Ms. Johnson is older than her sister (Hannah) by 2 years. If their ages add up to 52, how old is each sister? Let x represent Ms. Johnson age, and let y represent Hannah's age.

The HL theorem, also known as the Halpern-Lehman theorem, is a theorem in propositional logic which states that, given a set of premises, the conclusion of an argument is logically valid if and only if the premises are consistent and the conclusion follows logically from the premises.

The HL theorem is a fundamental concept in propositional logic which states that a conclusion is logically valid if the premises are consistent and the conclusion follows logically from the premises. The theorem is based on the principle of deduction, which states that if a set of premises is true, then any conclusion drawn from them must also be true. In other words, if the premises are consistent and the conclusion follows logically from them, then the conclusion must be accepted as valid. The HL theorem is important because it helps to determine the validity of an argument, and is thus a useful tool for evaluating logical arguments.

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a) The functions are classified as follows:

b) After seven years, John has $1,666.36 more in his balance than James.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

Hence James' function is exponential, as:

3456/2880 = 2880/2400 = 2400/2000 = 1.2.

The definition of the function is given as follows:

Ja(x) = 2000(1.2)^x.

Considering the initial balance of 2000.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

Hence John's function is classified as linear, as:

3500 - 3000 = 3000 - 2550 = 2550 - 2000.

The definition of the function is given as follows:

Jo(x) = 2000 + 500x.

The balances after seven years are given as follows:

Hence the difference is of:

7166.36 - 5500 = $1,666.36.

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Answer:

We can use trigonometry to solve this problem. The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the top of the building.

We are given the angle of elevation (41°) and the distance from the observer to the building (60 feet).

We can use the tangent function to find the height of the building:

tan(41°) = height / 60

To find the height of the building we can multiply both sides of the equation by 60:

height = tan(41°) * 60

The height of the building is approximately 41.56 feet

The difference of the given numbers after rounding to nearest thousand is 21,000.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Given that, 33,167-12,052.

Rounding the number 33,167 to the nearest thousand is 33,000.

Rounding the number 12,052 to the nearest thousand is 12,000.

Now, the difference is

33,000-12,000 =21,000

Therefore, the difference is 21,000.

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To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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We can solve the system of equations:

y = -3x + 1

2x + y = 1

By substitution, and we will get the solution x = 0, y = 1.

Here we have a system of linear equations:

y = -3x + 1

2x + y = 1

And we want to solve this.

To do so, we can use the substitution method, where we isolate one of the variables in one of the equations and then replace it on the other equation.

Here we can see that "y" is already isolated in the first equation, so we can replace that in the other equation, then we will get:

2x + y = 1

2x + (-3x + 1) = 1

Now we can solve that equation for x.

2x - 3x + 1 = 1

-x + 1 = 1

-x = 1 - 1

-x = 0

x = 0

To find the value of y, we can replace x by zero in any of the equations, we will get:

y = -3*0 + 1

y = 1

Then the solution of the system of equations is (0, 1).

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Argument of the given complex number (-5√3 +  5i) will be 150°.

The argument of a complex number is defined as the angle inclined from the real axis in the direction of the complex number represented on the complex plane. It is denoted by “θ” or “φ”. It is measured in the standard unit called “radians”.

Argument of a complex number:

If a complex number if Z = (x + yi),

Imaginary part = y

real part = x

Argument of the complex number will be,

arg z = [tex]\text{tan}^{-1}(\frac{y}{x})[/tex]

Given in the question,

Imaginary number 'z' = -5√3 + 5i

Imaginary pat 'y' = 5

Real part 'x' = -5√3

Therefore, arg z = [tex]\frac{y}{x}=\text{tan}^{-1}(\frac{5}{-5\sqrt{3} })[/tex]

[tex]arg z = \frac{y}{x}=\text{tan}^{-1}(\frac{-1}{\sqrt{3} })[/tex]

Since, tan is negative in IInd quarter,

arg z = (180 - 30)° = 150°

Therefore, argument of the given complex number will be 150°

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The argument of the complex number -5√3 + 5i is 150°.

The argument of a complex number is the angle between the positive real axis and the line connecting the origin to the complex number in the complex plane.

The complex number -5√3 + 5i can be written in polar form as rcos(θ) + irsin(θ), where r is the magnitude of the complex number and cos(θ) + isin(θ) is the complex number represented in polar form.

We can find the argument of - 5√3 + 5i by using the inverse tangent function to find the angle between the positive real axis and the line connecting the origin to the complex number in the complex plane. We can do this by dividing the imaginary part of the complex number by the real part:

arg(-5√3 + 5i ) = tan⁻¹(5 / (-5√3))

= tan⁻¹(-1/ √3)

= 150°

Therefore, the argument of -5√3 + 5i is 150 degrees.

