75% of the Pottery Club members paid their $5.00 dues. If there are 48 members, how many members paid?

The limit of the function (cos(12x) - cos(3x))/x^2 as x approaches 0 is approximately -99862.9534, as determined by evaluating the function at various values near x=0.

Let f(x) : (cos(12x) - cos(3x))/x^2

We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2

Step 1: Calculate the value of the function for x=0.2

fx = (cos(12(0.2)) - cos(3(0.2)))/(0.2)^2

fx = (cos(2.4) - cos(0.6))/0.04

fx = (0.92358 - 0.95105)/0.04

fx = -24.987664

Step 2: Calculate the value of the function for x=0.1

fx = (cos(12(0.1)) - cos(3(0.1)))/(0.1)^2

fx = (cos(1.2) - cos(0.3))/0.01

fx = (0.9589 - 0.9511)/0.01

fx = -98.998848

Step 3: Calculate the value of the function for x=0.05

fx = (cos(12(0.05)) - cos(3(0.05)))/(0.05)^2

fx = (cos(0.6) - cos(0.15))/0.0025

fx = (0.9802 - 0.9657)/0.0025

fx = -19.923683

Step 4: Calculate the value of the function for x=0.01

fx = (cos(12(0.01)) - cos(3(0.01)))/(0.01)^2

fx = (cos(0.12) - cos(0.03))/0.0001

fx = (0.9999 - 0.9998)/0.0001

fx = -99.853172

Step 5: Calculate the value of the function for x=0.001

fx = (cos(12(0.001)) - cos(3(0.001)))/(0.001)^2

fx = (cos(0.012) - cos(0.003))/0.000001

fx = (0.999983 - 0.999971)/0.000001

fx = -998.62855

Step 6: Calculate the value of the function for x=0.0001

fx = (cos(12(0.0001)) - cos(3(0.0001)))/(0.0001)^2

fx = (cos(0.0012) - cos(0.0003))/0.00000001

fx = (0.99999983 - 0.99999971)/0.00000001

fx = -9989.29525

Step 7: Calculate the value of the function for x=0.00001

fx = (cos(12(0.00001)) - cos(3(0.00001)))/(0.00001)^2

fx = (cos(0.00012) - cos(0.00003))/0.0000000001

fx = (0.9999999983 - 0.9999999971)/0.0000000001

fx = -99862.9534

Therefore, the limit of the function

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The deck of cards Jacob got has a volume of 6.833 cubic inches.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, Jacob received a deck of cards for his birthday. The length, width, and height of the card box are shown below.

Length = 3 1/2 = 7/2

Width = 2 1/2 = 5/2

Height = 2/3

From the general formula of volume:

volume = Length * width *Height

volume = 7/2 * 5/2 * 2/3

The volume of a pack of cards = 35/6 = 6.833

Therefore, the volume of the Deck of cards Jacob received is 6.833 cubic inches.

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Answer:

1. x/0=7

2.x+1=2

3. x=7

Step-by-step explanation:

1. you can't divide by zero so it's undefined

2. x=1

3. when you graph this on a graph, the line goes on forever, as long as it satisfies the equation x+1.

The puffs that the patient will take daily include:

1 puff every 4 hours for 24hrs = 6

1 puff every 6 hours for 24hrs =4

2 puffs every 4 hours for 24hrs =12

2 puffs every 6 hours for 24 hrs =8

From the information, a physician writes a prescription for Proair HFA (albuterol sulfate) for Chronic Obstructive Pulmonary Disease (COPD). The instructions state: Inhale 1 to 2 MDI puffs (90-180mcg) q 4-6 hours.

In this case, it should be noted that puff every 4 hours for 24hrs will be 6 times. Also, 1 puff every 6 hours for 24hrs will be 4 times.

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Answer:

11\4

Step-by-step explanation:

the lcm of 4 and 2 is 4. divide 4 by each denominator. your answer multiplied by the numerator. then you find the difference between the two numbers

Both buildings are 219 years old, with the newer one being 73 years old.

A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

In light of this, the buildings' combined age is 292 years.

Now,

If the newer structure is x years old, the older structure is 3 times that old.

The buildings here have a combined age of 292 years.

Therefore, we obtain: x + 3x = 292 x 4x = 292 x x = 73

Thus, the more recent structure is 73 years old, or x years old.

The older structure is also three times older.

219 years old is 3 times 73.

As a result, the older building is 219 years old, while the more recent structure is 73 years old.

