HELP 30 POINTS
In 2001, 36,500 people attended a public concert. The attendance at the annual event has decreased by 3% each year since. Which equation models the attendance, y, at the event x years after 2001?
A.
y = 36,500 – 0.03x

B.
y = 36,500(0.97)x

C.
y = 36,500(0.03)x

D.
y = 36,500(1.03)x

If instead, you had found the best-fit line t=c¯db¯, the slope d¯ is expected to be related to the slope d found in (a) through the formula: d¯=cd. Hence, the slope d¯ would be directly proportional to the constant c. This means that if the value of c changes, the value of d¯ will also change accordingly.

However, this relationship is only theoretical and is not true empirically because it assumes that the data points follow a linear relationship perfectly, which is rarely the case in real-world scenarios. In practical applications, there are often several factors that affect the relationship between two variables, and these factors cannot be accurately captured by a simple linear model. As a result, the actual relationship between the variables may be more complex than a straight line, and the slope may not be accurately represented by a single value such as d or d¯. Therefore, while the theoretical relationship between d and d¯ may be straightforward, it may not hold true in empirical situations where data is more complicated.

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Answer:

1262(2)^x

Step-by-step explanation:

Answer : The area of the figure composed of a parallelogram, a square and a rectangle is 126 in².

Step-by-step explanation :

Area of composed figure = Area of parallelogram + Area of square + Area of rectangle

First we have to calculate the area of parallelogram.

Area of parallelogram = Base × Height

Given:

Base = 10 in

Height = 3.5 in

Area of parallelogram = 10 in × 3.5 in

Area of parallelogram = 35 in²

Now we have to calculate the area of square.

Area of square = (Side)²

Given:

Side = 4 in

Area of square = (4 in)²

Area of square = 16 in²

Now we have to calculate the area of rectangle.

Area of rectangle = Length × Breadth

Given:

Length = 12.5 in

Breadth = 6 in

Area of rectangle = 12.5 in × 6 in

Area of rectangle = 75 in²

Now we have to calculate the composed figure.

Area of composed figure = Area of parallelogram + Area of square + Area of rectangle

Area of composed figure = 35 in² + 16 in² + 75 in²

Area of composed figure = 126 in²

Therefore, the area of the figure composed of a parallelogram, a square and a rectangle is 126 in².

The area of the given figure is 126in²

The given figure is a composite figure composed of a parallelogram, a square and a rectangle.

Get the area of the square

Area = L²

Area of the square = 4² = 16in²

Area of the rectangle = 6 * 12.5

Area of the rectangle = 75in²

For the parallelogram:

Area of the parallelogram = Base * Height

Area of the parallelogram = 10 * 3.5

Area of the parallelogram  = 35 in²

Area of the figure = 75in² + 35in² + 16in²

Area of the figure = 126in²

Hence the area of the figure is 126in²

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Answer:

-3

Step-by-step explanation:

p(x) = x^2-6x+5

Let x= 4

p(4) = 4^2-6(4)+5

Exponents first

       = 16 -6(4) +5

Multiply

     = 16 -24 +5

Add and subtract

    = -8+5

   = -3

Answer:

Step-by-step explanation:

hey buddy all you do is divide 0.45 by the number 18 so that aswer will be 0.025

Answer:

1/40

Step-by-step explanation:

0.45 divided by 18

rewrite 0.45 as 45/100 divided by 18:

\(\frac{\frac{45}{100}}{\frac{18}{1}}\)

\(\frac{45}{100} / 18 \\\\\frac{45}{100} * \frac{1}{18} \\\)

= 45/1800

1800 can be divided by 45 and gives 40.

so

1/40

Everything is correct except for option (a). That is PR = 3x is wrong while others are right.

An isosceles triangle is a type of triangle that has two sides of equal length. This means that two of the three sides of the triangle are congruent. The angles opposite the congruent sides are also congruent.

