let r be the region bounded by the following curves. find the volume of the solid generated when r is revolved about the​ y-axis.

Answer:The Algebra of Functions

Like terms, functions may be combined by addition, subtraction, multiplication or division.

Example 1. Given f ( x ) = 2x + 1 and g ( x ) = x2

+ 2x – 1 find ( f + g ) ( x ) and

( f + g ) ( 2 )

Solution

Step 1. Find ( f + g ) ( x )

Since ( f + g ) ( x ) = f ( x ) + g ( x ) then;

( f + g ) ( x ) = ( 2x + 1 ) + (x2

+ 2x – 1 )

= 2x + 1 + x2

+ 2x – 1

= x

2

+ 4x

Step 2. Find ( f + g ) ( 2 )

To find the solution for ( f + g ) ( 2 ), evaluate the solution above for 2.

Since ( f + g ) ( x ) = x2

+ 4x then;

( f + g ) ( 2 ) = 22

+ 4(2)

= 4 + 8

= 12

Example 2. Given f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ).

Solution

Step 1. Find ( f – g ) ( x ).

( f – g ) ( x ) = f ( x ) – g ( x )

= ( 2x – 5 ) – ( 1 – x )

= 2x – 5 – 1 + x

= 3x – 6

Step 2. Find ( f – g ) ( 2 ).

( f – g ) ( x ) = 3x – 6

( f – g ) ( 2 ) = 3 (2) – 6

= 6 – 6

= 0

Step-by-step explanation:

$50 can purchase 40 sports drinks.

A purchase is the acquisition of goods or services in exchange for money or other forms of payment. It is a common transaction that takes place in everyday life and can range from small purchases such as buying groceries, to larger purchases such as buying a car or a house.

When making a purchase, a buyer typically identifies a need or desire for a particular product or service, and then selects a seller or retailer who offers the desired item. The buyer then pays the seller the agreed-upon price, either in cash, by credit card, or through other forms of payment.

Purchases can take place in a variety of settings, including physical stores, online marketplaces, and through person-to-person transactions. The process of making a purchase may involve comparing prices, negotiating with the seller, and evaluating the quality and features of the product or service being purchased.

In addition to individual purchases, businesses and organizations also make purchases to acquire the resources and materials needed to operate and grow. This can include purchasing raw materials, equipment, and services from suppliers, as well as acquiring other businesses through mergers and acquisitions.

Overall, purchases are an important aspect of economic activity and play a crucial role in the functioning of markets and the economy as a whole.

Let's start by finding the cost of one sports drink:

$29.99 / 24 = $1.25 per sports drink

To find how many sports drinks can be purchased for $50, we divide $50 by the cost of one sports drink:

$50 / $1.25 per sports drink = 40 sports drinks

Therefore, $50 can purchase 40 sports drinks.

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Answer:

DB = approximately 16

Step-by-step explanation:

DEC is a right triangle => DC=10. Because all four sides are equal in a rhombus, then AD=AB=10. Then, because angle BAD is 53*2=106 degrees, we can use cosines. DB=sqrt(10^2+10^2-2*10*10cos(106deg))=15.9727102009.

If 0 is not an eigenvalue of a matrix, then it means that the matrix is invertible it implies that the matrix has a unique inverse .

The Eigenvalues are defined as the values which is associated with a square matrix.  

A non-zero vector is said to have an eigenvector of a matrix if when the matrix is multiplied by the vector, the result is a scalar multiple of the vector and that scalar multiple is known as the eigenvalue.

If a matrix has an eigenvalue of 0, it means that there exists a non-zero vector such that when the matrix is multiplied by the vector, the result is the zero vector. Such a matrix is said to be singular or non-invertible.

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The conversion of the weight 46 Kg to pounds (lbs) is 46 Kg is = 101.42 lbs .

The Pound and Kilogram are both units of measurement for weight or mass ; the unit used for pound is lbs , and for Kilogram the unit used is Kg .

The weight to be converted is = 46 Kg ,

We have to convert this weight to pounds ;

The conversion factor to convert the weight from Kilogram to pounds is : 1 Kg = 2.20462 lbs ;

On multiplying the given weight by the conversion factor ;

We get ;

⇒ 46 Kg = 46 × 2.20462 lbs ;

⇒ 46 Kg = 101.41252 ≈ 101.42 lbs .

Therefore , the weight 46 Kg is approximately equal to 101.42 lbs  .

