a)cos 165 in terms of sine and cosine of acute angle

The rational function graphed in this problem is given as follows:

B. f(x) = 1/(x - 3) + 2.

From the graph, the asymptotes of the rational function are given as follows:

Considering that the function has a vertical asymptote at x = 3, we have that:

f(x) = 1/(x - 3).

Considering the horizontal asymptote at y = 2, we have that:

f(x) = 1/(x - 3) + 2.

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Let's assume that the number of shirts that must be sold to cover the costs is x.

The revenue from selling x shirts is 12x dollars, and the total cost is the sum of the setup fee and the cost per shirt multiplied by the number of shirts, which is 65 + 7x dollars.

To break even, the revenue must be equal to the cost:

12x = 65 + 7x

Subtracting 7x from both sides:

5x = 65

Dividing both sides by 5:

x = 13

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the expression for the total cost:

65 + 7x = 65 + 7(13) = 156

So the total costs will be $156.

Answer:

The student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

Step-by-step explanation:

Let's call the number of shirts sold "x".

The revenue from selling x shirts at $12 each is:

The total cost of making x shirts is:

In order to break even (i.e. cover their costs), the revenue must equal the total cost:

[tex]\sf:\implies 12x = 7x + 65[/tex]

Solving for x:

[tex]\sf:\implies 5x = 65[/tex]

[tex]\sf:\implies \boxed{\bold{\:\:x = 13\:\:}}\:\:\:\green{\checkmark} [/tex]

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the total cost equation:

[tex]\sf:\implies Total\: Cost = 7(13) + 65 = \boxed{\bold{\:\:\$146\:\:}}\:\:\:\green{\checkmark} [/tex]

So the student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

The number written as a percentage is:

772.5666118%

To do this, just multiply the number by 100%.

For example, for any number A, the percentage form of A is:

p = A*100%

Here the number is  7.725666118, then the percentage form of this number will be:

N =  7.725666118*100% = 772.5666118%

That is the number as a percentage.

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The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.

The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.

However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.

Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.

Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.

The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

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The new volume of the inflatable ball after the radius becomes half of the original one is 16π.

The original volume of the ball is given as 96π

The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.

The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³

With this the original volume of the ball is

(4/3)π X r³

and the new volume of the ball after it's halved is

V₂ = (4/3)π X (r/2)³

After simplification

V₂ = (4/3)π X (r³/8)

The new volume of the ball is:

V₂ = (1/6) X πr³

So the new volume is (1/6) of the original volume. We can calculate this as

V₂ = (1/6) X 96π

= 16π

Therefore, the new volume of the inflatable ball is 16π.

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Answer:

The answer to 1+1 is 2.

Answer:

2

Step-by-step explanation:

The equation that can be written to show the total length of the bandages if they are placed end-to-end is expressed as: 2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3).

In the image given above that shows a line plot for the set of data representing the length of bandages, we have:

Two 1¼ = 2(5/4)

One 1 2/4 = 6/4

Three 1¾ = 3(7/4)

Four 2 = 4(2)

Six 3 = 6(3)

Thus, the equation that will represent the total length of the bandages can be expressed as:

2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3)

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Answer:

The third graph from the top could be the graph of f(x) = (2/5)^x. As x approaches infinity, f(x) approaches 0.

The greatest whole number that rounds to 500 when rounding to the nearest hundred is 550.

When rounding a number to the nearest hundred, you need to look at the digit in the tens place. If that digit is 5 or greater, you round up the hundreds digit; if it is less than 5, you round down the hundreds digit.

For example, let's say we have the number 2,548. The digit in the tens place is 4, which is less than 5, so we round down the hundreds digit (2) to get 2,500.

Now, if we are looking for the greatest whole number that rounds to 500 when rounded to the nearest hundred, we need to find the largest number that has 5 in the tens place and 0 in the ones place. That number is 550. When we round 550 to the nearest hundred, we get 500.

Therefore, the greatest whole number that rounds to 500 when rounded to the nearest hundred is 550.

