Bill paid $45in tax on a laptop that cost $500. What percent sales tax did Bill pay?

Sally put in 36 hours, Harold put in 30 hours, and Nora put in 15 hours.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let x be the work hours of Sally, y be the work hours of Harold and z be the work hours of Nora.

x+y+z=81

x=y+6

y=2z

x=2z+6

2z+6+2z+z=81

6+5z=81

5z=75

z=15

y=2z

=30

x=y+6

=30+6

=36

Sally worked for 36 hours while Harold worked for 30 hours and Nora worked for 15 hours.

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Answer:Answer Choice C

Step-by-step explanation:To solve this problem, we need to find the area of the rectangle by doing 9X5, which is 45. Next we have to find the area of the triangle, and then subtract it by the area of the rectangle to find the area of the figure. To find the area of a triangle, we do BaseXHeight divided by 2, and in this problem, we do 9X2 (which is 18) and 18 divided by 2 which gets us 9. Now we subtract 9 from 45, which gets us 36 which means 36m2 is the answer to this problem.

The given statement "when a transversal crosses two parallel lines, Corresponding angles are created, which are congruent to one another" is TRUE.

The angles created when a transversal intersects two parallel lines are known as corresponding angles.

Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.

Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Therefore, the given statement "when a transversal crosses two parallel lines, Corresponding angles are created, which are congruent to one another" is TRUE.

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Answer:

461.814 is part A

103.67 is part

The required probability is 7/18 that an eighth grader chosen at random will play the keyboard.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The total number of eighth-grade students in the School of Rock is 12 + 6 + 4 + 14 = 36 students.

The number of eighth-grade students playing the keyboard is 14 students.

So, the probability that an eighth grader chosen at random will play the keyboard is :

⇒ 14/36

In the simplest form, 14/36 can be reduced to 7/18.

Thus, the required probability is 7/18.

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Answer:

4.2571428571 (but you should probably round for 4.3 or 4.26)

Step-by-step explanation:

if he spent $7.45 and each pound costs $1.75 then just divide 7.45 by 1.75.

Anthony bought exactly 4.2571428571 pounds of trail mix. However, it can be rounded off to 4.3 pounds.

The total amount spent on trail mix= $7.45

1 pound of trail mix costs $1.75

Therefore, the amount of trail mix bought= total amount spent on it / the cost of 1 pound of the product

= 7.45 / 1.75

= 4.2571428571 pounds

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The expression is equal to f(x) g(x) is 77x⁷ + 78x⁶ - 27x⁵

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

In order to find which expression is equal to f(x) g(x), multiply (11x³ - 3x²) by (7x⁴ + 9x³). That is:

f(x) g(x) = (11x³ - 3x²)(7x⁴ + 9x³)

Expand the expression:

f(x) g(x) = 11x³ × 7x⁴ + 11x³ × 9x³ - 3x² × 7x⁴ - 3x² × 9x³

f(x) g(x) = 77x⁷ + 99x⁶ - 21x⁶ - 27x⁵

Combine like terms:

f(x) g(x) = 77x⁷ + 78x⁶ - 27x⁵

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Complete Question

Select the correct answer.

Consider functions f and g.

f(x) = 11x³ - 3x²

g(x) = 7x² + 9x³

Which expression is equal to f (x) g(x)?

A. 7x⁴ + 99x³ -3x²

B.77x¹² +99x⁹- 21x⁸ - 27x⁶

C. 18x⁷ + 10x⁶ + 6x⁵

D. 77x⁷ + 78x⁶ - 27x⁵

Answer:

67,43/10 = 6.743

When dividing any number by 10, you just move the decimal to the left. When multiplying, you move it to the right.

Step-by-step explanation:

Hope it helps! =D

The degree of the function is 3, and the end behavior is that as x gets very large or very small the function increases or decreases without bound respectively.

Generally, The degree of a polynomial function is the highest power of the variable in the function. In this case, the highest power of x is 3, so the degree of the function is 3.

The end behavior of a polynomial function refers to how the function behaves as the value of x gets very large or very small (i.e., as x approaches positive or negative infinity).

To find the end behavior, we look at the leading term, which is the term with the highest degree. In this case, the leading term is 3x³. Since the coefficient of x³ is positive, the end behavior of the function as x approaches positive infinity is positive infinity, and as x approaches negative infinity, the end behavior of the function is negative infinity.

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The comparison that can be be made between population of city A and B is City A < City B

The population of city A is eighty-four thousand two hundred-six

This is written in numerals as : 84,206

For Population B the size is said to be:

80,000 + 4000 + 200 + 10 +6

we would have to add this up

= 84216

Now we are to compare the value that is greater

84216 is greater than 84206

hence we would say that City A has a less population compared to City B which is greater

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Therefore , the solution of the given problem of unitary method is Boat is travelling at a speed of 21.6 miles /hour.