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Answer:

y = 22x - 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 22 , then

y = 22x + c ← is the partial equation

to find c substitute (1, 2 ) into the partial equation

2 = 22(1) + c = 22 + c ( subtract 22 from both sides )

- 20 = c

y = 22x - 20 ← equation of line

Using the formula, we can convert milliliters to teaspoons. 1 milliliter equals 0.202 teaspoons, thus 10ml equals 2.02 teaspoons.

The volume unit is milliliters. A teaspoon is also a volume measure, however it is a smaller unit that is commonly used at dinner settings.

One millilitre is equivalent to 0.202 US teaspoons using normal conversion rates.

As a result, we may define the link using the unit conversion idea.

One milliliter is equal to 0.202 teaspoons in the United States.

For example, 10 milliliters equals 2.02 teaspoons.

As a result, we'll need roughly 2 tablespoons to get 10 ml.

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The area of the triangular prism is 240 mm²

A triangular prism is a prism with three rectangular faces connecting its two congruent triangular faces. It consists of 5 faces, 6 edges, and vertices.

The sum of the areas of all the triangle's faces is the surface area. By using the net of a prim we can determine the area of the prism as given below. Here we calculate the individual parts of the net to get the total area.

Here we have

A right triangular prism and its net  

The area of the prism can be calculated by calculating the area of the 2 triangles and the areas of 3 rectangles in the given net

As we know Area of rectangle = Length × Width

Area of rectangle parts = [ 3 × 8 ] + [ 3 × 15 ] + [ 17 × 3 ]

= 24 mm² + 45 mm² + 51 mm²

= 120 mm²  

Area of triangle parts = 2 [ 1/2 (15 × 8) ]

= 120 mm²  

Total area of prism = 120 mm² + 120 mm² = 240 mm²

Therefore,

The area of the triangular prism is 240 mm²

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Answer:

15m3 + 16m5

Step-by-step explanation:

3m3 + 3m3 + 9m3 = 15m3

11m5 + m5 = 16m5

Answer:

-10m^5-3m^3

Step-by-step explanation:

3m^3+3m^3=6m^3-9m^3=-3m^3

-11m^5+m^5=-10m^5

Mover the larger exponent first so -10m^5-3m^3

99% confidence interval for the number of chocolate chips per cookie is

15.4 ± 1.1115

The mean of sample plus and minus the range of that sample constitutes a confidence interval.

Within a specific level of confidence, this is the range of values anticipated to fall within, if the test is repeated.

Number of cookies in the sample n = 55

Mean μ = 15.4

Standard deviation s = 3.2

Confidence = 99%

For 99% confidence interval Z-value = 2.576

Confidence interval

= μ ± Zs/√n

= 15.4 ± 2.576×3.2/√55

= 15.4 ± (8.2432/7.4162)

= 15.4 ± 1.1115

Hence, 15.4 ± 1.1115 is the 99% confidence interval for the number of chocolate chips per cookie.

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Answer:

The correct answer is B. Quantitative data, because the numbers represent numerical values that can be measured and compared.

The values of side lengths d and b in the triangles are d = 2.3 units and b = 8.5 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

TRIANGLE 1

sin 60° = 2/d    (Sine = opposite / hypotenuse)

0.8660 = 2/d

d = 2/0.8660

d = 2.3 units

TRIANGLE 2

sin 45° = 6/b    (Sine = opposite / hypotenuse)

0.7071 = 6/b

b = 6/0.7071

b = 8.5 units

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The value  converted from Celsius to Fahrenheit is given by 39.1 Celsius equals to 102.38 Fahrenheit.

Units  representing the measurement of the temperature in the standard form are Celsius and Fahrenheit .

Formula which relates the Celsius and Fahrenheit are given by

(°C × 9/5) + 32 =°F

Now Substitute the converted value 39.1 Celsius into Fahrenheit we get,

(39.1°C × 9/5) + 32

= ( 351.9 / 5 ) + 32

= ( 70.38 ) + 32

= 102.38°F

Therefore, the converted value from Celsius to Fahrenheit for the given temperature 39.1 Celsius is given by 102.38 Fahrenheit.

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The above question is incomplete , the complete question is:

What is the conversion of 39.1 °C to °F ?

Answer:

200 * 25/100 --> 25% of 200

200 * 15/100 --> 15% of 200

100 * 35/100 --> 35% of 100

Step-by-step explanation:

Percentages are always out of 100 ( e.g 60% is equivalent to 60/100) and whole numbers have a denominator of 1 meaning you could simply solve this sort of problem if you set it up right.

