express as a sum of logarithms
a, log3 5ab
​

The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)

Here, we need to construct a 99% confidence interval for population mean (μ) is given by

μ = x + Zα/2 * σ/√n   or    μ = x - Zα/2 * σ/√n

where, μ = population mean

x = sample mean

  = 3 inches

σ = population standard deviation

  = 0.3 inches

Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)

So, the upper limit would be,

μ = 3 + 1.645 * (0.3/√36)

μ = 3 + 1.646 * (0.3/6)

μ = 3.0823

And the lower limit would be,

μ = 3 - 1.645 * (0.3/√36)

μ = 3 - 1.646 * (0.3/6)

μ = 2.9177

Hence, the 99% confidence interval is (2.9177, 3.0823)

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The required number of associates is 2 and the number of partners is 4.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

daily rate charged to the client for each associate = $400

daily rate charged to the client for each partner = $900

According to question :

The law firm designated twice as many partners as associates , that means

P=2A                                 ---(1)

900*P +400A =4400       ---(2)

substitute the value of eqn (1) in (2).

900 *2A +400A = 4400

1800 A+400 A =4400

2200A =4400

A= 2

therefore P = 4.

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The leading coefficient of a polynomial is the coefficient of the leading term. In the above example 7+x−3x^2, the leading coefficient is −3.

A polynomial's leading coefficient is the coefficient of the leading term. In the preceding example, the leading coefficient is 3.

The leading coefficient of a polynomial is the coefficient of the leading term. In the preceding example, the leading coefficient is -3. (called that because the "standard notation" manner of writing polynomials has the terms organized from terms with high powers down to the constant term).

The term with the greatest power of x in a polynomial function is called the leading term. The leading coefficient is the leading term's coefficient.

The numbers written before the variable with the greatest exponent are known as leading coefficients. They, like regular coefficients, can be positive, negative, real, or imaginary, in addition to being whole numbers, fractions, or decimals. For example, the highest exponent in the equation  -7x^4 + 2x^3 - 11 is 4.

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No. Linear functions and quadratic functions are not the same.

Given,

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).

A polynomial function of degree 2 known as a quadratic function is expressed in the generic form f(x)=ax2+bx+c. Where a0, real numbers a, b, and c are used. The graph of the quadratic function f(x)=x2 that squares an input value is shown below.

When we graph a linear function, we get a straight line, however with a quadratic function, we get a parabola. In contrast to the slope of a linear polynomial, the slope of a quadratic polynomial is dynamic.

That is,

Linear functions and quadratic functions are not the same.

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The correct option d. All of the above are correct; for the sales of gasoline in local gasoline station.

According to the law of demand, for almost all things, demand decreases as price increases.

Because your neighbourhood gas station

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Over the past forty years, there has been a sharp rise in the quantity and variety of interest groups. .

In general, federal courts handle cases involving federal law, while state courts hear cases involving state law. Because most crimes are violations of local or state law, state courts typically hear criminal cases.

The 94 District Courts (trial courts), 13 Courts of Appeals (intermediate appellate courts), and the United States Supreme Court are the three main categories of federal courts within the federal system (the court of final review).

The three main causes of this surge are the "New Politics" movement, the increase of the role of government, and grassroots conservative action. Federal jurisdiction over a wide variety of public policy problems was expanded throughout the 1960s and 1970s, and there was a matching rise in the number of interest organizations that could exert pressure on elected officials

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If the required return is 10 percent then the profitability index for project 1 is 1.140 and project 2 is 1.284. If the company applies the profitability index decision rule, then project 2 should the firm accept.

In the given question, the michner corporation is trying to choose between the following two mutually exclusive design projects.

A1. Profitability index

Profitability index = present value of cash flow/initial investment

Project 1

Present value of future cash flows = 37600/(1+0.1)³

Present value of future cash flows = 93,505.634

Initial investment = 82,000

Now substitute values in formula

Profitability index = 93,505.634/82,000

Profitability index = 1.140.

Project 2

Present value of future cash flows = 11,200/(1+0.1)³

Present value of future cash flows = 27,852.742

Initial investment = 21,700

Now substitute values in formula

Profitability index = 27,852.742/21,700

Profitability index = 1.284

A2. Multiple choice.

The project with higher probability index should be accepted, therefore Project 2 should be accepted.

