Jack, Marta, Rand, Todd and 6 more students went apple picking. Every two of these 10 students pick a different number of apples. Combined, the ten students pick 45 apples. Suppose Jack and Marta pick a total of 16 apples; Marta and Rand pick a total of 15 apples; Rand and Todd pick a total of 13 apples. How many apples did Todd pick

Answer: A. To find the number of glass squares each student will receive, we need to divide the total number of squares by the number of students.

We can write this as:

x = number of glass squares per student

x = 1240 / 121

B. To find the number of squares each student will receive, we need to solve for x by dividing 1240 by 121.

1240 ÷ 121 = 10.246753246753247

C. Each student will get 10 whole glass squares.

D. The remainder in this context is the number of glass squares that cannot be distributed evenly among the students. In this case, the remainder is 30. It means that there will be 30 glass squares left over after each student has received 10 squares. It's like remainder in division where after dividing 1240 by 121 the quotient is 10 and the remainder is 30.

Step-by-step explanation:

An initial investment of $580, earning 3% annually-compounded interest, will take 18.429 years (investment period) to reach $1,000.

The period for the investment to accumulate to $1,000 at 3% compounded interest is computed using an online finance calculator.

The parameters required include identifying the interest rate, compounding period, present investment, and future value., from the given formula:

A = 580(1.03)^t

$1,000 = 580(1.03)^18.429

I/Y (Interest per year) = 3%

PV (Present Value) = $580

PMT (Periodic Payment) = $0

FV (Future Value) = $-1000

Results:

N = 18.429

= 18 years and 5 months

Total Interest = $420

Thus, for the account to reach $1,000, it will take 18 years and 5 months.

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A = 580(1.03)^t

Step-by-step explanation:

the range is (-32, 28)

note that when the bubble is not filled in it should be an open bracket

[tex]T=2\pi \sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\cfrac{\sqrt{L}}{\sqrt{g}}\implies T\sqrt{g}=2\pi \sqrt{L} \\\\\\ \sqrt{g}=\cfrac{2\pi \sqrt{L}}{T}\implies (\sqrt{g})^2=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2\implies g=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2 \\\\\\ g=\cfrac{(2\pi \sqrt{L})^2}{(T)^2}\implies g=\cfrac{4\pi ^2L}{T^2}[/tex]

The equation of the line that passes through the points (-4, -6) and (9, 2) is

y = (8/13)x - 46/13.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through points (-4, -6) and (9, 2).

Let the equation of the line y = mx + c.

Now,

m = (2 + 6) / (9 + 4) = 8/13

(-4, -6) = (x, y)

-6 = (8/13) x -4 + c
-6 = -32/13 + c

c = -6 + 32/13

c = (-78 + 32)/13

c = -46/13

Thus,

The equation of the line is y = (8/13)x - 46/13.

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Answer:

(2, -1)

Step-by-step explanation:

2(2)+ (-1) = 4-1 = 3.

The XYZ axis is called as X-axis, Y-axis, and Z-axis, respectively.

The term axis in math is defined as  a line with respect to which a curve or figure is drawn, measured, rotated, etc.

Here we have given that XYZ axis, in math are no standard names for the coordinates in the three axes

Based on these the coordinates are often denoted by the letters X, Y, and Z, or x, y, and z.

And these axes may then be referred to as the X-axis, Y-axis, and Z-axis, respectively.

Here in the graph x-axis and y-axis represent the first two dimensions where as the z-axis, the third dimension. Which is also defines the x and y denote width and height and the z denotes depth.

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For given inequality, graph number 3 is correct.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.

Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the numbers on the other by adding or subtracting quantities.

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The equation  y = x + 0.4x is the retail price y in dollars for an item with the original cost and a markup of 40% .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

So, we choose the first equation.

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If Elliot purchased 3 trick cameras and 4 fake snakes for $40 and  Kaci bought 7 trick cameras and 8 fake snakes for $85 , then the system of equations that can be used to find the cost of trick camera and fake snakes are [tex]3x+4y=40[/tex] and [tex]7x+8y=85[/tex] .

Elliot purchased 3 trick cameras and 4 fake snakes for $40  ;

Kaci purchased 7 trick cameras and 8 fake snakes for  $85 ;

let the number of trick cameras purchased be = x ;

let the number of fake snakes purchased be = y ;

So , the equation for Elliot's purchase is ⇒ [tex]3x+4y=40[/tex] ;

and the equation for Kaci's purchase is ⇒ [tex]7x+8y=85[/tex] ;

Therefore , the equations to solve for the number of trick cameras and number of fake cameras are  [tex]3x+4y=40[/tex] and [tex]7x+8y=85[/tex] .

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Using the method of simple random sampling, The answer is we select sample before collecting data.

Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.

A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.

