geoff is investigation fractions of the form (1)/(n), where n is an interger from 2 up to and including 20. How many of these fractions are equivalent to terminating decimals

Both the limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1. So, The function is continuous at x=1.

To determine if the function is continuous at x=1, we need to evaluate the left and right limits of the function at x=1 and see if they are equal.

Left limit as x approaches 1:

\lim_{x\to 1^-}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Right limit as x approaches 1:

\lim_{x\to 1^+}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Since both limits are indeterminate forms of 0/0, we can use L'Hopital's Rule to evaluate them.

Taking the derivative of the numerator and denominator of the original function, we get:

\lim_{x\to 1^-}\frac{4x-5}{1} = -1

\lim_{x\to 1^+}\frac{4x-5}{1} = -1

Both limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1.

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The value of the expression 7₂ + 3₃ is 10₅.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

An expression is 7₂ + 3₃.

To find the value of the expression, first, add 7 and 3.

That means, 7 + 3 = 10.

Now add 2 and 3,

2 +3 = 5

So, the value of the expression is 10₅.

Therefore, the result is 10₅.

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The equation for the line of best fit is y = 5.43x + 76.41.

The correlation coefficient is 0.79

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of hours would be plotted on the x-axis of the scatter plot while the test scores would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the number of hours and test scores, a linear equation for the line of best fit is given by:

y = 5.43x + 76.41

In conclusion, the type of correlation between the variables is a strong positive correlation.

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Answer:

Using the rules of arithmetic, we can simplify the given expressions as follows:

-8 - (-6) = -8 + 6 = -2

-3 - (-7) = -3 + 7 = 4

6 - (-7) = 6 + 7 = 13

-2 - (-15) = -2 + 15 = 13

-12 - 3 = -15

-4 - 12 = -16

9 - (-5) = 9 + 5 = 14

Therefore, the simplified expressions are:

-2, 4, 13, 13, -15, -16, and 14.

Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given is to write the transitive property of congruence.

The transitive property of congruence states that “ if two shapes are congruent to the third shape, then all the shapes are congruent to each other. So, we can conclude that option A is the correct answer.

Therefore, Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.

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The sale price of a pair of dress shoes originally at $69.98 with a 25% discount will be $52.49.

To find the sale price, you need to calculate the discount amount and subtract it from the original price.

Step 1: Find the discount amount by multiplying the original price by the discount percentage.
$69.98 x 0.25 = $17.49

Step 2: Subtract the discount amount from the original price to get the sale price.
$69.98 - $17.49 = $52.49

Therefore, the sale price of the dress shoes will be $52.49.

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Answer:

Your answer:

6. x = 8

8. x = 3

Step-by-step explanation:

Basic calculation involving adding/subtracting and multiplying and dividing.

Formula for Area of a Rectangle:

Area = Length * Width.

6. Given information

A = 165 cm^2

length = 4x + 1

width = 5

(4x + 1) * 5 = 165 cm^2

5 * (4x + 1)= 165

20x + 5 = 165

20x = 160

x = 8

8. Given information

A = 40 cm^2

length = 7x - 1

width = 2

(7x - 1) * 2 = 40 cm^2

2 * (7x - 1)= 40

14x - 2 = 40

14x = 42

x = 3

Step-by-step explanation:

the angles which occupy the same relative position at each intersection where a straight line crosses two others, are called corresponding angles. If the two lines are parallel, the corresponding angles are equal.

two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines, are called alternate angles. If the original two lines are parallel, the alternate angles are equal.

since we are only dealing with parallel lines here, the angles are always equal.

a)

a = 60°, alternate

b)

a = 75°, corresponding

c)

a = 108°, corresponding

The equation represents the 33.60+1.40=w that a shop will use to determine the markup from its wholesale price.

The definition of the an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or describe the whole situation, this is known as an equation.

Let w be the wholesale price, then the price after markup is:

w + 140%

[tex]w=w+1.4w=2.4w[/tex]

we know price after markup is $[tex]33.60[/tex]

2.4w = $33.60

we can solve w

w = $33.60 / 2.4 = $14.00

So the wholesale price before markup is $14.00.

The equation represents the 33.60+1.40=w

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The mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /) that represents a value or a calculation. It can contain variables, which are placeholders for unknown or changing values, and can be simplified or evaluated using mathematical rules and operations. Examples of expressions include 3x + 5, (a + b) / 2, and √(16 - 3y).

The mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

where x is the unknown number.

Therefore, the mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

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The 12th term of the geometric sequence 9, - 18, 36, is 18,432.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -18/9

Common ratio, r = -2

For the 12th term, we have:

a₁₂ = 9(2)¹²⁻¹

a₁₂ = 18,432.

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Answer:

c.

Step-by-step explanation:

the inner angle is half of the sum of both outer angles.