For example) 25% of 200

25/ 100  *  200/1

25 * 200 is 5000 and 100 * 1 is 100

So the answer would be 5000/100 (which you would simplify to get the right answer but that's just an example)

Hope you have a great day :)

Using angle relationship as reasons, the missing angles are:

1. m∠a = 108°

2. m∠b = 43°

3. m∠c = 114°

4. m∠d = 101°

5. m∠e = 82°

m∠f = 82°

6.  m∠g = 67°

m∠h = 113°

7. m∠i = 127°

m∠j = 53°

8. m∠k = 156°

m∠l = 24°

9. m∠m = 72°

10. m∠n = 86°

11. m∠p = 25°

12. m∠q = m∠r = 61°

The angle relationship that exist between the angles in question will determine how to solve for the missing angle measure in a figure. Some of them are:

1. m∠a = 108°,

Reason: alternate interior angles are congruent.

2. m∠b = 43°,

reason: corresponding angles are congruent.

3. m∠c = 114°,

reason: corresponding angles are congruent.

4. m∠d = 180 - 79

m∠d = 101°

Reason: same-side interior angles theorem (angle relationship)

5. m∠e = 82°,

reason: alternate interior angles are congruent.

m∠f = 82°

Reason: vertical angles are congruent.

6.  m∠g = 67°,

Reason: corresponding angles are congruent.

m∠h = 180 - 67 = 113°,

reason: same-side interior angles are supplementary.

7. m∠i = 127°

reason: corresponding angles are congruent.

m∠j = 180 - 127 = 53°

reason: linear pair angles are supplementary or have a sum of 180 degrees.

8. m∠k = 156°

reason: supplementary angles

m∠l = 24°

reason: alternate exterior angles are congruent

9. m∠m = 72°

reason: alternate exterior angles are congruent

10. m∠n = 180 - 94 = 86°

reason: supplementary angles

11. m∠p = 180 - 155 = 25°

reason: supplementary angles

12. m∠q = m∠r = 180 - 119 = 61°

reason: supplementary angles

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As x approaches positive infinity, f(x) approaches negative infinity , Option C is the answer.

What is a Function ?

Function is a mathematical statement that links two variables m a dependent and an independent variable with each other.

It is given that

f(x) = - [tex]\sqrt{x+6}[/tex]

as x----- > ∞  y ---->- ∞

as x -----> - ∞ y----> imaginary axis

Therefore , As x approaches positive infinity, f(x) approaches negative infinity , Option C is the answer.

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To calculate the optimal bundle, you need to find the combination of goods or services that maximizes the consumer's utility while staying within their budget constraint.

The optimal bundle can be found by using the consumer's utility function and their budget constraint. The utility function specifies how much utility the consumer gets from consuming various quantities of the goods or services, while the budget constraint specifies the combinations of goods or services that the consumer can afford given their income and the prices of the goods or services.

To find the optimal bundle, follow these steps:

Write down the consumer's utility function, such as U(x, y) where x and y are the quantities of two goods.

Write down the consumer's budget constraint, such as P_x x + P_y y = I where P_x and P_y are the prices of the goods, I is the consumer's income, and x and y are the quantities of the two goods.

Find the marginal utility of each good by taking the partial derivative of the utility function with respect to each good. For example, the marginal utility of x is given by dU/dx.

Set the marginal utility per dollar spent on each good equal to each other, since the consumer should allocate their spending so that the marginal utility per dollar spent is the same for both goods. That is, set dU/dx / P_x = dU/dy / P_y.

Solve the resulting equations for the quantities of the goods that maximize the consumer's utility subject to their budget constraint.

The resulting combination of goods that solves the optimization problem is the consumer's optimal bundle. It represents the combination of goods that maximizes the consumer's utility given their budget constraint.

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There is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

We can use the binomial distribution to calculate the probability of the Rangers winning a majority of their games against the Islanders, given their win percentage of 55.1%. Let's denote the probability of the Rangers winning a single game against the Islanders as p.

Since the Rangers and Islanders play seven games against each other, the number of games the Rangers win against the Islanders follows a binomial distribution with parameters n = 7 and p = 0.551.

To find the probability that the Rangers win a majority of these seven games, we need to sum the probabilities of all possible outcomes where they win four or more games. We can use the binomial probability formula to calculate each of these individual probabilities and then sum them up:

P(Rangers win 4 or more games) = P(Rangers win 4 games) + P(Rangers win 5 games) + P(Rangers win 6 games) + P(Rangers win 7 games)

[tex]= (7 choose 4) * 0.551^4 * (1 - 0.551)^3 + (7 choose 5) * 0.551 ^ 5 * (1 - 0.551)^2 + (7 choose 6) * 0.551^6 * (1 - 0.551) + (7 choose 7) * 0.551^7[/tex]

Using a binomial calculator or a spreadsheet, we can evaluate this expression and find that:

P(Rangers win a majority of their games against the Islanders) = 0.423

Therefore, there is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

The Binomial distribution is a discrete probability distribution that describes the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial can have only two outcomes (e.g., success or failure).

The distribution is defined by two parameters: the number of trials n and the probability of success in each trial p. The distribution gives the probability of obtaining k successes in n trials, where k can range from 0 to n.

The formula for the probability mass function of the Binomial distribution is:

[tex]P(k) = (n choose k) * p^k * (1 - p)^n-k[/tex]

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. The formula can be used to calculate the probability of obtaining k successes in n trials, given a fixed probability of success p.

The Binomial distribution is used in many areas of statistics, including quality control, epidemiology, and finance, among others. It is also a fundamental building block for more complex statistical models, such as the Poisson distribution and the normal distribution.

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Answer:

The expected number of times Henry would remove a strawberry chew from the bag is about 1041. This can be calculated by multiplying the total number of trials (23 + 1300 = 1323) with the relative probability of each type of chew (17/23 = 0.7391 for strawberry, 3/23 = 0.1304 for lemon, 3/23 = 0.1304 for peach). The expected number of times Henry would remove a strawberry chew from the bag is 0.7391 x 1323 = 1041.24, which can be rounded to 1041.

Answer:

Step-by-step explanation

The answer is 961 . I can explain because, it is really easy all you have to do is add 17 and 23 together because it is only asking about strawberry so lower number on top and higher on bottom you get 17/23 then u put this equation 1300 times 17/23 you will get 960 and some decimals round up to 961 there you go you've got your anwser.

Therefore, the n-th term of the sequence is 19 - 2n.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant value to the previous term. This constant value is called the common difference of the arithmetic sequence. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is obtained by adding 3 to the previous term.

The nth term of an arithmetic sequence can be expressed using the following formula:

an = a1 + (n - 1)d

where an is the nth term of the sequence, a1 is the first term, n is the number of the term, and d is the common difference.

The sum of the first n terms of an arithmetic sequence can also be calculated using the formula:

Sn = n/2(2a1 + (n - 1)d)

where Sn is the sum of the first n terms, a1 is the first term, n is the number of terms, and d is the common difference.

Here,

The first term of the sequence is 17 and the common difference between consecutive terms is -2 (i.e. subtracting 2 from the previous term to get the next term). So, we can write the n-th term of the sequence as:

a_n = 17 + (n-1)(-2)

Simplifying this expression, we get:

a_n = 19 - 2n

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(a) The translation in coordinate notation is (x', y') = (x-4, y-3)

(b) The translation as a vector in component is [tex]\vec v = \vec w + ( -4\hat i -3\hat j)[/tex].

The solution has been obtained by using the concept of transformation.

What is transformation?

A transformation is any operation that shifts a polygon or other two-dimensional object on a plane or coordinate system.

The two-dimensional shape that existing before any modification is referred to as the "inverse image" or "pre-image." The image is a representation of the altered shape.

From the given figure, we can see that the quadrilateral W'X'Y'Z' has been formed by translating quadrilateral WXYZ 4 units in x direction and 3 units in y direction.

So, the translation in coordinate notation is (x', y') = (x-4, y-3) and as a vector in component is [tex]\vec v = \vec w + ( -4\hat i -3\hat j)[/tex].

Hence, the required solution has been obtained.

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The missing figure for the question has been attached below.

Answer:

Step-by-step explanation:

x-3 is greater than or less than 7

The solution is, Ian walk in 4 1/2 days 81/4 = 20.25 miles.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

Ian walks 4 1/2 miles every day

i.e. in 1 day walks = 9/2 mile

so, Ian walk in 4 1/2 days is.

in 9/2 days walks = 9/2* 9/2 miles

                             =81/4 miles

Hence, The solution is, Ian walk in 4 1/2 days 81/4 = 20.25 miles.

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The value which is converted from inches to feet representing the length is given by 38 inches is equal to 3.1667 feet.

Formula which relates the inches and feet is equal to  :

1 inch is equal to 0.0833333 feet.

