A company can choose to package 12 cans into 3 rows of 4 or 6 rows of 2 which packaging uses more material?

Why would a company choose to package 12 cans one way instead of another?

The equation of parabola which opens up, has focus (2,12) and a focal diameter of 24 is,

⇒ (x - 2)² = 24 (y - 6)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

Focus of parabola = (2, 12)

Focal diameter = 24

We know that;

Focal Diameter also known as latus rectum is the segment which passes through Focus and intersects the Axis of parabola having end point at the wall of of parabola.

Hence, We get;

⇒ Focal diameter = 24

⇒ 4p = 24

⇒ p = 6

Now, To find the equation of parabola we need the vertex (h, v).

And, Vertex is a point on parabola which lies in same axis of symmetry at equidistant from the directrix and Focus and the distance is one fourth of latus rectum.

Hence, we get;

⇒ (h, v) = (h, k - p)

            = (2, 12 - 6)

            = (2, 6)

And, Equation of parabola is,

⇒ (x - h)² = 4a (y - v)

Substitute all the values, we get;

⇒ (x - 2)² = 24 (y - 6)

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The simplified form of the expression y⁻³/4y⁶ is option B: - 1/4y⁹

An algebraic expression consists of unknown variables, numbers and arithmetic operators such as addition, subtraction, multiplication, division etc. Therefore, let's simplify the expression.

The simplified form of the expression y⁻³/4y⁶ is:

To simplify this expression, you can use the rule of simplifying the powers of a variable.

It can be done by:

Therefore, The final step is to simplify the coefficient, 1/4 is a fraction, but to make it simpler we can divide 1 by 4, getting -1/4

Thus option B is correct.

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The Answer is Rs.408

step by step solution:

Given, P=5000

R=4%

T=2 years

Amount  A=P ( 1+ R/100 )^T

A=5000(1+ 4/100)^2

5000 (104/100)^2

= Rs.5408

Compound interest =A−P

 =5408−5000=Rs.408

​

If Yasmine's guests at her birthday party are exactly 26, based on the division operation, there will not be any ice cream left.

A division operation involves dividing the dividend (the numerator) by the divisor (the denominator) to obtain the quotient.

The quantity of ice cream purchased = 19¹/₂ (19.5).

The quantity of ice cream per guest = ³/₄ (0.75)

The number of guests that can be served = 26 (19¹/₂  x ⁴/₃) or (19

5/0.75)

Thus, using division operation, no ice cream will be left if the guests are not less than 26.

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Answer:

x = -3

y = -11

Step-by-step explanation:

These are the good questions someone can ask when trying to understand a problem.

What have you tried?

What happened?

What did you learn from this?

What else do you need?

What else can you do?

Answer:

[tex] \sf \: \frac{6}{7} \times 14 = 12[/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{6}{7} \times 14[/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{6}{7} \times 14[/tex]

[tex] \sf \rightarrow \frac{6}{\cancel{ \: 7 }} \times \cancel{14}[/tex]

[tex] \sf \rightarrow \: 6 \times 2[/tex]

[tex] \sf \rightarrow \: 12[/tex]

Hence, the answer is 12.

Answer:

Step-by-step explanation:

x=4

No, an equilateral triangle is not similar to a scalene triangle.

Two triangles are similar if they have the same shape, but they can be different sizes. In order for two triangles to be similar, the angles in the triangles must be congruent (equal in measure) and the sides of the triangles must be proportional. An equilateral triangle has three congruent angles, each measuring 60 degrees, and three congruent sides. A scalene triangle, on the other hand, has three sides that are all different lengths and three angles that are all different measures. Because the angles and sides of an equilateral triangle are not proportional to the sides and angles of a scalene triangle, the two triangles are not similar.

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The two triangles are not similar.

Now, According to the question:

An equilateral triangle is not similar to a scalene triangle because an equilateral triangle has all equal sides and the same angle measures, and a scalene triangle's sides are all different measures and the angles don't measure the same angle.

An equilateral triangle has three congruent angles, each measuring 60 degrees, and three congruent sides. A scalene triangle, on the other hand, has three sides that are all different lengths and three angles that are all different measures. Because the angles and sides of an equilateral triangle are not proportional to the sides and angles of a scalene triangle, the two triangles are not similar.

Hence, The two triangles are not similar.

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In a 1000g sample, 250g will be left undecayed and still radioactive after 11,400 years.

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay). The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite of life's exponential growth is time's doubling.