Given an isosceles triangle with the following properties:

PQ = x + 0.1

PR = 3x - 0.4

RQ = x + 1.4

But

PR = RQ (equal sides of isosceles triangle)

with this fact, we can calculate the value of x

Recall that:

PR = RQ

3x - 0.4 = x + 1.4

3x - x = 1.4 + 0.4

2x = 1.8

x = 0.9

Knowing the value of x now, we can substitute to the above equations:

Recall:

PQ = x + 0.1

     = 0.9 + 0.1

PQ = 1.0

RQ =  x + 1.4

     = 0.9 + 1.4

     = 2.3

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Answer:

Hi im filipino :))

Step-by-step explanation:

Thanks for the points

Answer:

Option B is the correct answer

Step-by-step explanation:

B. x2 + y2 = 25

To find the volume under a surface and above a rectangle, use a double integral. Integrate the surface function over the rectangle and approximate using Riemann sums or numerical methods to obtain an estimate of the volume

To find the volume under a surface and above a rectangle in three-dimensional space using a double integral, we can follow these steps:

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Answer:

jingle bell Rock Moana lolil

The expression is evaluated to give 36

Note that algebraic expressions are defined as expressions composed of terms, variables, constants, coefficients and factors.

These expressions are also identified with arithmetic operations, such as;

addition, subtraction, multiplication, division,  bracket, parentheses.

From the information given, we have that;

z²+yx+ z

Given that;

z = 5,  y = 2, x = 3

Substitute the values, we get;

(5)² + 2(3) + 5

find the square

25 + 6 + 5

Add the values

36

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Answer:

31, 32, 29, 31

u < 28

Step-by-step explanation:

To find if a value works for an inequality, one has to substitute in the value and simplify. If the resulting equation is true, then the value is a part of the solution set of the inequality.

When simplifying an inequality, one must follow all the same rules as simplifying an equation. The only difference is that when one multiplies or divides by a negative number one must flip the inequality sign for the inequality to remain true. In this case, this rule won't come into play.

\(\frac{u}{4}<7\)

*4   *4

u < 28

Answer:

12600 (ZAR)

Step-by-step explanation:

4.2*3000

Hey there!

7x + 3 - 4x - x

• First COMBINE your LIKE TERMS

(7x - 4x - x) + (3)

• x by itself is understood as an INVISIBLE ONE

(7x - 4x - 1x) =

(7x - 4x) = 3x

(3x - 1x) = 2x

➡️ 2x + 3

• Answer:

2x + 3

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

When Kate's math homework had a set of equations and one work problem, the number of equations will be 15.

It should be noted that an equation is used to illustrate the relationship between the variables.

It should be noted that in this case, Kate's math homework had a set of equations and one work problem and she took 3 minutes to solve each equation.

Let the number of equation be represented by x.

Therefore, the information illustrated shows that the equation will be:

3x + 7 = 52

Collect like terms

3x = 52 - 7

3x = 45.

Divide

x = 45 / 3

x = 15

Therefore, Kate's math homework had a set of equations and one work problem, the number of equations will be 15.

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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From the question we have been given the rate of conversion from kilograms to pounds, which is;

Therefore, for a dog that weighs 112 pounds, the weight in kilograms shall be calculated as follows;

This means the dog's weight in kilograms would be approximately 50.79 kilograms.

The prescription indicates 4.25 mg per kilogram of body weight. Hence, for a dog that weighs 50.79 kg, the dosage would be;

Next, if Denefor is available in 200ml/5mL, and the dog requires a total of 215.86 mg, then the prescription in mL would be;

This means the dog whose body weight is 112lb/50.79kg would be given 5.08ml of Denefor.

ANSWER:

If two lines are parallel, then they have the same slope.

If two lines are perpendicular, then the slope of one line is the negative reciprocal of the other line.

The equation of a given line is expressed as

y = mx + b

Where

m represents slope

c represents y intercept

Considering the first equa

The two triangles are similar by the Angle- Angle and also SIde -Side postulates.

A postulate is defined as a statement that is assumed to be true without any proof.

A theorem is defined as a true statement and is supported by a proof (or can be proven).

Here, two triangles can be said to be similar through many postulates :

1. △ABC and △DEF are similar if

angle ABC is equal to angle DEF; and

angle BCA is equal to angle EFD

(or any other two corresponding angles are same)

This can be said that △ABC and △DEF are similar with Angle- Angle (AA) postulate.