In simple random sampling, the sample size is determined before collecting data. There are several ways to determine the sample size, but one common method is to use a sample size calculation formula, such as: n = (z^2 * p * (1-p)) / e^2

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The probability that Mr. Espinoza will select the middle toll booth on Monday and Tuesday is 8%.

Probability refers to the odds of Mr. Espinoza selecting the middle toll booth on Monday and Tuesday when he could have selected toll booths 1, 2, 4, or 5.

The chances of selecting one out of five toll booths = 1/5 or 0.2

The likelihood of Monday and Tuesday out of the five working days = 2/5 or 0.4

The probability of selecting the middle toll booth on Monday and Tuesday = 1/5 x 2/5

= 0.2 x 0.4

= 0.08

= 8%

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Answer:

  10.35 kg

Step-by-step explanation:

Given a bag of sugar weighs 3.45 kg, you want the weight of 3 bags.

The weight of 3 bags will be three times as much as the weight of one bag:

  3 × 3.45 kg = 10.35 kg

Three such bags weigh 10.35 kg.

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Answer:

9 in.

Step-by-step explanation:

the sum of two sides in a triangle is always longer than the 3rd side. so 9 is the only answer that fits this condition.

The amount of GI is $35,468.

The amount of taxable income is $23,068.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Gross income = $35,468

Exemption = $12,400

Deduction = 0

Adjustment = 0

Taxable income.

= Gross income - Exemption

= 35,468 - 12,400

= $23068

Thus,

GI and taxable income are $35,468 and $23,068

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WeDeliver: The total cost of sending the parcel with WeDeliver is £64.00.

Total cost is the sum of all costs associated with a particular purchase, project, or investment. It includes the cost of materials, labor, and any other expenses incurred such as taxes, fees, and shipping. Total cost is an important factor in determining whether or not a project or purchase is feasible. When evaluating the total cost, one must consider any associated risks, such as the risk of a market downturn or currency fluctuations.

This is calculated by summing the three dimensions of the cuboid (10 cm + 20 cm + 40 cm) and then multiplying this sum by £0.80.

GoParcels: The total cost of sending the parcel with GoParcels is £48.00. This is calculated by multiplying the total area, in cm, of all 6 faces of the cuboid (10 cm x 20 cm x 2 + 10 cm x 40 cm x 2 + 20 cm x 40 cm x 2) by £0.02.

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Answer:

x = 11.2

Step-by-step explanation:

We know that the second triangle is just a smaller scale of the bigger triangle.

So, first, we take

28 divided by 25 = 1.12

Then we take

10 times 1.12 = 11.2

So, x = 11.2

The axis of symmetry of the function f(x) = -( x 9 )( x 21) is x = 15.

The axis of symmetry of a parabola is a line that divides the parabola into two exact mirror images. In this case, the parabola is defined by the quadratic function f(x) = -(x-9)(x-21). To find the axis of symmetry, we can take the average of the x-coordinates of the two solutions, which are 9 and 21. The average of 9 and 21 is 15, so the axis of symmetry is x = 15. This means that the parabola is symmetrical about the line x = 15, and the vertex of the parabola is located at the point (15,0).

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Therefore , the solution to the given problem of unitary method comes out to be he will have $870.

The unit method is a method of problem-solving that entails calculating the variable of one unit, multiplying that value, and then calculating the required value. To describe it simply, the unit method is employed to obtain a single entity value from a specified multiple. One pen costs 400 rupees, thus 40 needles would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Logic of matrices or operators, algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.

Here,

To address the issue,

if the person gets a gross biweekly salary of $840 and claims 2 extra withholding allowances,

their take-home pay would increase by $30.

thus,

They will have 840 + 30 = $870

Therefore , the solution to the given problem of unitary method comes out to be he will have $870.

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The formula becomes a times 1, which is merely a, when you swap out 0 for the exponent x. This is so because 1 equals any number raised to the power of 0. The value of a will always be the initial value for any function with this form since the initial value is the function's value with an input of 0.

By looking for an equation's constant, one can also locate initial values. Graph functions benefit from understanding the y-intercept.

Any number that is multiplied by 0 equals 1.

A number is equal to a number multiplied by 1.

The value of a multiplied by one will equal its starting value.

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The amount of money that the business will receipt is $44.

given:

Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt

From the above question:

24oz of Lemonade = 1 bottle

528 oz of Lemonade = x

Cross Multiply

24 × x = 528

x = 528/24

x = 22 bottles

We are told that: they sell each bottle for $2

Hence:

1 bottle = $2

22 bottles = y

Cross Multiply

y = 22 × $2

y = $44

Therefore, the amount of money that the business will receipt = $44

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The function f(x - 5/3) is translated 5/3 units right and the function f(x) - 5/3 is translated 5/3 units down.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, A function f(x) is transformed to f(x - 5/3) this results in f(x) is translated 5/3 units to the right along the x-axis.

And, The transformation f(x) - 5/3 is translated 5/3 units down along the y-axis.