Carbon-14 has a half-life of approximately 5700 years, which means that after 5700 years, half of the original amount of Carbon-14 will remain undecayed and still radioactive. After 11,400 years, there will be 1/4 of the original amount remaining, because two half-lives have passed. So, in a 1000g sample, 250g will be left undecayed and still radioactive after 11,400 years.

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The best scale for the length axis is 10 cm to represented 1 unit on the graph

Using this scale the value of A and B are 60 and 110 respectively

All conceivable data for the graph is represented by the numbers on the X and Y axes.

There are major and minor axes, the major axes contains smaller divisions of 5, the smaller divisions are the minor axes

The scale are based on the major axes. The scale of a graph is the units that the distance in the major axes stands for

The scale should go beyond the values to be plotted so as to contain all the possible values

Applying the scale of 1 unit on graph for 10 units points A = 60 and point B = 110

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Answer:

Step-by-step explanation:

Attached are the formula. (Ignore the point slope formula not needed)

For second part, just know that m= slope and b = y intercept in the slope-intercept formula. Just plug those in for each of those, I will do one for you and you try the rest ok

Slope = 1/3 and y-intercept = -1

Slope intercept formula is y = mx + b

y = 1/3 x + (-1)

y= 1/3 x -1

Now you try the rest.

Answer:

(2, 0 )

Step-by-step explanation:

- 5y = 10 - 5x → (1)

- 2y = 8 - 4x → (2)

multiplying (1) by - 2 and (2) by 5 and adding will eliminate y

10y = - - 20 + 10x → (3)

- 10y = 40 - 20x → (4)

add (3) and (4) term by term to eliminate y

0 = 20 - 10x ( add 10x to both sides )

10x = 20 ( divide both sides by 10 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (1)

- 5y = 10 - 5(2)

- 5y = 10 - 10 = 0 , then

y = 0

solution is (2, 0 )

You can purchase 126 or 10.5 dozen eggs in 105 cowry shells.

What is algebraic expression ?

An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

Have given ,

105 cowry shells and cost of a dozen eggs (12 eggs) 10 cowry shells,

To find how many eggs can you purchase in 105 cowry shells,

Let  x eggs can purchase in 105 eggs

x = [tex]\frac{a dozen eggs * 105}{10}[/tex]

x = [tex]\frac{12*105}{10}[/tex]

x = [tex]\frac{1260}{10}[/tex]

x = 126 eggs

Hence ,  You can purchase 126 or 10.5 dozen eggs in 105 cowry shells.

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The consecutive even integers are 6,8 and 10.

If an integer is divisible by two, or a multiple of two, it is said to be an even integer.

Examples include 2,4,6,... and 2,4,6,... being divisible by 2.

In other words, the numbers 2,4,6,... and 2,4,6,... are even numbers.

Since k is an integer, we may claim that the integer of the type 2k is an even integer.

Let the three consecutive even integers be x, x + 2, and x + 4.

We are given,

 x(x + 2) = x^2 + 2x = x + 4 + 38.

By rearranging this equation, we get

x^2 + x - 42 = 0

On factoring this quadratic equation, we get

 (x - 6)(x + 7) = 0.

Since, x must be an integer, x = 6 or x = -7.

Since -7 is an odd number

Therefore, x=6

=>The consecutive even numbers are 6,8 and 10.

Therefore, The consecutive even integers are 6,8 and 10.

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According to the linear cost function sneakers are produced in 8 hours is 4400.

Businesses employ a mathematical technique called a linear cost function to calculate the overall costs related to a certain level of production. When the cost of producing each item is constant regardless of the number of units produced, this approach of cost estimating can be used.

Given :

C(x) = 25x + 400

x(t) = 20t

∴ C(x) = 25(20t) + 400

∴ C(x) = 500t + 400

Now,

C(x(t)) =  C(x(8)) = 500t + 400

                         = 500(8) + 400

                         = 4400

∴   C(x(8)) =4400

sneakers are produced in 8 hours = 4400

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Answer: (b) RP PS SR BR YP YS YR RY PY PS PR SY SR SB

Each time the drum is spun, there are five possible colors that can end up on top: red, yellow, purple, silver, and black. Since the drum is spun twice, there are 5x5 = 25 possible outcomes for the two spins.

In the list provided (a), the possible outcomes are listed in the format of the color that was uppermost on the first spin followed by the color that was uppermost on the second spin. For example, "RR" would mean that red was the color uppermost on the first spin, and red was the color uppermost on the second spin.

In the list provided (b) the possible outcomes are all the possible combinations of the five colors, no order is specified here.

Each of the 25 possible outcomes listed in (a) and (b) are equally likely as long as the drum is well-balanced and spun fairly.

