Edna has been keeping an eye on an emerald ring she likes. She just noticed that it has been marked down to $28,394.70, which is 27.1% less than its original price. What was the original price of the ring?
Round your answer to the nearest cent.

(a) Commuters take both the bus and the subway = 10

(b) commuters take only the subway = 1120

What is a set?

A set is a collection of well-defined objects or elements. A set is represented by capital letter and their elements is represented by small letters.

Let U be the set representing the number of commuters in New york.

⇒n(U) = 1900

Let A be the set representing the commuters take subway

⇒n(A) = 1130

Let B be the set representing the commuters take bus

n(A) = 650

130 commuters do not take either the subway or the bus,

(a) commuters take both the bus and the subway

n(A∪B)=n(A) + n(B) - n(A∩B)

n(A∪B)=n(U)-130⇒1900-130=1770

1770=1130+650-n(A∩B)

⇒n(A∩B) = 10

(b) Commuters take only the subway,

n(A)-n(A∩B) = 1130-10=1120

Hence, commuters take both the bus and the subway is 10

commuters take only the subway is 1120

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a = 281.25 Gm / (1 - (-0.57)²) = 667.3 Gm

b = √(667.3 Gm² * (-0.57)²) = 420.3 Gm

c = √(667.3 Gm² - 420.3 Gm²) = 558.0 Gm

What is the hyperbola?

Hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.

To calculate the parameters a, b, c, and e for a hyperbolic orbit, we need to know the perihelion distance (p), semi-latus rectum (l), and eccentricity (e) of the orbit.

l = p / (1 + e)

where e is the eccentricity of the orbit. We can solve for e using the given distances:

e = (p - l) / l = (120 Gm - 281.25 Gm) / 281.25 Gm = -0.57

a = l / (1 - e²)

b = √(a^2 * e²)

c = √(a^2 - b²)

a = 281.25 Gm / (1 - (-0.57)²) = 667.3 Gm

b = √(667.3 Gm² * (-0.57)²) = 420.3 Gm

c = √(667.3 Gm² - 420.3 Gm²) = 558.0 Gm

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Answer:

Step-by-step explanation:

[tex]a_{1} =10\\a_{n}=-4a_{n-1}\\put~n=2,3,4\\a_{2}=-4a{1}=-4(10)=-40\\a_{3}=-4a_{2}=-4(-40)=160\\a_{4}=-4a_{3}=-4(160)=-640[/tex]

[tex]f(t) = 4 (1.25)^{t+3} = 4 \cdot (1.25)^{3} \cdot (1.25)^{t}[/tex] using the exponent rule [tex]a^n\cdot a ^m = a^{n+m}[/tex] in reverse.  (Using the rule to split apart the exponent.

Continuing to calculate out some values,

[tex]f(t) = 4 \cdot (1.25)^{3} \cdot (1.25)^{t} = 4 \cdot 1.953125 \cdot (1.25)^{t} = 7.8125 \cdot (1.25)^{t}[/tex]

So, [tex]f(t) = 7.8125 \cdot (1.25)^{t}[/tex] or [tex]f(t) = 7.81 \cdot (1.25)^{t}[/tex] rounded to the nearest hundredth.

Since the b-value is greater than 1, this is exponential growth.

The b-value of 1.25 means that for each increase by 1 unit in the t-value, the y-value will become 125% of what it had been.  The output will grown by 25%, which is your percent rate of change.

The b-value of your function is always a measurement from 100% or b=1.  

Answer:

D.

Step-by-step explanation:

The two parallel sides of the trapezoid are referred to as the bases of the trapezoid; the other two sides are called the legs of the trapezoid.

Therefore, the answer is D.

Hope it helped!

Answer:

Step-by-step explanation:

multiple by the domanatior to get the answer

The outputs for the given inputs are:

Input:   -2  -1   0  1

Output: 2   2  0  4

What is a linear function?

A linear function is a mathematical function that has a constant rate of change, or slope, between its input and output variables. In other words, the output of a linear function changes at a constant rate as the input changes.

The given function y = x(x + 3) is not a linear function because it contains a squared term (x^2) and thus has a non-constant rate of change.

To complete the table for the given function, we substitute each input value into the equation and simplify:

Input: -2

Output: (-2)(-2 + 3) = 2

Input: -1

Output: (-1)(-1 + 3) = 2

Input: 0

Output: (0)(0 + 3) = 0

Input: 1

Output: (1)(1 + 3) = 4

Therefore, the outputs for the given inputs are:

Input:   -2  -1   0  1

Output: 2   2  0  4

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Answer:

$100 account

Step-by-step explanation:

to double, $100 only need to earn 100 in interest, while $1000 account will need earn $1000 in interest.  because the interest is the same for both, so the $100 account will double first

A. The current account balance is a deficit of 130

B. The financial account balance is a deficit of 70

C. The trade balance is a deficit of 50.

D. The net factor payments are a deficit of 30.

Balance of payments is the method by which countries measure all of the international monetary transactions within a certain period.