2.  △ABC and △DEF are similar if

side AB/ BC is proportional to side DE/ EF;

(or ratio of two corresponding sides are similar)

This can be said that △ABC and △DEF are similar with Side Side (SS) postulate.

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Answer:

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

Step-by-step explanation:

The equation for the area of a triangle (\(A_{\bigtriangleup}\)) is:

\(A_{\bigtriangleup} = \frac{1}{2}\cdot b \cdot h\)

Where:

\(b\) - Base, dimensionless.

\(h\) - Height, dimensionless.

The expression for each triangle are described below:

First Triangle (\(b = 3\cdot x + 7\), \(h = 5\cdot x - 1\))

\(A_{\bigtriangleup,1} = \frac{1}{2}\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

Second Triangle (\(b = 3\cdot (3\cdot x+7)\), \(h = 2\cdot (5\cdot x -1)\))

\(A_{\bigtriangleup,2} = 3\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is:

\(\Delta A_{\bigtriangleup} = A_{\bigtriangleup,2}-A_{\bigtriangleup,1}\)

\(\Delta A_{\bigtriangleup} = 3\cdot (3\cdot x+7)\cdot (5\cdot x-1)-\frac{1}{2} \cdot (3\cdot x+7)\cdot (5\cdot x-1)\)

\(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

Answer:

Martin's Bowling cost = $5x

Isabelle Bowling cost = $5x + 3

where x is the total games Martin and Isabelle played.

Step-by-step explanation:

As given,

There are 2 people - Martin and Isabelle

Each game costs = $10

Let they both play total games = x

⇒total game cost = $10x

As they split the cost , it means the cost is divided into half

⇒Martin game cost = $5x

Isabelle game cost = $5x

Also, given that Isabelle pays $3 to rent shoes.

⇒$3 is added to the Isabelle game cost

∴ we get

Isabelle game cost = $5x + 3

so, we get

Martin's Bowling cost = $5x

Isabelle Bowling cost = $5x + 3

Answer:

$2.25

Step-by-step explanation:

5 lbs = $11.25

The unit price in this context means the price of a 1-pound bag of dog food so you would divide $11.25 by 5:

$11.25 ÷ 5 = $2.25

Hope this helps!

Answer:

2.25 ($) per pound

Step-by-step explanation:                                                                               11.25 /  5 = 2.25 per pound   Alternative workings we simply divide by 10  to find   11.25 / 10  = 1.125 then multiply by 2                                                      1.125 * 2  = 2.25 ($) per pound

With given angular speed/velocity,  the maneuver takes approximately 0.716 seconds.

Angular speed (ω) is a measure of how quickly an object is rotating around an axis or center point, and is given in units of radians per unit time (e.g., radians per second). It is also sometimes referred to as rotational speed.

Angular speed is related to the linear speed (v) of a point on the rotating object and the distance (r) of that point from the axis of rotation by the equation:

ω = v/r

Now,

As angular velocity

ω_avg = Δθ/Δt

where ω_avg is the average angular velocity, Δθ is the change in angle, and Δt is the time taken.

In this case, the gymnast rotates through half a revolution, or 0.5 × 2π radians = π radians. The initial angular velocity is ω1 = 3.40 rev/s, and the final angular velocity is ω2 = 5.40 rev/s.

We can use the formula for average angular velocity to find the time taken:

ω_avg = (ω1 + ω2)/2

ω_avg = (3.40 rev/s + 5.40 rev/s)/2

ω_avg = 4.40 rev/s

Δθ = π radians

Δt = Δθ/ω_avg

Δt = π/4.40 s

Δt ≈ 0.716 s

Therefore,

                The maneuver takes approximately 0.716 seconds.

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The volume of the solid can be found using the slicing method by integrating the cross-sectional area along the x-axis.

To find the volume, we can consider an infinitesimally small slice of width dx at an arbitrary x-coordinate. The cross-sectional area of this slice is given by the product of the curve y=32√(cosx) and the width dx.