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The correct number of beads is; 4 black, 8 red, and 4 blue. Option A

A molecular model is a depiction of molecules or chemical compounds made physically, visually, or mathematically in order to comprehend their behavior and characteristics. These models can range from real models made of plastic or metal to computer-generated graphics or mathematical formulae, and they can be straightforward or sophisticated.

There are four carbon atoms, eight hydrogen atoms and four oxygen atoms.

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They may choose to bring 4 chaperones or even more depending on their preferences and logistical constraints.

For the camping trip with 15 scouts, they will need at least 15/5 = 3 chaperones.

However, it's possible that they may want to have more than the minimum number of chaperones for additional supervision and safety. The number of chaperones they choose to bring may also depend on the ratio of chaperones to scouts that they want to maintain.

So, they may choose to bring 4 chaperones (1 chaperone for every 3.75 scouts), 5 chaperones (1 chaperone for every 3 scouts), or even more depending on their preferences and logistical constraints.

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The area of the composite figure is equal to 104 square feet.

In this question we have a composite figure formed by a part of a rectangle and an entire triangle. The area formulas for a rectangle and a triangle are introduced below:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the area of the mural:

A = (10 ft) · (8 ft) - 0.5 · (10 ft) · (5 ft) + 0.5 · (14 ft) · (7 ft)

A = 104 ft²

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If the dowel has a radius of 3.5 cm, we can round it to 4 cm and use the formula to find an estimated circumference of C ≈ 2π(4) ≈ 25.1 cm.

When Jayce cuts the cylindrical dowel in parallel to the base, she creates a circular cross section. The circumference of a circle is the distance around its perimeter, and it can be calculated using the formula C = 2πr, where C is the circumference, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.

Since the dowel is cylindrical, its cross section will also be a circle. Therefore, to find the circumference of the horizontal cross section of the dowel, we need to know the radius of the circle.

However, we can estimate the circumference by rounding the radius to the nearest whole number. For example, if the dowel has a radius of 3.5 cm, we can round it to 4 cm and use the formula to find an estimated circumference of C ≈ 2π(4) ≈ 25.1 cm. Rounded to the nearest whole number, the circumference would be 25 cm.

In summary, to find the circumference of the horizontal cross section of a cylindrical dowel that has been cut in parallel to the base, we need to know the radius of the resulting circle. We can estimate the circumference by rounding the radius to the nearest whole number and using the formula C = 2πr.

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Hi! I'd be happy to help you with your question. To find the volume of two laundry detergent boxes, each measuring 12 inches by 8 inches by 3 inches,

you can follow these steps:

Formula: Volume = Length × Width × Height

Step 1: Plug in the values for one box:
Volume = 12 inches × 8 inches × 3 inches

Step 2: Calculate the volume of one box:
Volume = 288 cubic inches

Step 3: Multiply the volume of one box by 2 to find the volume of two boxes:
Total volume = 288 cubic inches × 2

Solution: The total volume of two laundry detergent boxes is 576 cubic inches.

Your answer: The volume of two boxes of detergent is 576 cubic inches.

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Answer:

(x + 5)^2 + (y + 5)^2 = 16.

Step-by-step explanation:

(x - a)^2 + (y - b)^2 = r^2    where (a, b) is the centre and r =- the radius.

Here (a, b) = (-5, -5) and r = 4, so:

(x - (-5))^2 + (y - (-5))^2 = 4^2

(x + 5)^2 + (y + 5)^2 = 16

The two digit Combinations that never appear in any of the passcodes are 5 and 6.

There are 49 different passcodes that can be used. The sum of the six digits of the current passcode is 81, which is a square number. Therefore, the current passcode is made up of three different two-digit square numbers with the sum of their digits equal to 9.

The possible combinations are

(16, 25, 40),

(16, 49, 16),

(25, 36, 20),

(36, 49, 4),

(49, 64, 9),

(64, 81, 16), and

(81, 16, 64).

