d) What would be the total cost of purchasing the number of shirts needed to use your coupon—after your coupon is applied and a 7.5% sales tax is charged on the purchase?

Answers

Answer 1

Answer: Multiply 7.5% by the price after subtracting the coupon's value.

Step-by-step explanation:

Let's assume that the cost of the shirts is x. So the coupon would subtract y from x so that's x-y which gives us z. Then to find z, on a calculator just put in 7.5% x z. I used variables since I don't know the value of the coupon or the original price of the shirts.


Related Questions

Calculate and write a sentence interpreting each of the following descriptions of change over the specified interval. (Round your answers to three decimal places.) Before the merger of two other major airlines, a certain airline was the second-largest airline in the world. This airline flew 98.175 million enplaned passengers during 2007 and 92.772 million enplaned passengers during 2008. (a) Calculate the change. million enplaned passengers Explain the change. The number of paying passengers on the given airline decreased by million between 2007 and 2008. (b) Calculate the percentage change. % Explain the percentage change. The number of paying passengers on the given airline decreased by % between 2007 and 2008. (c) Calculate the average rate of change. million enplaned passengers per year Explain the average rate of change. The number of paying passengers on the given airline decreased by an average of million per year between 2007 and 2008.

Answers

(a) The change is -5.403 million enplaned passengers.

The number of enplaned passengers on the given airline decreased from 98.175 million in 2007 to 92.772 million in 2008, resulting in a decrease of 5.403 million enplaned passengers.

(b) The percentage change is -5.51%.

The percentage change is calculated using the formula: ((new value - old value) / old value) x 100%. In this case, the percentage change is ((92.772 - 98.175) / 98.175) x 100% = -5.51%. This indicates a 5.51% decrease in the number of paying passengers on the given airline between 2007 and 2008.

(c) The average rate of change is -2.702 million enplaned passengers per year.

The average rate of change is calculated by dividing the total change in the number of enplaned passengers by the number of years between 2007 and 2008. In this case, the average rate of change is (-5.403 / 2) = -2.702 million enplaned passengers per year.

This means that the number of paying passengers on the given airline decreased by an average of 2.702 million per year between 2007 and 2008.

For more questions like Average rate click the link below:

https://brainly.com/question/23715190

#SPJ11

kenzie bought a eight pack of apple juice boxes for $4.88. how much did one apple juice box cost?????????????

Answers

Answer:

$0.16

Step-by-step explanation:

$4.88 is how much 8 apple juice boxes cost

to find out how many 1 costs we divide by 8

$4.88÷8=$0.61

so 1 apple juice box costs $0.61

Direction: Draw a box() if it is an expression and a triangle (A) if it is an equation.
1. 2x + 9 =
2. 32 + 3 x 9) = 59
3. 3k + 7 = 34
4. 5 (b + 28) = 150
5. 9a + 7 =​

Answers

Among the given expressions and equations, two are equations represented by triangles (A), while the remaining three are expressions represented by boxes().

The first equation, "2x + 9 = 2," is represented by a triangle (A) because it contains an equal sign, indicating that both sides are equal. The second expression, "32 + 3 x 9) = 59," is represented by a box () as it does not have an equal sign, making it an arithmetic expression rather than an equation.

The third equation, "3k + 7 = 34," is an equation and represented by a triangle (A) because it has an equal sign, signifying an equality between two expressions. The fourth expression, "5 (b + 28) = 150," is an expression and represented by a box () because it lacks an equal sign. It involves arithmetic operations but does not establish an equality.  

Finally, the fifth equation, "9a + 7 =," is an equation and represented by a triangle (A). Although it appears incomplete, it still contains an equal sign, indicating that the expression on the left side is equal to an unknown value on the right side.  

In summary, two equations are represented by triangles (A) because they contain equal signs and establish equalities between expressions, while the remaining three are expressions represented by boxes () as they lack equal signs and do not create equalities.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ11

If f(x) is a polynomial, then is f(x^2) a polynomial?

Answers

If `f(x)` is a polynomial, then `f(x²)` is also a polynomial. Polynomials are mathematical expressions that consist of variables and coefficients with only the operations of addition, subtraction, multiplication, and non-negative integer exponents. We can prove this statement using the definition of a polynomial. Definition of a polynomial polynomial is an expression that can be written as follows:$$f(x)= a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdot\cdot\cdot +a_1x+a_0$$where `a0, a1, …, an` are constants, and `n` is a non-negative integer. This definition of the polynomial can be used to show that `f(x²)` is also a polynomial. Using the definition of a polynomial, we can write:$$f(x²)= a_n(x²)^n+a_{n-1}(x²)^{n-1}+a_{n-2}(x²)^{n-2}+\cdot\cdot\cdot +a_1(x²)+a_0$$Simplifying the terms of the expression, we get:$$f(x²)= a_nx^{2n}+a_{n-1}x^{2(n-1)}+a_{n-2}x^{2(n-2)}+\cdot\cdot\cdot +a_1x^2+a_0$$This proves that `f(x²)` is also a polynomial. Therefore, if `f(x)` is a polynomial, then `f(x²)` is also a polynomial.

