At the tri-county track meet Jada won the 100 meter race in 12 9/10 seconds. The runner up finished in 13 1/10 seconds how many seconds faster was Jada then the funner up?

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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The types of concurrent constructions that are needed to find the centroid of a triangle include the following: B. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex.

In Mathematics and Geometry, the centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.

Generally speaking, the centroid of a triangle simply refers to the point where the three (3) medians of the triangle meet or intersect. This ultimately implies that, a centroid is a point of intersection of the lines from each vertex of a triangle to the midpoint of the opposite sides.

In this context, the types of concurrent constructions would be modeled by answer option B.

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Complete Question:

What types of concurrent constructions are needed to find the centroid of a triangle.

A. intersection of the lines drawn from each vertex of a triangle and perpendicular to its opposite side.

B. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex.

C. intersection of the lines drawn to bisect each vertex of the triangle.

D. intersection of the lines drawn perpendicular to each side of the triangle through its midpoint

Answer:

x=2

Step-by-step explanation:

5x-7=5-x

6x-7=5

6x=12

x=2

Answer:

Q = 216 - 0.5P

Step-by-step explanation:

One approach to modeling the demand as a function of the cost is to use a linear demand equation of the form:

Q = a - bP

where Q is the quantity demanded, P is the price, and a and b are constants. To find these constants, we can use the two points given:

When P = $180, Q = 8 portraits, so 8 = a - b * 180

When P = $100, Q = 24 portraits, so 24 = a - b * 100

Solving the system of equations gives us:

a = 216

b = 0.5

So, the demand equation is:

Q = 216 - 0.5P

This represents the demand for portraits as a function of the price, where the demand decreases linearly as the price increases.

Answer:

2,047,291,874,697,000,000,000,000

Step-by-step explanation:

that is the answer to the multiplication statement xD

The extension cord is an illustration of unit rates, and the price per foot is $0.47 per foot

The given parameters are:

Length = 6 yards

Cost = $8.46

Convert the length from yard to feet.

So, we have:

Length = 6 feet * 3

This gives

Length= 18 feet

The price per foot is then calculated using:

Rate = Cost/Length

This gives

Rate = 8.46/18

Evaluate

Rate = 0.47

Hence, the price per foot is $0.47 per foot

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The augmented matrix is,

\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)

We have given system of linear equation is,

\(x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.\)

In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.

So, the first row is

\(1\ -1\ -4\ 5\)

the second row is

\(2\ 0\ 2\ 0\)

and the third row is

\(4\ 1\ 1\ 3\)

Therefore the augmented matrix for this linear system is,

\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)

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The augmented matrix for the given linear equations will be constructed as follows

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.

The given equation has three variables so the matrix form will be of \(3\times3\)

The given linear equations are

\(x-y-4z=5\\2x+0y+2z=0\\4x+y+z=3\)

From the above equations, we will make an augmented matrix.

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

The first equation will be followed by the first row of the matrix and the rest will be followed the same.

Thus the augmented matrix for the given linear equations will be constructed as follows

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

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Answer:

before the 0.32 in the tick is the 0.319

Step-by-step explanation:

So Simon has \(7/10\) of the original cakes left.

Simon gives 1/5 of the cakes to Sali:

= 30 * 1/5

= 6 cakes.

Simon gives 10% of the cakes to Jane:

= 10% * 30

= 3 cakes.

The total number of cakes Simon gives away is:

=  6 + 3

= 9 cakes.

So, Simon is left with 30 - 9 = 21 cakes.

To express this as a fraction of the original 30 cakes, we will simplify as:

= 21/30

= 7/10.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

y = -4 + 1.4

Step-by-step explanation:

y+3/5 = -4(x-1/2)

y + 3/5 = -4x + 2

y + 0.6 = -4x + 2

y = -4 + 1.4

The correct answer is d. Chi-square. The chi-square method for finding confidence intervals should be used only when the population distribution is chi-square.

The method for finding confidence intervals with the chi-square distribution is specifically designed for situations where the data follows a chi-square distribution.

The chi-square distribution is a probability distribution that arises in inferential statistics, particularly in hypothesis testing and constructing confidence intervals for categorical data.

When the data does not follow a chi-square distribution, such as when the distribution is normal, skewed, or bimodal, using the chi-square distribution for constructing confidence intervals may lead to incorrect results.

In those cases, other methods appropriate for the specific distribution should be used. The correct answer is d. Chi-square.

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Answer: triangle sum , x= 9

Step-by-step explanation:

The triangle angle sum theorem states that the 3 interior angles of a triangle sum to 180 degrees. Add all of the angle measures together and set equal to 180. (3x-4)+(5x-7)+(13x+2) = 180. Combine like terms. 21x -9 = 180. Add 9 to both sides. 21x= 189. Divide both sides by 21. X = 9

The statement given "every then or else block of an if-then statement is reachable by some value, regardless of the test conditions specified by the if statement." is false  because the "then" block of an if-then statement is only executed when the specified test condition is true, and not all values will satisfy the test condition.

The "then" block of an if-then statement is executed only when the specified test condition in the if statement evaluates to true. If the test condition is false, the "then" block is skipped, and the program proceeds to the next statement following the if-then statement. The "else" block, if present, is executed when the test condition is false. Therefore, not every "then" or "else" block is reachable by any value, but rather by the evaluation of the test condition.

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Therefore, the work done in this problem comes out to be 144 ft pound.

The work a force does is calculated as the product of the object's displacement and the components of the applied force of the object in the displacement direction. Pushing a block with some force and accelerating the body results in work being completed.

Here,

Given : an 8 lb mass

a height = 18ft

So, we find the work done

Using formula

=> Work done = m*g*h

=>  Work done = weight * height

=>   Work done = 8*18

=> Work done=144 ft pound

Therefore, the work done in this problem comes out to be 144 ft pound.

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Answer: Ix - 5I ≥ 5.

Step-by-step explanation:

We want the set:

[0, 10]

to be the solution of:

Ix - bI ≤ c

So we need to find the values of c and b.

The first step is to find the middle point in our segment.

We can do that by adding the extremes and dividing it by 2.

M = (10 + 0)/2 = 5

And we also want to find half of the difference between the extremes, this is:

D = (10 - 0)/2 = 5.

Now, this set will be the set of solutions of:

Ix - MI ≥ D

Then in our case, we have:

Ix - 5I ≥ 5.

so we have that b = 5, and c = 5.

The value of x for the given polygon is 126º.

The given pentagon with angles (x-30)°, (x-30)°, (x-30)°, x° and x°.

We need to find the value of x.

A pentagon is a flat 2D shape that has five sides and five vertices.

The word “pentagon” comes from the Greek word “pentagons”, which means “five-angled”. A regular pentagon has five internal angles that form corners. The angles in all the corners add up to 540º.

Now, (x-30)°+(x-30)°+(x-30)°+x°+x°=540º

⇒5x-90=540

⇒5x=630

⇒x=126º

Therefore, the value of x for the given polygon is 126º.

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Here, \(det(5B^T) = -2 * (5^n)\) and d\(et(SB^T) = (S^n) * (-2)\), where n is the dimension of B and S is the scaling factor of the scalar matrices S.

The determinant of the product of the scalar and matrices transpose is equal to the scalar multiplication of the matrix dimensions and the determinant of the original matrix. So \(det(5B^T)\)can be calculated as \((5^n) * det(B)\). where n is the dimension of B. In this case B is an n × n matrix, so \(det(5B^ T) = (5^n) * det(B) = (5^n) * (-2) = -2 * (5^ n )\).

Similarly, \(det(SB^T)\) can be calculated as \((det(S))^n * det(B)\). A scalar matrix S scales only the rows of B so its determinant det(S) is equal to the higher scale factor of B 's dimension. Therefore,\(det(SB^T) = (det(S))^n * det(B) = (S^n) * (-2)\). where\(S^n\) represents the n-th power scaling factor. 

The determinant of a matrix is ​​a scalar value derived from the elements of the matrix. It is a fundamental concept in linear algebra and has many applications in mathematics and science.

To compute the determinant of a square matrix, the matrix must have the same number of rows and columns. The determinant is usually represented as "det(A)" or "|"A"|". For matrix A 

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Answer:

8 feet.

Step-by-step explanation:

     Before remodeling:

                   width = 9 ft

                 Area   = 108 ft²

                 \(\boxed{length = \dfrac{Area}{width}}\)

                              \(=\dfrac{108}{9}\\\\= 12 \ ft\)

After remodeling:

               width = 9 ft

               Area = 180 ft²

             \(length = \dfrac{180}{9}\\\)

                        = 20 ft

length after remodeling = 20 ft

To find the length of the added portion, subtract the length of the living room before modeling from the length after remodeling.

    length of the added portion = 20 - 12

                                                   = 8 ft

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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Step-by-step explanation:

I just answered this. so here again :

let's start with

1 inch = 2.54 cm

1 ft = 12 in = 2.54×12 = 30.48 cm

1 yd = 3 ft = 3×30.48 = 91.44 cm

1 meter = 100 cm

this should be enough to answer the problems :

a.)