The only combination that has the same first and sixth digits is (16, 25, 40), so the current passcode is 162540.

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The probability of selecting a brown M&M from this bag is 0.

Since there are no brown M&Ms mentioned in your bag, the probability of selecting a brown M&M is 0. In probability terms, we can express this as:

Probability of selecting a brown M&M = Number of brown M&Ms / Total number of M&Ms

There are 0 brown M&Ms, and there are a total of 4 green + 6 yellow + 7 purple + 3 red = 20 M&Ms in the bag. So the probability is:

Probability = 0 / 20 = 0

Thus, the probability of selecting a brown M&M from this bag is 0, meaning it's impossible with the given information.

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The perimeter of Rebakh's new mural is 9 meters.

Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.

So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.

Therefore, the perimeter of Rebakh's new mural is 9 meters.

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The factored form of the equation is 1/2(y - √5)

To factor this expression, we need to look for any common factors that can be pulled out of both terms. We can see that both terms contain a factor of 1/2, so we can factor that out:

1/2(y - 5 1/2)

Now we need to see if there are any further factors that we can find. The term inside the parentheses, y - 5 1/2, cannot be factored any further using real numbers. However, we can write the expression as y - √5, which shows that it involves the square root of 5.

So the final factored form of the expression is:

1/2(y - √5)

This means that if we multiply 1/2 by (y - √5), we get back the original expression 1/2y - 5 1/2.

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No, 2352 is not a perfect square.

To find the smallest number by which 2352 must be multiplied so that the product is a perfect square, we need to factorize 2352 into its prime factors.

2352 = 2^4 x 3 x 7^2

To make it a perfect square, we need to multiply it by 2^2 and 7, which gives us:

2352 x 2^2 x 7 = 9408

Now, we can take the square root of 9408:

√9408 = √(2^8 x 3 x 7) = 2^4 x √(3 x 7) = 16√21

Therefore, the smallest number by which 2352 must be multiplied so that the product is a perfect square is 2^2 x 7, which gives us the square root of 9408 as 16√21.

Answer:

The smallest number by which 2352 must be multiplied so that the product is a perfect  square = 3

The square root of the new number = 84

Step-by-step explanation:

√2352 ≈ 48.5 so not a perfect square

Prime factorization of 2352 yields

2352 = 2 x 2 x 2 x 2 x 7 x 7 x 3

In exponential form this is
2⁴ x  7² x 3¹

So
[tex]\sqrt{2352} = \sqrt{2^4 \cdot 7^2 \cdot 3}\\\\= \sqrt{2^4} \cdot \sqrt{7^2} \cdot \sqrt{3}\\\\= 2^2 \cdot 7 \cdot \sqrt{3}\\\\= 28 \sqrt{3}[/tex]

To get rid of the radical in the square root and get a whole number, all you have to do is multiply [tex]\sqrt{2352}[/tex]  by √3

[tex]28 \sqrt{3} \cdot \sqrt{3} = 28\cdot 3 = 84\\\\84^2 = 7056 = 2352 \cdot 3\\[/tex]

This means that if you multiply 2352 by 3 it will become a perfect square

Check:
[tex]2352 \cdot 3 = 7056\\\\\sqrt{7056} = 84[/tex]

5.58g of catalyst is required for 900g of reactants.

If 500g of reactants require 3.1g of catalyst, then for 900g of reactants, we can use the following proportion:

500g reactants / 3.1g catalyst = 900g reactants / x

Where x is the amount of catalyst required for 900g of reactants.

To solve for x, we can cross-multiply:

500g reactants * x = 3.1g catalyst * 900g reactants

Then, we can divide both sides by 500g reactants to isolate x:

x = (3.1g catalyst * 900g reactants) / 500g reactants

Simplifying this expression gives:

x = 5.58g catalyst

Therefore, 5.58g of catalyst is required for 900g of reactants.

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Answer:Go to the 6 number on the bottom line.Then go up until you reach 2

Step-by-step explanation:
|      
|
|
|
|        .  
|______

Should look like that-ish

Answer:

Step-by-step explanation:

Put the point to the right 6 times and up two times

The artist used a total of $0.33 worth of paint for the project.