Yes, if f(x) is a polynomial, then f(x²) is also a polynomial.

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents. It can include addition, subtraction, and multiplication operations. The terms in a polynomial can be in the form of axⁿ, where a is the coefficient, x is the variable, and n is a non-negative integer exponent.

When we substitute x² into f(x), each occurrence of x in the polynomial f(x) is replaced by x². Since x² is still a variable with a non-negative integer exponent, the resulting expression f(x²) remains a polynomial. The coefficients and exponents may change, but the essential structure of a polynomial is preserved.

Therefore, if f(x) is a polynomial, then f(x²) is also a polynomial.

Learn more about polynomial here

https://brainly.com/question/11536910

#SPJ4

Express the mass of these planets and moons in both standard and scientific notation. If necessary, round the numbers so that the first factor goes only to the hundredths place

Answers

Here are the masses of some planets and moons expressed in both standard and scientific notation:

Planet Mass in Standard NotationMass in Scientific Notation:

Venus = 4,870,000,000,000,000,000,000,000 kg4.87 × 10²⁴ kg

Earth = 5,970,000,000,000,000,000,000,000 kg5.97 × 10²⁴ kg

Mars = 6,420,000,000,000,000,000,000,000 kg6.42 × 10²⁴ kg

Jupiter = 1,898,000,000,000,000,000,000,000,000 kg1.90 × 10²⁷ kg

Saturn = 568,000,000,000,000,000,000,000,000 kg5.68 × 10²⁶ kg

Uranus = 86,800,000,000,000,000,000,000 kg8.68 × 10²⁵ kg

Neptune = 102,000,000,000,000,000,000,000 kg1.02 × 10²⁶ kg

Moon = 7,340,000,000,000,000,000 kg7.34 × 10²² kg

Io = 8,930,000,000,000,000,000 kg8.93 × 10²² kg

Ganymede = 1,480,000,000,000,000,000,000 kg1.48 × 10²³ kg

To learn about the masses here:

https://brainly.com/question/86444

#SPJ11

I need help with the answer to this question

Answers

Ryan needs to contribute $1000.07 per month.

How much does Ryan need to contribute monthly?

To determine the monthly contribution needed, we will use the formula for monthly payment [tex]FV = P * [(1 + r)^n - 1] / r,[/tex]

Plugging values:

[tex]208,000 = P * [(1 + 0.078/12)^{11*12} - 1] / (0.078/12).\\208,000 = P * [1.0065^{132} - 1] / 0.0065.[/tex]

Rearranging to solve for P

[tex]P = 208,000 * 0.0065 / [1.0065^{132} - 1].[/tex]

P = 208,000 * 0.0065 / 1.35190003004

P = 1000.07394775

P = $1000.07

Read more about monthly payment

brainly.com/question/28106777

#SPJ1

find the general antiderivative of n(x)=x8 5x4x5.

Answers

The general antiderivative of n(x) = x⁸ + 5x⁴ + x⁵ is N(x) = (1/9)x⁹ + (1/5)x⁵ + (1/6)x⁶ + C.

To find the antiderivative of n(x) = x⁸ + 5x⁴ + x⁵, we apply the power rule for integration, which states that ∫x^n dx = (xⁿ⁺¹)/(n+1) + C, where C is the constant of integration.

1. For the first term, x⁸, integrate using the power rule: ∫x⁸ dx = (1/9)x⁹ + C₁.
2. For the second term, 5x⁴, integrate: ∫5x⁴ dx = 5(1/5)x⁵ + C₂ = x⁵ + C₂.
3. For the third term, x⁵, integrate: ∫x⁵ dx = (1/6)x⁶ + C₃.

Now, add the results of each integration and combine the constants: N(x) = (1/9)x⁹ + x⁵ + (1/6)x⁶ + (C₁ + C₂ + C₃). Since the constants are arbitrary, we can represent them as a single constant, C: N(x) = (1/9)x⁹ + (1/5)x⁵ + (1/6)x⁶ + C.

To know more about  power rule click on below link:

https://brainly.com/question/23418174#

#SPJ11

a set of x and y scores has ssx = 21, ssy = 9, and sp = 55. what is the slope for the regression equation? round your answer to 2 decimal places.

Answers

The slope for the regression equation is given by:

b = sp / ssx

where sp is the sum of products of deviations, and ssx is the sum of squared deviations of x scores.

Substituting the given values, we get:

b = 55 / 21

b ≈ 2.62

Rounding to 2 decimal places, we get the slope as 2.62.

