You are baking cupcakes for your class. There are 30 total students in your class and you have baked 15 cupcakes. Write and
solve an equation to find the additional number of cupcakes you need to bake in order to have 3 cupcakes for each student.
Write your equation so that the units on each side of the equation are cupcakes per student.
Equation:
= 3
Number of cupcakes: x=

Answer:

\(\huge\boxed{\sf 1}\)

Step-by-step explanation:

f(x) = 3x - 4

Put x = 3

f(3) = 3(3) - 4

f(3) = 9 - 4

Also,

g(x) = x²

Put x = 2

g(2) = (2)²

Subtract Eq. (2) from Eq. (1)

= 5 - 4

\(\rule[225]{225}{2}\)

Answer:

F(3) -g(2) = 1

Step-by-step explanation:

F(3)= 3(3) -4= 5

g(2)= \(2^{2}\) = 4

f(3) -g(2)= 5-4 =1

The best definition of random variation is: "Common variation inherent in a process occurring by chance."

In mathematics, random variation refers to the inherent variability that arises in the outcome of a random experiment. It is a type of natural variability that cannot be predicted with certainty and is due to chance. For example, if we toss a fair coin multiple times, we can expect to see some variation in the number of heads and tails that appear, even though the coin is fair and each toss is independent of the previous ones. This variation is random and follows a probability distribution that can be modeled mathematically. Understanding random variation is important in statistical inference and modeling, as it allows us to estimate the uncertainty in our results and make informed decisions based on probabilistic reasoning.

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Volume of the cube  is 840 cubic centimeters and volume of cylinder is 904.32 cubic feet

Let us calculate the volume of the cube which has a length of 7 cm , width is 8 cm and height is 15 cm

Volume = Length×width×height

=7×8×15

=840 cubic centimeters

Now let us find the volume of cylinder which has diameter 12 ft and height of 8 ft

Radius of cylinder is 6 ft

Volume of cylinder= πr²h

=3.14×6²×8

=3.14×36×8

=904.32 cubic feet

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Answer:

x=-2

Step-by-step explanation:

3x-8x = -5x

8+2= 10

5x = 10

simp: x=-2

Answer:

B $10.45

Step-by-step explanation:

Fist you find how much the 2 boxes of cracker cost

$3.50 * 2 = $7

Then subtract the amount of 2 crackers by the $0.80 coupon

$7 - $0.80 = $6.20

Then add that amount to the cost of a jar of peanut butter

$6.20 + $4.85 = $11.05

Then add that about for with the amount of a package of juice boxes

$11.05 + $2.40 = $13.45

Then subtract the total amount to the $3.00 coupon

$13.45 - $3.00 = $10.45

B $10.45 is your answer

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

x = 1/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 2 from both sides.

Step 3: Divide both sides by -4.

15.3/0.012=??????????????

Answer: 1275

Answer:

x=7

y=10

Step-by-step explanation:

I -7x + 4y = -9 | *3

II 5x - 3y = 5   | *4

Ia   -21x + 12y = -27

IIa  20x - 12y =20

IIa + Ia = IIb

IIb -x = -7  |*(-1)

      x=7

x in I

-7*7 + 4y = -9

-49 + 4y = -9   |+49

        4y = 40  |/4

          y =10

(a) The solutions for x* and y* are given by equations (6) and (7), respectively. (b) When I = $24, Pₓ = $4, and Pᵧ = $2, the optimal values of x* and y* are x* = 16 and y* = 20, respectively.

(a) To solve for x* and y* in terms of Pₓ, Pᵧ, and I, we need to find the utility-maximizing bundle that satisfies the budget constraint.

The utility function is given as U(x, y) = x^(1/2) * y^(1/2).

The budget constraint is expressed as Pₓ * x + Pᵧ * y = I.

To maximize utility, we can use the Lagrange multiplier method. We form the Lagrangian function L(x, y, λ) = U(x, y) - λ(Pₓ * x + Pᵧ * y - I).

Taking the partial derivatives of L with respect to x, y, and λ and setting them equal to zero, we get:

∂L/∂x = (1/2) *\(x^(-1/2) * y^(1/2)\)- λPₓ = 0   ... (1)

∂L/∂y = (1/2) *\(x^(1/2) * y^(-1/2)\) - λPᵧ = 0   ... (2)

∂L/∂λ = Pₓ * x + Pᵧ * y - I = 0               ... (3)

Solving equations (1) and (2) simultaneously, we find:

\(x^(-1/2) * y^(1/2)\)= 2λPₓ   ... (4)

\(x^(1/2) * y^(-1/2)\)= 2λPᵧ   ... (5)

Dividing equation (4) by equation (5), we have:

\((x^(-1/2) * y^(1/2)) / (x^(1/2) * y^(-1/2))\) = (2λPₓ) / (2λPᵧ)

y/x = Pₓ/Pᵧ

Substituting this into equation (3), we get:

Pₓ * x + (Pₓ/Pᵧ) * x - I = 0

x * (Pₓ + Pₓ/Pᵧ) = I

x * (1 + 1/Pᵧ) = I

x = I / (1 + 1/Pᵧ)        ... (6)

Similarly, substituting y/x = Pₓ/Pᵧ into equation (3), we get:

Pᵧ * y + (Pᵧ/Pₓ) * y - I = 0

y * (Pᵧ + Pᵧ/Pₓ) = I

y * (1 + 1/Pₓ) = I

y = I / (1 + 1/Pₓ)        ... (7)

Therefore, the solutions for x* and y* are given by equations (6) and (7), respectively.

