The island of Martinique has received $32,000 for hurricane relief efforts. The island’s goal is to fundraise at least y dollars for aid by the end of the month. They receive donations of $4500 each day. Write an inequality that represents this
situation, where x is the number of days.

The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.

To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.

A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.

To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°

Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.

The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)

So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.

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The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x))​ is 1

Given that

f(x) = 3 - 2x

Rewrite as

g(x) = -x² + x + 1

Express as vertex form

g(x) = -(x - 0.5)² + 1.25

Express as equation and swap x & y

x = -(y - 0.5)² + 1.25

Make y the subject

y = 0.5 + √(1.25 - x)

So, the inverse is

g⁻¹(x) = 0.5 + √(1.25 - x)

Here, we have

f(g(x)) = g(f(x))​

This means that

f(g(x)) = 3 - 2(-x² + x + 1)

g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1

Using a graphing tool, we have

f(g(x)) = g(f(x))​ when x = 1

Hence, the value of x is 1

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Complete question

f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers

Find the inverse of G and the value for x for which f(g(x)) = g(f(x))​.

Answer:

f(x) = (5/6)x - (1/4)

f(-8) = (5/6)(-8) - (1/4)

f(-8) = (5/3)(-4) - (1/4)

f(-8) = (-20/3) - (1/4)

f(-8) = (-80-3)/12

f(-8) = -83/12

Answer:

A is correct

Step-by-step explanation:

Whatever value you put in for "y" will keep both of the equations equal

In set theory, two sets are considered equal if they have the same elements. In this case, A is a set containing the elements 1, 2, and 3, while B is an empty set (also known as the null set),

A contains three distinct elements, and B contains none, we can conclude that A and B are not equal, i.e., A is not equal to B.

A ≠ B

Set theory is a branch of mathematics that studies collections of objects, called sets, and the relationships between them. A set is defined as a well-defined collection of distinct objects, which can be anything from numbers and letters to more abstract concepts like functions and geometrical shapes. The set theory provides a foundation for other areas of mathematics, including algebra, topology, and logic.

One of the fundamental concepts of set theory is the notion of membership, which states that an object either belongs to a set or does not. Sets can also be combined through operations such as union, intersection, and complementation, and the relationships between sets can be represented using Venn diagrams.

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Among the given factors, global competition does not contribute to the quest for quality. The correct answer is Option A.

In today's business environment, quality has become an important factor that can make or break a company's success. A successful firm must focus on the quality of the products and services they offer, as this can help them maintain their competitive advantage and ensure customer loyalty.

Quality is important for a variety of reasons, including customer satisfaction, reduced costs, increased productivity, and increased revenue. When firms focus on quality, they can provide better products and services to their customers, which can lead to increased customer loyalty and repeat business. This can help firms build a strong reputation in the market and maintain a competitive advantage.

Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage. When firms face global competition, they need to ensure that their products and services are of high quality to compete effectively in the global market. High-quality products and services can help firms differentiate themselves from their competitors and gain a competitive advantage. This can help firms increase their market share and revenue.

Several factors contribute to the quest for quality. These include:

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Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.

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The exponential distribution is a probability distribution that models the time between events in a Poisson process, where events occur randomly and independently at a constant average rate.

It is commonly used in reliability theory, queuing theory, and other fields to model the failure or waiting times of systems.

(a) The mean time to decay for Cobalt-60 is 5.27 years.

(b) The standard deviation of the decay time is 2.6355 years.

(c) The 99th percentile is 13.6825 years.

(d) The mean time of the experiment is 15.8175 years and the standard deviation is 4.86788 years.

Note: The answers are calculated based on the exponential distribution of radioactive decay with a half-life of 5.27 years for Cobalt-60.

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Answer:

the chance of a blizzard tommorrow is 5%. write the complement of this event

Step-by-step explanation:

The complement of an event is the event that it does not happen, so the complement of a blizzard occurring tomorrow with a 5% chance is that a blizzard does not occur tomorrow with a probability of:

100% - 5% = 95%

Therefore, the complement event is that there is a 95% chance that a blizzard does not occur tomorrow.

from the given circle having tangents, the value of x is 130°.

A line that touches a curve at one point, y = f(x), is said to be the curve's tangent line. (x0, y0). The point at which it is drawn is substituted into the derivative f'(x) to find its slope (m), and y - y0 = m is used to find its equation. (x - x0).

In geometry, a tangent is a straight line that touches a curve or a surface at a single point, without intersecting it at that point. In the case of a curve, the tangent line at a point on the curve has the same slope as the curve at that point.

In trigonometry, the tangent is a mathematical function that relates the angles of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side.

From the given figure,

We know that

50 + AB = 180

AB = 180 - 50

AB = 130

The value of x or arc AB is 130°.

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Answer:

Step-by-step explanation:

It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.

Answer:

120 minutes / 2 hours

Step-by-step explanation:

time = distance / velocity

[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]

Step-by-step explanation:

There are 8 fluid ounces in a cup....

   divide the number of ounces by 8 to find the number of cups

# ounces /  8 ounces/cup    =    cups

The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).

The fraction represents a portion or part of a whole.

There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.

The fractional distance traveled on day one = ²/₅

The remaining fractional distance = ³/₅ (1 - ²/₅)

The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)

The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)

Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.

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An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.

In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:

Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:

89 = 1 x 55 + 34

The gcd of 55 and 89 is 1.

Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89

   The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.