To learn more about  regression equation refer below:

https://brainly.com/question/30738733

#SPJ11

Alexandria ate at most two hundred fifty calories more than twice the number of calories her infant sister ate. Alexandria ate eighteen hundred calories. If i represents the number of calories eaten by the infant, which inequality represents the situation?
1,800 less-than-or-equal-to 250 + 2 i
1,800 less-than 250 + 2 i
1,800 + 250 greater-than 2 i
1,800 + 250 greater-than-or-equal-to 2 i

Answers

Answer:

Step-by-step explanation:

Answer:

A. 1,800≤250+2i .

Step-by-step explanation:

Determine whether the matrix is in echelon form, reduced echelon form, or neither. [1 0 5 41 O 1-5 -3 0 0 0 0 0 0 0 0] a) Neither. b) Echelon form. c) Reduced echelon form

Answers

To determine whether the matrix is in echelon form, reduced echelon form, or neither, let's first write the given matrix clearly:

[1 0 5 4]
[0 1 -5 -3]
[0 0 0 0]
[0 0 0 0]

Now, let's analyze its form:

a) Echelon form requires:
1. All nonzero rows are above any rows of all zeros.
2. The leading coefficient (pivot) of a nonzero row is always to the right of the pivot of the row above it.

This matrix satisfies both conditions, so it is in echelon form.

b) Reduced echelon form requires:
1. The matrix is in echelon form.
2. The pivot in each nonzero row is 1.
3. Each pivot is the only nonzero entry in its column.

This matrix fulfills the first two conditions, but the third condition is not met due to the presence of '5' in the first row and the same column as the pivot '1' in the second row.

Therefore, the matrix is in echelon form (option b) but not in reduced echelon form.

Learn more about Reduced echelon: https://brainly.com/question/30153510

#SPJ11

If the pencil is going to be enlarged by a scale factor of 425% for a poster, what will be the length of pencil? Original Length 7units and width 1. 5

Answers

The length of the enlarged pencil will be 29.75 units.The original length of the pencil is 7 units, and the width is 1.5 units. The scale factor is 425%.

We need to find the new length of the pencil after it is enlarged by the given scale factor of 425%.

The formula for calculating the new length of the pencil is:New Length of Pencil = Original Length × Scale Factor/100 Adding the given values in the above formula,

To find the length of the enlarged pencil, we need to multiply the original length by the scale factor.

The scale factor is given as 425%, which can be written as a decimal as 4.25.

Length of enlarged pencil = Original length * Scale factor

= 7 units * 4.25

= 29.75 units

Therefore, the length of the enlarged pencil will be 29.75 units.

to know more about width visit :

https://brainly.com/question/30282058

#SPJ11

NEED HELP ASAP PLEASE!

Answers

Answer:

Step-by-step explanation:

From top to bottom:  T (true), F (false)

T

F

T  51/109 x 100 = 47%

F  (49 + 58)/221 x 100 = 48%

F  109 < 112

A random sample of size n=200 is to be taken from a uniform population with α=24 and β=48. Based on the central limit theorem, what is the probability that the mean of the sample will be less than 35?

Answers

The probability that the mean of the sample will be less than 35 is approximately 0.0205, or 2.05%.

To solve this problem, we'll use the central limit theorem, which states that for a large enough sample size, the distribution of sample means approximates a normal distribution, regardless of the shape of the population distribution.

Given that the population follows a uniform distribution with α = 24 and β = 48, we know that the mean (μ) of the population is given by the formula:

μ = (α + β) / 2

Substituting the values, we have:

μ = (24 + 48) / 2 = 72 / 2 = 36

The standard deviation (σ) of the population is given by the formula:

σ = (β - α) / √12

Substituting the values, we have:

σ = (48 - 24) / √12 = 24 / √12 = 24 / 3.464 = 6.928

According to the central limit theorem, the distribution of sample means follows a normal distribution with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n). Therefore:

μ_s = μ = 36

σ_s = σ / √n = 6.928 / √200 ≈ 0.490

To find the probability that the mean of the sample will be less than 35, we need to find the area under the normal distribution curve to the left of 35. We'll use a standard normal distribution with a mean of 0 and a standard deviation of 1, and then transform it using the mean and standard deviation of the sample distribution.

Let's calculate the z-score for 35:

z = (x - μ_s) / σ_s = (35 - 36) / 0.490 ≈ -2.041

Using a standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of -2.041. The probability that the mean of the sample will be less than 35 is approximately 0.0205, or 2.05%.

To know more about central limit theorem refer to

https://brainly.com/question/18403552

#SPJ11

let d={4,7,9}, e={4,6,7,8} and f={3,5,6,7,9}. list the elements in the set (d ∪ e) ∩ F
(d ∪ e) ∩ F = ___
(Use a comma to separate answers as needed. List the element)

Answers

the right answer on this question is 7,9

Thus, list the elements in the set (d ∪ e) ∩ F is {4, 6, 7, 9}.



To find the elements in the set (d ∪ e) ∩ F, we first need to determine what the union of d and e is.

Given that:

d={4,7,9}, e={4,6,7,8} and f={3,5,6,7,9}.

The union of two sets, denoted by the symbol ∪, is the set of all elements that are in either one or both of the sets.

So, in this case, d ∪ e would be the set {4, 6, 7, 8, 9}.

Next, we need to find the intersection of the set {4, 6, 7, 8, 9} and f.

The intersection of two sets, denoted by the symbol ∩, is the set of all elements that are in both sets.

So, the elements in the set (d ∪ e) ∩ F would be the elements that are common to both {4, 6, 7, 8, 9} and {3, 5, 6, 7, 9}. These elements are 4, 6, 7, and 9.