(a) The current account balance can be calculated as follows:

Current Account Balance = (Exports of goods + Service exports) - (Imports of goods + Service imports + Income payments to foreigners - Income receipts from abroad)

= (275 + 50) - (325 + 40 + 70 - 40)

= 325 - 455

= -130

So, the current account balance is a deficit of 130.

(b) The financial account balance can be calculated as follows:

Financial Account Balance = Increase in home country assets abroad - Increase in foreign assets in home country

= 350 - 420

= -70

So, the financial account balance is a deficit of 70.

(c) The trade balance can be calculated as follows:

Trade Balance = Exports of goods - Imports of goods

= 275 - 325

= -50

So, the trade balance is a deficit of 50.

(d) The net factor payments can be calculated as follows:

Net Factor Payments = Income receipts from abroad - Income payments to foreigners

= 40 - 70

= -30

So, the net factor payments are a deficit of 30.

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a). The formula that expresses v in terms of t is v = 22 - 2t, b).  As t increases from 3 to 5, v varies from 16 to 12, c). As t varies from 3 to 5, v changes by 16 - 12 = 4.

What is the volume?

'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3, etc. Sometimes, volume is also termed capacity.

a). The volume of water in the tank, v, decreases by 2 gallons per hour, so the formula for v in terms of t is v = 22 - 2t.

b). As t increases from 3 to 5, v varies from 16 to 12. That is, as t goes from 3 to 5, v decreases from 22 - 2(3) = 16 to 22 - 2(5) = 12.

c). As t varies from 3 to 5, t changes by 5 - 3 = 2, and v changes by 16 - 12 = 4.

Hence,  a). The formula that expresses v in terms of t is v = 22 - 2t, b).  As t increases from 3 to 5, v varies from 16 to 12, c). As t varies from 3 to 5, v changes by 16 - 12 = 4.

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Answer:

Below

Step-by-step explanation:

Gravel is  4 / (4+3+2) = 4/9 ths of the total

    4/9 x 27 m^3 = 12 m^3 gravel

Similarly  sand is 3/9th    3/9 * 27 = 9 m^3

  and the rest is cement   6 m^3

The complete equation is 2Fe(s) + 3Cl₂(g) -> 2FeCl₃(s) ΔH = -400 kJ

A thermochemical equation is a chemical equation that includes information about the energy change that occurs during a chemical reaction. The energy change is represented by the symbol ΔH (delta H), which stands for the change in enthalpy, or heat energy, of the system. The equation shows the reactants on the left side and the products on the right side, and includes the amount of heat energy evolved or absorbed during the reaction.

For example, consider the reaction:

2H2(g) + O2(g) → 2H2O(l) ΔH = -571 kJ/mol

This equation shows that two molecules of hydrogen gas react with one molecule of oxygen gas to form two molecules of liquid water. The reaction releases 571 kJ of heat energy per mole of hydrogen and oxygen that react.

The complete thermochemical equation for the reaction of Fe(s) with Cl₂(g) to form FeCl₃(s) is:

2Fe(s) + 3Cl₂(g) -> 2FeCl₃(s) ΔH = -400 kJ

This means that the reaction releases 400 kJ of energy for each mole of Fe(s) that reacts. The negative sign indicates that the reaction is exothermic, meaning it releases heat.

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Answer:

Step-by-step explanation:

The area of Mrs Brown’s classroom is

63 m2

. The area of Mr Black’s

classroom is 64 m2

. Mr Black’s

classroom is bigger.

The amount of the sales tax is $9.75.

The percentage is defined as a ratio expressed as a fraction of 100.

The taxable amount of the sale: $150

Sales tax percentage: 6.5%

To calculate the sales tax, you can multiply the taxable amount of the sale by the sales tax percentage.

Sales Tax = Taxable Amount × Sales Tax Percentage

Sales Tax = $150 × 6.5%

Sales Tax = $150 × 0.065

Apply the multiplication operation, and we get

Sales Tax = $9.75

So, the amount of the sales tax is $9.75.

