04. We can then divide the sales tax by the price of the cupboard and multiply by 100% to find the sales tax rate as a percentage:

$7.04 / $85.78 * 100% = 8.2%

Rounding to the nearest tenth, the sales tax rate was 8.2%.

Answer:

8.2% (rounded to the nearest tenth)

Step-by-step explanation:

$92.82-$85.78= $7.04

100%= $85.78

1%= $85.78÷100

= $0.8578

$7.04÷$0.8578= 8.2% (rounded to the nearest tenth)

The distance apart is given as 1/3 inches

Since the original scale was 2 inches = 45 miles, the highway length on the original map was 8 inches * 45 miles/2 inches = 180 miles.

So, each of the 17 rest stops was spaced 180 miles / (17 - 1) = 10 miles apart on the highway.

With the new scale of 1 inch = 30 miles, each inch on the map represents 30 miles on the highway.

Thus, each rest stop on the new map is 10 miles / 30 miles/inch = 10/30 inches = 1/3 inch apart.

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