An item is priced at $13.75. If the sales tax is 7%, what does the item cost including sales tax?

(a) To sketch the graph of f(t) = {sin(t) 0 ≤ t < π, 0 π ≤ t}, we can observe that the function is equal to zero for t greater than or equal to π. Thus, the graph of f(t) consists of a sine wave from 0 to π, and then it becomes zero from π onwards.

(b) To express f(t) in terms of the Heaviside function u(t - a), we can write f(t) as {0 0 ≤ t < 3, t² 3 ≤ t}. This means that for t less than 3, the function is zero, and for t greater than or equal to 3, the function is t squared. We can rewrite this using the Heaviside function as f(t) = t²u(t - 3).

To find the Laplace transform L{f(t)}, we can apply the Laplace transform to each part of the function separately. Using the Laplace transform properties, we have L{f(t)} = L{t²u(t - 3)}. By applying the time-shifting property, the Laplace transform of t²u(t - 3) is given by L{t²u(t - 3)} = e^(3s)/s^3, where s represents the Laplace variable.

The graph of f(t) consists of a sine wave from 0 to π, and then it becomes zero from π onwards. The function f(t) can be expressed as f(t) = t²u(t - 3) using the Heaviside function. The Laplace transform of f(t) is L{f(t)} = e^(3s)/s^3.

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Answer:

454.96

Step-by-step explanation:

Suppose that the total price of worth clothes equal : x

Rachel bought them with 12% off which means , Rachel bought them :

( x ) - ( 12x / 100 )

As the question told the above equation must equal 517$ , So :

( 100x / 100 ) - ( 12x / 100 ) = 517

100x - 12x / 100 = 517

88x / 100 = 517

multiply sides by 100

88x = 51700

Divide sides by 88

x = 587.5 $

Thus the total price is 587.5 $ .

Answer:

13

Step-by-step explanation:

25 - 12 = 13

Answer:

13

Step-by-step explanation:

12 + 13 = 25 or 25 -12 = 13

Answer:

-92  - 10 + 2(145 - 7) + 174

Step-by-step explanation:

Answer:

just do 115 for 2 days come to 230

Answer:

230 pounds

Step-by-step explanation:

Since it is for 2 days, 115(2)

which gives u 230

The solution to the system of differential equations with the given initial condition is:

x₁(t) = (-6/17) × exp(-t) + (44/17) × exp(2t)

x₂(t) = (-15/17) × exp(-t) + (108/17) × exp(2t)

The system of differential equations

x₁'(t) = -52x₁(t) + 22x₂(t)

x₂'(t) = -110x₁(t) + 47x₂(t)

Let's find the solution X(t) = [x₁(t), x(t)] with the initial condition x₀ = [-3, -3].

To solve the system, we'll start by finding the eigenvalues and eigenvectors of the coefficient matrix.

The coefficient matrix of the system is

A = [[-52, 22], [-110, 47]]

To find the eigenvalues, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix

| -52 - λ 22 |

| -110 47 - λ | = 0

Expanding the determinant, we have

(-52 - λ)(47 - λ) - (-110)(22) = 0

Simplifying, we get

(λ + 1)(λ - 2) = 0

Solving this quadratic equation, we find two eigenvalues

λ₁ = -1

λ₂ = 2

Now let's find the corresponding eigenvectors for each eigenvalue.

For λ₁ = -1, we solve the equation (A - λ₁I)v = 0

| -51 22 | | v₁ | | 0 |

| -110 48 | | v₂ | = | 0 |

Simplifying, we get the equation

-51v₁ + 22v₂ = 0

-110v₁ + 48v₂ = 0

Solving this system of equations, we find the eigenvector v₁ = [2, 5].

For λ₂ = 2, we solve the equation (A - λ₂I)v = 0

| -54 22 | | v₁ | | 0 |

| -110 45 | | v₂ | = | 0 |

Simplifying, we get the equation

-54v₁ + 22v₂ = 0

-110v₁ + 45v₂ = 0

Solving this system of equations, we find the eigenvector v₂ = [11, 27].

Therefore, the eigenvalues in ascending order are

λ₁ = -1

λ₂ = 2

The corresponding eigenvectors are

v₁ = [2, 5]

v₂ = [11, 27]

To find the solution X(t), we can write it as a linear combination of the eigenvectors:

X(t) = c₁ × v₁ × exp(λ₁ × t) + c₂ × v₂ × exp(λ₂ × t)

Substituting the given values for x₁(t) and x₂(t) into the equation, we can find the coefficients c₁ and c₂:

x₁(t) = c₁ × 2 × exp(-t) + c₂ × 11 × exp(2t)

x₂(t) = c₁ × 5 × exp(-t) + c₂ × 27 × exp(2t)

Using the initial condition x₀ = [-3, -3], we can solve for c₁ and c₂

-3 = c₁ × 2 × exp(0) + c₂ × 11 × exp(0)

-3 = c₁ × 5 × exp(0) + c₂ × 27 × exp(0)

Simplifying, we get:

-3 = 2c₁ + 11c₂

-3 = 5c₁ + 27c₂

Solving this system of equations, we find

c₁ = -3/17

c₂ = 4/17

Substituting these values back into the solution equation, we have

x₁(t) = (-3/17) × 2 × exp(-t) + (4/17) × 11 × exp(2t)

x₂(t) = (-3/17) × 5 × exp(-t) + (4/17) × 27 × exp(2t)

Therefore, the solution to the system of differential equations with the given initial condition is:

x₁(t) = (-6/17) × exp(-t) + (44/17) × exp(2t)

x₂(t) = (-15/17) × exp(-t) + (108/17) × exp(2t)

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The question is incomplete the complete question is :

Answer:

DC = 1332.95 feet

Step-by-step explanation:

From the figure attached,

Let the measure of DC = h ft

And measure of side BC = a ft

By applying tangent ratio in ΔBCD,

tan(56°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

             = [tex]\frac{DC}{BC}[/tex]

             = [tex]\frac{h}{a}[/tex]

h = a[tan(56°)] --------(1)

By applying tangent rule in ΔACD,

tan(22°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

tan(22°) = [tex]\frac{DC}{BC+AC}[/tex]

             = [tex]\frac{h}{a+2400}[/tex]

h = (a + 2400)tan(22°) ------- (2)

Equating the values of h from equations (1) and (2),

a[tan(56°)] = (a + 2400)tan(22°)

a[tan(56°) - tan(22°)] = 2400[tan(22°)]

1.0785a = 968.6629

a = 899.085 ft

From equation (1),

h = 899.085[tan(56°)]

h = 1332.948

h ≈  1332.95 ft

Answer:

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(173≤X≤174) = 0.0936

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 175

Given that the standard deviation of the Population = 6

Let 'x⁻' be the mean of the random sample

Given that  x₁⁻ = 173

[tex]Z_{1} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{173-175}{\frac{6}{\sqrt{60} } } =-2.58[/tex]

Given that  x₂⁻ = 174

[tex]Z_{2} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{174-175}{\frac{6}{\sqrt{60} } } = -1.29[/tex]

Step(ii):-

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(X₁≤X≤X₂)      = P(Z₁≤Z≤Z₂)

                       = P(Z≤Z₂) - P(Z≤Z₂)        ( both values 'Z' values are negative)

                       = 0.5 -A(Z₁) - (0.5 -A(Z₂))

                      = |A(Z₂) -A(Z₁)|

P(173≤X≤174)     =   | A(2.58)-A(1.29)|

                  = 0.4951 - 0.4015       (∵ from normal table)

                = 0.0936

Final answer:-

The probability that the mean of this sample of home purchases is between 173 and 174 homes

P(173≤X≤174) = 0.0936

Answer:

$2100 will be his new salary

Step-by-step explanation:

Well since a 5 percent raise is basically 105% of his pay, we can multiply 105% with 2000

since its a percent in decimal form its 1.05

1.05*2000=2100

$2100 is his new salary

It is important to remember the definitions of binomial, continuous, discrete, interval, nominal, ordinal, and ratio variables because these are different types of data which need different methods of analysis.

Nominal variables are variables used for identification or categorization. Nominal data cannot be ranked, ordered, or compared. The gender, ethnicity, religion, and hair color of an individual are all examples of nominal variables.

Ordinal variables are variables that can be ranked or ordered, but the difference between each point on the scale is not constant. For example, we could use an ordinal variable to describe the class ranks of students: 1st, 2nd, 3rd, and so on. While there is a clear order to the data, the difference between each rank is not necessarily the same.

Interval variables have equal distances between each value, and they also have a true zero point. For example, a temperature measurement is an interval variable because the difference between 20 degrees Celsius and 30 degrees Celsius is the same as the difference between 30 degrees Celsius and 40 degrees Celsius.

Ratio variables have equal intervals between each value and have a true zero point. For example, weight is a ratio variable because a weight of zero means that there is no weight.

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The minimum sample size required is 94 to obtain a margin of error of 0.04236.

To find the minimum sample size required to obtain a margin of error of 0.04236.

we need to use the formula for sample size determination for proportions:

n = (Z² × p × (1 - p)) / E²

Where:

n = required sample size

Z = Z-score corresponding to the desired level of confidence (we'll assume a 95% confidence level, so Z ≈ 1.96)

p = estimated proportion (from the available data)

E = margin of error

Given:

Total adults in the town = 88

Adults with health insurance = 69

First, we calculate the estimated proportion (p) of adults with health insurance:

p = (69 / 88)

Next, we substitute the values into the formula and solve for n:

n = (1.96² × (69/88) × (1 - 69/88)) / (0.04236²)

n = 93.966

The minimum sample size required is 94 to obtain a margin of error of 0.04236 (or 4.236%).

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Answer:

9

Step-by-step explanation:

8/12=6/x

cross multiply to get 9

Answer:

99 oak trees

Step-by-step explanation:

Given data

Ratio= 8:3

Number of pine tree= 264

Let the number of oak trees be x

Let us apply the part to part method

8/264= 3/x

cross multiply

264*3= 8x

792=8x

x= 792/8

x=99 oak trees

The owner of the tree farm planted 99 oak trees.

An equation is an expression used to show the relationship between two or more numbers or variables.

Given that a farmer plants pine trees and oak trees in a ratio of 8:3. If 264 pine trees are planted, let y represent the total number of trees hence:

264 = (8/11) * y

y = 363 trees

Number of oak trees = (3/11) * 363 = 99 trees

Therefore the owner of the tree farm planted 99 oak trees.

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Answer:

You need the minimum cost for renting the meeting room given the following info

Reservation Fee = $18

Hourly Rate = $5

The renter wants to keep the cost below $58

So the cost will vary with the time, t you use the inequality below

5t + 18 ≤ 58

You can solve this to get that minimum

You can check you answer by graphing it.

I hope this helps!<3

Answer:

x = 0

Step-by-step explanation:

hi there!

im not sure if the x between the 2's is a x as in a variable or if it is multiplication sign. im going to solve the problem as if it is a multiplication sign but if that is wrong then please let me know!

2 * 2 + x - 4 = 0

is our equation that we are working with ^

first step is, following the pemdas we multiply *2 with its self

( ^ parentheses, exponents, multiplication/ division making sure to solve it left to right, addition and subtraction still making sure to follow the left to right rule )

2 * 2 + x - 4 = 0

2 * 2

= 4 + x - 4 + 0

then we add positive 4 and negative 4 together, canceling eachother out the giving us the answer of  x = 0

4 + x - 4 + 0

4 + - 4 = 0

x = 0

i hope this helps you! have a good rest of your day :)

When  we rolled a fair, 6-sided die 1000 times. out of 1,000 rolls, the actual number of even rolls may vary due to the inherent randomness of the process.

If we assume that the die is fair and unbiased, each of the six sides has an equal probability of landing face-up. Since we are interested in the number of times the die comes up even (2, 4, or 6), we need to consider that half of the possible outcomes are even numbers.

Out of the six possible outcomes (1, 2, 3, 4, 5, 6), three are even (2, 4, 6). Therefore, the probability of rolling an even number on a fair six-sided die is 3/6 or 1/2.

If we roll the die 1000 times, we can expect that the die would come up even approximately half of the time, as per the probability. Half of 1000 is 500, so we would expect the die to come up even around 500 times out of 1000 rolls.

It's important to note that this is an expected value based on probability, and in practice, the actual number of even rolls may vary due to the inherent randomness of the process.

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Answer:

$85.09

Step-by-step explanation:

Answer: A. Bruno accidentally used the diameter instead of the radius to find the area of the base. B. The correct volume is 602.88

Step-by-step explanation: Area of a cylinder is (r^2)(pi)(h) not (d^2)(pi)(h)

Answer:

Question?

Step-by-step explanation:

What is the question?

Since option b correctly represents the set LA as the set of all singletons of X, and the other options are incorrect, the correct answer is option d.

Let's break down the given options:

a) LA = {∅}:

This option represents the set LA, which is the set of all singletons of X. A singleton is a set that contains only one element. Since X is the set of integers, a singleton of X would be a set containing a single integer. However, the notation LA suggests that the singletons are related to the set A, not X. Therefore, option a is not correct.

b) LA = {{a} | a ∈ X}:

This option represents the set LA, which is the set of all singletons of X. Here, the notation {{a} | a ∈ X} denotes the set of all sets that contain a single element, where that element belongs to X. In other words, LA is the set of all possible singletons of X. This option correctly represents the set LA, so option b is correct.

c) LA = {∅, {X}}:

This option represents the set LA as a set containing two elements: the empty set (∅) and the set {X}. However, this representation does not align with the definition of LA as the set of singletons of X. The set LA should only contain sets with a single element, not the empty set or the set {X}. Therefore, option c is not correct.

d) None of the above:

Since option b correctly represents the set LA as the set of all singletons of X, and the other options are incorrect, the correct answer is option d.

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Answer: Cost of one hosta = $11

Cost of one pot of ivy = $11

Step-by-step explanation:

Let the the cost of one hosta be represented by x.

Let the cost of one pot of ivy be represented by y.

The information given in the question can be formed into an equation as:

8x + 4y = 132 ............ i

2x + 2y = 44 ............. ii

Multiply equation i by 2

Multiply equation ii by 4

16x + 8y = 264 ........ iii

8x + 8y = 176 ........ iv

Subtract iv from iii

8x = 88

x = 88/8

x = 11

One hosta cost $11

From equation ii

2x + 2y = 44

2(11) + 2y = 44

22 + 2y = 44

2y = 44 - 22

2y = 22

y = 22/2

y = 11

One pot of ivy cost $11

Answer:

2/5, option 4.

Step-by-step explanation:

When you are dividing 2 fractions, the first fraction stays the same, and the 2nd fraction becomes the reciprocal, and the division sign becomes a multiplication sign.

The reciprocal of 2/3 is 3/2.

Now you need to change the division sign to a multiplication sign.

The equation will now become 4/15 x 3/2.

4 times 3 is 12, and 15 times 2 is 30.

12/30 isn't an option, so you will need to simplify.

Find a common factor, then divide.

6 is a common factor, so you divide both 12 and 30 by 6, to get 2 and 5.

2/5 is what you are left with.

Option 4.

4/15 divided by 2/3 is 2/5.

Answer:

hi

Step-by-step explanation:

[tex] \frac{4}{15} \div \frac{2}{3} = \frac{4}{15} \times \frac{3}{2} = \frac{2}{5} [/tex]

have a nice day

The mean GPA is greater than 2.75.

Here, we have,

A= 4.0, A- = 3.7, B+ = 3.

three, and many others.

Total the first-class factors, and overall the credit hours. Divide the overall satisfactory points by means of the overall credit score hours.

Grade Point Average (GPA):

Grade point average (GPA) is the measure used to summarize your instructional fulfillment at Griffith. After the e-book of final grades every trimester, your software and career.

GPA is calculated and could be utilized by the college to tell choices, which include the subsequent: educational progression.

Divide the total range of grade factors earned with the aid of the total number of letter-graded units undertaken.

Mean GPA = total / 50    

                 = 2.75.

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The inverse of the matrix (AAB)- can be found by taking the inverse of A, the inverse of B, and the inverse of AAB.

To find the inverse of the matrix (AAB)-, we can utilize the properties of matrix inverses.

Given that A and B are invertible n x n matrices, we can express the inverse of (AAB)- as the product of the inverses of A, B, and AAB in the reverse order.

In mathematical notation, the inverse of (AAB)- can be represented as (AAB)-1 = B-1A-1(AAB)-1.

To confirm that the obtained inverse is correct, we can evaluate the expression (AAB)-1(AAB)- and verify that it equals the identity matrix.

Similarly, we can multiply (AAB)- with (AAB)-1 and check if it results in the identity matrix.

By performing these calculations and observing that the resulting product is indeed the identity matrix, we can confirm the correctness of the inverse.

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Answer:  the answer is 9.9

Step-by-step explanation:

Answer:

94.88 cubic units

Step-by-step explanation:

Volume of the prism = Area of base * Height

[tex] = 5( \frac{1}{2} \times 2.75 \times 4) \times 3.45 \\ \\ = 5 \times 2.75 \times 2 \times 3.45 \\ \\ = 10\times 2.75 \times 3.45 \\ \\ = 94.875 \\ \\ \approx 94.88 \: cubic \: units[/tex]

The set A ∩ B = {3}

The intersection of sets, denoted as A ∩ B, refers to the set that contains elements that are common to both sets A and B. In this case, set A consists of the elements {1, 2, 3, 6}, and set B consists of the elements {3, 4, 5}.

The intersection of A and B, written as A ∩ B, represents the set of elements that appear in both sets simultaneously.

To find the intersection of sets A and B, we examine each element of set A and check if it is also present in set B. In this case, the element 3 is the only element that exists in both sets.

Therefore, the intersection of sets A and B is {3}.

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