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Answer:

about 1.67

Step-by-step explanation:

24x=40

A polynomial f (x) of degree 4 that has the following zeros, 0, 6 (multiplicity 2), -2 is: x (x+2) (x-6)²

A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminate's and coefficients. Nearly all areas of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

given that,

a polynomial f(x) of degree 4 and has the zeros are 0, 6 (multiplicity 2), -2

We know that If a polynomial P(x) is, of degree 4 and has Zeros are a, b, c (multiplicity 2) then polynomial P(x) will be:

P(x) = (x - a)' (x - b)' (x - c)²

P(x) = (x - a)' (x - b)' (x - c)²

So, here polynomial of degree 4 will be:

F(x) = (x- (-2)) [x-6]² (x-0)

F(x) = x (x+2) (x-6)²

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The complete statement is -

If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.

Elastic demand is when the price of a product has a large impact on the quantity purchased.

Given is that the demand for apples is highly elastic and the supply is highly inelastic.

If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.

Therefore, the complete statement is -

If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.

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Answer:

She received a 35% discount    :)).  

Step-by-step explanation:

By applying probability concept, it can be concluded that the experimental probability of rolling each is P(1) = 1/6, P(2) = 1/7,  P(3) = 1/3,  P(4) = 2/21,  P(5) = 1/7, and P(6) = 5/42.

Probability is a value used to measure the degree of occurrence of a random event.

P(E) = n(E)/n(S)

n(E) = number of desired events

n(S) = total number of events

We have the following information about a die rolling 42 times:

One    Two    Three   Four     Five     Six

 7          6          14         4          6        5

The theoretical probability of rolling any number on a six-sided die is  7/42 or 1/6.

Now we can calculate the probability of each side by substituting the value in the table into the equation:

P(E) = n(E)/n(S)

P(1) = 7/42

      = 1/6

P(2) = 6/42

      = 1/7

P(3) = 14/42

      = 1/3

P(4) = 4/42

      = 2/21

P(5) = 6/42

      = 1/7

P(6) = 5/42

Thus, the experimental probability of rolling each is P(1) = 1/6, P(2) = 1/7,  P(3) = 1/3,  P(4) = 2/21,  P(5) = 1/7, and P(6) = 5/42.

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The list in highest tο lowest οrder is as follows :

0.2

27%

25​

Percentage is a way οf expressing a number as a fractiοn of 100. It is often used to cοmpare or describe relative values, such as prοportions, growth rates, or percentages of a whole.

Percentage is calculated by dividing a part of sοmething by the whole and then multiplying by 100. Fοr example, if a class has 25 students and 5 οf them are absent, we can find the percentage οf absent students by dividing the number οf absent students (5) by the tοtal number of students (25) and then multiplying by 100

Accοrding to given information:

The list in οrder from highest to lowest is:

0.2

27%

25​

Petruta Ciοran 13

8%

0.19 << < < <<

4

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The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.

What is plane?

In two dimensions, a plane can continue on forever. The lack of breadth. A plane is an example of coordinate geometry. A point's location in a plane is determined by its coordinates.

A plane is a two-dimensional, flat surface that never ends in mathematics. A plane is a two-dimensional equivalent of a three-dimensional equivalent that contains three spatial dimensions, a line, and a point. Planes can resemble subspaces in some higher-dimensional situations, as if the room's walls had been substantially stretched. These walls have their own existence, exactly as in the context of Euclidean geometry.

A flat surface in three dimensions can be represented using the plane equation. There are several approaches for determining the equation for a given function.. The equation for the plane can be expressed in either cartesian form or vector form.

Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0

Now,

For given two points in (x1,y1),(x2,y2) in coordinate plane

distance between them will be = √((x2-x1)²+(y2-y1)²)

So, distance between  N=(-2,-1) and L=(3,-4)=√((3+2)²+(-4+1)²)

=√(25+9)

=√34

hence,

          The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.

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Answer:

351.68

Step-by-step explanation:

Given:

The radius of the cylinder = r = 4 cm

Height of the cylinder = h = 7 cm

The volume of the cylinder is given by the formula:

V = πr²h

Using π = 3.14

so, the volume of the cylinder will be:

[tex]3.14 X4^{2} X7 = 3.14 X 16 X 7 = 351.68[/tex]

Volume of the cylinder = 351.68

The approximate circumference of the smaller circular base, in the remaining section of the cone, is c. 3.36 feet.

To find the circumference, the formula is :

= π x diameter

So, you need to find the diameter of the smaller circle. If a distance of 14 feet corresponds to 3 feet of diameter , then 5 feet to the smaller circle would be :

= ( 5 x 3 ) / 14

= 1. 0714 feet

The circumference is therefore :

= 3. 14 x 1. 0714

= 3. 36 feet

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The cost of the meal that cost $40 in 2000 would have cost $32.16 in 1992.

The average rate at which the prices of goods and services change within a year is called the average inflation rate.