The artist purchased 2 liters of paint, which is equivalent to 2,000 milliliters of paint. This amount of paint was used to complete a project, and after the project was finished, there were 350 milliliters of paint left over.

To determine how much paint was used for the project, we subtract the amount of leftover paint from the total amount of paint purchased, which gives us 2,000 - 350 = 1,650 milliliters of paint used for the project.

The cost of the paint is 2 cents per milliliter, which is equivalent to $0.02/100 milliliters or $0.0002 per milliliter. To determine the cost of the paint used for the project, we multiply the amount of paint used by the cost per milliliter.

Therefore, the cost of 1,650 milliliters of paint used for the project can be calculated by multiplying 1,650 milliliters by $0.0002 per milliliter, which gives us $0.33.

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The value of x is 32.

A set of angles that are between the two line parallels but on each side of the transverse are referred to as alternate external or exterior angles. The measure of the alternate external or exterior angles is equal.

According to the alternate outside angle theorem, alternate exterior angles are regarded as congruent angles or degrees of equal magnitude when two parallel lines intersected by a transversal.

Given that the lines m and n are parallel, and the angles are [tex](3x-2)^{0}[/tex] and [tex](2x+30)^{0}[/tex].

The given angles are alternate external or exterior angles. So, they must be equal.

[tex](3x-2)^{0} = (2x+30)^{0}[/tex]

Rearrange the above equation to find the value of x as follows,

[tex]3x-2x=30+2[/tex]

[tex]x=32[/tex]

Hence, the value of x is 32.

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If Mrs. Smith's estimation only accounted for a 4-week month, it would be incorrect. However, if she factored in the additional 10 days, then her estimation of serving 40,000 people soup with 1 cup per person over 2 weeks is correct.

Soup kitchens are community-based organizations that provide meals, primarily soup, to people in need. These facilities are often run by volunteers and rely heavily on donations from local businesses and individuals to provide food for those who cannot afford it.

Mrs. Smith, the soup kitchen chef, estimates that they will serve 40,000 people soup, giving each person 1 cup of soup over 2 weeks, and with the month having 5 weeks.

To determine if Mrs. Smith's estimation is correct, we need to do some calculations. One cup of soup per person over two weeks means that each person will receive 2 cups of soup in total. Therefore, to serve 40,000 people with 2 cups of soup each, the soup kitchen would need to provide a total of 80,000 cups of soup.

With the month having 5 weeks, it means that there are 10 days extra in the month compared to a standard 4-week month. Therefore, the soup kitchen will need to serve an additional 1/5 of the total amount of soup to cover the additional 10 days.

So, to determine if Mrs. Smith's estimation is correct, we can multiply the total cups of soup needed (80,000) by 1/5, which equals 16,000 cups. We then add this to the original total, which gives us 96,000 cups of soup needed for the month.

In conclusion, if Mrs. Smith's estimation only accounted for a 4-week month, it would be incorrect. However, if she factored in the additional 10 days, then her estimation of serving 40,000 people soup with 1 cup per person over 2 weeks is correct.

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Evaluation of S12(x3 – 2x)dx is- 92.875

We can use the definition of the Riemann Sum to evaluate S12(x3 – 2x)dx as follows:

First, we need to choose the width of our intervals.