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The value of TU is 117.

What is a line segment?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

Here, we have

Given: U is between T and V. If TU = 11x − 15, UV = 10x, and TV = 20x − 3.

We have to find the value of TU.

TV = TU + UV

20x − 3 = 11x − 15 + 10x

20x − 3 = 21x - 15

-3 + 15 = 21x - 20x

12 = x

Now, we have TU = 11x − 15.

We put the value of x on TU and we get

TU = 11x − 15

TU = 11(12) - 15

TU = 132 - 15

TU = 117

Hence, the value of TU is 117.

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Answer:

96 and 270

Step-by-step explanation:

12×8=96

90

×13

180

+90

270

To determine the service fee as a percentage of the deposited amount, we can use the following formula:

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Service fee percentage = (Service fee / Deposited amount) x 100

In this case:

Service fee percentage = (31.74 / 2239.10) x 100 = 1.41%

So, the service fee for depositing the amount of R2239.10 was 1.41% of the deposited amount.

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The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.

The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.

y_2(t) = t^2v'(t) + 2t v(t) - y_1(t)

Substituting y_1(t) and y_2(t) in the given equation, we get

t^2v''(t) + 2tv'(t) - 2v(t) = 0

This is a first order linear differential equation and can be solved as

v'(t) = -2v(t)/t

Integrating both sides, we get

v(t) = c/t^2

Therefore, the second solution of the given equation is

y_2(t) = c/t

The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.

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Answer:

The area of the shaded region is 36.

Step-by-step explanation:

First, let's find the area of the rectangle as a whole, which will be 5*10 = 50. How did we get 50? The right side is 5 (from 2+3), and the top is 10 (3+7). Multiplying those numbers together will give you the area.

Now, the problem asks to find the shaded region. Let's solve for the area of the non-shaded region: (7*2) = 14.

Now, we can subtract the whole rectangle area minus the non-shaded region to find the shaded region:

50 - 14 = 36

A wire that supports telegraph poles is joined to them at intervals of 6 metres above the ground and 2.5 metres from the pole's foot for a total length of 7.3 metres.

Assume that x is the wire's length. [tex]$x^2=2.5^2+6^2$[/tex] Pythagorean theory [tex]$x^2=6.25+36$[/tex]

[tex]$x^2=6.25+36$\\ $x^2=42.25$[/tex]

As [tex]$x > 0, x=\sqrt{42,2 \sqrt{2}}=6, \sqrt{m}$[/tex]

Total length [tex]$=6.5+2.8=7.3 \mathrm{~m}$[/tex]

There are 50 metres between each telephone pole. Utility poles are made more stable by guy wires. The pole is covered by a ground wire the entire way around. Any power on the pole is safely directed underground by this device. This is a representation of the essential hardware that can differ depending on where you are found on a distribution pole. Typically, lineside telegraph poles are placed 60 to 70 yards apart, a little closer, and ideally within curves.

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Two lines are parallel when their slopes are the same

Two lines are perpendicular when the product of their slopes is -1

Two lines are intersect when their slopes are different

Let's define our slopes as m1 and m2, != means not equal

Solution:

1) m1 = m2        Parallel

2) m1*m2=-1     Perpendicular

3) m1*m2=-1     Perpendicular

4) m1=m2         Parallel

5) m1=m2   (-4 = -4)  Parallel

6) m1 != m2     Neither

7) m1 != m2     Neither

8) m1*m2=-1    Perpendicular

The Vales of x in the equations are : 1) 3 (2) 1  (3) 5  (4) 14  (5) 10 respectively

A linear equation in one variable is that in which the highest power of its variable is 1

The given equations and their solutions are

2x +1 = 7

By collecting like terms we have

2x = 3

x = 3

2) The given equation is 4x +7 = 11

By collecting like terms we have

4x = 4

Making x the subject we have

x = 1

3) 2x -3 = 7

By collecting like terms we have

2x = 10

Making x the subject we have

x = 5

4) 1/2 x - 3 = 7

By collecting like terms we have

1/2x = 7

x= 14

5) The given equation is 3x - 11 = 19

By collecting like terms we have

3x= 30

Therefore x= 10

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Answer: 20,009

Step-by-step explanation:

pk you you have to divide it by 100 sk its 1% then multiply it by 12 sibce its two years

19,616 Answer:

Step-by-step explanation: you divide

Answer: the answer I don’t know

Step-by-step explanation:

The correct choice is b. There are no local maxima. The intervals where the function is increasing. Since the square of any real integer is always positive, the function 3x² will always be growing right since it will never be less than 6 right.

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Attending a business conference is the activity she should engage in.

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What is the average easiness rating of Foothill-De Anza Community College instructors? What are the distributions of easiness ratings for instructors with a photo, chili pepper, and no chili pepper? Is there a relationship between gender and easiness ratings?

To answer these questions, we first need to open the MINITAB file rateMP.mpj. Upon opening the file, we can see that it contains data on 700 instructors from Foothill-De Anza Community College, including the college they teach at, their gender, the department and division they teach in, the number of ratings they have received, their overall quality rating, and their easiness rating. To answer the first question, we can use the average function on the easiness column to find the overall average easiness rating of Foothill-De Anza Community College instructors. To answer the second question, we can use a bar chart to compare the distributions of easiness ratings for instructors with a photo, chili pepper, and no chili pepper. To answer the third question, we can use a two-way table to examine the relationship between gender and easiness ratings. After creating these graphs and tables, we can then interpret our results.

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The two equivalent expressions that could be used to find the total number of chocolate pieces that Luisa has are given as follows:

To obtain the number of pieces that Luisa has, we must consider that:

Hence the multiplication operation giving the number of pieces is given as follows:

4 x 10 x 8.

The associative property of multiplication states that the order in which 3 or more terms are multiplied does not change the product, hence the equivalent expressions are given as follows:

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The monthly cost of x messages is 0.43x + 6 dollars.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given

Cost of message plan for one month = $6

cost for each text = $0.43

The monthly cost is calculated by adding the price of the message plan for one month to the cost of each text message multiplied by the number of messages sent in a month.

Total number of messages sent in a month = x

monthly cost for x text messages = (0.43 * x) + 6

Monthly cost for x text messages = 0.43x + 6 dollars

Hence the cost is 0.43x + 6 dollars.

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The ΔBAE is congruent to ΔDAE. ΔBAE and ΔDAE have three corresponding angles that are congruent, so they are congruent.

The Triangle Congruence Theorem states that if two triangles have three corresponding angles that are congruent, then the triangles are congruent.

This can be seen by looking at the angles BAE, BAE, and DAE. All three of these angles are equal, so they are congruent. Additionally, the side lengths of the triangles are the same, so the triangles are also congruent. The Triangle Congruence Theorem is an important tool for determining the congruence of two triangles.

It is used to compare the angles and side lengths of two triangles, and if the angles and side lengths are the same, then the triangles are congruent. When ΔBAE and ΔDAE have the same angles and side lengths, then it is clear that they are congruent.

According to question,

E is the midpoint of,

AC⊥ BD,

As given E is the midpoint of the line ,

So, BE = ED,

further, line AE = AE, because this is the common line between the two triangles.

Also, ∠BED =∠DEA =90°, as AC⊥ BD.

Therefore, the ΔBAE is congruent to ΔDAE.

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y = ln( [tex]\frac{x^2+1}{2}[/tex])  is the required equation.

In a graph of an equation, the x-intercept is the point at which the graph of the equation crosses the x-axis. It is the point where the y-coordinate is equal to 0. The x-coordinate of the x-intercept is the solution of the equation when y = 0.

Given that the slope at point (x,y)

and we know that slope at any find is dy/dx

so dy/dx = [tex]xe^-^y[/tex]

=> dy/[tex]e^-^y[/tex] = xdx

=> [tex]e^y[/tex] dy = x dx

intergrating both side we get:

[tex]e^y[/tex] = x²/2 + c

where c is a constant

given x intercept is 1

[tex]e^0[/tex] = 1²/2 + c

=> 1 = 1/2+c

=>  c= 1/2

so [tex]e^y[/tex] = x²/2 + 1/2

taking ln on both side we get:

y = ln( [tex]\frac{x^2+1}{2}[/tex])  is the required equation.

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Trigonometry is the study of relationships between angles and sides of a triangle.

The six trigonometric functions—sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot)—are used to describe the relationships between the angles and sides of any triangle.

The unit circle is a circle of radius one centered at the origin of a Cartesian coordinate system. When we determine the coordinates of points on the unit circle, we are using the six trigonometric functions. The unit circle is used to find the values of the trigonometric functions for angles of measures 0°, 30°, 45°, 60°, and 90°.

In the interval [0, 2π], we can use the unit circle to calculate the trigonometric functions of the angles in both degrees and radians. For example, sin 0° = 0, cos 0° = 1, tan 0° = 0, csc 0° = undefined, sec 0° = 1, cot 0° = undefined. The corresponding values in radians are sin 0 = 0, cos 0 = 1, tan 0 = 0, csc 0 = undefined, sec 0 = 1, cot 0 = undefined.

By using the unit circle, we can find the value of all six trigonometric functions for any angle in the interval [0, 2π], given in degrees or radians. We can also use the unit circle to find the trigonometric functions for any angle in any interval.

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Karen divided 560.9 by 10³ and got a quotient of 0.5609 ,therefore he is right.

What do you mean by division?

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

What do you mean by quotient ?

In mathematics, the outcome of dividing two numbers is called the quotient. In other words, the result quotient is obtained by dividing a dividend by a divisor.

How to Divide a Long Number by Decimals?

Hence, Karen divided 560.9 by 10³ and got a quotient of 0.5609.

It is Right answer for the this division, and steps are uploaded in mage kindly see the image also.

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The answer is D. I and II only. The number of people who chose A as their favorite brand could be 30 or 35 since x is rounded to the nearest integer, which is 3. However, it cannot be 45 since 3 is the nearest integer.

1. x is rounded to the nearest integer, which is 3

2. If x is equal to 30, then the number of people who chose A as their favorite brand would be 30

3. If x is equal to 35, then the number of people who chose A as their favorite brand would be 35

4. If x is equal to 45, then the number of people who chose A as their favorite brand would be 45

5. Since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45

6. Therefore, the answer is D. I and II only.

1,150 respondents were asked to select their preferred brand among brands A, B, and C of laundry detergent. x% of those polled indicated that A was their preferred brand. The outcome is 3 if x is rounded to the nearest integer. This means that x could be 30, 35, or 45. However, since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45. Therefore, the answer is D. I and II only, meaning that the number of people who chose A as their favorite brand could be 30 or 35. This is because if x is equal to 30, then the number of people who chose A as their favorite brand would be 30 and if x is equal to 35, then the number of people who chose A as their favorite brand would be 35.

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The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.

The probability of randomly landing in a particular region of a circular dartboard is 1/6. This means that each region of the dartboard is equivalent in size, and thus has the same central angle. Since the dartboard is circular, the total measure of the central angles must add up to 360 degrees. Therefore, the measure of the central angle of each section of the dartboard is 360 divided by 6, which is equal to 60 degrees.

The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.  of randomly landing in a particular region of a circular dartboard is 1/6.

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According to the question of equilateral triangles, 6.7√3 cm is the vertical height of the hexagon.

An equilateral triangle is a triangle with all three sides having the same length and all three angles measuring 60 degrees. It is one of the three basic shapes in geometry and is considered to be the most symmetrical triangle. The sides of an equilateral triangle are always congruent, meaning all three sides have the same length. The sides of an equilateral triangle are also always perpendicular, meaning all three angles are equal to 60 degrees. The area of an equilateral triangle can be calculated using the formula A = (1/2)bh, where b is the length of the base and h is the length of the height.

The vertical height of the hexagon can be calculated using the Pythagorean Theorem. The length of each side of the equilateral triangle is x/2 and the height of the triangle is x√3/2.

The total vertical height of the hexagon is therefore 6 x x√3/2, which is equal to 6.7√3 cm.

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Answer:

2/5 of income put into savings

Step-by-step explanation:

Let Kory's income be X

1/3 of his income goes to taxes so taxes are X/3

Remaining is (1-  2/3) of income = (2/3 ) X

He spends 4/5 of this remaining amount

So balance after expenditure = (1- 4/5) = 1/5 of the remaining income and this amount is put into savings

Fraction of income in savings = 1/5 x 2/3 X = (2/15)X

So fraction put into savings account is 1/5 of total income

If you find it confusing to work with fractions such as these, I suggest an alternate approach which may make it easier to understand

Pick an amount for total income. Since the denominators are 3 and 5, choose an amount which is divisible by both 3 and 5 or in other words divisible by 15

Let's choose 300, a convenient number

Tax Paid = 1/3 x 300 = 100

Income after tax = 300 - 100 = 200
which is same as 2/3 x 300

Spending = 4/5 x 200 = 160

Balance in savings = 200 - 160 = 40 same as 1/5 x 200

So amount in savings as a fraction of income = 40/300 = 2/15