14 1/2 x 6 1/2 x 6 1/2

The trade discount rate for the wholesaler at the net price is 0.45 or 45%.

A trade discount is a cut in the list price of products or services provided by a seller to a customer who makes frequent or significant purchases of such items. A trade discount is intended to encourage the customer to make further purchases from the supplier. The discount might change depending on the volume or regularity of purchases and is often given as a percentage of the list price. Retailers or wholesalers that purchase products from producers or suppliers to resell to consumers frequently receive trade discounts.

The discount rate is given by the following formula:

Trade Discount Rate = (List Price - Net Price) / List Price

Substituting the given values, we get:

Discount Rate = (13600 - 7480) / 13600

Discount Rate = 0.45 or 45%

Hence, the trade discount rate for the wholesaler is 0.45 or 45%.

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Answer: 59, 218

Step-by-step explanation:

5 ten thousands = 50,000

9 thousands = 9,000

2 hundreds = 200

1 ten = 10

8 ones = 8

50,000 + 9,000 + 200 + 10 + 8 = 59,218

Answer: 59,218

Step-by-step explanation:

The number that has 5 ten thousands, 9 thousands, 2 hundreds, 1 ten, and 8 ones is 59,218.

Answer:

$36,500 per employee

Step-by-step explanation:

$730,000/20 employees

Answer: They all have the same unit rate

Step-by-step explanation:

3:1 is the unit rate if you multiply it by 2, it's 6:2. If multiplied by 3, it is 9:3. Multiplied by 4, its 12:4

Answer:

-7 and -1

Step-by-step explanation:

Remember, a negative times a negative equals a positive

Using expressions, we get that$836 will be paid in total throughout the first 12 months.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression.

Given is that the starting balance is 62. As a result, the sum rises by 4%.

The time period is 12, but he will pay for 11 extra months, not including the first month's 62 dollars.

The formula is: y=62(1+0.11

y=62(1.04) ^11

The amount to be paid in the previous month is: y=95.45$

This geometric sequence has r equal to 1.04 in this case. The total will be determined as follows:

Sum = 62(1.04¹¹-1)/1.04-1

Sum = $836

Hence, $836 will be paid in total throughout the first 12 months.

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The probability that the next person will purchase no costume is 80%.

What is the difference between a probability and an odds?

The possibility of an event occurring can be expressed using odds and probability, but they are computed and understood in different ways.

Probability, which is stated as a number between 0 and 1 (or between 0% and 100%), is the possibility that an event will occur. By dividing the number of positive possibilities by the total number of potential outcomes, the probability of an event happening is determined.

The possibility of an event happening is expressed differently by odds, which are expressed as a ratio of the number of favourable events to the number of negative outcomes. It is possible to state odds as "odds for" or "odds against."

Now,

The total number of visitors who purchased costumes is:

71 (exactly one) + 12 (more than one) = 83

The total number of visitors who did not purchase a costume is: 349

The probability that the next person will purchase no costume is:

349 / (349 + 83) = 349 / 432 ≈ 0.8079

Hence, the probability that the next person will purchase no costume is 80%.

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Answer:

1a. Decay

1b. r = 0.43

1c. a = 35

1d. y = 6.481755

2a. Growth

2b. r = 2.23

2c. a = 225

2d. y = 340.4025

Step-to-Step Explanation:

1.

  (a)Decay

  (b) [tex]y=a(1-r)^{x}[/tex]

       r = rate of decay, a is the initial value

       1-r=0.57 = r=1-0.57 = r = 0.43

  (c) a = 35

  (d) [tex]y=35(0.57)^{3}\\\\y=35(0.185193)\\y=6.481755[/tex]

2.

   (a) Growth

   (b)[tex]y=a(1+r)^{x} \\[/tex]

        r = rate of growth, a is the initial value

         1+r=1.23 = r=1+1.23 = r = 2.23

   (c) a = 225

   (d) [tex]y=225(1.23)^{2} \\y=225(1.5129)\\y=340.4025[/tex]

Problem 1

Set the base of the exponent equal to 1+r and solve for r.

1+r = 0.57

r = 0.57-1

r = -0.43

The result is negative, which tells us we have exponential decay. Notice that b = 0.57 fits the interval 0 < b < 1.

The rate of decay is 43%

The initial value is a = 35 since this is the first value mentioned in the equation. Plugging x = 0 into the equation will lead to y = 35.