Given that, a meal in a restaurant cost $40 in 2000, we need to find its price in 1992 dollars,

The dollar had an average inflation rate of 2.45% per year between 1992 and today,

The year change = 2000 - 1992 = 8

Therefore, the $40 in 1992 =

= 40 - (40 × 8 × 2.45 / 100)

= 40 - (7.84)

= 32.16

Hence, the cost of the meal that cost $40 in 2000 would have cost $32.16 in 1992.

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We can use trigonometry to find the length of side SU in triangle TSU. We can use the tangent function, where tangent is equal to the opposite side divided by the adjacent side. In this case, the opposite side is SU and the adjacent side is ST.

What is basic trigonometry?

The study of the relationship between the sides and angles of the right-angle triangle is the main objective of the field of mathematics known as "trigonometry." Trigonometric formulas, functions, or identities can consequently be used to determine the missing or unknowable angles or sides of a right triangle.

We know that angle TUS is 37 degrees, so we can use that angle to find the tangent of the angle:

tan(37) = SU / 0.6

Solving for SU:

SU = 0.6 * tan(37)

The exact length of SU can be found by using a calculator or a table of trigonometric values. To a good approximation, the value of SU is approximately 0.73.

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Answer: (b) To find the cost per lock, we need to divide the total cost by the number of locks.

For Home Hardware, the cost per lock is 120 / 4 = $30.00.

For Rona, the cost per lock is 192 / 6 = $32.00.

So, Home Hardware has the lower cost per lock at $30.00, compared to Rona's cost of $32.00.

(i) Some other factors to consider when buying a lock include:

Security: The level of security offered by the lock is important to consider, especially for locks that will be used for homes, businesses, or other valuable assets.

Durability: It's important to choose a lock that is durable and resistant to weather and wear-and-tear.

Ease of use: Consider the ease of use of the lock, including how easy it is to install and how user-friendly the lock mechanism is.

Brand reputation: Consider the reputation of the brand, as well as customer reviews and ratings of the product.

Warranty: Look for a lock that comes with a warranty, and consider the length and terms of the warranty.

Step-by-step explanation:

The value of x such that the probability of the sample mean being between 13.6-0.89 and 13.6+0.89 is 0.6827 is approximately x = 0.89.

Central Limit Theorem states that as the sample size increases the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, for a sample of 8 two-lined salamanders, the standard deviation of the sample means is:

σ = σ/√n = 2.2/√8 = 0.89

We are looking for the value of x such that the probability of the sample mean being between 13.6-x and 13.6+x is 0.6827. This corresponds to the area under the normal curve within x standard deviations of the mean.

We can use a standard normal table or calculator to find the value of x corresponding to 0.6827. The result is approximately x = 0.89.

So, the value of x such that the probability of the sample mean being between 13.6-0.89 and 13.6+0.89 is 0.6827 is approximately x = 0.89.

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The estimated overhead costs for ICU and other are $970 per patient day, or $19,400,000 divided by 20,000 patient days.

There is a connection between one set of values about one variable and an other number of values. direct variation With the equations y = mx + b, you have the direct variant function y = mx (often written y = kx). Equations that describe the relation between independent variables in a language also explain how those variables vary between one another. There are various types of variations, including linear, inverse, joint, among combination variations. If y and x are said to be directly connected, then y must equal kx, where k is a number that is every now and again referred to as the perpetual of variation. If y and x have such an inverse connection, then y equals k/x, where k is just the variance constant.

given

1a. Every patient day, the predetermined overhead rate is $970.

compute the combined expected overhead expenses for the ICU and other:

ICU: $3,200,000 plus $236 each patient-day multiplied by 2,000 patient-days equals $3,672,000.

$14,000,000 plus ($96 for each patient day)

(15,728,000 patient-days) divided by 18

Add the anticipated overhead expenses for ICU and Other:

$3,672,000 + $15,728,000 = $19,400,000

19,400,000 divided by 20,000 patient days equals 970 each patient day.

1b. The overall expense allocated to Patients A and B.

The estimated overhead costs for ICU and other are $970 per patient day, or $19,400,000 divided by 20,000 patient days.

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The given statement is False because if the price of avocados increases by 11% for four consecutive months, then the price of avocados did not increase by 48.64% over the four-month period.

If the price of avocados increases by 11% for four consecutive months, then the price of avocados did not increase by 44% over the four-month period. The calculation of percentage increase is cumulative, meaning that the increase in price in the second month will be based on the increased price from the first month, and so on.

In this case, if the price starts at $1 and increases by 11% each month, the price after four months will be $1 * 1.11 * 1.11 * 1.11 * 1.11 = $1.4864, which represents an increase of 48.64% over the four-month period, not 44%.

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