(b) Given I = $24, Pₓ = $4, and Pᵧ = $2, we can substitute these values into equations (6) and (7) to find the values of x* and y*.

x* = 24 / (1 + 1/2) = 16

y* = 24 / (1 + 1/4) = 20

So, when I = $24, Pₓ = $4, and Pᵧ = $2, the optimal values of x* and y* are x* = 16 and y* = 20, respectively.

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Suppose U(x,y)=x  1/2  y  1/2  and P  x ​  x+P  y ​  y=I a. Solve for x  ∗  (P  x ​  ,P  y ​  ,I) and y  ∗  (P  x ​  ,P  y ​  ,I). b. What are the values of x  ∗  (P  x ​  ,P  y ​  ,I) and y  ∗  (P  x ​  ,P  y ​  ,I) if I=$24,P  x ​  =$4 and,P  y ​  =$2?

We may easily get the following conclusion from the provided graphic regarding the pair of lines:

AB and BD: Perpendicular lines

BD and CA: Parallel lines

CD and AB: Parallel lines

AC and AB: Perpendicular lines

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross.

Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

Perpendicular lines are those that cross at a straight angle to one another.

Examples include the opposite sides of a rectangle and the steps of a straight staircase.

The sign that indicates two perpendicular lines is: ⊥

So, according to the given image, we can easily conclude the pair of lines as follows:

AB and BD: Perpendicular lines

BD and CA: Parallel lines

CD and AB: Parallel lines

AC and AB: Perpendicular lines

Therefore, we may easily get the following conclusion from the provided graphic regarding the pair of lines:

AB and BD: Perpendicular lines

BD and CA: Parallel lines

CD and AB: Parallel lines

AC and AB: Perpendicular lines

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Zoe gets the number of 476 building blocks if they share building blocks in the ratio of 19:28.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Max and Zoe share building blocks in the ratio 19:28 which is given in the question.

Max has 323 building blocks.

We have to determine the number of building block got by Zoe

Let the number of building blocks got by Zoe would be x

As per the given condition, the ratio can be also written as

⇒ 19:28 = 323 : x

⇒ 19/28 = 323 / x

⇒ x = (323)(28) / 19

⇒ x = 476

Therefore, the number of building blocks got by Zoe would be 476.

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Coterminal angles are those whose ultimate positions are identical but whose number of full revolutions varies.

No, coterminal angles have the same angle measure. Two angles are coterminal if they have the same initial side and the same terminal side, meaning that they differ by an integer multiple of 360 degrees (or 2π radians) or by a multiple of 360 degrees plus or minus any number of full rotations (i.e., adding or subtracting 360 degrees or 2π radians any number of times).

For example, 30 degrees and 390 degrees are coterminal angles because 390 - 30 = 360, which is a multiple of 360 degrees. Similarly, 45 degrees and 405 degrees are coterminal because 405 - 45 = 360

However, two angles that differ by a non-integer multiple of 360 degrees are not coterminal. For example, 30 degrees and 390.5 degrees are not coterminal because they differ by 360.5 degrees, which is not a multiple of 360 degrees.

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For a NaCl crystal has six slip systems,

A) The exact slip planes are \([\bar 1 1 0] \), \([0 \bar1 1] \), \([\bar 1 0 1] \), [ 1 1 0], [0 1 1] and [ 1 0 1] and slip direction are (110), (011), ( 101) , \(( \bar 1 1 0) \), \((0 \bar 11 ) \) and \(( \bar1 0 1) \) of te six systems.

B) The sketch of the slip plane and slip direction for each slip system is present in attached figure.

C) Slip systems (ii), (iii), (v) & (vi) are the suitable ones.

We have a NaCl crystals has slip on {110} < 110 > slip systems. Total number of possible systems = 6

The slip plane refers to the plane of maximum atomic density, and the slip direction is the closest folded direction in the slip plane.

A) For six possible systems, slip planes and slip directions are the following:

plane : \([\bar 1 1 0] \).

Plane : \([0 \bar1 1] \)

plane : \([\bar 1 0 1] \)

plane : [ 1 1 0]

plane : [0 1 1]

plane : [ 1 0 1]

B) Using the standard cubic representations, the slip plane and slip direction of each system is present in attached figure.

C) Shear is y stress would at assis ; suitable 21 be highest in the direction which either x axis and y axis parallel to system (ii), (iii), (v) & (vi) are the suitable ones. Hence, we resolved all parts.