Now Substitute the value 38 inches which needs to convert  into another unit of length feet we get,

1 inch = 0.0833333 feet

⇒ 38 inches = ( 38 ) × ( 0.0833333 ) feet

⇒ 38 inches = 3.1666654 feet.

⇒ 38 inches =  3.1667 feet ( round upto the four decimal places )

Therefore, the converted value from inches to feet  for the 38 inches is equal to 3.1667 feet.

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An example of a double replacement reaction is given below:

AgNO3 + NaCl → AgCl + NaNO3

A double replacement reaction, also known as a double displacement reaction or metathesis reaction, is a type of chemical reaction in which two compounds react with each other and swap cations or anions to generate two new compounds.

A general double replacement reaction is expressed as follows:

AB + CD → AD + CB

A double replacement reaction is illustrated below:

AgNO3 (silver nitrate) + NaCl (sodium chloride)  → AgCl (silver chloride) + NaNO3 (sodium nitrate)

Silver nitrate and sodium chloride are combined in this process. Silver chloride (AgCl) is formed when the silver ion (Ag+) in silver nitrate replaces the sodium ion (Na+) in sodium chloride, whereas sodium nitrate (NO3-) is formed when the nitrate ion (NO3-) replaces the chloride ion (Cl-) in sodium chloride (NaNO3).

This reaction's balanced equation is:

AgNO3 + NaCl → AgCl + NaNO3

This sort of reaction is often utilised in salt synthesis and precipitation processes.

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A logarithmic differentiation calculator is an online tool used to calculate the derivative of a function using logarithmic differentiation.

A logarithmic separation mini-computer is a web-based instrument that utilizes logarithmic separation to work out the subordinate of a capability. Logarithmic separation is a procedure used to separate capabilities that are challenging to separate utilizing customary techniques. The cycle includes taking the normal logarithm of the two sides of the capability, then separating utilizing the principles of logarithms and the chain rule. The subsequent articulation can be streamlined to give the subsidiary of the first capability. An internet based logarithmic separation number cruncher robotizes this interaction, permitting clients to enter a capability and accept its subsidiary. This can be helpful for understudies and experts in fields like math, physical science, and designing, who need to rapidly and precisely work out subsidiaries of perplexing capabilities. There are numerous logarithmic separation number crunchers accessible on the web, some of which additionally give bit by bit clarifications of the interaction used to compute the subsidiary.

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Answer:

8.5 cm

Step-by-step explanation:

A regular pentagon has 5 congruent sides , then

length of each side = perimeter ÷ 5 = 42.5 ÷ 5 = 8.5 cm

The negative solution of the statement is -1

From the question, we have the following parameters that can be used in our computation:

6 times a number is 7 less than the square of that number

When represented as an equation, we have

6x = x^2 - 7

So, we have

x^2 - 6x - 7 = 0

Factorize

x^2 + x - 7x - 7 = 0

This gives

(x + 1)(x - 7)

Solve for x

x = -1 and x = 7

So, the negaive solution is -1

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Answer:

see explanation

Step-by-step explanation:

(a)

the sum to infinity of a geometric progression is

S∞ = [tex]\frac{a_{1} }{1-r}[/tex] : | r | < 1

where a₁  is the first term and r the common ratio

here a₁ = 20 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{16}{20}[/tex] = [tex]\frac{4}{5}[/tex] = 0.8

S∞ = [tex]\frac{20}{1-0.8}[/tex] = [tex]\frac{20}{0.2}[/tex] = 100

(b)

the sum to n terms of an arithmetic progression is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 20 , d = a₂ - a₁ = 16 - 20 = - 4 and [tex]S_{n}[/tex] = - 160

substitute values into formula and solve for n

[tex]\frac{n}{2}[/tex] [ (2 × 20) - 4(n - 1) ] = - 160 ( multiply both sides by 2 to clear the fraction )

n(40 - 4n + 4) = - 320

n(- 4n + 44) = - 320

- 4n² + 44n = - 320 ( add 320 to both sides )

- 4n² + 44n + 320 = 0 ( divide through by - 4 )

n² - 11n - 80 = 0 ← in standard form

(n - 16)(n + 5) = 0 ← in factored form

equate each factor to zero and solve for n

n - 16 = 0 ⇒ n = 16

n + 5 = 0 ⇒ n = - 5

now n > 0 , then n = 16

there are 16 terms in the arithmetic progression

Answer:1 l = 2.2 lb wt.

Step-by-step explanation: