2xy^2 ( - 3x^2 y^2 + 4x)​

The weight of the melted ice cream would be the same as the weight of the original ice cream, which is 5 ounces.

a quantity or thing weighing a fixed and usually specified amount. : a heavy object (such as a metal ball) thrown, put, or lifted as an athletic exercise or contest. 3. : a unit of weight or mass see Metric System Table.

When the ice cream melts, it undergoes a change in state from solid to liquid, but the total mass or weight remains unchanged. Therefore, the weight of the melted ice cream is still 5 ounces.

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Answer: 5/12

Step-by-step explanation:

Since the first customer bought 1/2 of the pan of brownies. This means that the pan of brownies left will be:

= 1 - 1/2

= 1/2

The The second customer bought 5/6 of what was left of the pan of brownies, the fraction that the second customer bought will be:

= 5/6 × 1/2

= 5/12

Answer:

5/12

Step-by-step explanation:

At a bake stall there is a large square pan of chocolate brownies. Customers can buy any fraction of the pan of brownies they like.

The first customer bought 1/2 of the pan of brownies.

The amount of brownies that was left over is given as:

1 - 1/2 = 1/2 brownies left ove

The second customer bought 5/6 of what was left of the pan of brownies.

The amount of brownies the second customers bought is calculated as:

5/6 of 1/2

= 5/6 × 1/2

= 5/12

What fraction of the whole pan did the second customer buy

Answer:

5.7 feet

Step-by-step explanation:

Given:

\(\text{Height of triagle: 5 ft}\)

Formula;

\(\text{Area of triangle}= \dfrac{1}{2} \times \text{Base} \times \text{Height}\)

Substitute the height and the area in the formula;

\(\implies\text{Area of triangle}= \dfrac{1}{2} \times \text{Base} \times \text{Height}\)

\(\implies14.25 = \dfrac{1}{2} \times \text{Base} \times 5\)

Use cross multiplication;

\(\implies14.25 = \dfrac{1}{2} \times \text{Base} \times 5\)

\(\implies14.25 \times 2= \text{Base} \times 5\)

Simplify the left hand side;

\(\implies14.25 \times 2= \text{Base} \times 5\)

\(\implies28.5= \text{Base} \times 5\)

Divide both sides of the equation by 5;

\(\implies\dfrac{28.5}{5} = \dfrac{\text{Base} \times 5}{5}\)

\(\implies \text{Base} = \dfrac{28.5}{5} = 5.7 \ \text{ft}\)

Therefore, the measure of the base is 5.7 feet.

Answer:

5.7 feet

Step-by-step explanation:

The area formula for a triangle: A=(1/2) Base x Height

1. What we know: 14.25=(1/2)Base x 5

2. Now isolate "base" to get the answer. First, divide by 1/2. Dividing by 1/2 is the same as multiplying by 2. Leaves us with: 28.5=Base x 5.

3. The last thing we have to do is divide 5: 5.7=base.

4. To make sure, check with the formula: (1/2) 5.7 x 5=14.25

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

Answer:

D. x-91

Step-by-step explanation:

x will stand for the unknown number.

x minus 91 is the word form of x-91, so this is the answer.

The required regression equation is y=−15.9x+1081.6 and new cases for 2008 is 950.

To find the linear regression equation that represents the given set of data, we need to find the slope and y-intercept of the line of best fit.

We can use the following formulas to find the slope and y-intercept:

\($\begin{align*}\text{slope } b &= \frac{\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y})}{\sum_{i=1}^{n}(x_i - \overline{x})^2} \\text{y-intercept } a &= \overline{y} - b\overline{x}\end{align*}\)

where n is the number of data points, \($x_i$\) and \($y_i$\) are the i th values of x and y, respectively, \($\overline{x}$\) and\($\overline{y}$\) are the means of x and y, respectively.

Using the given data, we can calculate:

\(\overline{x} &= \frac{0+1+2+3}{4} = 1.5 \\overline{y} &= \frac{998+1047+1106+1084}{4} = 1058.75\)

\(\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y}) &= (0-1.5)(998-1058.75) + (1-1.5)(1047-1058.75) \&\quad+ (2-1.5)(1106-1058.75) + (3-1.5)(1084-1058.75) \&= -79.5 \\sum_{i=1}^{n}(x_i - \overline{x})^2 &= (0-1.5)^2 + (1-1.5)^2 + (2-1.5)^2 + (3-1.5)^2 \&= 5 \\end{align*}\)

Therefore, the slope is:

\($\begin{align*}b &= \frac{-79.5}{5} \&= -15.9 \\end{align*}\)

The y-intercept is:

\(\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)\($\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)

So the linear regression equation is:

y=−15.9x+1081.6

To find the projected number of new cases for 2008 (which is 8 years after 2000), we substitute x=8 into the equation and round to the nearest whole number:

\($\begin{align*}y &= -15.9(8) + 1081.6 \&= 949.8 \&\approx \boxed{950}\end{align*}\)

Therefore, the projected number of new cases for 2008 is 950.