Let's choose Δx = 1/2, which means we will have 24 subintervals.
Now, we can use the formula for the Riemann Sum to calculate the sum of the areas of the rectangles.
S12(x3 – 2x)dx ≈ ∑[f(xi)Δx] from i=1 to i=24
where xi is the right endpoint of the ith subinterval,

f(xi) = x[tex]i^3[/tex] – 2xi is the height of the rectangle, and Δx = 1/2 is the width of the rectangle.
Evaluating this sum using the given formula, we get:
S12(x3 – 2x)dx ≈ [f(1/2) + f(1) + f(3/2) + ... + f(11)](1/2)
≈ [[tex](1/2)^3[/tex] – 2(1/2) + (1)^3 – 2(1) + (3/2[tex])^3[/tex] – 2(3/2) + ... + (11[tex])^3[/tex] – 2(11)](1/2)
≈ [- 2361/16](1/2)
≈ - 92.875
4) we can simply evaluate the given integral:
S2x2+x=2 = ∫(2[tex]x^2[/tex] + x)dx from 0 to 2
= [[tex]2/3 x^3 + 1/2 x^2[/tex]] from 0 to 2
= [[tex]2/3 (2)^3 + 1/2 (2)^2[/tex]] - [[tex]2/3 (0)^3 + 1/2 (0)^2[/tex]]
= 16/3
5), we can use the following formulas

to find the displacement and distance traveled by the particle over the given time interval:
Displacement = ∫v(t)dt from 1 to 5
Distance traveled = ∫|v(t)|dt from 1 to 5
where v(t) is the velocity function.
a) To find the displacement, we evaluate the integral:
∫v(t)dt = ∫(8 – 2t)dt from 1 to 5
= [8t – t^2] from 1 to 5
= [[tex]8(5) – (5)^2[/tex]] - [8(1) – [tex](1)^2[/tex]]
= 18 meters
b) To find the distance traveled, we evaluate the integral:
∫|v(t)|dt = ∫|8 – 2t|dt from 1 to 5
= ∫(8 – 2t)dt from 1 to 4 + ∫(2t – 8)dt from 4 to 5
= [8t – [tex]t^2[/tex]] from 1 to 4 + [-t^2 + 8t -16] from 4 to 5
= [8(4) – [tex](4)^2[/tex]] - [8(1) – [tex](1)^2[/tex]] + [[tex]-(5)^2[/tex] + 8(5) -16 -(-[tex](4)^2[/tex] + 8(4) -16)]
= 26 meters

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This will show that each family gets 5/16 of a pizza.

Sure, I'd be happy to help you with your question!

So, Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive?

Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families.

To illustrate both students' solutions, we can use Scratchpad. For Savannah's solution, we can draw 5 rectangular pizzas and then divide them into 4 equal parts each. Then, we can shade in 1 whole pizza and divide the remaining pizza equally among the 4 families. This will show that each family gets 1 whole pizza and a quarter of a pizza.

For Josiah's solution, we can draw 5 rectangular pizzas and then divide each pizza into fourths. Then, we can divide the fourths equally among the 4 families.

This will show that each family gets 5/16 of a pizza.

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The probability of getting an even number or a number less than 8 is:

P = 0.83

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.

The numbers that are even or less than 8 are:

{1, 2, 3, 4, 5, 6, 7, 8, 10, 12}

So 10 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 10/12 = 0.83

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Here is a two way table that shows the type of music a person likes compared to their gender:

|               | Males | Females | Total |
|---------------|-------|---------|-------|
| Jazz          | 13    | 0       | 13    |
| Rock          | 54    | 27      | 81    |
| Country       | 0     | 66      | 66    |
| Total         | 67    | 93      | 200   |

In this table, we can see that out of the 94 males surveyed, 13 of them liked jazz. Out of the 106 females surveyed, 27 of them liked rock and 66 of them liked country. Overall, out of the 200 people surveyed, 81 of them liked rock, 13 of them liked jazz, and 66 of them liked country.

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Examining the expression the value of r/2c is

We can use algebra to calculate the value of r/2c with 3r/c as the variable.

First, let's reduce the expression 3r / c = 126 by multiplying both sides by c / 3:

3r/c * c/3 = 126 * c/3

r/1 = 42c

Now we can obtain r / 2c by dividing both sides by 2c:

solving for the left hand side of the equation

r /2c = (r/1)/(2c)

solving for the right hand side of the equation

42c = (42c)/(2c) = 21

Equation the left hand side to the right hand side of the equation

r/2c = 21

Therefore, r/2c = 21.

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