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Angle DFE=30 -Vertically Opposite Angle

DFE=FDE=30 -Base angles of an isosceles triangle

y+x+30=180 -sum of angles of a triangle

y+30+30=180

y+60=180

y=180-60

y=120

Answer:

5 and -15

Step-by-step explanation:

5 × -15 is -75.

5 + -15 is -10

By subtracting the sum of the two known angles from 180, we can find the measure of the unknown angle. In this example, the size of angle ABC is 105 degrees.

105 degrees

To find the size of angle ABC, use the formula 180 - (A + B) = C.

A = 30 degrees

B = 45 degrees

Therefore, C = 180 - (30 + 45) = 105 degrees

Therefore, the size of angle ABC is 105 degrees to the nearest degree.

To find the size of angle ABC, use the formula 180 - (A + B) = C. In this case, A = 30 degrees and B = 45 degrees. Therefore, C = 180 - (30 + 45) = 105 degrees. The size of angle ABC is then 105 degrees, rounded to the nearest degree. This can be useful when trying to calculate the measure of an angle in a triangle. Knowing the measure of the other two angles, you can use this formula to find the measure of the third angle. By subtracting the sum of the two known angles from 180, we can find the measure of the unknown angle. In this example, the size of angle ABC is 105 degrees.

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If an economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. the 80% confidence interval for the mean per capita income in thousands of dollars is: 36.3,  36.9.

X = Sample mean = $36.6

σ =Population standard deviation = $8.5

n = Sample size = 1012

Z =Z score for 80% confidence interval = 1.2816

Using this formula

X ± Z σ/√n

Let plug in the formula

36.6 ±  1.2816 × 8.5/√1012

36.6 ±  0.34246

(36.6 -  0.34246) , (36.6 + 0.34246)

36.3,  36.9

Therefore the confidence interval is 36.3,  36.9.

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The percentage of temperatures that are below 55° include the following: D. 25%.

In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the box-and-whisker plot (box plot) shown above, the five-number summary for the given data set include the following:

Generally speaking, the first quartile is also referred to as the 25th percentile and it is the value at which 25% of a value in a data set lies below and 75% of the answers lie above in a box plot.

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Using the concept of ratios and proportions and with the provided ratio and total number of students, The answer is 55 .

A ratio is a way of comparing two or more quantities by using division. It is a way of expressing a relationship between numbers, typically represented by a fraction. The numbers being compared are called the "terms" of the ratio. For example, a ratio of 3:5 compares the value of 3 to the value of 5. It can also be written as 3/5. Ratios can be used to compare many different types of quantities, such as lengths, weights, or time. Ratios are also used to express the relationship between different parts of a whole, for example, the ratio of girls to boys in a class, or the ratio of water to flour in a recipe.

A proportion is a statement that two ratios are equivalent. It is an equation that compares two ratios to see if they are equal. Proportions are written in the form of "a/b = c/d" where a, b, c, and d are numbers. For example, "3/5 = 6/10" is a proportion because it states that the ratio of 3 to 5 is equal to the ratio of 6 to 10. A proportion can also be used to find a missing value when we have a proportion and the value of three of the terms. This method is called cross-multiplication.

3x+17x+18x = 690

x=690/38

teacher number = x*3 = 690/38 * 3 = 55

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Therefore , the solution to the given problem of Perimeter comes out to be Perimeter = 2(9+12) = 42 and diagonal = √(9² + 12²) = √225 = 15 and So the sides are 9 and 12.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Here,

L+W equals 21, thus we know that perimeter is 42.

Diagonal = 15, thus we know L2 + W2 = 152.

Let's create a quadratic equation and define L as 21-W:

(21-W)² + W² = 15² 441 - 42

441 - 42W + W² + W² = 225

2W² - 42W + 216 = 0

W² - 21W + 108 = 0

(W-9)(W-12) = 0

W = 9 or 12

Therefore , the solution to the given problem of Perimeter comes out to be Perimeter = 2(9+12) = 42 and diagonal = √(9² + 12²) = √225 = 15 and So the sides are 9 and 12.

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Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Answer: 2000

Step-by-step explanation:

Let X be the number of subscribers the magazine had last year.

The magazine had 69% fewer subscribers this year than it had last year, which means that the number of subscribers this year is 100% - 69% = 31% of the number of subscribers last year.

We can set up the following equation to represent this situation:

620 = 0.31X

To solve this equation for X, we can divide both sides by 0.31:

X = 620 / 0.31

This simplifies to:

X = 2000

Therefore, the magazine had 2000 subscribers last year.

Lisa needs 39 cards to sell on Friday to make a profit.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

Lisa makes a profit when sells 140 cards.

Number of cards sold by Lisa from Monday to Thursday are 15, 7, 14, 45.