25 ft = 25 × 30.48 cm = 762 cm = 762/100 m = 7.62 m

b.)

67 m = 6700 cm = 6700/2.54 in = 2,637.795276... in

c.)

8.5 yd = 8.5 × 91.44 cm = 777.24 cm

d.)

90 cm = 90/2.54 in = 35.43307087... in

Answer:

It will take 5 hours and 5 minutes to fill the tank

Step-by-step explanation:

Here, we want to get the time taken to fill the tap

Let us have the rate per hour

A fills in 6 hours; so the fraction filled in an hour is 1/6

B fills in 8 hours, so the fraction filled in an hour is 1/8

C empties in 10 hours, so the fraction removed per hour is 1/10

So factoring the supply and removal, where removal is on a negative basis

we have it that in an hour, the fraction retained is;

1/6 + 1/8 - 1/10

= (20 + 15 - 12)/120

= 23/120

So this is the fraction retained per hour

The number of hours it will take to have a whole is simply the reciprocal of this fraction

That would simply be 120/23 = 5 5/23

5 hours and 5 minutes

Using the normal distribution, the probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.

Normal distribution refers to a continuous probability distribution wherein values lie in a symmetrical fashion mostly centered around the mean. In a normal distribution, the probability is calculated using the z-score of a measure X. A Z-score refers to a numerical measurement that defines a value's relationship to the mean (of a group of values).

In order to determine the probability of the sample proportion, the z-score of a measure X is determined.

z-score = (X - µ)/σ where µ is the mean and σ is the standard deviation.

The standard deviation σ = √(p(1-p)/n

From the given data:

n = no of random sample = 145

p = probability of success (household spending more than $125) = 0.32

Hence,

σ = √((0.32(1-0.32)/145) = 0.0387

Calculating the z-score when X = 0.3

z-score = (0.3 – 0.32)/0.0387 = -0.516

From the table, the probability of z = -0.516

P(X<z) = 0.30293 or 30.29%

The probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.

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Answer: None of the above

Step-by-step explanation:

Present value of Loan payment 1 = \($1000 / (1 + (0.12/365))^{60\)

Present value of Loan payment 2 = \($1200 / (1 + (0.12/365))^{(-30)\)

The single payment required 90 days from now to pay off the two obligations would be the total present value calculated in Step 3.

To calculate the single payment required to pay off the two obligations with a 12% interest rate, we can use the concept of present value. Present value is the current worth of a future payment, taking into account the interest rate and time.

Let's break down the given information:

Loan payment 1: $1000 due 60 days ago

Loan payment 2: $1200 due in 30 days

To find the single payment required 90 days from now, we need to calculate the present value of each payment and then add them together.

Step 1: Calculate the present value of Loan payment 1.

The time period for Loan payment 1 is 60 days ago.

To bring it to the present, we need to calculate the interest accrued for 60 days at a 12% annual interest rate.

Step 2: Calculate the present value of Loan payment 2.

The time period for Loan payment 2 is 30 days in the future.

To bring it to the present, we need to calculate the interest accrued for 30 days at a 12% annual interest rate.

Step 3: Add the present values of Loan payment 1 and Loan payment 2.

Total present value = Present value of Loan payment 1 + Present value of Loan payment 2

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The correct weekly profit of company B as represented by quadratic  inequality is as below:

y≤−50x2+19950x+20,000 y less than or equal to negative 50 x squared plus 19950 x plus 20,000

What is the initial weekly profit?

The initial weekly profit is determined as the initial price of $10 multiplied by 2,000 units sold in one week.

However, a change in price by $5, I mean an increase of $5 means that the quantity sold falls from 2,000 units to 1,990 units, however, it is evident that volume falls but the profit would increase the increase in profit by $5 on 1,990 units is more than the decrease in sales revenue by 10 units, hence, the equation should have an equal to sign and less than not just less than.

Profit after decrease of 10 units=1990*($10+$5)

Profit after decrease of 10 units=$19,950(the option that $19,950 and > or = signs is correct)

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