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The process to show the vector field V(x,y,z) as conservative is show  below and the scalar potential f is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex]   .

A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .

The Gradient is vector that is made from partial derivatives of potential function .

The Vector function is given as , V(x,y,z) = [tex](yz^{2} )i + (xz^{2} )j + (2xyz)k[/tex] ,

So , we can write the partial derivatives function of potential function as :

[tex]\frac{\partial f}{\partial x} = yz^{2}[/tex] ; [tex]\frac{\partial f}{\partial y} = xz^{2}[/tex] ; [tex]\frac{\partial f}{\partial z} = 2xyz[/tex],

On Antidifferentiating any of the above three partial derivatives ,

we get ; [tex]f=xyz^{2} + C[/tex] , here the constant C can take any value ,

so , we take C as [tex]e^{\pi }[/tex] .

Therefore , the potential Function is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .

The given question is incomplete , the complete question is

Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .

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Yes, the order of the quantities in an inequality matters, and examples are given to show why.

The four inequality symbols, along with their meaning, are presented as follows:

It is known that the number 5 is greater than the number 3, hence the inequality that describes these numbers is given as follows:

5 > 3.

However, if we tried to apply the commutative property, that is, changing the order of the numbers, we would have that:

3 > 5.

Which is a false statement, as the number 3 is less than the number 5, and not more.

This shows that the order of the symbols in an inequality in fact does matter.

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Answer: To divide two rational expressions, you need to first find the least common denominator (LCD) of the two expressions. The LCD is the least common multiple of the two denominators.

In this case, the rational expressions are x/(3x-1) and (x-2)/(2x). The LCD of these two expressions is (3x-1)(2x), which can be factored as 6x(x-1).

To divide the two rational expressions, you need to express each expression as a fraction with the LCD as the denominator.

The first expression, x/(3x-1), can be rewritten as (x * (2x))/(3x-1 * (2x)) = (2x^2)/(6x^2-2x).

The second expression, (x-2)/(2x), can be rewritten as ((x-2) * (3x-1))/(2x * (3x-1)) = (3x^2-3x+2)/(6x^2-2x).

To divide these two expressions, you can divide the numerators and the denominators separately:

(2x^2)/(6x^2-2x) ÷ (3x^2-3x+2)/(6x^2-2x)

= (2x^2) ÷ (3x^2-3x+2)

= (2/3)x^2 ÷ (x^2-x+2/3)

Therefore, the quotient of the rational expressions x/(3x-1) and (x-2)/(2x) is (2/3)

Step-by-step explanation:

The paper is folded into 5 folds before the area is less than 1 square inches.

What is area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Here the area of the folded paper after n folds is,

A = 90[tex](\frac{1}{3})^n[/tex]

Now put n=0 into given formula,

A = 90[tex](\frac{1}{3})^0[/tex]=90×1 = 90 square inches.

Here Area of the paper before being fold is 90 square inches.

Now area is less than 1 square inches then

=> 90[tex](\frac{1}{3}) ^n[/tex] < 1

=> [tex](\frac{1}{3}) ^n < \frac{1}{90}[/tex]

Here if n= 4 then  [tex](\frac{1}{3}) ^4 > \frac{1}{90} = \frac{1}{81} > \frac{1}{90}[/tex] then n=5.

Hence the paper is folded into 5 folds before the area is less than 1 square inches.

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The candies left for Kyla were 10 based on the amount given to her sister and friend from total 20 candies.

Firstly we will calculate the remaining candies from twenty after giving to her sister. Next calculation will be the final answer representing candies left for Kyla herself.

Remaining candies = total number of candies - 1/5×total candies

Keep the values in formula

Remaining candies = 20 - 1/5×20

Remaining candies = 20 - 4

Remaining candies = 16

Total candies for Kyla = remaining candies - 3/8×remaining candies

Candies for Kyla = 16 - 3/8×16

Candies for Kyla = 16 - 3×2

Candies for Kyla = 16 - 6

Candies for Kyla = 10

Thus, Kyla received 10 candies.

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The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Place the arithmetic symbol between the 6 times 6 to become one. Then we have

⇒ 6 + 6 - 6 - 6 + 6 / 6

⇒ 1

The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.

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a. The current sale price for the computer system is given as follows: $618.4.

b. The amount paid by the club members, with the discount, is given as follows: $587.48.

The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.

The selling price is of:

$773.

The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:

0.8 x 773 = $618.4.

Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:

0.95 x 618.4 = $587.48.

The problem is given by the image presented at the end of the answer.

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The percentage of people who are satisfied with the car are 60%.

In mathematics →

Given is that in a survey of 2000 people who owned a certain type of​ car, 1200 said they would buy that type of car again.

The percentage of people who are satisfied with the car are -

{x}% = (1200/2000) x 100

{x}% = (12/20) x 100

{x}% = 12 x 5

{x}% = 60

Therefore, the percentage of people who are satisfied with the car are 60%.

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