The unit method is a way of problem-solving where you first calculate the worth of a single group, subsequently multiply that value to get the answer. Simply expression, a single system value is extracted from a specified multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint or reciprocal are equivalent. (Linear Algebra, Mathematical Interpretation, Mathematics of Matrix or Operators)

Here,

A boat has a speed = 36 km/hour

a km is about 60% of a mile.

1 km = 60/100 mile = 0.6 mile

the boat has a speed = (0.6 × 36) mile/hour

                                   = 21.6 miles/ hour

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Based on the table, the equation of the function h(x) is h(x) = f(x) - 1

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

The functions f(x) and h(x)

When the x values of both functions are compared, we can see that they have the same x values

However, for the y values

The function h(x) is 1 lesser than the function f(x)

This means that

h(x) = f(x) - 1

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The errors of quadratic equation is [tex]x=4 \pm \sqrt{24} &[/tex].

The given quadratic equation is [tex]8x^{2}-x-1=0[/tex]

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

where x is the unknown variable and a, b and c are the constant terms.

Standard Form of Quadratic Equation is [tex]ax^{2} + bx + c = 0[/tex] where a,b,c are real number and a≠0

Therefore the roots of the given equation can be found by:

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

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

⇒[tex]$$8 x^2-x-1=0$$[/tex]

Multiply both sides by 8.

⇒[tex]8\left(8 x^2-x=1\right)[/tex]

[tex]x^2-8 x=8 & \\x^2-8 x+16=8+16 & \\(x-4)^2=24 & \\x-4=\pm \sqrt{24} & \\x=4 \pm \sqrt{24} &[/tex]

Therefore, the x is [tex]x=4 \pm \sqrt{24} &[/tex].

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Price of gasoline is with Time:

The term "rate of change" (ROC) describes the rate which something alters over time.

For the stated graph.

Price of gasoline is fixed for Time: A , C, E, and G.

Price of gasoline is increasing rate for Time: D

Price of gasoline is decreasing rate for Time: B, and F

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Using Law of exponents, The value of [tex]5\sqrt{\frac{8xz^{2} }{y^{3} } }[/tex]   [tex](\frac{8xz^{2} }{y^{3} } )^{\frac{1}{5} }[/tex]

Exponent rules are the laws that are applied to simplify exponent-based expressions. The principles of exponents make it simple to carry out numerous arithmetic operations, such as addition, subtraction, multiplication, and division, in a short amount of time. Additionally, these rules aid in the simplification of numbers with complex powers incorporating roots, fractions, and decimals.

Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These guidelines are useful for reducing the complexity of expressions whose exponents are decimals, fractions, irrational numbers, or negative integers.

Given,

[tex]5\sqrt{\frac{8xz^{2} }{y^{3} } }[/tex]

⇒ [tex](\frac{8xz^{2} }{y^{3} } )^{\frac{1}{5} }[/tex]

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Therefore , the solution of the given problem of unitary method comes out to be  56 tablespoons in 3 1/2 cups of vinegar .

The unit technique is a method for resolving variable problems that includes multiplying the value of a unit by the required number of units. A unified force number can be extracted from a given many using the unit function, to put it simply. The price of 40 needles is 400 rupees, or about $1.50. It might be possible to verify this using a regular procedure. simply one nation. Everything possesses a unique quality.

Here,

Given :

=> 3 1/2 cups or 7/2 cups or 3.5 cups

16 tablespoons in one cup ,

=> 16 * 3.5

=> 56 tablespoons

Therefore , the solution of the given problem of unitary method comes out to be  56 tablespoons in 3 1/2 cups of vinegar .

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Answer: ±1.4

Step-by-step explanation:

f(x)=ax^2+c

The graph passes through (2,2) and (-2,2)

Vertex:(0,-2)

f(x)=ax^2-2

4a-2=2

4a=4

a=1

f(x)=x^2-2

if f(x)=0

x^2-2=0

x^2=2

x=±[tex]\sqrt{2}[/tex]=±1.414

x=±1.4

The x-intercepts of the graph of the equation are (8,0) and (-6,0).

What are intercepts?

A point on the y-axis known as an intercept is where the line's slope passes.

X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.

Now, in order to find the x- intercepts, we need to put y=0 because at that point the line crosses the x- axis and therefore, y=0 at that point.

So,

x^2-2x+(0)^2-3(0)=48

⇒x^2-2x=48

⇒x^2-2x-48=0

⇒x^2+6x-8x-48=0

⇒x(x+6)-8(x+6)=0

⇒(x-8)(x+6)=0

So, x= 8,-6

Hence, the x-intercepts of the graph of the equation are (8,0) and (-6,0).

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Answer:

The area of a circle is given by the formula A = πr^2, where A is the area, r is the radius, and π is approximately equal to 3.14. Since the diameter of the dartboard is 30 millimeters, the radius is half of that, or 15 millimeters. Therefore, the area of the dartboard is A = π(15^2) = 225π square millimeters.

