Find the indefinite integral. (Use C for the constant of
integration.) 8sin xcos x dxFind the indefinite integral. (Use C
for the constant of integratioFind the indefinite integral. (Use C
for the con

The equation will be changed into = f(x)= 32

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Hence, The equation will be changed into = f(x)= 32

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Answer:

2674

Step-by-step explanation:

add all of them together like this

2000

600

70

4

-------

2674

Answer: 2,674

Step-by-step explanation: Add all of the numbers. An easier way to do it is just to take the first number of each addend and piece them all together.

Extra Example: 400 + 20 + 7

400: Take the 4.

4

20: take the 2.

42

7: Take the 7.

427

Therefore, 400 + 20 + 7 in standard form is 427

Answer:

48

Step-by-step explanation:

Its the most logical one of them all

The final answers are given below

\(10.\)L

\(11.\) \(3\) (the number should be \(1,000,000\), which has six zeros)

\(00000\)

\(12\)  | |

\(00000\)

|

\(00000\)

\(15. 31 16 48 29 53 47 22 37 98 26 2025\)

A number is an arithmetic value that is used to calculate and represent a quantity.

The numbers that are more than \(20\) but less than \(30\) are \(22\) and \(26\), so they should be crossed out:

\(31 16 48 29 53 47\) X \(37 98\) X \(2025\)

Therefore the answers are given below.

\(10.\)L

\(11.\) \(3\) (the number should be \(1,000,000\), which has six zeros)

\(00000\)

\(12\)  | |

\(00000\)

|

\(00000\)

\(15. 31 16 48 29 53 47 22 37 98 26 2025\)

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Answer:

x=4

Step-by-step explanation:

x²-16=0

x²=0+16

x²=16

x=√16

x=4

The phone is worth $128 after 2 years, which is option C.

What is exponential decay ?

Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.

Calculating the worth of the phone :

The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.

Let's use the formula for exponential decay: \(A = A_0(1 - r)^t\), where A is the final amount, \(A_0\) is the initial amount, r is the decay rate, and t is the time elapsed.

In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:

\(A = 800(1 - 3/5)^2\)

\(A = 800(2/5)^2\)

\(A = 800(4/25)\)

\(A = 128\)

Therefore, the phone is worth $128 after 2 years, which is option C.

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The rate at which the angle between the ladder and the wall changes is 30√75 ft/sec and the rate at which the base of the ladder slides away from the wall at this instant is 13.2 ft/sec.

When a 10-foot ladder slides down a wall at a rate of 3 ft/sec, the rate at which the (acute) angle between the ladder and the wall changes when the foot of the ladder is 5 feet from the wall and the rate at which the base of the ladder slides away from the wall are required to be calculated.

Let's mark the length of the ladder as ‘l’ and the distance of the ladder from the wall as ‘x’.If the ladder has slid x feet down the wall at time t, the triangle formed by the ladder, the wall, and the ground is such that l² = x² + y². The angle is θ, then sin θ = y/l, cos θ = x/l, and tan θ = y/x.

Thus, we have the following equation:(l)² = (x)² + (y)²Differentiate with respect to t.2(l)(dl/dt) = 2(x)(dx/dt) + 2(y)(dy/dt)

Solve for dy/dt when x = 5ft and dx/dt = 3 ft/sec.dy/dt = (l/x)(dx/dt)√[l² - x²]dy/dt = (10/5)(3)√[10² - 5²]dy/dt = 30√75 ft/sec

Now, let's differentiate the equation l² = x² + y² with respect to time:2l(dl/dt) = 2x(dx/dt) + 2y(dy/dt)

We have already calculated the value of dy/dt from the previous step. Substituting, l = 10, x = 5 and dx/dt = 3, we get: 20(dl/dt) = 10(3) + 2(5)(30√75)dl/dt = 13.2 ft/sec

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Answer:

the first one is. hope helps

Answer: 12

Step-by-step explanation:

12 can go into 12 and 36, and 6 but its the least common factor.

Answer:

A. 2x(x+1)(x-6);x=0,-1,6

Step-by-step explanation:

Take out 2x and factorise:

2x(x² - 5x - 6)

We can factorise (x² - 5x - 6)

What two numbers multiply to make -6 and add to give -5? That is -6 and 1 which is written as:

(x - 6)(x + 1)

Now the fully factorised polynomial is:

2x(x - 6)(x + 1)

Equate each of them to 0

2x = 0, x - 6 = 0, x + 1 = 0

Solve for x

x = 0, x = 6, x = -1

Answer:

7

Step-by-step explanation:

Answer:

no answer

Step-by-step explanation:

2(-2)+3=-2

simplify

-4+3=-2

simplify

-1=-2

No answer

If there's something along the lines of no answer and it's multiple choice click that.

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Answer:

n2=v2n1/v1

Or B

Step-by-step explanation:

P, R, and T are constant, then the volume is directly proportional to the mole. Then the correct option is A.