Therefore, the answer to the question is (d ∪ e) ∩ F = {4, 6, 7, 9}.

Know more about the union

https://brainly.com/question/18909282

#SPJ11

How do you find a equation from a table

Answers

First you need to identify the type of equation in the table, then you can set up the correspondent equation or system of equations to find your equation.

How to find an equation from a table?

To find an equation from a table, you will need to identify the pattern or relationship between the given inputs and outputs (so the first thing you need to do, is identify which type of equation is represented by the table)

There are different methods depending on the type of relationship and the data provided. Here are a few common approaches:

Linear Relationship (y = ax + b)

If the table data suggests a linear relationship between the inputs (x-values) and outputs (y-values), you can use the method of finding the equation of a straight line. This can be done by calculating the slope (m) and the y-intercept (b) using two data points from the table.

Quadratic Relationship (y = ax² + bx + c)

If the table data suggests a quadratic relationship, meaning the outputs change according to a quadratic function of the inputs, you can use the method of finding the equation of a quadratic function. This involves using three data points from the table and solving a system of equations to determine the coefficients of the quadratic equation.

Exponential Relationship (y = A*bˣ)

If the table data suggests an exponential relationship, where the outputs change exponentially with respect to the inputs, you can use the method of finding the equation of an exponential function. This involves determining the base and exponent of the exponential function by examining the ratios between the outputs.

Please notice that these are only 3 types of equations, but there are a lot more, like logarithmic functions, trigonometric functions, cubic functions.

And each one will have a different way of setting up equations to find the equation represented in the table.

Learn more about tables at:

https://brainly.com/question/15602982

#SPJ1

f sin ( θ ) = 24 /26 , 0 ≤ θ ≤ π 2 , thencos ( θ )=tan ( θ )=sec ( θ )=

Answers

Starting with the given equation F sin(θ) = 24/26, we can use trigonometric identities to find expressions for cos(θ), tan(θ), and sec(θ).

First, we square both sides of the equation to get:

F^2 sin^2(θ) = (24/26)^2

Then, we use the identity sin^2(θ) + cos^2(θ) = 1 to solve for cos(θ):

cos^2(θ) = 1 - sin^2(θ)

cos^2(θ) = 1 - (24/26)^2

cos(θ) = ± √(1 - (24/26)^2)

Since 0 ≤ θ ≤ π/2, we know that cos(θ) must be positive, so we take the positive square root:

cos(θ) = √(1 - (24/26)^2)

Next, we can use the fact that tan(θ) = sin(θ)/cos(θ) to find an expression for tan(θ):

tan(θ) = sin(θ)/cos(θ)

tan(θ) = (F sin(θ))/cos(θ)

tan(θ) = (F sin(θ))/√(1 - (24/26)^2)

Finally, we can use the fact that sec(θ) = 1/cos(θ) to find an expression for sec(θ):

sec(θ) = 1/cos(θ)

sec(θ) = 1/√(1 - (24/26)^2)

So, in summary, we have:

cos(θ) = √(1 - (24/26)^2)

tan(θ) = (F sin(θ))/√(1 - (24/26)^2)

sec(θ) = 1/√(1 - (24/26)^2)

Note that we cannot simplify these expressions any further without more information about the value of F.

To know more about value of F, visit:

https://brainly.com/question/13527898

#SPJ11

A system of equations is given.

Equation 1: 5x − 2y = 10
Equation 2: 4x − 3y = 15

Explain how to eliminate x in the system of equations.

Source
StylesFormatFontSize

Answers

Answer:

To eliminate x, you need a positive coefficient in front of x for one equation and its negative counterpart in front of the other equation as a positive number plus its negative opposite equals 0 (e.g., -4 + 4 = 0 and -80 + 80 = 0)

Step 1:  Therefore, we can eliminate x by first determining the least common multiple (LCM) between 5 and 4.  We know that 5 * 4 = 20 and 4 * 5, so the LCM between 5 and 4 is 20.

Step 2:  In order to have 20 as coefficient for x in one equation and -20 for x as a coefficient in the other equation, we can multiply the entire first equation by 4 and the entire second equation by -5:

Equation 1 multiplied by 4:  4 * (5x - 2y = 10) = 20x - 8y = 40

Equation 2 multiplied by -5:  -5* (4x - 3y = 15) = -20x + 15y = -75

Step 3:  Adding the two equations shows that the xs cancel as 20x - 20x = 0, leaving us with 15y - 8y = 40 - 75, which simplifies to 7y = -35

Answer: See below.

Step-by-step explanation:

       First, we are already given these equations in standard form.

5x − 2y = 10

4x − 3y = 15

       Next, we need to make the coefficients of the x variables opposites (as in 5 and -5, etc), since we want to eliminate the x's. To do this, we will find a common multiple (here, the Lowest Common Multiplb is 20). Then, we will multiply every term by the number that makes the coefficient of x our common multiple.

       We will make the first equation with a coefficient of 20 for the x and the second with a coefficient of -20 for the x.

       See this visually below.