Let's now plug in x = 3

y = 35*(0.57)^x

y = 35*(0.57)^3

y = 35*0.185193

y = 6.481755

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

======================================================

Problem 2

We'll follow similar steps as problem 1.

1+r = 1.23

r = 1.23-1

r = 0.23

The r value is positive, so we have growth this time. Notice that b = 1.23 fits the interval b > 1.

The growth rate is 23% since r = 0.23 converts to this.

The initial value is a = 225. Compare y = a(1+r)^x to y = 225(1.23)^x to see how the terms match up. If you want you can think of it like y = 225(1+0.23)^x. Plugging x = 0 into the equation will lead to y = 225.

Let's plug in x = 2.

y = 225*(1.23)^x

y = 225*(1.23)^2

y = 225*1.5129

y = 340.4025

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

The required values of exponent a, b, and c are 6, 8, and 9 respectively.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Given expression,
[tex][x^{24}y^{32}]^{1/4} \times (x^{-3}z^{27})^{1/5} = x^ay^bz^c[/tex]

We have to determine the value of a, b, and c in the exponents, so in order to get the solution we have to simplify the given expression.

[tex][x^{7}y^{8}] \times (x^{-1}z^{9}) = x^ay^bz^c\\x^{7 -1}y^8z^9 = x^ay^bz^c\\x^{6}y^8z^9 = x^ay^bz^c[/tex]

Comparing the exponent across the equal sign we get,
a = 6
b = 8
z = 9

Thus, the required value of exponent a, b, and c are 6, 8, and 9 respectively.

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It would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

A square meter is a unit of measurement that denotes the surface area of a two-dimensional object or surface that is one metre long and one meter broad. It is frequently used to determine the dimensions of rooms, structures, and other areas as well as the surface area of land or other objects. The imperial method of measurement converts one square metre into 10.764 square feet. Science, engineering, and other fields frequently utilise the square metre, a core unit of the International System of Units (SI).

The area of the room is:

Area = 5m x 5m = 25 square meters

Then, we multiply the area by the cost per square meter:

Cost = 25 square meters x N5.00 per square meter = N125.00

Hence, it would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

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Amount of money do you need to save to purchase the home is  $15,000. The total amount the bank will be loaning you is $235,000.  You can expect to pay around $1,332.29 per month.

A down payment is a payment made upfront when purchasing a large ticket item, such as a home or a car. It is a percentage of the total purchase price that the buyer pays out of their own pocket, with the remainder of the price financed through a loan.

To calculate the down payment, we need to multiply the purchase price by the percentage:

Down payment = 0.03 x $250,000 = $7,500

To calculate the closing costs, we also need to multiply the purchase price by the percentage:

Closing costs = 0.03 x $250,000 = $7,500

So the total amount of money needed to purchase the home is the sum of the down payment and the closing costs:

Total cost = $7,500 + $7,500 = $15,000

The amount the bank will be loaning you is the purchase price minus the down payment and the closing costs:

Loan amount = $250,000 - $15,000 = $235,000

To calculate the monthly payments, we need to use the formula for a fixed-rate mortgage:

M = P [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ⁻¹]

where:

M = monthly payment

P = loan amount

i = monthly interest rate (5.5% / 12 = 0.0045833)

n = total number of payments (30 years x 12 months = 360)

Plugging in the numbers, we get:

M = $235,000 [ 0.0045833(1 + 0.0045833)³⁶⁰ ] / [ (1 + 0.0045833)³⁶⁰ – 1]

M ≈ $1,332.29

So you can expect to pay around $1,332.29 per month for 30 years to pay off the mortgage.

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A point that represents the ordered pair (0, -3) is: D. Point G.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the ordered pair (0, -3), we can logically deduce that the coordinates would be located in quadrant IV as shown in the image attached below.

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With the discount, each dresser would cost $450.

What is the discount?

A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. It is a form of incentive that is used to encourage customers to purchase goods or services, often by making them more affordable or attractive.

To calculate the amount of discount off each item, we need to know the original price of each dresser and the percentage discount that is being offered. Let's assume that the original price of each dresser is $500, and the discount being offered is 10%.

To calculate the discount off each item, we can use the following formula:

Discount amount = Original price x Discount rate

where the discount rate is the percentage discount expressed as a decimal (e.g., 10% = 0.1).

So, for each dresser, the discount amount would be:

Discount amount = $500 x 0.1 = $50

Therefore, each dresser would be discounted by $50. This means that the new price for each dresser would be:

New price = Original price - Discount amount

New price = $500 - $50 = $450

Hence, with the discount, each dresser would cost $450.