An ideal gas is a theoretical composed of a set of randomly moving gas particles that interacts only through elastic collision.

Given

A balloon containing 0.040 mol of a gas with a volume of 5.0 mL was expanded to 1.0 L.

\( \rm V_1 = 5 \ mL\\ V_2 = 1000 \ mL\\ n_1 = 0.040 \ mol \)

We know the equation of the ideal gas.

\( \rm PV = nRT \)

where P, R, and T are the constant, then

\( P \propto n\)

Then we have

\( \rm \dfrac{V_2}{V_1} = \dfrac{n_2}{n_1} \\\\ V_2 = n_2 *\dfrac{V_1}{n_1} \)

Thus, the correct option is A.

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15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

What is the question, is their answer options or...?

Answer:

See attached

Step-by-step explanation:

The linear equation that gives the height on the x-th month is:

y = 2.5*x + 74.5

This will be modeled with a linear equation of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that for a line with the points (x₁, y₁) and (x₂, y₂), the slope is given by:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

Here we have the two points (3, 82) and (7, 92). Where the first value is the number of months and the second value is the height.

So the slope is:

\(a = \frac{92 - 82}{7 - 3} = 10/4 = 2.5\)

Then the linear equation is:

y = 2.5*x + b

To get the value of b, we use the fact that when x = 3, we have y = 82,

82 = 2.5*3 + b

82 = 7.5 + b

82 - 7.5 = b = 74.5

Then the linear equation is:

y = 2.5*x + 74.5

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a) (f∘g)(4) = 3.

b) (g∘f)(25) = 18.

c) (g∘f)(x) = g(f(x)) = (f(x))^2 + 2.

d) f(x) = x^5 and g(x) = 4x + 7.

To determine the values for each of the given expressions, let's go through them one by one:

a. To find (f∘g)(4), we need to substitute the value 4 into g(x) first, and then use the result as the input for f(x).

First, let's find g(4):
g(4) = 4^2 + 2 = 16 + 2 = 18

Now, substitute g(4) into f(x):
f(g(4)) = f(18) = sqrt(18 - 9) = sqrt(9) = 3

Therefore, (f∘g)(4) = 3.

b. To find (g∘f)(25), we need to substitute the value 25 into f(x) first, and then use the result as the input for g(x).

First, let's find f(25):
f(25) = sqrt(25 - 9) = sqrt(16) = 4

Now, substitute f(25) into g(x):
g(f(25)) = g(4) = 4^2 + 2 = 16 + 2 = 18

Therefore, (g∘f)(25) = 18.

c. To find (g∘f)(x), we need to substitute f(x) into g(x).

(g∘f)(x) = g(f(x)) = (f(x))^2 + 2

d. The domain of (g∘f)(x) would be the same as the domain of f(x). Since f(x) = sqrt(x-9), the domain would be x ≥ 9, as the expression inside the square root must be non-negative.

For question 2, we are given h(x) = (4x+7)^5 and we need to determine two functions f(x) and g(x) such that h(x) = f(g(x)).

One possible solution would be:

Let f(x) = x^5 and g(x) = 4x + 7.

Then, h(x) = f(g(x)) = (g(x))^5 = (4x+7)^5.

In this case, f(x) = x^5 and g(x) = 4x + 7 would satisfy the given condition.

Keep in mind that there may be multiple correct answers for the second part, as long as f(x) and g(x) can be composed to produce h(x).

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Answer:

Whole numbers

Step-by-step explanation:

Integers and whole numbers are similar, but integers contain negatives and whole numbers do not. Since a city cannot have a negative population count, we'd prefer whole numbers.

Rational numbers allow for non-whole numbers, but again, a city can't havea population of something and a half person. We again prefer whole numbers.

Answer:

Whole Numbers

Step-by-step explanation:

So cities Have complete number the represent it so integers are negative numbers and fractions and rational numbers are fractions so whole number is the only number that are complete and is not a fraction so therefore the only answer it could be is whole numbers

Answer:

D and E

Step-by-step explanation:

remote interior angles are not adjacent to a given angle. or basically 1 is our exterior angle, so the opposites of 1 and the remote interior angle.

The remote interior angles of Z1 are ∠4 and ∠3. The correct options are D and E.

A triangle's remote interior angles are the two angles that are not adjacent to a given exterior angle. An exterior angle of a triangle is formed by extending one of the triangle's sides.

The following theorem can be used to calculate the remote interior angles of a triangle:

A triangle's remote interior angles are equal in size to the exterior angle that is not adjacent to them.

In other words, if we know the measure of one of a triangle's exterior angles, we can find the measure of the distant interior angles by subtracting that measure from 180 degrees.

Thus, the correct options are D and E.

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Answer:

a = 47

b = 23.87

c = 90

d = 35.59

Step-by-step explanation:

I can only help this much. Not sure what the other two others below are asking

The simplified form of 1 and 3 over 4 times, 2 and 2 over 3 is 4/3.