Step-by-step explanation:

To determine the probability that the sample mean for French is greater than that of the Americans, we need to use the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means will become more and more normal, regardless of the distribution of the population from which the samples are drawn.

So, we can assume that the sample means of both American and French adults will be normally distributed with a mean of 43.5 hours/week and 36 hours/week respectively and a standard deviation of 4.6/sqrt(110) and 5.1/sqrt(135) respectively.

We can use these assumptions and the Z-score formula to find the probability that the sample mean for French is greater than that of Americans.

Z = (36 - 43.5) / (sqrt((4.6/sqrt(110))^2 + (5.1/sqrt(135))^2))

The resulting Z-score will be negative, meaning that the probability that French sample mean is greater than American sample mean is low and it's a rare event.

The expression that shows how much the individual earns everyday if they sell n items would be = $5 × n = $5n.

A salesperson is an individual that helps in the marketing and selling of goods and products for a company and who is equally rewarded with bonus after each sale that is made.

The amount of money that the salesperson makes = $10/day

The amount of money given as bonus for each item sold = $5

Therefore when the number of items sold = n, the amount made = $5 × n = $5n

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The standard deviation of the data-set is given as follows:

2.24.

The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

The sum of the differences squared between each observation and the mean is given as follows:

4 x (6 - 9.28)² + 5 x (7 - 9.28)² + (8 - 9.28)² + 4 x (9 - 9.28)² + 5 x (10 - 9.28)² + 4 x (11 - 9.28)² + 6 x (12 - 9.28)² = 144.75.

Dividing by the number of values, we have that:

144.75/(4 + 5 + 1 + 4 + 5 + 4 + 6) = 5.

Taking the square root, the standard deviation is given as follows:

2.24.

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The Gold Standard was a system under which nearly all countries fixed the value of their currencies in terms of a specified amount of gold, or linked their currency to that of a country which did so.

Step-by-step explanation:

Answer:

No longer used.

Step-by-step explanation:

Due to too much paper money being printed, some countries did not have enough gold reserves to exchange for the excessive amounts of paper promissory notes. (China's overprinting of printed money during the 9th and 15th centuries foreshadowed England's overprinting during WWI some 200 years later.) This rendered the paper money worthless. (One of the causes of the Great Depression.)

The gold standard is no longer used now, but the system it inspired is currently used between nations.

a. The probability that X is less than 95 is approximately 0.0668

b. The probability that X is between 95 and 97.5 is approximately 0.1359

c. The probability that X is above 102.2 is approximately 0.0228

d. The value of X for 65% chance is 99.23

We know, z=(X-mean)/ (S.D./sqrt N)

Thus, putting in the values for the respective cases, we get

(a) z value corresponding to X=95 is,

z=(95-100)/(10/sqrt 25)= -2.5

Therefore, required probability= area under the standard normal curve left to

z= -2.5 = 0.5000- 0.4938= 0.0062

(b) z value corresponding to X=95 is -2.5 and X=97.5 is,

z=(97.5-100)/(10/sqrt 25)= -1.25

Therefore, required probability= area under the standard normal between

z= -2.5 and z= -1.25= 0.4938- 0.3944= 0.0994

(c) z=(102.2-100)/(10/sqrt 25)= 1.1

Therefore, required probability= area under the standard normal curve right to

z= -2.5 = 0.5000- 0.3643= 0.1357

(d) 65%= 0.6500 is an area on the left side of the z value.

Or, we can say 35%= 0.3500 is on the right side of the z value.

therefore, the corresponding z value is -0.385 approximately.

Thus, for X value,

-0.385= (X-100)/(10/sqrt 25)

-0.385= (X-100)/2

-0.77= X-100

X= 99.23

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The value of y is 2/3, and RS = 9 and ST = 9.

What is the value of​ y?

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Answer:

Step-by-step explanation:

$126-$70 =

False, Shapes can be both 2 dimensional (L*W) and 3 dimensional (L*W*H) whereas Form gives us the typical significance of the shape

Points, line segments, circles, and curves are used to build closed geometric objects. We can see these forms all around us. Examples of geometric shapes include circles, rectangles, triangles, and others. Pizza is a cylinder with triangle pieces.

3.1 Euclidean geometry.

3.2 Differential geometry. 3.2.1 Non-Euclidean geometry.

3.3 Topology.

3.4 Algebraic geometry.

3.5 Complex geometry.

Hence from the given arguments we see

Shapes can be both 2 dimensional (L*W) and 3 dimensional (L*W*H) whereas Form gives us the typical significance of the shape

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There is no number that satisfies this criteria

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: let the two numbers be x and y then

we have x+y=1 and xy=7

Solving these two equations we get x²-x+7=0

∴x=1±√1-28 /2 but this is not a real number

Hence, such a number doesnt exist.

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