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The single transformation that maps shape A onto shape C is a translation of 4 units to the right.

A single transformation is a mathematical operation that changes the position, orientation, or size of a geometric figure. It can be a translation, reflection, rotation, or dilation. It is a way to describe how a figure is transformed to obtain a new figure.

To map shape A onto shape C, we need to perform a sequence of transformations.

First, shape A is reflected in the line x = 2 to give shape B. This is a reflection in the vertical line passing through x = 2.

Next, shape B is reflected in the line x = 6 to give shape C. This is a reflection in the vertical line passing through x = 6.

To find the single transformation that maps shape A onto shape C, we can combine these two reflections into a single transformation.

The composition of two reflections in vertical lines is a translation.

In this case, the distance between the vertical lines x = 2 and x = 6 is 4 units. Since shape A is reflected in the first vertical line and shape C is reflected in the second vertical line, the movement is from the first line to the second line, which is to the right.

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The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let three consecutive numbers are, (x - 1) , x , (x + 1).

Hence, By given condition we get;

⇒ (x - 1)² + 2 (x + x + 1) = 38

⇒ x² - 2x + 1 + 4x + 2 = 38

⇒ x² + 2x - 35 = 0

⇒ x² + 7x - 5x - 35 = 0

⇒ x (x + 7) - 5 (x + 7) = 0

⇒ (x - 5) (x + 7) = 0

⇒ x = 5 or x = - 7

When, x = 5

All the integers are,

x - 1 = 5 - 1 = 4

x = 5

x + 1 = 5 + 1 = 6

When x = - 7

All the integers are,

x - 1 = - 7 - 1 = - 8

x = - 7

x + 1 = - 7 + 1 = - 6

Thus, The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

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The role of GCF, its placement and verification has been explained below. The solution has been obtained by using the concept of Greatest Common Factor.

The greatest common factor, or largest number, is the product of two or more numbers (GCF). The greatest number (factor) that separates them yields a natural number.

1. The GCF is a factor that all terms in a polynomial share.

For instance, if the polynomial has the form R * S + R * T, the GCF is R because both terms share the factor R.

2. The GCF is positioned in front of the remaining polynomials, outside of the parenthesis, once we have factored out the GCF.

R * S + R * T, given the prior example, is R (S + T).

3. By allocating the GCF to the polynomial enclosed in parenthesis, we can verify that our factoring is accurate.

Hence, the above stated is the role of GCF in factoring a polynomial.

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Answer: question 1 is 62° and radius is 1.0821  

question 2 is 454.91794m

question 3 is 855.57622m

Step-by-step explanation:

Given c=969 and ∠α=28°,

a = 454.91794

b = 855.57622

∠β = 62° = 1.0821 rad

h = 401.6687

area = 194,608.48704

perimeter = 2,279.49416

inradius = 170.74708

circumradius = 484.5

im only in 8th grade so don't trust me on this but i think im right

Answer:

It is impossible, because u can say x is 5 and y is 1 or x is 9 and y is 3

The value of the variables are as follows:

The value of the variables is given as follows:

sin 45° = 39/z

z = 39/sin 45°

sin 45° = 1/√2

z = 39 / 1/√2

z = 39√2

Let the height of the triangle be h;

cos 45 = h/39√2

cos 45 = 1/√2

h = 39√2 * 1/√2

h = 39

tan 60° = 39/y

tan 60° = √3

y = 39/√3

y = 13√3

sin 60° = 39/x

x = 39 / sin 60°

sin 60° = √3/2

x = 39 /√3/2

x = 26√3

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Yes, 5x=7y is a linear equatiοn.

First οrder equatiοns include linear equatiοns. In the cοοrdinate system, the linear equatiοns are defined fοr lines. A linear equatiοn in οne variable is οne in which there is a hοmοgeneοus variable οf degree 1 (i.e., οnly οne variable). Multiple variables may be present in a linear equatiοn. Linear equatiοns in twο variables, fοr example, are used when a linear equatiοn cοntains twο variables.

Linear equatiοn is an algebraic equatiοn in οne οr mοre variables where the pοwer οf each variable is less than οr equal tο 1.

Fοr example,

y = mx + c , an equatiοn in this fοrm can be called as linear equatiοn.

Sο in equatiοn 5x = 7y

We can write this equatiοn as 7y = 5x + 0.