Given,

1 and 3 over 4 times

2 and 2 over 3 times

We can convert this to mathematical form:

That is,

1 and 3 over 4 times = (1 + 3) / 4

2 and 2 over 3 times = (2 + 2) / 3

Now, equate the above terms:

We get,

(1 + 3) / 4 x (2 + 2) / 3

= (4 / 4) x (4 / 3)

= 1 x (4 / 3)

= 4 / 3

That is, the simplified form of 1 and 3 over 4 times and 2 and 2 over 3 times is 4/3.

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The price of one ticket without discount is 90 dollars.

5 friends use an online coupon to get $9 off of each ticket to go to a concert.

They spent a total of $405 for the tickets.

Therefore,

let

the price of the one ticket without discount = x

Hence,

Each price with discount = x - 9

Therefore,

5(x - 9) = 405

5x - 45 = 405

5x = 405 + 45

5x = 450

divide both sides by 5

x = 450 / 5

x = 90 dollars

Therefore, the price of one ticket without discount is 90 dollars.

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Step-by-step explanation:

3/5 - 1/3 = 4 /15

5/6 - 2/3 = 5/6 - 4/6 = 1/6

7/9 - 2/3 = 7/9 - 6/9 = 1/9

5/8 - 1/6 = (15 - 4) /24 = 11/24

(All the above ones I have taken common factor and subtracted them)

5 x 9/10 = 45/10 = 9/2 (simplified)

2/7 x 3 = 6/7

3 x 2/15 = 6/15

4x 2/6 = 8/6 = 4/3 (simplified form)

Hope this helps!!!

The standard normal distribution can roughly statistic estimate the t-value for small sample sizes, though it grows less sensitive to changes in sample size for large sample sizes.

The test statistic for something akin to a Z-test has been the Z-statistic, which shows the usual normal null hypothesis to be correct. Suppose you perform a 2 X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also defined as a Z-value). 0.0124 is the p-value for the this Z-value.

Here,

When the population size is small (typically less than 30) or when it is unclear what the population standard deviation will be, the t-value is a statistical measure that is used to determine the statistical significance of a difference of the two means.

This is so that there will be less sampling error and more accurate information the about population provided by the bigger sample size. As the sample size grows, the t-distribution gets more constrained and resembles the average more closely.

In conclusion, the t-value tends to rise as sample size rises, indicating the increased accuracy of the sample mean.

The standard normal distribution can roughly estimate the t-value for small sample sizes, though it grows less sensitive to changes in sample size for large sample sizes.

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Answer:

241

Step-by-step explanation:

Given the equation to evaluate :

2^8 −10−15÷3

2^8 = 256

256 - 10 - 15 ÷ 3

From BODMAS principle, we evaluate the divison before subtraction :

-15 ÷ 3 = - 5

256 - 10 -5

256 - 15

= 241

A system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0) can be found as follows:

Suppose that the line through the points (1, 1, 1) and (3, 5, 0) can be represented by the vector equation (x, y, z) = (1, 1, 1) + t(2, 4, -1), where t is a scalar parameter. Then we have x = 1 + 2t, y = 1 + 4t, z = 1 - t. This vector equation can be rewritten as a system of linear equations by equating each component of the vectors.

We have:

x = 1 + 2t, y = 1 + 4t, z = 1 - t

So, the system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0) is:

x - 2t = 1, y - 4t = 1, z + t = 1.

To find a system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0), we can use the parametric equation of a line in three dimensions. Suppose that the line through the points (1, 1, 1) and (3, 5, 0) can be represented by the vector equation (x, y, z) = (1, 1, 1) + t(2, 4, -1), where t is a scalar parameter.

This vector equation means that the coordinates of any point on the line can be obtained by adding a scalar multiple of the direction vector (2, 4, -1) to the point (1, 1, 1).

In other words, if we let t vary over all real numbers, we obtain all the points on the line. Then we can rewrite the vector equation as a system of linear equations by equating each component of the vectors. We have:

x = 1 + 2t,y = 1 + 4t, z = 1 - t .

This system of equations represents the line passing through (1, 1, 1) and (3, 5, 0) in three dimensions. The first equation tells us that the x-coordinate of any point on the line is 1 plus twice the t-coordinate. The second equation tells us that the y-coordinate of any point on the line is 1 plus four times the t-coordinate.

The third equation tells us that the z-coordinate of any point on the line is 1 minus the t-coordinate. Therefore, any solution of this system of equations gives us a point on the line through (1, 1, 1) and (3, 5, 0). Therefore, the system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0) is:

x =1+ 2t, y - 4t = 1, z + t = 1

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Answer: 5.450 x 10^-4 x 3.550 x 10^-7

19.3475 x 10^-11

1.935 x 10^10

Answer:

1.93475 x 10^-10

Step-by-step explanation:

5.450X10^-4 * 3.550X10-7

= 1.93475 x 10^-10

Answer:

C is the answer your looking for