5x − 2y = 10 ➜ 4(5x) − 4(2y) = 4(10) ➜ 20x - 8y = 40

4x − 3y = 15 ➜ -5(4x) − -5(3y) = -5(15) ➜ -20x + 15y = -75

       Lastly, add these two equations together. The x's are eliminated. This also will let us solve for y.

      20x - 8y = 40

+   -20x + 15y = -75

--------------------------------

7y = -35

y = -5

decide whether the statement is true or false. 5 is in {1, 2, 3, 4, 5}

Answers

The statement given "5 is in {1, 2, 3, 4, 5}" is true because 5 is included in  the set given {1, 2, 3, 4, 5}.

In set notation, the curly brackets {} represent a set. The set {1, 2, 3, 4, 5} contains the elements 1, 2, 3, 4, and 5. So, when we check if 5 is in this set, we find that it is indeed present. Therefore, the statement is true. Option A is the correct answer.

A set is an unordered collection of unique elements. In this case, the set {1, 2, 3, 4, 5} includes the numbers 1, 2, 3, 4, and 5. When we check if the number 5 is in this set, we find that it is one of the elements in the set. Thus, the statement "5 is in {1, 2, 3, 4, 5}" is true.

You can learn more about sets at

https://brainly.com/question/13458417

#SPJ11

an item is selected randomly from a collection labeled {1,2,...,n}. Denote its label by X. Now select an integer Y uniformly at random from {1,2,...X}. Find :
a) E(Y)
b) E(Y^(2))
c) standard deviation of Y
d) P(X+Y=2)

Answers

(a) The expected value of Y is :

E(Y) = (n+1)/3

(b) The value of E(Y^2) = (2n^2+5n+1)/6

(c) The variance of Y = (2n^2+5n+1)/6 - [(n+1)/3]^2

(d) P(X+Y=2) = 1/n

a) To find the expected value of Y, we use the law of total probability:

E(Y) = ∑ P(X=k)E(Y|X=k) for k=1 to n

Since Y is uniformly distributed on {1,2,...,X}, we have E(Y|X=k) = (k+1)/2.

Therefore,

E(Y) = ∑ P(X=k)(k+1)/2 for k=1 to n

To find P(X=k), note that X can take on any value from 1 to n with equal probability, so P(X=k) = 1/n for k=1 to n. Thus,

E(Y) = ∑ (k+1)/2n for k=1 to n

E(Y) = [1/2n ∑ k] + [1/2n ∑ 1] for k=1 to n

E(Y) = [1/2n (n(n+1)/2)] + [1/2n n]

E(Y) = (n+1)/3

b) To find E(Y^2), we use the law of total probability again:

E(Y^2) = ∑ P(X=k)E(Y^2|X=k) for k=1 to n

Since Y is uniformly distributed on {1,2,...,X}, we have E(Y^2|X=k) = (k^2+3k+2)/6. Therefore,

E(Y^2) = ∑ P(X=k)(k^2+3k+2)/6 for k=1 to n

Using the same values of P(X=k) as before, we get:

E(Y^2) = ∑ (k^2+3k+2)/6n for k=1 to n

E(Y^2) = [1/6n ∑ k^2] + [1/2n ∑ k] + [1/6n ∑ 1] for k=1 to n

E(Y^2) = [1/6n (n(n+1)(2n+1)/6)] + [1/2n (n(n+1)/2)] + [1/6n n]

E(Y^2) = (2n^2+5n+1)/6

c) The variance of Y is given by Var(Y) = E(Y^2) - [E(Y)]^2. Therefore,

Var(Y) = (2n^2+5n+1)/6 - [(n+1)/3]^2

d) To find P(X+Y=2), we note that X+Y=2 if and only if X=1 and Y=1. Since X is uniformly distributed on {1,2,...,n}, we have P(X=1) = 1/n. Since Y is uniformly distributed on {1,2,...,X}, we have P(Y=1|X=1) = 1. Therefore,

P(X+Y=2) = P(X=1)P(Y=1|X=1) = 1/n

To learn more about variance visit : https://brainly.com/question/9304306

#SPJ11

use properties of the indefinite integral to express the following integral in terms of simpler integrals: ∫(−3x2 5x 6xcos(x))dx

Answers

The given integral can be expressed in terms of simpler integrals as:

[tex]\int (−3x^2 + 5x + 6x cos(x)) dx = -x^3 + (5/2)x^2 + 6x sin(x) + 6 cos(x) + C[/tex](

To express the given integral in terms of simpler integrals, we can use the properties of the indefinite integral, including the linearity property and integration by parts.