Total number of cards sold by Lisa from Monday to Friday = 15 + 7 + 14 + 45 = 81

Since, Lisa makes profit after selling 140 cards.

Therefore, Lisa needs to sell cards on Friday = 140 - 81 = 39

Hence, Lisa needs to sell 39 cards to make a profit.

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Therefore, mean of the chi-square distribution has now become 0 and is not a characteristic of the chi square distribution, hence this is how the given chi square problem is resolved.

To compare actual outcomes with predictions, statistical tests like the chi-square test are performed. This test's goal is to establish whether a discrepancy between observed and expected data results from chance or a connection between the variables under study.

Here,

The characteristics of the a chi square test must be discovered.

1. Untrue

A chi square distribution's mean is the same as its degree of freedom.

B) True

Asymmetry exists in the chi-square distribution.

C) True

Both 0 and 1 are valid values for the chi square.

Its foundation is a sum of the squared differences, hence it will never be negative.

D) True

For every degree of freedom, there is a separate chi-square distribution.

The freedom level is n - 1 when working with a singular population variance.

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We will get the solution of the matrix X after completing the calculations as: [tex]$$\mathrm{X}=(\mathrm{A}-\mathrm{CB})^{-1} \mathrm{CD}$$[/tex]

If and only if another matrix B of the same dimension exists, such that AB = BA = I, where I is the identity matrix of the same order, then matrix A of dimension n x n is said to be invertible. The inverse of matrix A is known as matrix B.

If and only if another matrix B of the same dimension exists, such that AB = BA = I, where I is the identity matrix of the same order, then matrix A of dimension n x n is said to be invertible. The inverse of matrix A is known as matrix B.

We have the matrix: [tex]$$\mathrm{AX}(\mathrm{D}+\mathrm{BX})^{-1}=\mathrm{C}$$[/tex]

Now, multiplying (D+X) on both sides of the equation,

We will get it as:

[tex]\mathrm{AX}(\mathrm{D}+\mathrm{BX})^{-1}(\mathrm{D}+\mathrm{BX})=\mathrm{C}(\mathrm{D}+\mathrm{BX})[/tex]

AX1=CD+CBX

AX=CD+CBX

AX-CBX=CD

(A-CB)X=CD

[tex]\mathrm{X}=(\mathrm{A}-\mathrm{CB})^{-1} \mathrm{CD}[/tex]

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To find the measure of an angle in a triangle that is isosceles, you can use the fact that the two equal sides of the triangle are congruent to each other.  The measure of each of these angles can be found by subtracting the measure of the third angle from 180 degrees.

Determine which two sides of the triangle are equal in length (these are called the "congruent sides").

Find the measure of the angle opposite one of the congruent sides. This angle is called the "base angle."

Subtract the measure of the base angle from 180 degrees. This will give you the measure of the other two angles in the triangle (since the three angles in any triangle must add up to 180 degrees).

For example, if the measure of the base angle is x degrees, then the measure of the other two angles would be (180-x) degrees.

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The measure of angles in an isosceles triangle can be found using the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.

To find the measure of an angle in a triangle isosceles, you can use the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.

Let's look at an example. Suppose you have an isosceles triangle and you know that two of its angles measure 50 degrees and 60 degrees. To find the measure of the third angle, you would subtract 110 (the sum of the two known angles) from 180. This gives you 70 degrees as the measure of the third angle.

In addition to the Triangle Angle Sum Theorem, you can also use the Isosceles Triangle Theorem to find the measure of an angle in an isosceles triangle. The Isosceles Triangle Theorem states that the angles opposite the two equal sides of an isosceles triangle are equal. This means that if you know one of the angles in the triangle, you can determine the measure of the other two angles, since they will both be equal to the measure of the known angle.

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Answer:

x = 5

Step-by-step explanation:

to find the value of x that makes the expressions equal, equate them

8x - 24 = 4x - 4 ( subtract 4x from both sides )

4x - 24 = - 4 ( add 24 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

then

4x - 4 = 4(5) - 4 = 20 - 4 = 16

8x - 24 = 8(5) - 24 = 40 - 24 = 16

the value x = 5 makes the 2 expressions equal

The coordinates of the image (2,4) under the transformation are (4, -14)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The image of the point A (2, 4) with respect to the point T (3, -5)

Suppose the image of A is B

B, T, and A are collinear and T is the mid point of segment BA

by section formula we can calculate the coordinates of B

3 = ( 2 + x)/2

x = 6–2 = 4

Now -5=(4+y)/2

-10=4+y

-14=y

The image B = (4, -14)

Hence, the coordinates of the preimage are  (4, -14).

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The number that is not a solution of the inequality

6x - 11 ≥ 4x - 13

Is x = -2, option a.