65 = 1/2 × (36 + x)

130 = 36 + x

x = 130 - 36 = 94°

The fourth term a₄ of the sequence is -343

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

a₁= -1

aₙ = 7aₙ₋₁

The above definitions imply that we simply multiply 7 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = 7 * -1

a₂ = -7

Also, we have

a₃ = -7 * 7

a₃ = -49

Lastly, we have

a₄ = -49 * 7

Evaluate the equation

a₄ = -343

Hence, the value of a₄ is -343

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The coefficient a in the factorization [ x²+a x y+b y²=(x+5 y)(x-4 y) ] is -1. The correct answer is C

Terms are the sum of the numbers or variables, factors are the sum of the numbers or variables multiplied, and coefficient is the number multiplied by the variable.

To find the coefficient a, we can expand the right side of the equation and compare it to the left side.

Expanding the right side gives us: [ (x+5 y)(x-4 y)=x²-4 x y+5 x y-20 y² ]

Simplifying the right side gives us: [ x²+x y-20 y² ]

Comparing this to the left side of the equation, we can see that the coefficient a is -1.

Therefore, the correct answer is c. ( -1 ).

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We start by isolating the square root on one side of the equation:

3x - 3 = sqrt(3x^2 + 177)

Squaring both sides of the equation gives:

(3x - 3)^2 = 3x^2 + 177

Expanding the left-hand side gives:

9x^2 - 18x + 9 = 3x^2 + 177

Simplifying gives:

6x^2 - 18x - 168 = 0

Dividing both sides by 6 gives:

x^2 - 3x - 28 = 0

We can now solve for x using the quadratic formula:

x = (3 ± sqrt(3^2 + 4128)) / 2

x = (3 ± 7) / 2

Therefore, the solutions are x = -2 and x = 5, and their sum is -2 + 5 = 3.

Thus, the answer is (C) 3.

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The ratio of all points scored up to the moment when Alex left the ground was 25 : 100. This means that out of all the points scored, 25% were Alex's hits.

Ratio is a comparison between two or more numbers. It is usually expressed in the form of a fraction, with the numerator being the first number and the denominator being the second number. Ratios can also be expressed in terms of a percentage or a proportion. Ratios help to compare two or more values and can be used to indicate relationships between different parts of a system. For example, if the ratio of apples to oranges is 2:3, then for every two apples, there are three oranges.

The reason for this is that when Alex entered the game, Alphas had a score of 20 points out of a total of 120 points. After his reverse substitution, Alphas had a score of 50 points out of a total of 100 points. This means that Alex scored 30 points in total during his time in the game. Therefore, the ratio of Alex's hits to the total points scored is 30 : 100, or 25%.

This shows the impressive contribution that Alex made in the game. Despite playing for a relatively short period of time, he was able to score a quarter of all the points in the game. This highlights Alex's skill and shows what a difference an individual player can make in a team sport.

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Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

To write vector u as a linear combination of the vectors in set S, we need to find scalars a, b, and c such that:

u = a[1] + b[2] + c[-2]

Substituting the given values of u and the vectors in S, we get:

[3] = a[1] + b[2] + c[-2]

To solve for the scalars a, b, and c, we can set up a system of equations:

3 = a + 2b - 2c

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

a = 1, b = 1, c = 0

Substituting these values back into the equation, we get:

[3] = 1[1] + 1[2] + 0[-2]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [1] + [2]

Similarly, for the second set of vectors, we need to find scalars d, e, and f such that:

u = d[2] + e[3] + f[-5]

Substituting the given values of u and the vectors in S, we get:

[8] = d[2] + e[3] + f[-5]

To solve for the scalars d, e, and f, we can set up a system of equations:

8 = 2d + 3e - 5f

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

d = 2, e = 2, f = 0

Substituting these values back into the equation, we get:

[8] = 2[2] + 2[3] + 0[-5]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

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Answer:

60m^2

Step-by-step explanation:

15.1×10.3=155.53

155.53÷2=77.765

2.8×6.5=18.2

77.765-18.2= 59.565

rounded to nearest 10th = 60m^2

a. False. If we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44) = (0.43, 0.69).

b. True. We may get a different odds ratio value if we treat marijuana use as the response variable than if we treat alcohol use as the response variable.

c. False. Interchanging two rows or interchanging two columns in a contingency table does have an effect on the value of the X2 or G-chi-squared statistics. Thus, these tests treat both the rows and the columns of the contingency table as nominal scale, and if either or both variables are ordinal, the test takes that information into account.

d. False. Income and gender are not necessarily independent in the 2 x 2 marginal table, even if they are conditionally independent given the type of job.

e. False. The estimated odds ratio between opinion on global warming and whether one is a Democrat or a Republican does not equal 2.96 x 2.08 = 6.2, it equals (2.96/2.08) = 1.42.

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The volume of the Cylinder is 24.11 cubic feet.

Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.

The radius of the cylinder is half the diameter of the circular base, so:

r = 2.6/2 = 1.3 feet

The volume of the cylinder is given by:

V = πr²h

Substituting the values given:

V = 3.14 × 1.3² × 4.4 ≈ 24.11 cubic feet

Rounding to the nearest hundredth:

V ≈ 24.11 cubic feet

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The correct answer is B. The graph shows the amount of water in a sink after several minutes, so it is a decreasing function.