Step-by-step explanation:

The lengths of the sides of a right triangle are in the extended ratio 5:12:13. The perimeter of the triangle is 120 inches are: 20, 48, 52.

The first side has length 5x

The second side has length 12x

The third side has length 13x

Then the expression for this can be written as : 5x + 12x + 13x = 120

x = 120/(5 + 12 + 13) = 120/30 = 4

Then,

The first side has length 5x= 5*4=20

The second side has length 12x=1`2*4=48

The third side has length 13x= 13*4 = 52

Then the The lengths of the 3 sides are 20, 48, 52

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The Indian rupees do you receive when you exchange $13 will be 601.2 rupees.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The expression 62.4d-210 gives the number of Indian rupees you receive when you exchange dollar d at the local currency exchange.

The Indian rupees do you receive when you exchange $13 will be:

= 62.4d - 210

= 62.4(13) - 210

= 601.2 rupees

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Answer: 12...12...12...57

The range of this exponential function  y=7ˣ is (0,∞), {y|y>0}

The range of a function is the set of its possible output values

The given function is y=7ˣ

Now we need to find the range of y=7ˣ

Let us take few values of x and y

x     -2       -1    0     1    2

y     1/49   1/7    1     7   49

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y=0. Horizontal Asymptote:  y=0

The Range is: (0,∞), {y|y>0} from the graph

Hence, the range of this exponential function  y=7ˣ is (0,∞), {y|y>0}

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Given functions are inverse of each other.

What are inverse functions?

A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the inverse of a function f. (y). Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.

Here, we have

Given: f(x) = 5x + 2

g(x) = (x-2)/5

We have to inverse one another function.

f(x) = 5x + 2

g(x) = (x-2)/5

f(g(x)) = f( (x-2)/5)

f(g(x)) = 5×(x-2)/5 + 2

f(g(x)) = x - 2 + 2

f(g(x)) = x these functions are inverse of each other.

Hence, given functions are inverse of each other.

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In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown." x is a variable in x + 2 = 7, but we can figure it out.

Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

To determine the value of X in a multiplication operation, the usual form is

Product = Multiplicand x Multiplier

Consider Multiplier as x.

Product = Multiplicand x

The equation to determine the value of x is then

X = product/multiplier

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Answer:

juniors- 43, seniors-155, veterans- 65, total-263

Step-by-step explanation:

so you divide each my 4 then subtract that from the original number and that's your answer

Juniors- 57 divide by 4=14, 57-14=43

Seniors- - 209 divide by 4=52, 209-52=155

veterans- 86 divide by 4=21, 86-21=65

Than add all 3 numbers together

:)

Answer: avg speed for the round trip is 2*4*6/(4+6) = 4.8 km/hr

RT distance = 4.8*0.75 = 3.6 km

sorry if this is wrong answer

The z-score corresponding to an observation of 470 is -0.97.

Given that the observation x is 470.

mean, is 570

standard deviation, σ is 103

For the occurrence score,

z = (x - μ)/σ

z = (470 - 570)/103

z = -0.97

The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalizing is the process of transforming a raw score into a standard score (however, "normalizing" can refer to many types of ratios; see normalization for more).

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The polynomial function would be [tex]g(x)=x^4 + x^3 -7x^2 -x -6[/tex].

Option (C) is correct.

What is a polynomial function?

A polynomial function is a function of the form:

[tex]f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0[/tex]

Where n is the degree of the polynomial, x is the variable, and [tex]a_0, a_1, a_2, ... a_n[/tex] are the coefficients. The degree of a polynomial is the highest power of the variable in the function.

A polynomial function in standard form with zeroes 1, 2, -3 and -1 is

g(x)=(x-1)(x-2)(x+3)(x+1)

So, (x-1)(x-2)(x+3)(x+1)

= (x^2 -3x +2)(x^2 +4x +3)

=[tex]x^4 + x^3 -7x^2 -x -6[/tex]

Hence, the polynomial function would be [tex]g(x)=x^4 + x^3 -7x^2 -x -6[/tex].

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The vertex of the data set of the table: (-3, 0) and the range is {y I 0 ≤ y < ∞}. The correct answer is A.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Given:

From the table,

we interpreted the graph of data set.

Which is given in the attached image.

And from the graph,

we have the vertex = (-3, 0)

To find the range:

y have the value y = 0

And never take the value from negative y.

And expands to over positive infinity.

So, the range is 0 ≤ y < ∞

Therefore, the vertex = (-3, 0) and the range is 0 ≤ y < ∞.

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