To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:

   55 x 34 = 1870

   11 = 1 x 11 + 0

Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:

55 x 34 ≡ 0 |89|

Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:

55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|

Therefore, the inverse of 55 modulo 89 is indeed 34.

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The answer is (001). This is because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family.

The question is asking which of the planes (A), (B), (C), and (D) is not part of the {100} family for a tetragonal crystal.A tetragonal crystal is a three-dimensional structure made up of four faces that intersect at right angles, forming a unit cell. Each face of the unit cell is defined by a Miller index. A Miller index is a set of three integers written in the form {hkl}, which describes the orientation of the face relative to the crystal lattice. In a tetragonal crystal, the {100} family is the set of faces described by {hkl} such that h = k = 0 and l ≠ 0.

Therefore, A (010), C (110), and E (all of these planes are in the {100} family) are all part of the {100} family for a tetragonal crystal, while B (001) is not.  because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family. In conclusion, the correct answer to the question is B (001).

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New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

The area of the tennis court is given by:

A = lw

where l is the length of the court and w is the width of the court.

Substituting the given values, we have:

[tex]$$260.7569 = l \cdot 10.97$$[/tex]

Solving for l, we get:

[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]

To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:

w' = w - 0.25w = 0.75w

Substituting the given values, we have:

[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]

where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:

[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]

Therefore, the new area of the court is reduced by 25%.

To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:

[tex]$w' = 0.75w$$[/tex]

Dividing both sides by w, we get:

[tex]$\frac{w'}{w} = 0.75$$[/tex]

This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

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The power dissipated by the heater is 1260 watts (W).

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.

Given:

Current (I) = 10.5 A

Potential Difference (V) = 120 V

Unknown:

Power (P) = ?

The formula to calculate the power is:

P = VI

Substituting the given values:

P = 120 V × 10.5 A

P = 1260 W

It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:

P = 1260 W (rounded to three significant digits).

Therefore, the power dissipated by the heater is 1260 watts (W).

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Answer:

x = 4

Step-by-step explanation:

Alternative interior angles means these angles are equal in magnitude and sign

[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]

Thus, the ratio for the number of blueberries to banana is 4:1.

A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.

A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.

The given data for preparing fruit smoothie:

Then,

ratio of  blueberries to banana:

blueberries/banana = 4/1

Thus, the ratio for the number of blueberries to banana is 4:1.

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The value of m∠B is 212 - 24x.

The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.

As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.

To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.

Thus,

m∠A + m∠B + m∠C + m∠D = 360

Substituting the given values, we get:

(16x)° + m∠B + (8x+20)° + 128° = 360

Simplifying and solving for m∠B, we get:

m∠B = 360 - (16x)° - (8x+20)° - 128°

m∠B = 212 - 24x

Therefore, the value of m∠B is 212 - 24x.

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The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.

The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:

[tex]b^2 - 4ac[/tex]

[tex]= 8^2 - 4(1)(c)[/tex]

[tex]= 64 - 4c[/tex]

Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).

In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.

Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.

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Answer:

Using the property of logarithms that says log_a(a^b) = b, we can simplify the expression:

7^(log_7(12)) = 12

Therefore, the value of the expression is 12.

The resultant value of the given expression 4(x²+3)-2y is 157 respectively.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.

Here, we refer to these letters as variables.

An expression is a group of words with operators between them.

The equation is the union of two expressions joined by the symbol "equal to" (=).

For instance, 3x-8. Ex: 3x-8 = 16.

So, the value would be:

4(x²+3)-2y

Insert values as follows:

=4((-6)²+3)-2(-1/2)

=4(36+3)+1=157

Therefore, the resultant value of the given expression 4(x²+3)-2y is 157 respectively.

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Complete question:

What is the value of this expression when x= -6 and y= -1/2? 4(x2+3)-2y

The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.

We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:

x_1 = y

x_2 = y'

x_3 = y''

with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.

The resulting system of equations is:

x_1' = x_2

x_2' = x_3

x_3' = (2t^2 - t)x_2 - 4x_3 + 2t

This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.

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[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Lwh}{3} ~~ \begin{cases} L=\stackrel{base's}{length}\\ w=\stackrel{base's}{width}\\ h=height\\[-0.5em] \hrulefill\\ L=6L\\ w=6w \end{cases}\implies V=\cfrac{(6L)(6w)h}{3}\implies \stackrel{ \textit{36 times the volume} }{V=\cfrac{Lwh}{3}(36)}[/tex]

Answer:

$63 more in tax

Step-by-step explanation:

Takis is 5.25 in tax  

PlayStation is 68.25

well, we know the tax is 10.5% so let's get them for both.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]

[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]

Therefore, the measure of ∠D is approximately 60.96 degrees.

A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.

by the question.

To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:

[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]

Taking the inverse tangent of both sides, we get:

[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]

Rounding this to the nearest hundredth, we get:

[tex]angleD = 60.95 degrees =60.96 degree.[/tex]

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Answer:

Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.

Answer:

(1,3)

Step-by-step explanation:

Given system of equations is :-

We can solve this by using substitution method by substituting the value of y from equation (1) into equation (2) as ,

2x + 1 = x + 2

Subtract x on both sides,

2x - x + 1 = 2

Simplify,

x = 2 - 1

x = 1

Substitute this value of x into equation (2) as ,

y = 1 + 2

y = 1 + 2

y = 3

Hence the required answer is (1,3) .

and we are done!

If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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