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Slope intercept form of equation of a line is described by y - y1 = m(x - x1)

The are three kinds of equation of a line

a) point intercept form

b) slope point form

c) point point form

The formula y - y1 = m(x - x1) is usually described as the 'point-slope form' for the equation of a line.

where m represents the slope of the line and x1 and y1 is the point given through which the line passes.

It is useful when one point on a certain line and the slope of that certain line is known, then the equation of the line can be structured using this form.

Thus, the slope intercept form of equation of a line is described by y - y1 = m(x - x1)

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The number line which represents the solution set for the inequality is

x ≤ -5.

What is number line?

In elementary mathematics, a number line may be a image of a graduated line that is visual illustration of the important numbers. each purpose of variety|variety} line is assumed to correspond to a true number, and each real to a degree.

Main body:

[Given]=

-4(x + 3) ≤ -2 - 2x

Using the distributive property of multiplication on LHS

-4x-12 ≤ -2 - 2x

By transposing the terms with variables on one side and the constant on the other side

- 4x + 2x ≤ –2 + 12

By further calculation

- 2x ≤ 10

Divide both sides by -2

x ≤ -5

Therefore, x ≤ -5 represents the solution set.

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The value of x is 24

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

2/10 = 3/(x-9)

Do cross multiplication

2(x-9) = 10*3 = 30

2x-18=30

2x=30+18=48

x=48/2=24

So, the value of x is 24

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A y-intercept of the continuous function in the table is;  (0, –6)

The y-intercept of a function is defined as the point where the graph intersects the y-axis. This means the point where the x-value is zero.

Now, from the function table given, we can see the coordinates of the function are given as;

(-4, 10)

(-3, 0)

(-2, 0)

(-1, -4)

(0, -6)

(1, 0)

Now, from the coordinates above , we can see that the only coordinate that has the x-value as zero is the one (0, -6) and as such by definition, it is the y-intercept.

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The rule in function notation for the courier company charge on delivery is

C = 15 + 1.6x

Independent variables  are the ones that you include in the model to explain or predict changes in the dependent variable.

The dependent variable is what you want to use the model to explain or predict. The values of this variable depend on other variables. It is the outcome that you’re studying. It’s also known as the response variable, outcome variable, and left-hand variable.

Given in the question,

A courier company charges $15 plus $1.60 per pound to deliver packages

Here , the dependent variable is cost of delivery because it is depending on how much a packages is weighting

The independent variable here is the weight of package because it doesn't depend on anything.

Let the cost of delivery be C and weight of package be x

The function for the charge will be :

C = 15 + 1.6x

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Two positive numbers that satisfy x=21 and y=7

XY = 147

x +3y = x + 3(147/x) = (x²+ 441)/x = f(x)

0= f'(x) = (x ( 2x) - x² - 441)/x²

         = 2x² - x² -441)/x²

         = (x² - 441)/x²

So then x² - 441 = 0

             x = 21 , as x>0

x=21 and y=7,

the max sum is 21 +3(7) = 42

Related to best a regular and a primary-order (linear) time period, in which m is the slope and b is the y-intercept. every so often, the above is referred to as a "linear equation of variables," where y and x are the variables. a linear feature is defined as a feature that has both one or two variables without exponents. it is a function that graphs to the direct line.

A linear equation in two variables is of the shape Ax + by way of + C = zero, in which A and B are the coefficients, C is a consistent term, and x and y are the two variables. Linear functions are those whose graph is an instant line. A linear feature has the subsequent shape. y = f(x) = a + bx. A linear characteristic has one impartial variable and one based variable. The independent variable is x and the base variable is y.

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The Empirical Rule given helps in determining Let x = the time it takes an NFL running back to run the 40-yard dash and that P(x < 4.23) is =95%.

In Football, every play is made from both yardage benefit or yardage loss that is a calculation of a poor or advantageous number. With every byskip or run that the offense attempts, you need to upload the yardage that they made collectively to apprehend wherein they've superior to at the field.

Here we have that,

NFL= 40 yard run

x = the time it takes an NFL running back

[tex]mu=4.59 \\sigma= 0.12[/tex]

Using Empirical rule,

[tex](A)P(X)P(4.35 < x > = P( -2 < Z > = P\\\\(Zthe usage of empirical rule=95%/2 + 95%/2=47.5%+47.5%=95 %[/tex]\

Thus the P(x < 4.23) = 95%.