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Step-by-step explanation:

Since u and w are orthogonal, their dot product is 0. Thus,

u · w = 0

Using the Pythagorean Theorem,

||u - w||^2 = ||u||^2 + ||w||^2 - 2(u · w)

Since u and w are unital (i.e., their lengths are 1), we have

||u||^2 = ||w||^2 = 1

Substituting these values and u · w = 0, we get

||u - w||^2 = 1 + 1 - 0 = 2

Taking the square root of both sides, we get

||u - w|| = √2

Therefore, we have shown that if u and w are unital orthogonal vectors, then ||u - w|| = √2.

By analytic geometry, the equation of the line y = - (1 / 12) · x + 11 is perpendicular to the line y = 12 · x + 3.

In accordance with analytic geometry, lines are described by algebraic equations of the form:

y = m · x + b

Where:

The relationship between the slopes of two perpendicular lines:

m · m' = - 1

First, write the original line:

y = 12 · x + 3

Second, write the slope and the intercept of the original line:

m = 12, b = 3

Third, the slope and the intercept of the perpendicular line:

m = - 1 / 12, b = 11

Fourth, write the equation of the perpendicular line:

y = - (1 / 12) · x + 11

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Answer:

am not sure

Step-by-step explanation:

I will help you but yeh so y=20

The evaluation of the inequalities are presented as follows;

2. x ≤ -5

3. x  ≤ -14

4. x ≤ 4

5. x < -10

An  inequality is an expression or comparison of two expressions that posses different values using an inequality sign.

2. -14·x + 1 ≥ 71

-14·x + 1 - 1 ≥ 71 - 1

-14·x  ≥ 70

x ≤ 70/(-14) = -5

x ≤ -5

3. -3·x - 1 ≥ 41

-3·x - 1  + 1 ≥ 41 + 1 = 42

-3·x - 1  + 1 ≥ 42

-3·x  ≥ 42

x ≤ 42/(-3) = -14

x ≤ -14

4. (x/2) + 11 ≤ 13

(x/2) + 11  - 11 ≤ 13 - 11  = 2

x/2  ≤ 2

x ≤ 2 × 2

x ≤ 4

5. x/(10) - 6  < -7

x/(10)  - 6 < -7

x/(10) -6 + 6 < -7 + 6 = -1

x/(10) < -1

x  < -10

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Answer: H: (7, 1)

Step-by-step explanation: If the endpoints of A and B are (3, 5) and (11, -3), you just have to find the middle of the x and y coordinate for each endpoint. The middle of 3 and 11 is 7, and the middle of -3 and 5 is 1, therefore the middle point would be (7, 1).

The ratio as fraction is 36/ 55.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have to find the ratio for  3 feet to 55 inches.

So, 3 feet to 55 inches

= 3 feet/  55 inches

= 3 feet : 55 inches

= 3 x 12 inches : 55 inches

= 36 inches : 55 inches

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The probability that at least 5 of the callers received a busy signal is given as follows:

0.3712 = 37.12%.

The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

n = 1000, p = 0.004.

The probability of less than 5 busy signals is:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X < 5) = 0.6288.

Hence the probability of at least 5 busy signals is of:

P(X >= 5) = 1 - P(X < 5)

P(X >= 5) = 1 - 0.6288

P(X >= 5) = 0.3712.

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A) R = -19t + 1890 B) 11 years from now, the total oil reserves will be 1681 billions of barrels. C)  The world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now.

The slope of a line represents the rate of change between the x and y variables, or the rise over the run. A positive slope means that the line is increasing from left to right, while a negative slope means that the line is decreasing from left to right. A slope of zero means that the line is horizontal, while an undefined slope means that the line is vertical.

A) The rate of decrease in oil reserves is 19 billion barrels per year, which can be represented as a slope of -19. The initial oil reserves are 1890 billion barrels, which is the y-intercept. Therefore, the linear equation for the total remaining oil reserves R, in terms of t (the number of years since now) is:

R = -19t + 1890

B) To find the total oil reserves 11 years from now, we can substitute t = 11 into the equation:

R = -19(11) + 1890

R = -209 + 1890

R = 1681 billion barrels

Therefore, 11 years from now, the total oil reserves will be 1681 billions of barrels.

C) If no other oil is deposited into the reserves, the reserves will be completely depleted when R = 0. We can use the linear equation to find how long it will take for the reserves to reach 0:

0 = -19t + 1890

19t = 1890

t = 99.47 years

Therefore, the world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now, assuming no new reserves are discovered or added.

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Answer:

E

Step-by-step explanation:

Acellus