We can first break down the integrand using linearity:

[tex]\int (−3x^2 + 5x + 6x cos(x)) dx = \int (-3x^2) dx + \int (5x) dx + \int (6x cos(x)) dx[/tex]

Now, we can integrate each term separately:

[tex]\int (-3x^2) dx = -x^3 + C1[/tex] (where C1 is the constant of integration)

[tex]\int (5x) dx = (5/2)x^2 + C2[/tex] (where C2 is another constant of integration)

To integrate ∫(6x cos(x)) dx, we can use integration by parts with u = 6x and dv = cos(x) dx:

∫(6x cos(x)) dx = 6x sin(x) - ∫(6 sin(x)) dx

= 6x sin(x) + 6 cos(x) + C3 (where C3 is another constant of integration)

Putting everything together, we have:

[tex]\int (−3x^2 + 5x + 6x cos(x)) dx = -x^3 + C1 + (5/2)x^2 + C2 + 6x sin(x) + 6 cos(x) + C3[/tex]

So the given integral can be expressed in terms of simpler integrals as:

[tex]\int (−3x^2 + 5x + 6x cos(x)) dx = -x^3 + (5/2)x^2 + 6x sin(x) + 6 cos(x) + C[/tex](where C = C1 + C2 + C3 is the overall constant of integration)

for such more question on   integral

https://brainly.com/question/22008756

#SPJ11

Rewrite the product as a sum or difference. 16 sin(28x) sin(11x) Rewrite the product as a sum or difference. sin(-x) sin(9x)

Answers

The product as a sum or difference is:

1) 16 sin(28x) sin(11x) = 8[cos(17x) - cos(39x)]
2) sin(-x) sin(9x) = ([tex]\frac{1}{2}[/tex])[cos(-10x) - cos(8x)]

1) 16 sin(28x) sin(11x)
We can use the Product-to-Sum identity: sin(A)sin(B) = (1/2)[cos(A-B) - cos(A+B)]
So, 16 sin(28x) sin(11x) can be rewritten as:
8[cos(28x - 11x) - cos(28x + 11x)] = 8[cos(17x) - cos(39x)]
2) sin(-x) sin(9x)
Again, we use the Product-to-Sum identity: sin(A)sin(B) = ([tex]\frac{1}{2}[/tex])[cos(A-B) - cos(A+B)]
So, sin(-x) sin(9x) can be rewritten as:
([tex]\frac{1}{2}[/tex])[cos(-x - 9x) - cos(-x + 9x)] = ([tex]\frac{1}{2}[/tex])[cos(-10x) - cos(8x)]

Learn more about Product-to-Sum identity here:

https://brainly.com/question/29016343

#SPJ11

how many distinct ways are there to arrange 3 yellow marbles 5 blue marbles and 5 green marbles in a row

Answers

The number of distinct ways to arrange 3 yellow marbles, 5 blue marbles, and 5 green marbles in a row will be 5625.

What is a permutation?

A permutation is an act of arranging items or elements in the correct order.

There are 3 yellow marbles, 5 blue marbles, and 5 green marbles.

The number of distinct ways to arrange 3 yellow marbles, 5 blue marbles, and 5 green marbles in a row will be

[tex]\Rightarrow (3 \times 5 \times 5)^2[/tex]

[tex]\Rightarrow 75^2[/tex]

[tex]\Rightarrow 5625[/tex]

More about the permutation link is given below.

brainly.com/question/11732255

Lindsey would like to know the number of people at a movie theater who will buy a movie ticket and popcorn, Based on past data, the probability that a person who is selected at random from those that buy movie tickets will also buy popcorn is 0.6. Lindsey designs a simulation to estimate the probability that exactly two in a group of three people selected randomly at a movie theater will buy both a movie ticket and popcorn. For the simulation, Lindsey uses a number generator that generates random numbers. • Any number from 1 through 6 represents a person who buys a movie ticket and popcorn Any number from 7 through 9 or 0 represents a person who buys only a movie ticket. . For each trial, Lindsey generates three numbers. Lindsey ran 30 trials of the simulation and recorded the results in the following table; 266 342 847 672 567 268 252 465 573 100 818 139 730 910 494 922 155 585 426 593 903 556 981 966 491 186 865 044 147 311L 12 AM PARTA In the simulation, one result was "100. What does this result simulate? a. A No one in a group of three randomly-chosen people who buy movie tickets also buys popcorn. b. Exactly one person in a group of three randomly-chosen people who buy movie tickets also buys popcom. c. Exactly two people in a group of three randomly-chosen people who buy movie tickets also buy popcorn
d. All three people in a group of three randomly-chosen people who buy movie tickets also buy popcorn

Answers

The result "100" in the simulation simulates that exactly one person in a group of three randomly chosen people who buy movie tickets also buys popcorn.


In the simulation, Lindsey generated three random numbers for each trial to represent the behavior of three people at the movie theater. According to the given rules, any number from 1 through 6 represents a person who buys a movie ticket and popcorn, while any number from 7 through 9 or 0 represents a person who buys only a movie ticket.

To estimate the probability that exactly two in a group of three people selected randomly at a movie theater will buy both a movie ticket and popcorn, Lindsey needed to run multiple trials of the simulation. In one of the trials, the result was "100", which means that one of the three randomly-chosen people bought both a movie ticket and popcorn, while the other two only bought a movie ticket.

Therefore, the result "100" in the simulation simulates that exactly one person in a group of three randomly-chosen people who buy movie tickets also buys popcorn.


Based on the simulation results, Lindsey can estimate the probability of exactly two people buying both a movie ticket and popcorn out of a group of three randomly chosen people who buy movie tickets at the theater. By analyzing all 30 trials of the simulation, Lindsey can calculate the relative frequency of this event and use it as an estimate of the probability.

To learn more about probability visit:

https://brainly.com/question/30034780

#SPJ11

determine the volume of this cube. height = 7 cm length = 14 cm width = 7 cm a. a. 432 cm³. b. b. 682 cm³. c. c. 2744 cm³. d. d. 343 cm³.

Answers

This is closest to option d) 343 cm³,  The volume of the cube is 343 cm³. which is the correct answer.

The volume of a cube is given by the formula [tex]V = s^3,[/tex] where s is the length of any side of the cube. In this case, the height, length, and width are all equal to 7 cm. Thus, the length of any side of the cube is also 7 cm.

Substituting s = 7 cm into the formula for the volume of a cube, we get:

V = s^3 = 7^3 = 343 cm³

Therefore, the volume of the cube is 343 cm³. This is closest to option d) 343 cm³, which is the correct answer.

Learn more about volume  here:

https://brainly.com/question/31606882

#SPJ11

pls help lol my grade’s a 62 rn & grades are almost due !

Answers

The triangle in the image is a right triangle. We are given a side and an angle, and asked to find another side. Therefore, we should use a trigonometric function.

Trigonometric Functions: SOH-CAH-TOA

---sin = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent

In this problem, looking from the angle, we are given the adjacent side and want to find the opposite side. This means we should use the tangent function.

tan(40) = x / 202

x = tan(40) * 202

x = 169.498

x (rounded) = 169 meters

Answer: the tower is 169 meters tall

Hope this helps!

In ΔCDE, the measure of ∠E=90°, CD = 9. 2 feet, and DE = 8. 3 feet. Find the measure of ∠C to the nearest tenth of a degree

Answers

The answer of the given question based on the triangle is , - 15.75 ,  this is not possible as the length cannot be negative.

We are given:

In ΔCDE, the measure of ∠E = 90°, CD = 9.2 feet, and DE = 8.3 feet.

To find:

The measure of ∠C to the nearest tenth of a degree.

Solution:

In ΔCDE, applying Pythagoras theorem:

CE² + CD² = DE²CE² + (9.2)² = (8.3)²

CE² = (8.3)² - (9.2)²CE²

= 68.89 - 84.64CE²

= - 15.75

This is not possible as the length cannot be negative.

Hence, the given values are not possible.

So, there is no such triangle ΔCDE, which satisfies the given conditions.

Hence, we cannot find the measure of ∠C.

To know more about Pythagoras theorem visit:

https://brainly.com/question/32626180

#SPJ11

A number p, when rounded to 3 decimal places it is equal to 0.079
Find the upper and lower bound of p

Answers

To find the upper and lower bounds of p, we need to consider the range of values that could be rounded to 0.079 when rounded to 3 decimal places.

The midpoint between 0.0785 and 0.0795 is (0.0785 + 0.0795) / 2 = 0.079. Any value between 0.0785 and 0.0795 would round to 0.079 when rounded to 3 decimal places.

Therefore, the lower bound of p is 0.0785 and the upper bound of p is 0.0795.

In interval notation, we can write:

p ∈ [0.0785, 0.0795]

Suppose that when your friend was​ born, your​ friend's parents deposited ​$5000 in an account paying ​4. 7% interest compounded. What will the account balance be after 18 years?

Answers

After 18 years, the account balance will be calculated based on a $5000 deposit with a 4.7% interest compounded.

To calculate the account balance after 18 years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final account balance
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount is $5000, the annual interest rate is 4.7% (or 0.047 as a decimal), the interest is compounded annually (n = 1), and the time period is 18 years (t = 18).
Using the formula, we can calculate the account balance:
A = $5000(1 + 0.047/1)^(1*18)
= $5000(1 + 0.047)^18
= $5000(1.047)^18
≈ $5000 * 1.990
≈ $9949.92
Therefore, after 18 years, the account balance will be approximately $9949.92.

Learn more about interest Compounded here
https://brainly.com/question/14295570



#SPJ11

An article presents the following fitted model for predicting clutch engagement time in seconds from engagement starting speed in m/s (x1), maximum drive torque in N·m (x2), system inertia in kg • m2 (x3), and applied force rate in kN/s (x4) y=-0.83 + 0.017xq + 0.0895x2 + 42.771x3 +0.027x4 -0.0043x2x4 The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error. Predict the clutch engagement time when the starting speed is 18 m/s, the maximum drive torque is 17 N.m, the system inertia is 0.006 kg•m2, and the applied force rate is 10 kN/s.

Answers

The predicted clutch engagement time is approximately 1.81 seconds when the starting speed is 18 m/s, the maximum drive torque is 17 N.m, the system inertia is 0.006 kg•m2, and the applied force rate is 10 kN/s.