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Answer:

85,000 and 90,000

Step-by-step explanation:

Answer:

y = -6 + 2x/3 = 2x/3 -6

where

2/3 is the slope and -6 is the intercept

Step-by-step explanation:

4x-6y = 36

Simplify

2x - 3y = 18

put y on the LHS

-3y = 18 - 2x

divide by -3

y = -6 + 2x/3 = 2x/3 -6

where

2/3 is the slope and -6 is the intercept

Answer:It should be 49.365

Step-by-step explanation:

Answer:

the answer is 49.365

Step-by-step explanation:

because if you line the decimals up and just add normal

hope this helped

Best-case analysis refers to finding the scenario in which an algorithm performs most efficiently, requiring the fewest number of operations.(option c)

This analysis is useful for understanding the lower bound or the best-case time complexity of an algorithm. In contrast, worst-case analysis considers the scenario where the algorithm performs least efficiently and requires the maximum number of operations.

Average-case analysis takes into account the expected or average input and calculates the average number of operations. Usual-case analysis is not a commonly used term in computer science and may not be as relevant in this context. Therefore, best-case analysis is the term that specifically addresses the fewest number of operations required for a given n.

The term that determines the fewest number of operations required for a given n is the best-case analysis.  It focuses on the best possible input that the algorithm can encounter.

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Answer:

y=5

Step-by-step explanation:

The curve stops at the y value of 6. And we need a horizontal line for the asymptote, so we don't need an x value only a y-value. So the y-value is 5 on the y-axis, which means your equation will be y=5.

-Hope this helped

Using simple trigonometry, the flagpole's height was determined to be 14.28 metres.

The difference in direction between two lines or planes defines angle, a two-dimensional measure of a turn. Theta is the symbol used to represent it; it is typically expressed in degrees or radians. Angles might be right, straight, reflex, full, obtuse, acute, or any combination of these. Right angles measure precisely 90 degrees, straight angles measure 180 degrees, reflex angles measure more than 180 degrees, and full angles measure 360 degrees. Acute angles are less than 90 degrees, obtuse angles are larger than 90 degrees, and right angles measure exactly 90 degrees.

The transit is shown to be 1.6 metres high and 12 metres away from the flagpole. The flagpole's top is elevated at an angle of 58°.

Basic trigonometry can be used to determine the flagpole's height (h) using the following equation:

h = 12 tan 58°

As a result, the flagpole's height is determined to be:

h = 12 tan 58° = 14.28m

As a result of utilising fundamental trigonometry, the flagpole's height was determined to be 14.28 metres.

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Graph attached below,

There are the number of pods of peas are  = 38

A number is split in the straightforward action of division. It's simpler to visualize it as a set of items being distributed to a certain group of individuals, as in the scenario given above. Naturally, in the interest of fairness, you should always offer each person the same amount.

One of the four fundamental operations of arithmetic, or how to mix numbers to create new ones, is division. Addition, subtraction, and multiplication are the other operations.

total number of peas = 288

peas have per pod  = 6

total number of pods required  = 288/6

                                                    = 38

there are the number of pods of peas are  = 38

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I understand that the question you are looking for is:

George Mendel is examining peas to try to understand how traits are passed from parents to offspring. Today Gregor has 228 peas to examine . The pods have 6 peas per pod. How many pods of peas are there?

The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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Answer:

6,250$ is the overhead for department a

The distribution of overhead to Department A based on sales is $6250.

A recurring cost of running a firm is referred to as overhead or overhead charge. While operating expenses like material and labor, overheads could easily be linked to or recognized with any one revenue unit.

They are operating costs for a business that cannot be connected to the creation or production of a good or service. They are really the costs a business must pay to remain open, independent of how successful it is.