Therefore, the volume of the solid can be obtained by integrating the cross-sectional area over the interval [-π/2, π/2]:

V = ∫[(-π/2) to (π/2)] (32√(cosx)) dx

To evaluate this integral, we can make a substitution u = cosx, which gives du = -sinx dx. The limits of integration change accordingly to u(-π/2) = 0 and u(π/2) = 0.

After the substitution, the integral becomes:

V = ∫[0 to 0] (32√u) (-du)

Since the limits of integration are the same, the integral evaluates to zero.

Therefore, the volume of the solid is zero.

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The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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y= -1 x + 4

found the slope and then rearranged y=mx+b to find b

lmk if you need any other help :)

Using the given natural abundances of titanium-46, titanium-47, and titanium-48, we find that the average atomic mass of titanium on this planet is approximately 46.4 amu.

To calculate the average atomic mass of titanium on another planet, we need to consider the natural abundances of its isotopes. The average atomic mass is calculated by multiplying the mass of each isotope by its relative abundance and summing up these values.

Let's assume that the three isotopes of titanium on this planet are denoted as titanium-46, titanium-47, and titanium-48. The natural abundances of these isotopes are given as follows:

Isotope Natural Abundance

Titanium-46 70%

Titanium-47 20%

Titanium-48 10%

To calculate the average atomic mass, we multiply the mass of each isotope by its relative abundance and sum up these values. The atomic masses of titanium-46, titanium-47, and titanium-48 are approximately 46.0 amu, 47.0 amu, and 48.0 amu, respectively.

Average Atomic Mass of Titanium:

(46.0amu×70%)+(47.0amu×20%)+(48.0amu×10%)

=(32.2amu)+(9.4amu)+(4.8amu)

=46.4amu

Therefore, the average atomic mass of titanium on this planet is approximately 46.4 atomic mass units (amu).

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1. The volume of the box is given by:

Volume = length x width x height = 9 in. x 2 in. x 12 in. = 216 cubic inches

So, the answer is 216 cubic inches.

2. The surface area of the box is given by:

Surface Area = 2lw + 2lh + 2wh = 2(9)(12) + 2(9)(2) + 2(2)(12) = 216 + 36 + 48 = 300 square inches

So, the answer is 300 square inches.

3. The surface area of the cereal box is 300 sq. in.

If cardboard costs $0.01 per square inch, then the cost of manufacturing this cereal box would be:

300 sq. in. x $0.01/sq. in. = $3.00

Therefore, the correct answer is -3.00.

4. The volume of the rectangular prism is given by:

Volume = length x width x height = 9 in. x 2 in. x 12 in. = 216 cubic inches

To find the surface area of the sphere, use the formula:

A = 4πr²

Plugging in r = 3.7 in.:

A = 4π(3.7 in.)² ≈ 172.11 square inches

Rounding this to the nearest square inch gives us:

A ≈ 172 square inches

5. The rectangular prism with dimensions of 9 in. x 2 in. x 12 in. would cost less in packaging.

6. The volume of the cylinder is given by:

Volume = πr²h = 390 cubic inches

Solving for r:

r ≈ 4 inches

Therefore, the approximate radius of the cylinder should be 4 inches to hold the same volume of cereal as the rectangular prism.

7. The surface area of the travel-size cereal box is given by:

Surface Area = 2lw + 2lh + 2wh = 2(3)(1.5) + 2(3)(4.5) + 2(1.5)(4.5) = 9 + 27 + 13.5 = 49.5 square inches

To find the length of each side in the cube with the same surface area, we use the formula:

Surface Area of Cube = 6s²

49.5 = 6s²

s ≈ 2.2 inches

So, the length of each side in the cube would be approximately 2.2 inches.

8. The rectangular prism with dimensions of 3 in. x 1.5 in. x 4.5 in. holds more volume than the cube with a side length of approximately 2.2 inches.

9. Some factors that a cereal company may consider in creating their packaging include how well it stacks for shipping and storing on shelves, how easy it is to hold and pour, and how much advertising space there is on the front of the design.

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