We want to see which of the given numbers is not a solution of the inequality below:

6x - 11 ≥ 4x - 13

To check that, we just need to evaluate the inequality in the given values and see for which value we have a false inequality.

For example, from the first value we will get:

x = -2

6*-2 - 11 ≥ 4*-2 - 13

-12 -11 ≥ -8 - 13

-23 ≥ -21

This is false, thus this is the correct option.

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Yes, 'Rounding to the nearest cent means to round off the amount to the hundredths place' is the correct definition for Rounding to Nearest Cent.

Rounding to the nearest cent is a method of rounding an amount to the hundredths place. This means that any decimal value will be rounded up or down depending on the value of the decimal point.

For example, if the value is 0.45, it will be rounded down to 0.00 and if the value is 0.55, it will be rounded up to 1.00. This method of rounding can be used in accounting, finance and other business calculations.

Rounding to the nearest cent is a common practice used to accurately estimate an amount. It involves rounding off the amount to the hundredths place, so if the number is something like 12.356, it would be rounded off to 12.36.

Although a part of your question is missing, you might be referring to this question:

Is Rounding to the nearest cent means to round off the amount to the hundredths place the correct definition of Rounding to Nearest Cent.

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The domain and range of f(x) = 5√x + 4 are

[0, ∞) and [4, ∞).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 5√x + 4

If we take the negative value of x it becomes an imaginary number as

√-1 = i.

Thus x can never be a negative value.

The domain of the function.

= [o, ∞)

The value of f(x) when x = 0 to ∞ is the range of f(x).

f(0) = 5 x 0 + 4 = 4

f(1) = 5 + 4 = 9

The f(x) value will increase as x increases.

So,

The range of f(x) is [4, ∞}

Thus,

The domain of f(x) is [0, ∞).

The range of f(x) is [4, ∞).

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Pedro had 1744 hits and Ricky had 1469 hits.

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The solution is 15 feet

The scale of the model is given by the equation A = 15 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The height of the Lincoln statue = 60 feet

The model height of the chamber = 4 inches

And , the equation is

So , the scale of the model = height of the Lincoln statue / model height of the chamber

Substituting the values in the equation , we get

The scale of the model A = 60/4

The scale of the model A = 15 feet

Therefore , the value of A is 15 feet

Hence , the equation is A = 15 feet

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The price one year from now would be $3.10.

The price a year ago would be $2.87.

The equation that models the information is Price in a year = present price x (1 + inflation rate). It represents an exponential growth.

The year I would expect the price of to be $3.50 is 4.02 years.

Inflation is the rate at which the general price levels in an economy increases.

Price in a year = present price x (1 + inflation rate)

Price in a year = 2.98 x (1 + 0.04)

Price in a year = 2.98 x 1.04 = $3.10

Price last year = price this year / (1 + inflation rate)

= 2.98 / 1.04 = $2.87

Year the price would be $3.50 = (IN FV / PV) / r

(IN 3.50 / 2.98) 0.04 = 4.02 years

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You need 38 randomly selected employers (minimum number) must we contact in order to guarantee a margin of error of no more than 4% (at 95% confidence).

To determine the minimum number of employers you need to contact in order to guarantee a margin of error of no more than 4% (at 95% confidence), you can use the following formula:

n = (Z² * p * (1-p)) / e²

Where:

So, for example, if you estimate that 50% of the employers you are interested in have a certain characteristic (p=0.5) and you want to have a margin of error of no more than 4% (e=0.04), you would need to contact at least 38 employers (n=38).

Keep in mind that this formula assumes a simple random sample, meaning that every employer in the population has an equal chance of being selected. If you are using a different sampling method, the formula for determining the minimum sample size may be different.

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If you estimate that 50% of the employers you are interested in have a certain characteristic (p=0.5) and you want to have a margin of error of no more than 4% (e=0.04), you would need to contact at least 38 employers (n=38).

Now, According to the question:

Finding Sample Size for Estimating a Population Proportion

We use the formula :

n = [tex](\frac{z^*}{M} )^2p(1-p)[/tex]

We use p = p (bar)

M is the margin of error

p(bar) is an estimated value of the proportion

We want to construct a 95% confidence interval for p with a margin of error equal to 4%.

Because there is no estimate of the proportion given, we use p(bar) = 0.50 for a conservative estimate.

For a 95% confidence interval, [tex]z^*[/tex] = 1.960

n = [tex](\frac{1.960}{0.04} )^2(0.5)(1-0.5)[/tex] = 600.25

This is the minimum sample size, therefore we should round up to 601. In order to construct a 95% confidence interval with a margin of error of 4%, we should obtain a sample of at least n = 601.

if you estimate that 50% of the employers you are interested in have a certain characteristic (p=0.5) and you want to have a margin of error of no more than 4% (e=0.04), you would need to contact at least 38 employers (n=38).

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