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The possible formula for P(x) would be \(P(x)=x^5+x^4-5x^3+3x^2\).

What is a polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The polynomial of degree 5.

Each root corresponds to a linear factor, so we can write:

        \(P(x) = x^2(x-1)^2(x+3)\\\\P(x)=x^2(x^2-2x+1)(x+2)\\\\P(x)=x^5+x^4-5x^3+3x^2\)

Hence, the possible formula for P(x) would be \(P(x)=x^5+x^4-5x^3+3x^2\).

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a) the margin of error is 1.675. b) the sample mean is 22.425. c) If the true mean turned out to be 19.45, I would be surprised.

a) The margin of error can be found by taking the difference between the upper limit and the lower limit of the confidence interval and dividing by 2. So, the margin of error is (24.10 - 20.75)/2 = 1.675.

b) The sample mean can be found by taking the average of the upper limit and the lower limit of the confidence interval. So, the sample mean is (24.10 + 20.75)/2 = 22.425.

c) If the true mean turned out to be 19.45, I would be surprised because it falls outside of the 95% confidence interval (20.75, 24.10). This means that there is only a 5% chance that the true mean would fall outside of this interval, so it would be surprising if it did.

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Answer:

Fourth choice, 19/30

Step-by-step explanation:

Add 38 and 22 together, it's 60

Out of 60 times, he flipped heads 38 times, so it's 38/60

Simplify 38/60 with 2, 19/30

The correct answer is Point A onto Point D, and AB onto DE.Since the triangles are congruent, we know that they have the same shape and size.

what is  congruent?

In mathematics, congruent means having the same size and shape. In geometry, two figures are congruent if they have the same size and shape, which means that all corresponding sides and angles are equal.

In the given question,

Based on the given information, we know that triangle ABC and triangle DEF are distinct acute triangles such that ZBZE. We are also told that AABC is congruent to ADEF, and we need to determine which sequence of rigid motions maps the triangles onto each other.

The correct answer is Point A onto Point D, and AB onto DE.

Since the triangles are congruent, we know that they have the same shape and size. Therefore, we need to find a sequence of rigid motions that will map one triangle onto the other.

The first step is to map point A onto point D, which can be done with a translation. The second step is to map AB onto DE, which can be done with a rotation about point D. This sequence of rigid motions will map triangle ABC onto triangle DEF.

Option 1, ZA onto ZD and ZC onto ZF, does not necessarily map the rest of the triangles onto each other.

Option 2, AC onto DF and BC onto EF, is incorrect because it only maps two sides of the triangle and does not guarantee congruence.

Option 4, ZC onto ZF and BC onto EF, also does not necessarily map the rest of the triangles onto each other.

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The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer:

standard or standards

Step-by-step explanation:

Mikos is required to repay it on September 13 of the same year based on simple interest.

When there is only one compounding every time period, simple interest is applied.

Following t years, the amount of money is predicted by:

A(t) = A(0) (1 + rt)

That where:

The initial amount is A(0).

The interest rate in decimal form is r.

In this issue:

The starting sum is A(0) = 100000.

R = 0.105 is the interest rate.

The maturity value is 104375 for A(t).

Therefore, we must find t; as a result,

A(t) = A(0)(1 + rt)

104375 = 100000(1 + 0.105t)

1 + 0.105t = 104375 / 100000

1 + 0.105t = 1.04375

0.105t = 1.04375

t = 0.04375 / 0.105

t = 0.4166

The time in years, then in days, is as follows:

On September 13, which is 152 days after April 14 (0.4166 x 365).

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Given :

The diagonals of rhombus ABCD intersect at E.

∠CAD = 20°.

To Find :

The angle ∠CDA.

Solution :

We know, diagonals of a rhombus bisects each other perpendicularly.

So, ∠DEA = 90°.

In triangle ΔEAD :

∠EAD + ∠AED + ∠EDA = 180°

20° + 90° + ∠EDA = 180°

∠EDA = 70°

Now, we know diagonal of rhombus also bisect the angle between two sides .

So, ∠CDA = 2∠EDA

∠CDA = 2×70°

∠CDA =140°

Therefore, ∠CDA is 140°.

Multiple regression analysis is applied when analyzing the relationship between one dependent variable and two or more independent variables. The goal is to determine the extent to which the independent variables predict the dependent variable.

Multiple regression analysis is a statistical technique used to explore and quantify the relationship between a dependent variable and multiple independent variables. It allows researchers to examine how changes in one or more independent variables impact the dependent variable, while controlling for the effects of other variables. By estimating the coefficients for each independent variable, the analysis provides insights into the strength, direction, and significance of their relationships with the dependent variable. This method is commonly employed in various fields, such as economics, social sciences, and business, to understand complex relationships and make predictions based on the interplay of multiple factors.

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Answer: The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Step-by-step explanation:

The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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Answer:

3hr. and 15min. each : )

Step-by-step explanation: Thank me for intelectual skills even if im wrong... Im very wise

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation: