Find the exact coordinates of the centroid for the region bounded by the curves y = x, y = 1/x, y = 0, and x = 2. = = 13 II c II Y

The intital amount deposited was  $18485.82.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + \dfrac{r}{n})^{nt}\)

An account has $26,000 after 15 years. The account received 2.3 percent interest compounded continuously.

A = 26000

R = 0.02.3

\(a = p(1 + \dfrac{r}{n})^{nt}\)

\(26000 = p(1 + \dfrac{2.3}{100})^{15}\\\\26000 = p \times 1.4064\\\\\P= 18485.82\)

Therefore, the intital amount deposited was  $18485.82.

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The largest 3 digit number that is divisible by 9 and 7 is 945.

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.

If a number is divisible by 7 and 9 it shows that 7 and 9 are factors of the number. Since the number is a three digit number, the product of 7and 9 which is 63 will also be a factor.

the highest three digit multiple of 63 is 945.

This means that 945 can be divided by 7 and 9. i.e 945/7 = 135 and 945/9 = 105

Therefore the largest three digit number that can be divisible by both 9 and 7 is 945

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Answer:

true

Step-by-step explanation:

add

Answer:

Two systems that work very closely together are our cardiovascular and respiratory systems. The cardiovascular system includes your heart and blood vessels, which function to remove deoxygenated blood from and return oxygenated blood throughout your body. ... The heart then sends the oxygenated blood out to the body.

Step-by-step explanation:

Answer:

Two systems that work very closely together are our cardiovascular and respiratory systems. The cardiovascular system includes your heart and blood vessels, which function to remove deoxygenated blood from and return oxygenated blood throughout your body. ... The heart then sends the oxygenated blood out to the body.

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

We can unsquare the squareroots:

x^2=36

Becomes

x=6 (because 6*6 is 36)

similarly,

y^2=81

Becomes:

y=9(because 9*9=81)

When you have a squareroot no matter if it’s negative or positive the result is a positive number.

Now we can solve and eliminate possible solutions.
For A) -9+(-6)=(-15)

For B) (-9)+6=(-3)

For D)(-6)+9=3

For E) 9+6=15

The only one that cannot be made is C)0

In the "Let's Roll" game, the probability of winning a prize by rolling a number less than 6 is 1/3, or approximately 33.33%.

The "Let's Roll" game. In this game, a number cube with numbers 2, 4, 6, 8, 10, and 12 is used, and there are prizes for rolling any number less than 6.

To determine the probability of winning a prize, we need to find the probability of rolling a number less than 6. There are two numbers on the cube that meet this criterion: 2 and 4. Since there are six numbers in total on the cube, the probability of rolling a number less than 6 is 2/6, which simplifies to 1/3.

So, in the "Let's Roll" game, the probability of winning a prize by rolling a number less than 6 is 1/3, or approximately 33.33%.

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9514 1404 393

Answer:

  A.  the y-intercept is positive

  D.  the y-intercept is negative

Step-by-step explanation:

A proportional relationship is characterized by the equation ...

  y = kx

The y-intercept of this equation is zero--the line intersects the origin.

If the y-intercept is not zero (is positive or negative), then the relation is nonproportional.

Step-by-step explanation:

8c-(3×3)=5

8c-9+9=5+9

8c=14

c=7/4

Equation of the statement eight less than the product of 3 and a number is equal to 5 is 3c - 8 = 5

Equation : When the value of two mathematical expressions are same is called as equation.

Given, that eight less than the product of 3 and a number is equal to 5.

So, converting the statement into equation form.

Statement : Eight less than the product of 3 and a number is equal to 5.

By using c as a variable,

Firstly,

Product of 3 and c = 3c

Next,

Eight less than the product = 3c - 8

Finally,

3c - 8 = 5

The required equation is  3c - 8 = 5 .

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The solution to the integral \(\(\int \frac{x^3}{x^4-6}dx\)\) using the substitution \(\(u=x^4-6\)\) is \(\(\frac{1}{4}\ln|x^4-6| + C\)\), where \(\(C\)\) represents the constant of integration.

To evaluate the integral \(\(\int \frac{x^3}{x^4-6}dx\)\) by making the substitution \(\(u=x^4-6\)\), we can follow these steps:

1. Differentiate the substitution variable \(u\) with respect to \(x\) to find \(du\):

 \(\(\frac{du}{dx} = \frac{d}{dx}(x^4-6)\) \\ \(\frac{du}{dx} = 4x^3\)\)

  Rearranging, we have \(\(dx = \frac{du}{4x^3}\)\).

2. Substitute the expression for \(\(dx\)\) and the new variable \(\(u\)\) into the original integral:

 \(\(\int \frac{x^3}{x^4-6}dx = \int \frac{x^3}{u}\cdot\frac{du}{4x^3}\)\)

  Simplifying, we get \(\(\int \frac{1}{4u} du\)\).

3. Integrate the new expression with respect to \(\(u\)\):

\(\(\int \frac{1}{4u} du = \frac{1}{4}\int \frac{1}{u} du\)\)

  Taking the antiderivative, we have \(\(\frac{1}{4}\ln|u| + C\)\).

4. Substitute the original variable \(\(x\)\) back in terms of \(\(u\)\):

  \(\(\frac{1}{4}\ln|u| + C = \frac{1}{4}\ln|x^4-6| + C\).\)

Therefore, the solution to the integral \(\(\int \frac{x^3}{x^4-6}dx\)\) using the substitution \(\(u=x^4-6\)\) is \(\(\frac{1}{4}\ln|x^4-6| + C\)\), where \(\(C\)\) represents the constant of integration.

The complete question must be:

Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.)

\(\int \:\frac{x^3}{x^4-6}dx,\:u=x^4-6\)

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The product of 2 and 1/10 times -7 times 5/12 is -7/12, which is a fraction.

The product of 2 and 1/10 times -7 times 5/12 can be found stepwise by multiplying the numbers together.
1. Convert the mixed fraction 1/10 to an improper fraction: 1/10 = 1 ÷ 10 = 1/10.
2. Multiply the numbers together: 2 × 1/10 × -7 × 5/12 = -70/120.
3. Simplify the fraction: -70/120 = -7/12.
Therefore, the product of 2 and 1/10 times -7 times 5/12 is -7/12.

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Answer:

i didnt have this yet

Step-by-step explanation:

Answer:

y = 3/2x + 2

Step-by-step explanation:

let eqn be y = mx + c

m = (5-2)/(2-0) = 3/2

sub (0, 2):

2 = 3/2 (0) + c

c = 2

therefore, the equation is y = 3/2x + 2

Answer: i agree with the other guy ↑

Since Tony is self-employed, he will have to pay all of the tax himself.

Take his adjusted earnings times the tax rate

58238.74 * 2.9%

58238.74 * .029

1688.92346

Rounding to the nearest cent

1688.92

sin(2t) + cos(t) simplifies to cos(t)(2sin(t) + 1). This form provides a consolidated expression that combines both trigonometric functions into a single term.

To solve the expression sin(2t) + cos(t) using the double angle formula for sine, we can rewrite sin(2t) as 2sin(t)cos(t).

Here is the step-by-step solution:

Replace sin(2t) in the expression with 2sin(t)cos(t):

2sin(t)cos(t) + cos(t)

Now, we have a common factor of cos(t). Factor out cos(t) from both terms:

cos(t)(2sin(t) + 1)

Therefore, sin(2t) + cos(t) can be simplified to cos(t)(2sin(t) + 1).

To solve the expression sin(2t) + cos(t) using the double angle formula for sine, we need to use the trigonometric identity sin(2t) = 2sin(t)cos(t). This identity relates the sine of twice an angle to the sine and cosine of that angle.

By applying the double angle formula, we can rewrite sin(2t) as 2sin(t)cos(t). Substituting this expression back into the original equation, we have 2sin(t)cos(t) + cos(t).

Next, we can factor out the common factor of cos(t) from both terms:

cos(t)(2sin(t) + 1).

Therefore, sin(2t) + cos(t) simplifies to cos(t)(2sin(t) + 1). This form provides a consolidated expression that combines both trigonometric functions into a single term.

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Burt saves $1,500 from each pay check.

What is the percentage?

A percentage is a way of expressing a number or quantity as a fraction of 100. It is commonly used to express the proportion of one quantity relative to another or the amount of change between two quantities.

For example, if you received a score of 80 out of 100 on a test, you can express that score as a percentage by dividing 80 by 100 and multiplying by 100. The result is 80%, which means you scored 80% of the total possible points.

Percentages are often used in finance, such as when calculating interest rates, taxes, and discounts. They are also used in statistics to express the probability or likelihood of an event occurring.

Understanding percentages are important in everyday life, as they are commonly used to compare and evaluate different quantities and values.

Burt earns a semi-monthly income of $3,250, which means he earns $6,500 per month.

He spends 24% of his income on his mortgage, which is:

0.24 x $6,500 = $1,560

He spends 6.5% of his income on utilities, which is:

0.065 x $6,500 = $422.50

He spends 15% of his income on food, which is:

0.15 x $6,500 = $975

He spends 8% of his income on miscellaneous items, which is:

0.08 x $6,500 = $520

Therefore, his total expenses are:

$1,560 + $422.50 + $975 + $520 = $3,477.50

To find out how much he saves from each paycheck, we need to subtract his total expenses from his monthly income:

$6,500 - $3,477.50 = $3,022.50

Since he gets paid semi-monthly, he saves half of this amount from each paycheck:

$3,022.50 / 2 = $1,511.25

Rounding this amount to the nearest $100, we get:

$1,500

Therefore, Burt saves $1,500 from each paycheck.

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To determine whether the series ∑(n=1 to infinity) 7n/n is convergent or divergent, we can apply the ratio test. The ratio test helps us determine the convergence or divergence of a series by examining the limit of the ratio of consecutive terms.

In this case, let's calculate the ratio of consecutive terms using the formula for the ratio test:

lim(n→∞) |(7(n+1)/(n+1))/((7n/n)|

Simplifying the expression, we get:

lim(n→∞) |7(n+1)/n|

As n approaches infinity, the limit evaluates to:

lim(n→∞) |7(n+1)/n| = 7

Since the limit is a finite positive value (7), which is less than 1, the ratio test tells us that the series is convergent.

However, you mentioned identifying an (term) in the series, and it seems there may be an incomplete part of the question. Please provide additional information or clarification about identifying an term in the series so that I can provide a more specific answer.

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Answer:

5

Step-by-step explanation:

if two equals 10 then 5 makes 25

Answer:

(1) 6x + 3 = 15

(2) x = 2

Step-by-step explanation:

The expressions which represents the slope of a tangent to the curve \(y=\frac{1}{x+1}\) at any point (x, y) are:

                                ​\(f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}\)

Mathematically, the slope of a tangent line to the curve is given by this equation:

\(f'(x) =limh \rightarrow 0\frac{f(x+h)-f(x)}{h}\)

Given the function:

\(f(x)=y=\frac{1}{x+1}\)

When (x + h), we have:

\(f(x+h)=y=\frac{1}{x+h+1}\)

Next, we would find the derivative of f(x):

\(f'(x) =limh \rightarrow 0\frac{\frac{1}{x+h+1} -\frac{1}{x+1}}{h}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -(x+h+1)}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -x-h-1}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}\\\\f'(x) = \frac{-1}{(x+1)(x+1)} \\\\f'(x) = \frac{-1}{(x+1)^2}\)

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Answer: 8 posters

Step-by-step explanation:

From the question, we are informed that Lincoln has 16 pins in one box and 17 pins in another box and that he uses 4 pins to hang each posters posted. The total number of posters he can hang with the pins goes thus:

We should first calculate the total number of pins he has.

= 16 + 17 = 33 pins

Since he uses 4 pins to hang a poster, we then divide 33 pins by 4.

= 33 ÷ 4

= 8.25

This means that he can hang 8 posters with the pin

Answer:

238

Step-by-step explanation:

First, you must find the ratio between the one measurement of the larger octagon and the smaller octagon. Just divide 28 by 4 to get 7. This is what you have to multiply the perimeter by to get the larger octagon's perimeter.  34 times 7 equals 238. There are multiple ways to do this problem but this way is the simplest. If this helped you, please click the "Thanks" button!