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The correct statements for least square estimates is the 3rd and 4th statements.

Least square estimates is method to predicted the observed Y value with minimized the sum of squared errors when using the fitted line.

The first and second statements is about simple linear regression. Simple linear regression is refers to linear line as parameter for fitting a model.

All statements are correct, but since the question asks for which statement is correct for least squares estimation, only the third and fourth statements are correct.

Thus, the 3rd and 4th statements is correct for least square estimates.

Your question is incomplete, but most probably your full question was (image attached)

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The eigenvector of matrix A4 is 4096.

The eigenvalue of the matrix A-1 is 1/8.

(A+4I) has an eigenvalue of 12.

40 is the eigenvalue of 5Av.

The collection of scalar values known as the eigenvalues of a matrix are connected to the set of linear equations that are most likely contained within the matrix equations.

The eigenvectors are also known as the characteristic roots.

If the matrix A's eigen vector v is linked to an eigen value.

Av then equals lamda v.

The fact that v is an eigen vector of A with the value eight is assumed.

hence, Av = 8v.

We must determine the eigenvalue of A4.

A4*v equals A3(8v) = 84*v equals 4096v.

As a result, the eigenvalue of A4 is 4096.

Suppose A has an eigenvalue of 8. The eigenvalue of A-1 is thus 1/8.

It is calculated that the eigenvalue of (A+4I) is (A +4In)v = Av + 4v = 8v + 4v =12v.

(A+4I) has an eigenvalue of 12.

The value of 5Av's eigenvalue is 5Av = 5*8v = 40v.

40 is the eigenvalue of 5Av.

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The midpoint of line PQ is (4,4).

What is the midpoint?

A location that is halfway between two other points is considered to be a line segment's midway. The distance between the midway and each endpoint is the same.

Midpoint formula:

{(x₁ + x₂)/2, (y₁ + y₂)/2}

Here, we have

Given points P(1,6) and Q(7,2)

Now we apply the midpoint formula and get

= {(x₁ + x₂)/2, (y₁ + y₂)/2}

= {(1 + 7)/2 , (6 + 2)/2}

= (8/2, 8/2)

= (4,4)

Hence, the midpoint of line PQ is (4,4)

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(-14, -5) is the image point of (-9, -5) after the transformation T(-5,0)

Transformation is defined as the change in the position of a point, a line or a geometric figure

Given:  point (-9, -5) with transformation T (-5,0)

This implies there is a change in the position of the original point by (-5, 0). Thus, the image point can be determined as follows:

image point = (-9, -5) + (-5,0)

                    = (-9+(-5), -5+0)

                    = (-14, -5)

Therefore, the image point is (-14, -5)

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The maximum absolute values of the shear and bending moment is 2P and 3Pₐ respectively.

(a) Diagram is shown in image.

From A to B:

+∑Fy = 0: V = -P

+∑M₁ = 0: M = -P

From B to C:

+∑Fy = 0:

-P-P-V = 0

⇒ V = -2P

+∑M₂ = 0:

Pₓ+P(x - a)+M =0

⇒

M = -2Pₓ + Pₐ

(b) The maximum bending moment occurs in a beam, when the shear force at the section is zero or changes the sign because at point of contra fixture the bending moment is zero.

Therefore

|V|max = 2P

|M|max = 3Pₐ

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Answer:

undefined slope

Step-by-step explanation:

a vertical line parallel to the y- axis has an undefined slope

Answer:The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

Step-by-step explanation:

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

Prime multiples are numbers that add to make a prime. The sum of the factors 1 and 7 is 7. Consequently, 1 and 7 are the prime multiples of 7.

In the given question we have to explian about the prime multiple.

The numbers that result from multiplying the original number by any whole number are the multiples of that number. Prime multiples are hence numbers that add to make a prime. The sum of the factors 1 and 7 is 7. Consequently, 1 and 7 are the prime multiples of 7.

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The proof for the difference between the squares of any two consecutive integers is equal to the sum of these two integers is done.

Let x stand in for any integer.

The next integer (the one that comes after) should then be x+1.

The assertion calls for proof;

(x+1)² - x² = x+(x+1)

Address the left side;

= x² + x + x + 1² - x²

= 2x+1 (Left Hand Side Solution)

Now, work on the right side.