The given regression model for predicting clutch engagement time (y) based on four predictor variables (x1, x2, x3, x4) is:

[tex]y = -0.83 + 0.017x1 + 0.0895x2 + 42.771x3 + 0.027x4 - 0.0043x2x4[/tex]

To predict the clutch engagement time when x1 = 18 m/s, x2 = 17 N.m, x3 = 0.006 kg•m2, and x4 = 10 kN/s, we simply substitute these values into the regression equation:

[tex]y = -0.83 + 0.017(18) + 0.0895(17) + 42.771(0.006) + 0.027(10) - 0.0043(17)(10)\\y = -0.83 + 0.306 + 1.5215 + 0.256626 + 0.27 - 0.731[/tex]

y = 1.809126

Therefore, the predicted clutch engagement time is approximately 1.81 seconds when the starting speed is 18 m/s, the maximum drive torque is 17 N.m, the system inertia is 0.006 kg•m2, and the applied force rate is 10 kN/s.

To know more about clutch engagement  refer here:

https://brainly.com/question/28257224

#SPJ11

use part one of the fundamental theorem of calculus to find the derivative of the function. f(x) = 0 1 sec(7t) dt x hint: 0 x 1 sec(7t) dt = − x 0 1 sec(7t) dt

Answers

The derivative of the function f(x) = 0 to x sec(7t) dt is sec^2(7x) * tan(7x).

The derivative of the function f(x) = 0 to x sec(7t) dt is sec(7x).

To see why, we use part one of the fundamental theorem of calculus, which states that if F(x) is an antiderivative of f(x), then the definite integral from a to b of f(x) dx is F(b) - F(a).

Here, we have f(x) = sec(7t), and we know that an antiderivative of sec(7t) is ln|sec(7t) + tan(7t)| + C, where C is an arbitrary constant of integration.

So, using the fundamental theorem of calculus, we have:

f(x) = 0 to x sec(7t) dt = ln|sec(7x) + tan(7x)| + C

Now, we can take the derivative of both sides with respect to x, using the chain rule on the right-hand side:

f'(x) = d/dx [ln|sec(7x) + tan(7x)| + C] = sec(7x) * d/dx [sec(7x) + tan(7x)] = sec(7x) * sec(7x) * tan(7x) = sec^2(7x) * tan(7x)

Therefore, the derivative of the function f(x) = 0 to x sec(7t) dt is sec^2(7x) * tan(7x).

Learn more about derivative here

https://brainly.com/question/31399608

#SPJ11

Other Questions
Does profit equal revenue minus expenses? How does Orwell use satire to support his purpose in this passage he uses parody? Kinds of plan after 5 year career development plan find two whole numbers that are closest to v42. explain your reasoning Your elder sister has written a letter to you that she want to elope why her lover. Write a letter given her at least five reason why she must wait for you parent lesson before marriage QuestionFor which intervals is the function increasing?Select each correct answer.(1,2)(0,1)(,0)(2,) Lab-Kinematics in 1 Dimension: Determine Total Distance and Net Displacement from Velocity vs. Time Graphs tammy frequently _________ cash amounts reported to the audit committee. IM NOT SURE IF THIS IS RIGHT CAN SOMEONE PLEASE HELP MEEEEE!!!!! Which of the following is NOT a difference between anaphase I and anaphase II?A. At the end of anaphase I, each chromosome is composed of two chromatids and at the end of anaphase II, sister chromatids have separated, becoming daughter chromosomesB. Anaphase I occurs in a haploid cell while anaphase II occurs in a diploid cell.C. Sister chromatids separate during anaphase II while homologous chromosomes separate during anaphase I.D. The cell undergoing anaphase II is genetically different from what it contained while undergoing anaphase I. PLEASE HELP ASAP *VERY IMPORTANT* I WILL GIVE BRAINLIEST infants are often referred to as belly breathers because 5 starts and a thanks+brainliest find the slope of the line passing through the point and perpendicular to the given line [tex](-5,2) 4x-3y=12[/tex]options: -3/4 or -4/3 What advantage does a predator have over the prey? What does Opinion is the medium between knowledge and ignorance. Mean which of the following refers to the transformation of stimulus energy into neural impulses? responses perception perception bottom-up processing bottom-up processing top-down processing top-down processing transduction transduction psychophysics (Two-Step Linear Inequalities MC)Which graph represents the solution to the inequality 2(b + 2) > 24? number line with open point at 10 with arrow pointing left number line with closed point at 10 with arrow pointing left number line with closed point at 10 with arrow pointing right number line with open point at 10 with arrow pointing right Verb Usage 8.2-Question 4Is the following sentence in active voice or passive voice?The computer was used by the student. Determine the Fourier series coefficients for each of the following discrete-time periodic signals. Plot the magnitude and phase of each set of coefficients ak. a. Each x[n] depicted in Figure P3.28 (a) - (c) b. x[n] = sin(2 pi n/3)cos(2 pi n/2) c. x[n] periodic with period 4 and x[n] = 1 - sin pi n/4 for 0 < n < 3 d. x[n] periodic with period 12 and x[n] = 1 - sin pi n/4 for 0 < n < 11 e. Solve the following problem. Water has a specific heat of4184 J/kg C. How much energy is needed to increase thetemperature of 3 kg of water 15 C ?