Graph is a mathematical structure used to represent connections or relationships between objects. It consists of nodes, which are connected by edges. Graphs are used in computer science and other fields to represent networks of communication, data organization, computational devices, the flow of computation, and other objects. Graphs are also used to represent the abstract connections between objects in a more visual way. Graph theory is the study of graphs and their properties.

Option B, y = -3/2x + 5, is a linear function with a negative slope, which is the correct representation for this situation. This equation can be used to find the amount of water in the sink after any given number of minutes.

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The  value of the inequality for the expression is:  x >  -8

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

To solve the inequality, we need to isolate the variable, x.

We begin by simplifying the expression inside the parentheses:

2(3x - 2) = 6x - 4

Now we can substitute this expression into the original inequality:

-52 < 6x - 4

Add 4 to both sides:

-48 < 6x

Divide both sides by 6:

-8 < x

So the solution to the inequality is x > -8.

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Step-by-step explanation:

well, we don't need to look for any fancy calculation tricks.

all we need to do is calculate the amounts in both cases and then calculate the difference.

bachelor's degree income in 30 years :

59,100×30 = $1,773,000

high school diploma income in 30 years :

35,250×30 = $1,057,500

the difference is

$1,773,000 - $1,057,500 = $715,500

a person with a bachelor's degree would earn

$715,500

more over a period of 30 years than a person with only a high school diploma.

this is not considering the changes of the income levels over the period of 30 years (that adds insult to injury ...).

The measure of angle A is 85^o.

A quadrilateral is any form of plane figure which is bounded by four straight sides. Examples include: square, rhombus, rectangle trapezium etc. Each example of quadrilateral has differentiating properties.

The given quadrilateral ABCD inscribed in the circle has the shape of a rhombus. So we have:

the measure of opposite internal angles of a rhombus are congruent, so that;

x + (2x + 1) + 148 + (2x + 1) = 360

5x + 150 = 360

5x = 360 - 150

5x = 210

x = 210/ 5

  = 42

x = 42^o

Thus measure of angle A = (2x + 1)

                              = 2*42 + 1

                              = 85^o

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Answer: We can start by translating the given sentence into an equation:

950 + 0.40(950) = x

where x is the unknown amount after the 40% increase.

To solve for x, we can simplify the right-hand side of the equation:

950 + 0.40(950) = x

950 + 380 = x

1330 = x

Therefore, the unknown amount after the 40% increase is 1330.

Rounding 1330 to the nearest tenth gives 1330.0, and converting to a percent gives 133000%.

Step-by-step explanation:

The length of the legs are 2 units and 3.464 units

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

The triangle

The legs can be calculated using sine and cosine ratios

Using the above as a guide, we have the following:

sin(30) = PQ/Hyp

cos(30) = RQ/Hyp

Substitute the known values in the above equation, so, we have the following representation

PQ/4 = 0.5

RQ/4 = 0.8660

So, we have

PQ = 4 * 0.5

RQ = 4 * 0.8660

Evaluate

PQ = 2

RQ = 3.464

Hence, one of the leg is 3.464 units

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1. Elimination

2. Variable

3. Equation

4. Solve

5. Equation

6. Variable

7. Substitution

My best estimate

Elimination , variable ,equation , Solve , equation, variable, substitution .

An equation is a mathematical statement that asserts that two expressions are equal. It consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=). The expressions on both sides of the equation can be numbers, variables, or a combination of both, and the equal sign indicates that the two expressions have the same value.

Equations are used in mathematics to represent relationships between quantities, to solve problems, and to describe various phenomena. They are used in many areas of science, engineering, and economics, as well as in everyday life.

For example, the equation "2x + 3 = 7" represents the relationship between an unknown quantity x and the value 7. By solving this equation, we can find the value of x that makes the equation true. In this case, the solution is x = 2.

Identify elimination as the best method for the problem.

Find a variable with equal or opposite coefficients in the system.

Add or subtract one equation from the other.

Solve the one-variable equation.

Substitute the value of that variable into the other equation.

Solve for the second variable.

Check your answer. Use substitution and/or graphing.

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Answer:

How to calculate 8 + 3(5 - 7)​

Use Pemdas

Pemdas

8 + 3(5 - 7)​

5 - 7

= -2

8 + 3 ⋅ -2

Pemdas

8 + 3 ⋅ -2

3 x -2

= -6

8 + -6

Pemdas

8 + -6

Step-by-step explanation:

You're welcome.

Answer:

8+3(5-7)=-2

You will use the"Bracket Of Division Multiplication Addition and Subtraction(BODMAS)" method. Hence solve the one in the bracket first. So it's going to be 5-7 which is -2.Then you continue with the multiplication of 3 by the -2 you got making -6. Finally add the 8 to the -6 making 2.

18% of the total inventory was sold.

A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.

Given that, 30% of the inventory is sold over the weekend, on the second day only 15% of the inventory that was left in the store to be sold,

Let x be the total inventory,

Sold inventory = 30% of x,

The second day = x - 30% of x is sold

x -30% of x = 15% of x

x - 0.3x = 0.15x

x = 0.3x+0.15x

x = 0.18x

x = 18% of x,

Hence, 18% of the total inventory was sold.

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