= x + (x + 1)

= 2x + 1

Since, the LHS=RHS (left hand side=right hand side) is obvious, subtracting the difference between two successive squared numbers equals adding the two integers.

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Answer:

8.06 m

Step-by-step explanation:

Assuming the tree forms a right angle with the ground, the distance from the student to the tree represents the hypotenuse of a right triangle.

The hypotenuse can be found using the Pythagorean Theorem.

[tex]a^2+b^2=c^2\\a=8m\\b=1m\\c^2=(8m)^2+(1m)^2\\c^2=65m^2\\c=\sqrt65m^2\\c=8.06m[/tex]

Using tangent line approximation formula,

the tangent line approximation at x= 29.2 is

L(x) = 2x - 1 or L(29.2) = 57.4

Given a function f differentiable at tangent

x=a, we can find that the slope of the tangent of y=f(x) at (a,f(a)) can be found by writing . ). The resulting tangent line through (a,f(a)) and the gradient m=f'(a) is the point-gradient given by

y−f(a)=f'(a)(x−a) has an equation of the form This can also be expressed as y=f'(a)(x−a)+f(a).

Replacing the variable y by the expression L(x) yields

points (a, f( a)) called L(x)=f′(a)(x−a)+f(a). , L(x) is just the new name for the tangent, and

f(x)≈L(x) for x near a.

For example, suppose the function y=f(x) is known to have a tangent approximation at the point (1, 3) given by L(x)=3−2(x−1), but the function Other things about f.

we have given that,

f(x) = 2x - 1

x= 29.0 near to 29.2

f(29.0) = 58 - 1 = 57

f'(x) = 2

so, the point is (29.0, 57) and slope of tangent is 2 .

tangent line , 57 = 2(29) + b

=> b = -1

then equation is 2x - 1 = y

we to calculate tangent line approximation give as an approximation for at x = 29.2

tangent line approximation,

y = 2 (29.2) - 1 = 57.4

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Complete question:

suppose and f (x) = 2x - 1 , what does the tangent line approximation give as an approximation for x= 29.2??

The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

In the question ,

it is given that ,

The random variable X is said to be normally distributed  ,

the mean is given as , μ = 70 , and

standard deviation of normal distribution is  (σ) = 10

probability that X is between 72 and 84 is written as P(72 < X < 84)

= P((72 - 70)/10 [tex]<[/tex] Z [tex]<[/tex] (84 - 70)/10)

= P(0.2 < Z < 1.4)

= P(0 [tex]<[/tex] Z [tex]<[/tex] 1.4) – P(0 [tex]<[/tex] Z [tex]<[/tex] 0.2)

From the z table , we get the values as

= 0.4192 – 0.0793

= 0.3399

≈ 0.340

Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

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The area of a sector from the given figure is 50.24 square units.

From the given figure, radius of sector =8 units and the central angle =90°.

The area of a sector is the space inside the section of the circle created by two radii and an arc. It is a fraction of the area of the entire circle.

The formula to find the area of a sector = [tex]\frac{\theta}{360^o} \times\pi r^2[/tex].

Here, r=8 units and θ=90°

Using the area of a sector formula, we get

90°/360° ×3.14×8²

= 0.25×3.14×64

= 50.24 square units

Therefore, the area of a sector from the given figure is 50.24 square units.

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Answer: 1.72

Step-by-step explanation:

18.92 ÷ 11 can be rewritten as: [tex]\frac{18.92}{11}[/tex].

Use long division to find the answer, as shown below:

The sample space is all the cards in the deck if an experiment involves choosing one card from a deck of playing cards.

Given statement,

If an experiment is selecting a card from a deck of cards, then the sample space is,

For the given case,

The sample space in this case is " all the cards in the deck "

Therefore, If an experiment is selecting a card from a deck of cards, then the sample space is all the cards in the deck.

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Answer:

146304 marbles

Step-by-step explanation:

We do not need to worry about the color part, at least right now

One box contains 576 marbles

To find how many are in 2 boxes we would do 576 * 2

To find 254, we would do 576 * 254

Now, I would suggest using lattice multiplication here. If you do not know how to do that, long multiplication works fine.

I can't show that here, but I can show the answer:

576 * 254 = 146304

So, there are 146304 marbles is 254 boxes