Step-by-step explanation: I think it is 18 tell me if I am wrong

Answer:

-30b

Step-by-step explanation:

By using the distributive property,

→ -3b(6 + 4)

→ -3b × 10

→ -30b

Hence, the solution is -30b.

The method of sampling that is based on dividing a population into subgroups, sampling a set of subgroups, and conducting a complete census within the subgroups sampled is known as cluster sampling.

This method of sampling is often used when the population is too large to be sampled as a whole or when it is difficult to obtain a comprehensive list of the population.

In cluster sampling, the population is divided into smaller subgroups, or clusters, that are more manageable in size. These clusters are then randomly selected, and a complete census is conducted within each of the selected clusters. This means that every individual within the selected clusters is included in the sample.

Cluster sampling can be more efficient and cost-effective than other sampling methods because it reduces the amount of resources required to sample large populations. It is important to note, however, that cluster sampling can lead to increased sampling error if the selected clusters are not representative of the population as a whole.

In summary, cluster sampling is a method of sampling that involves dividing a population into subgroups, sampling a set of subgroups, and conducting a complete census within the selected subgroups. This method can be an effective way to sample large populations, but it is important to ensure that the selected clusters are representative of the population to minimize sampling error.

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The space would cost at, $833.34 per month.

:: Total area = 1000 square feet

:: Cost per feet per year = $10

Therefore,

Total cost per year would be, equal to the product of total area and cost per unit area per year.

That is,

Total cost per year = 1000 x $10

That is, $10,000.

Now, we know, there are 12 months in an year.

So, cost per month is, ( total cost per year / 12 )

That is, therefore,

Cost per month = ($10,000 / 12)

Which equals to, $833.34 per month. (rounded off)

So,

The space cost at, $833.34 per month.

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The space cost you $833.33. per MONTH

To calculate the monthly cost, we first need to determine the annual cost of the space.

Given that the cost is $10 per square foot per year, we know, there are 12 months in an year and the space is 1,000 square feet, the annual cost of the space would be:

Annual cost = the space  * cost

Annual cost = 1,000 square feet * $10/square foot = $10,000

To convert this to monthly cost, we divide the annual cost by 12 (the number of months in a year):

Monthly cost = $10,000 / 12 = $833.33

Therefore, the monthly cost of the 1,000 square feet of space in the new building would be $833.33.

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Total time used= 15+45+30=90 mins

Initial time=7:45

final time will be 1 hr 30 mins more than initial Time

final time= 9:15 am

Answer:

The correct option is;

The graph is a line that rises steeply from left to right and passes through the origin

Step-by-step explanation:

The given equation is y = 110·x

Comparing the given equation to the general equation of a straight line, y = m·x + c

Where;

m = The slope of the straight line graph

c = The y-intercept

We have;

The slope of the given equation, y = 110·x = 110

The y-intercept, which is given by the constant c in the given equation = (0, 0)

Therefore, by the slope of the equation, for each unit increase in x, y increases by 110, therefore, the graph is a straight line that rises steeply and passes through the origin

The true option is (2) The graph is a line that rises gradually from left to right and passes through the origin.

The linear function is given as:

y = 110x

A linear function that passes through the origin has the form y = mx.

This means that:

m = 110

When m > 0, then the line of the graph rises from left to right.

Hence, the true option is (2)

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Answer:

y = x - 5

Step-by-step explanation:

Using the 'y=mx+c' form,

Since m = 1,

y = x + c

Substituting (1, -4) into the above equation:

-4 = 1 + c

c = -5

Hence,

y = x - 5

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The component form of the vector that translates A to A' is (11, -17)

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

In translation, the shape of the figure does not change but its size may change.

Other transformation processes are reflection and rotation.

The component form of the vector is governed by the rule; A' - A

so we subtract corresponding x- coordinates and corresponding y- coordinates

A' - A = (7, -9) - (-4, 8)

       = ( 7 - - 4, -9 - 8)

       -= ( 11, -17)

In conclusion, the vector that translates A to A' is ( 11, -17 )

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