Which of these is a mathematical expression?

A

B

4 - 3r


C

4 - 3r = 1


D

"Happily ever after"

PLEASE HELP ITS ON A QUIZ AND ITS DUE IN TEN MINUETS

68.26% percent of months have maintenance costs in the range of $200 to $300

The monthly maintenance cost per square foot is calculated by dividing the total cost by the property's total area. It is multiplied by the unit area of each home to determine the individual maintenance contributions.

Your home's square footage can also be used to estimate your yearly maintenance expenses. If you follow this guideline, you should begin by figuring annual maintenance expenditures at $1 per square foot. Your estimated annual maintenance cost for a 2,000 square foot home is $2,000.

Costs incurred during normal measures to maintain an asset's original state are referred to as maintenance costs. Simple electrical repairs, bulb replacement, paint touch-ups, pool cleaning, etc. are a few examples of maintenance charges.

Remember that, [tex]P(X < A) = P(Z < (A - \mu )/\sigma)[/tex]

and given that \mu = [tex]$250\ and \ \sigma = \$50[/tex]

So, P(maintenance cost is in the range $200 to $300) = P(200 < X < 300)

= P(X < 300) - P(X < 200)

= P(Z < (300 - 250)/50) - P(Z < (200 - 250)/50)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

= 68.26%

Thus, 68.26% percent of months have maintenance costs in the range of $200 to $300

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The equation 4 2/7 = can be represented by the question: "What is 2/7 of 4?"

What is the arithmetic expressions?

An arithmetic expression is a mathematical phrase that can contain numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division.

The equation 4 2/7 = is asking for the value of 2/7 times 4. The right side of the equation is a mathematical expression that represents the product of 2/7 and 4. The value of this expression can be found by performing the calculation and replacing the expression with the resulting numerical value. In this case, 2/7 of 4 can be found by dividing 2 by 7 and then multiplying that result by 4. The answer to this question would give the value of 2/7 times 4.

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The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).

To find the pseudoinverse of a matrix A, the first step is to take the singular value decomposition (SVD) of A, which can be written as A = UΣV^T, where U and V are orthogonal matrices and Σ is a diagonal matrix with nonnegative singular values. The pseudoinverse of A is given by A^+ = VΣ^+U^T, where Σ^+ is the same as Σ except that the nonzero elements of Σ are replaced by their inverses.

Next, the projection matrices are given by AtA and AA+, which are used to project a vector onto the column space and the row space of A, respectively.

The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).

Whether a solution is exact or unique depends on the rank of A and the number of linearly independent columns and rows. If the rank of A is equal to the number of columns, then the solution is unique, otherwise, the solution may not be unique.

Therefore, The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).

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Answer: 75.2 °F

Step-by-step explanation: (24°C × 9/5) + 32 = 75.2°F

The calculation would be (24 x 9/5) + 32 = 75.2°F.

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Answer: k = 24, y = 24x

Step-by-step explanation:

y = kx (the variables x and y varies directly)
when x = 3, y = 72
k = y/x = 72/3 = 24
y = 24x

To determine the number of rectangles needed to achieve a desired accuracy, one could start with a small number of rectangles, calculate the approximation error, and then increase the number of rectangles until the error is within the desired range.

The number of rectangles to use in a rectangle approximation of a definite integral depends on several factors:

The desired accuracy: The smaller the desired accuracy, the more rectangles will be required.

The shape of the function: If the function is highly curved, more rectangles will be required to capture the shape of the function than if the function is more linear.

The range of integration: The larger the range of integration, the more rectangles will be required.

In general, to determine the number of rectangles needed to achieve a desired accuracy, one could start with a small number of rectangles, calculate the approximation error, and then increase the number of rectangles until the error is within the desired range. Alternatively, one can use mathematical techniques such as adaptive quadrature methods that automatically adjust the number of rectangles to achieve a desired accuracy.

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The truth about the end behavior of the graph is

The end behavior of function typically says the characteristics of the function at the ends

Examining the given graph it can be deduced that end behavior is  described as

x ⇒ -∞ f(x) ⇒ ∞

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Answer:

Step-by-step explanation:

The truth about the end behavior of the graph is

D. As the x-values go to negative infinity, the function's values go to positive infinity.

Answer:

$81.15

Step-by-step explanation:

So to find the total amount of money, you take the original price and add the sales tax.

We need to find the sales tax first, which is telling us to multiply the original price by 0.065.. so lets do that

(79.95)(0.065) = 5.19675

Since we got that answer there, we add that to the original price

$79.95 + $5.19675 = $81.14675

Which rounds to $81.15

The probability that the selected ride will be closed is given as follows:

E. 0.77.

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

For this problem, the percentages are given, hence we must just identify the correct percentages.

The probability of the park being closed is defined as follows:

Hence the probability that the park is closed is obtained as follows:

p = 0.75 + 0.08 x 0.25

p = 0.75 + 0.02

p = 0.77.

Meaning that option E is the correct option.

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The probability of the selected ride being closed is 0.77

Let R be the event that a ride is closed due to icy weather, and

M be the event that a ride is closed due to mechanical problems.

So, we have

Using the Law of Total Probability, we have:

P(M) = P(R) + P(M | R') * P(R')

So, we have

P(M) = 0.75 + 0.08 * (1 - 0.75)

Evaluate

P(M) = 0.77

Hence, the probability is 0.77

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The number of houses that can be built are 94.

A division is a process of splitting a specific amount into equal parts.

Given that, a construction company plans to build houses. The company will use [tex]23\frac{1}{2}[/tex] acres of land to build houses. Each house will be built on a 1/4 acre lot.

We need to find the number of houses that can be built,

To find the number of houses, we will divide total area by area of one house.

Therefore,

Number of house =  [tex]23\frac{1}{2}[/tex] ÷ 1/4

= 47/2 ÷ 1/4

= 47 x 2

= 94

Hence, the number of houses that can be built are 94.

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The linear system of equations in the question are resolved as follows;

Question 4

The true statements are;

Question 6

A linear system consists of two or more linear equations that operate simultaneously.

Question 4;

The system of equations is presented as follows;

Equation 1: 10·x - 2·y = 15

Equation 2: 4·x + y = 6

Plugging in the values of x = 1.5, y = 0, we get;

10 × 1.5 - 2 × 0 = 15

4 × 1.5 + 0 = 6

The point (1.5, 0), satisfies both equations in the system of equations, therefore, the point (1.5, 0) is a solution of the system of equations.

The true statements are therefore;

Question 6;

The linear system of equation is presented as follows;

-4·x - 8·y = 5

x = 4·y + 7

The substitution method can be used by plugging in the value of x = 4·y + 7, in equation (1) as follows;

-4·x - 8·y = 5

-4·(4·y + 7) - 8·y = -24·y - 28 = 5

Adding 28 to both sides, we get;

-24·y - 28 + 28 = 5 + 28

-24·y + 0 = 5 + 28 = 33

-24·y = 33

y = 33/(-24) = -11/8

y = -11/8 = -1.375

x = 4 × (-11/8) + 7

x = -11/2 + 7 = (-11 + 14)/2 = 3/2

x = 3/2 = 1.5

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Yes, the implications of leaving farm fields unused for the economy's PPF diagram can be seen in the output of agricultural products.

The PPF diagram shows the maximum output of two products that an economy can produce at a given time, and it is shaped like a curve. When farm fields are left unused, the amount of agricultural products that can be produced is decreased, resulting in a shift in the PPF curve inwards. This means that the economy has to sacrifice other goods to maintain the same level of production of agricultural products, leading to an opportunity cost. Thus, leaving farm fields unused has implications for the economy's PPF diagram, as it reduces the output of agricultural products, resulting in a shift in the PPF curve inwards.

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The selling price of the house that Laurie sold was $562,000.

The selling price is the amount paid by the customer to purchase the goods. The actual selling price is the amount paid by the customer for a product or service. This is the price that is more than the cost of products and includes a proportion of profit.

The cost price of an item is the amount spent to buy it or the price at which it is manufactured.

Let's call the selling price of the house "P".

The commission fee of 2.5% on the selling price of the house is equal to 0.025 * P.

Since Laurie made a commission of $14,050, we can set up the following equation:

0.025 * P = 14050

Dividing both sides by 0.025:

P = 14050 / 0.025 = 562000

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All parts of the probelm given regarding probability have been solved and provided below.

We have been told that a personnel director interviewed 11 senior engineers for four job openings and had scheduled six interviews for the first day and five for the second day of interviewing. Now let us assume that the candidates are interviewed in a random order.

(a) The probability that any quantity, lets say x, of the top four candidates are interviewed on the first day can be calculated using -

= h(x; 6,4,11) = (4;x) (7;6-x) / (11;6)

(b) The expected number of candidates, if top four candidates to be interviewed on the first day can be found out using -

= E[X]=nM/N

=  6*4 / 11

= 2.1812

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As a result, the radius of convergence, R, is equal to one. As a result, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 +...) = x + 16x^2 + 64x^3 +... This is the function f's power series representation (x).

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example.

Here,

The power series representation for f(x) = x(1 + 8x)^2 can be found by expanding the function (1 + 8x)^2 as a Taylor series centered at x = 0:

(1 + 8x)^2 = 1 + 16x + 64x^2 + ...

So, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 + ...) = x + 16x^2 + 64x^3 + ...

This is the power series representation for the function f(x).

To determine the radius of convergence, R, we use the formula:

R = 1 / limsup |a_n|^(1/n)

where a_n is the nth coefficient in the power series and limsup refers to the limit superior of the sequence {|a_n|^(1/n)}.

In this case, a_n = 16n x^n, so |a_n|^(1/n) = |16n|^(1/n) * |x|^(1/n). Since |16n|^(1/n) is a constant, the limit superior is just equal to |x|^(1/n). Therefore,

R = 1 / limsup |a_n|^(1/n) = 1 / |x|^(1/n) = 1

So, the radius of convergence, R, is equal to 1. So, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 + ...) = x + 16x^2 + 64x^3 + ... This is the power series representation for the function f(x).

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When dealing with complicated expressions that involve the addition and subtraction of positive and negative numbers, it is important to remember the following rules.

Nobody's a mathematical object used to count level and measure it is in the fundamental concept in mathematics and you used in many different way number can be used to represent anything from quantity of object to ideas in the concept additionally number are used to describe relationship between different object or concept.

First, when adding or subtracting two numbers with the same sign, the sum or difference will have the same sign as the numbers. For example, adding 5 + 3 gives 8 and subtracting 5 – 3 gives 2, both of which are positive numbers.

Second, when adding or subtracting two numbers with different signs, the sum or difference will have the sign of the number with the largest absolute value. For example, adding 5 + (-3) gives 2 and subtracting 5 – (-3) gives 8, both of which are positive numbers.

Third, when multiplying and dividing positive and negative numbers, the product or quotient will have the sign of the number with the largest absolute value. For example, multiplying 5 x (-3) gives -15 and dividing 5 / (-3) gives -1.67, both of which are negative numbers.

Finally, when dealing with expressions with multiple operations, it is important to use the correct order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This allows for the correct evaluation of an expression.

By remembering these rules, it is possible to add and subtract positive and negative numbers in complicated expressions.

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We can use (A) V = 16lw as a volume function.

Because the volume of a rectangular box is given by the product of its length, width, and height. In this case, the height is fixed at 8 cm, so the volume would be calculated as V = 16 x l x w, where l = 2w.

A three-dimensional space's volume is measured. t is frequently expressed numerically using units derived from SI (such the cubic Meter and litre) or by different imperial or US customary units (such as the gallon, quart, cubic inch). Volume and length (cubed) are related concepts.

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0.453592 kilograms are in a pound.

How many kilograms are in a pound?

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Answer:

x −2 −1 0

y −1 0 1

Step-by-step explanation:

Condition:

A linear relationship is proportional if the ratio of the change in the dependent variable to the change in the independent variable is constant. This constant is known as the proportionality constant and can be represented by "k" in the equation y = kx. When a linear relationship is proportional, there is a direct relationship between the variables and as one increases, the other increases and vice versa.

The second table (x = -2, -1, 0 and y = -1, 0, 1) represents a linear relationship that is also proportional. A proportional relationship means that the ratio of y to x remains constant, or in other words, y is a constant multiple of x. In this table, for every 1 unit increase in x, y increases by 1 unit, making it proportional.

The third table represents a linear relationship that is also proportional.

Your foot measure in centimeter is 4.25 centimeters and the proportion is 10.8 inches / 2.54 centimeters = x centimeters.

A proportion is an equation that states that two ratios are equal. It's often used to convert from one unit of measurement to another.

In your case, you want to convert 10.8 inches to centimeters, so you'll use a proportion to help you do that.

Here the correct proportion to use is 10.8 inches / 2.54 centimeters = x centimeters.

In this proportion, the first ratio on the left side of the equation represents 10.8 inches in terms of centimeters, and the second ratio on the right side of the equation represents x centimeters in terms of inches.

Since we know the conversion factor between inches and centimeters, 2.54 centimeters per inch, we can substitute that into the proportion.

=> 10.8 inches / 2.54 centimeters = x centimeters

=> 10.8 inches / 2.54 centimeters

=> 10.8 / 2.54 centimeters = 4.25 centimeters.

Therefore, 10.8 inches is equal to 4.25 centimeters.

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If there is a pattern 1 tree then 2 bead.  If there are a total of 42 tree and bead, then 84 bead is needed to complete the pattern as 42 tree and 84 bead.

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Answer:

25/3

Step-by-step explanation:

Let's call the number of students who picked sport "s" and the number of students who picked painting "p". We know:

p + s = 5 (the number of students who picked painting and sport)

42 - p - s = 8 (the number of students who did not pick either)

s = 2p (twice as many picked sport as painting)

From the first equation, we can solve for p:

[tex]\sf:\implies{p + 2p = 5}[/tex]

[tex]\sf:\implies{3p = 5}[/tex]

[tex]\sf:\implies{p = 5/3}[/tex]

So, 5 students picked painting and 10 students picked sport. And the number of students who picked sport but not painting is:

s - p = 10 - 5/3 = 10 - 5/3 = 25/3.

The interest on the loan is: $375.44

The maturity value is: $4,775.44.

Maturity value and interest on a loan can be calculated as follows:

Maturity value: it is the amount of the loan plus the interest charged on it. It can be calculated using the formula:

MV = P + I

where MV is the maturity value, P is the principal (original loan amount), and I is the interest charged on the loan.

Interest: it is the amount charged by the lender for the use of their money. It can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the term of the loan (in years or days).

Therefore:

Exact interest: 4,400 * 6% * 172/365 = $375.44

Maturity value: 4,400 + 375.44 = $4,775.44

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A rhombus has reflectional symmetry over either of its diagonals.

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Answer: Guaranteed

Step-by-step explanation:

Answer: Certain to happen

Hope this helps :)

Step-by-step explanation:

It's important to remember that when regarding probabilities with decimals, 0 is considered least likely, and 1 is most likely.

Answer:

Step-by-step explanation:

A sequence can be generated by using an=an−1+17, where a1=15 and n is a whole number greater than 1. The first 5 terms in the sequence are:

a2 = a1 + 17 = 15 + 17 = 32

a3 = a2 + 17 = 32 + 17 = 49

a4 = a3 + 17 = 49 + 17 = 66

a5 = a4 + 17 = 66 + 17 = 83

So the first 5 terms in the sequence are:

15, 32, 49, 66, 83

The lowest necessary yield strength for the axle material is 113.88 M/mm^2.

Torsional moment of Mv = 2×10^7 Nmm.

Bending moment of Mb = 1×10^7 Nmm

Axial force = 10^3 kN

Axial Stress = Axial Force/(πd^2/4)

Axial Stress = 10^3 × 10^3/(π(100)^2/4)

Axial Stress = 4 × 10^6/3.14 × 10^4

Simplifying

Axial Stress = 1.274 × 10^2

Axial Stress = 127.4

The combined tension of a torsional moment and a bending moment is known as shear stress.

τ = 16/πd^3√(Mv^2 + M^2)

τ = 16/π(100)^3√[(2×10^7)^2 + (1×10^7)^2]

τ = 16/π(10)^6√[4×10^14 + 10^14]

τ = 16/π(10)^6√[5×10^14]

After solving, we get

τ = 113.88 M/mm^2

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The complete question is:

The figure shows a circular axial made of steel that is loaded by a torsional moment of Mv=2×10^7 Nmm, a bending moment of Mb = 1×10^7 Nmm and an axial force of 10^3 kN. If a safety factor against yielding of 1,5 is required, what is the lowest necessary yield strength for the axle material?

Function is continuous everywhere expect x = 6 and  x = -6

What does a math interval mean?

In mathematics, an interval is quantified in terms of numbers. The range of numbers between any two specific numbers is known as the interval.

                         Every real number between those two values is included in this range. All kinds of numbers, including imaginary ones, are real numbers.

The function will not be continuous if the denominator becomes zero .

   f(x)  =  x+6/(x² - 36 )

to become denominator zero -

      x² - 36  = 0

    (x + 6) ( x - 6 ) =0

    x = 6  or   x = -6

so at x = 6 and x = -6 the function is not continuous .

  the interval for continuity is -

      = ( -∞ , - 6), ( -6 , 6) , ( 6, ∞ )

  In other words function is continuous everywhere expect x = 6 and

x = -6

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The rule for the translation is (-3, -4).

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

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

JKL is the original figure.

J'K'L' is the transformed figure after applying cetain rule.

We obtain J'K'L' by translating the original image left 3 units and down by 4 units.

The rule should be (-3, -4)

Hence,  the rule for the translation is (-3, -4).

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