Department A has sales of $200,000

Department B has sales of $600,000

Therefore the ratio between the two departments will be:

200000: 600000

= 1 : 3

The overhead expense for both the department combined are $25,000

The share of department A will  be at

= 25000 * (1/4)

= $6250  

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To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

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Using the properties of similar triangle and parallel lines we calculate the length of GF as √65 units.

It is given that GH is parallel to DE or GH || DE in the trapezium GHDE .

Therefore in the triangles ΔFDH and ΔFDE , we can say that

ΔFDH is similar to ΔFDE by angle angle angle axiom of similarity.

Now using the properties of similar triangles we can say that :

FG / DF = GH / DE

Now let us consider the length of GF be x.

Therefore DE = x

Now using the properties of similar triangles and substituting the values we get:

x / 13 = 5 / x

or, x² = 65

or, x = √65

Therefore the length of DE and GF is equal to √65.

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Answer:

0.166667

Step-by-step explanation:

Answer:

slope: 4/5

Step-by-step explanation:

If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.

To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;

C² = a² + b²

where;

a= 80

b= 100

c= ?

That is;

c²= 80²+100²

= 6400+10000

= 16,400

c = √16400

= 128.1m

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Joshua can determine the number of hours he can rent a kayak by dividing his budgeted amount by the rental rate per hour. He has two options: 1) He can inquire about the rental rate per hour at the kayak rental facility, or 2) He can check the rental website or contact the rental company to obtain the hourly rental rate.

To determine the number of hours Joshua can rent a kayak for himself, he needs to divide his budgeted amount of $50 by the rental rate per hour. There are two options for obtaining the rental rate per hour:

1) Inquire at the kayak rental facility: Joshua can directly contact the kayak rental facility and ask about their hourly rental rate. The staff at the facility will provide him with the current rate per hour, and then he can divide his budgeted amount by that rate to determine the number of hours he can rent the kayak.

2) Check the rental website or contact the rental company: Joshua can visit the rental company's website or contact them via phone or email to obtain information about their hourly rental rates. Most rental companies provide detailed information about their rates, including the cost per hour. By checking the website or contacting the company, Joshua can find the rental rate per hour and calculate the number of hours he can afford with his budget.

By utilizing one of these options, Joshua can determine the number of hours he can rent a kayak within his budgeted amount of $50.

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Yes, there exists a vector field g on ℝ3 such that curl(g) = x sin(y), cos(y), z − 3xy.

To find such a vector field g, we can use the fundamental theorem of vector calculus. Let g(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k be the vector field we are looking for.

Since the curl of g is given by curl(g) = ( ∂R/∂y - ∂Q/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂Q/∂x - ∂P/∂y ) k, we can equate the components of curl(g) with the given function x sin(y), cos(y), z − 3xy to obtain a system of partial differential equations:

∂R/∂y - ∂Q/∂z = x sin(y)

∂P/∂z - ∂R/∂x = cos(y)

∂Q/∂x - ∂P/∂y = z − 3xy

Solving this system of equations, we can obtain the expressions for P, Q, and R. One possible solution is:

P(x,y,z) = z cos(y) - yz^2/2 + C1

Q(x,y,z) = x sin(y) + xz^2/2 - C2

R(x,y,z) = xz - y cos(y) - C3

where C1, C2, and C3 are constants of integration. It can be verified that the curl of this vector field is indeed equal to the given function.

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The ordered pair (1, 2) is not included in the solution set to the system of inequalities y < x^2 + 3 and y > x^2 - 2x + 8.

To determine which ordered pair is included in the solution set to the given system of inequalities, we need to evaluate each ordered pair by substituting the values into the inequalities and checking if they satisfy the conditions.

Let's consider the ordered pair (1, 2) as a candidate solution:

Substituting x = 1 and y = 2 into the first inequality:

2 < 1^2 + 3

2 < 4 (True)

Substituting x = 1 and y = 2 into the second inequality:

2 > 1^2 - 2(1) + 8

2 > 1 - 2 + 8

2 > 7 (False)

Since the second inequality is not satisfied, the ordered pair (1, 2) is not included in the solution set to the given system.

Therefore, the ordered pair (1, 2) is not included in the solution set.

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Answer:yes

Step-by-step explanation:

it is a line or segment

Answer: The barrel can only hold less than 42 gallons of water, which means w<42.

Answer:

Abby rode the fastest

Hope that helps!

Answer:

Abby rode the fastest.

Step-by-step explanation:

Eddie rode the second fastest, since they the second highest line. Greg rode second to last, and Michelle rode the slowest, since they have the lowest line.