A manufacturer has 576 square inches of material available to construct the 6 faces of a carton, which will be in the shape of a rectangular prism. To maximize the volume, the carton will have dimensions such that the length and width are each twice the height.

Answer:

15 °C

Step-by-step explanation:

°C = (°F - 32) * (5/9)

Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.

Initial temperature: 77 °F

Converting to Celsius:

°C = (77 - 32) * (5/9)

°C ≈ 25

The temperature dropped by 10 °C, so the final temperature is:

Final temperature = Initial temperature - Temperature drop

Final temperature ≈ 25 - 10 = 15 °C

Therefore, the temperature after the storm was approximately 15 °C.

Data set: 6, 8, 10, 12, 14, 16, 18

To draw a dot plot representing this data set, we can place a dot above the corresponding value on a number line. Here's the dot plot:

Value    |

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

   6    |      o

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

   8    |      o

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

  10    |      o

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

  12    |      o

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

  14    |      o

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

  16    |      o

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

  18    |      o

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

In the dot plot, each "o" represents a data point. The values are shown on the left side, and the dots are placed above their respective values on the number line.

Answer:

  15.  f(-2) = 2

  17.  f(x) = 1 for x = ±1.7

Step-by-step explanation:

You want various values of the function and its inverse relation for f(x)=x²-2.

The value of f(x) is found by locating the value x on the x-axis and following the vertical line until it intersects the graph. Find the y-coordinate of that point.

The value of x for f(x) = k is found by locating k on the y-axis and following the horizontal line to the points of intersection with the graph. The x-coordinates of the points are the values of interest. Interpolation is often required.

The graph intersects the vertical line at x=-2 where y = 2.

  f(-2) = 2

The horizontal line at y=1 intersects the graph in two places, located symmetrically about the y-axis. The leftmost point is approximately (-1.7, 1). The rightmost point is approximately (1.7, 1).

  x ≈ -1.7 or +1.7

__

Additional comment

The instructions are to use the figure to answer the question. We interpret that to mean that you are to read the answers from the graph.

You can also use the figure to determine the equation for the graph (part of our problem statement, above). Then you can find the solutions by using the equation.

  f(x) = 1

  x² -2 = 1

  x² = 3

  x = ±√3 ≈ ±1.732 . . . . the values for problem 17

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The expression √(x²y²)  when simplified is i. xy

From the question, we have the following parameters that can be used in our computation:

√(x²y²)

When the expression is expanded, we have

√(x²y²) = √(x² * √(y²)

Evaluae the exponents in the expression

So, we have

√(x²y²) = x * y

Evaluae the products in the expression

So, we have

√(x²y²) = xy

Hence, the expression when simplified is i. xy

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Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

Step-by-step explanation:

To find the area of the square all you need to do is to find the length of the hypotenuse of the triangles

this will help us find the length of the square if we are given the values of the shorter lengths as shown up

we can calculate the length of the hypotenuse by using the Pythagorean theorem

[tex] \sqrt{a^{2} + b^{2} } = c[/tex]

we are given the sides of the shorter lengths being 5 and 3 we can then substitute them into the formula

let us label the missing length the hypotenuse as x

[tex] \sqrt{ {3}^{2} + {5}^{2} } = x[/tex]

[tex] \sqrt{34} = x[/tex]

[tex]5.83[/tex]

we get that 5.83 rounded to two decimal places is the length of the hypotenuse

we also know that it is the length of the square so

5.83 × 5.83 = Area of Square

34cm² = Area of Square

The perimeter of the trapezoid is 106 meters.

The area of the trapezoid is 1360 square meters.

To calculate the perimeter and area of an isosceles trapezoid, we need to use the given measurements:

The length of the minor base (34 m), the height (20 m), and the length of the oblique side (29 m).

First, let's calculate the length of the major base (the other parallel side). In an isosceles trapezoid, the major base and minor base have the same length.

So, the length of the major base is also 34 m.

The perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter can be calculated as follows:

Perimeter = length of minor base + length of major base + 2 × length of oblique side

Perimeter = 34 m + 34 m + 2 × 29 m

Perimeter = 34 m + 34 m + 58 m

Perimeter = 106 m

To calculate the area of the trapezoid, we can use the formula:

Area = (sum of the lengths of the bases) × height / 2

Area = (34 m + 34 m) × 20 m / 2

Area = 68 m × 20 m / 2

Area = 1360 m²

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Answer: -3 and -17

Step-by-step explanation:

     When completing the square we add and subtract [tex]\frac{b}{2} ^2[/tex] in the form ax² + bx + c.

[tex]\frac{b}{2} ^2 = \frac{-6}{2} ^2=(-3)^2=9[/tex]

x² - 6x - 8 = (x - __)² - __

(x² - 6x) - 8 = (x - __)² - __

(x² - 6x + 9) - 8 - 9 = (x - __)² - __

(x - 3)² - 17 = (x - __)² - __

     The blanks are 3 and 17.

The number of students who passed with I, II, and III divisions are 35, 70, and 49, respectively.

We have,

Let's denote the number of students who passed with I, II, and III divisions as x, y, and z, respectively.

Given that the total number of students who appeared in the examination is 210, and 56 students failed, we can calculate the number of students who passed:

Number of students who passed = Total students - Number of students who failed

= 210 - 56

= 154

According to the given ratio, the number of students who passed with I, II, and III divisions are in the ratio of 5:10:7.

We can express this ratio in terms of x, y, and z as:

x : y : z = 5 : 10 : 7

To find the actual number of students who passed with I, II, and III divisions, we can set up the following equation based on the ratio:

5k + 10k + 7k = 154

22k = 154

k = 154 / 22

k = 7

Now, we can find the number of students who passed with I, II, and III divisions:

Number of students who passed with I division = 5k = 5 x 7 = 35

Number of students who passed with II division = 10k = 10 x 7 = 70

Number of students who passed with III division = 7k = 7 x 7 = 49

Therefore,

The number of students who passed with I, II, and III divisions are 35, 70, and 49, respectively.

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According to the figure of the trapezoid

angle XMZ = 115 degrees

angle XMY = 102 degrees

Angle YMZ = 78 degrees

The given figure is an isosceles trapezoid, hence

angle XMZ + angle XYZ = 180

angle XYZ = 39 + 26 = 65

angle XMZ + angle XYZ = 180

angle XMZ = 180 - 65

angle XMZ = 115 degrees

angle XMY

angle XMY =  180 - 39 - 39 = 180 - 78 = 102 degrees

Angle YMZ + angle XMY = 180 (angle on a straight line)

Angle YMZ = 180 - angle XMY = 180 - 102 = 78 degrees

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Answer:

Let's assume the number of adults attending the performance is represented by 'x', and the number of children attending is represented by 'y'.

According to the given information, the entrance fee for adults is R50 each, and for children is R20 each.

The total amount raised by the school is R31,400. We can write an equation based on the total amount raised:

50x + 20y = 31,400

This equation represents the total value of the entrance fees paid by adults and children.

To solve this equation, we need another equation to relate the variables 'x' and 'y'.

Since we don't have any other information about the number of adults or children, we cannot determine their relationship based on the given information. Therefore, we cannot find a unique solution for 'x' and 'y' unless there is additional information provided.

If there is additional information or if you have any specific values for 'x' or 'y', I can assist you in solving the equation and finding the number of adults and children attending the performance.

Step-by-step explanation:

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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The volume of the container is 180 cubic meters.

Given,

Length of the container = 4 meters

Width of the container = 3 meters

Height of the container = 15 meters

Let the container is a cuboid, as the shape of the container isn't mentioned.

Now, we know that,

The volume of a cuboid = Length of the cuboid × Width of the cuboid × Height of the cuboid

Therefore, the volume of the given container of cuboid shape = 4 × 3 × 15 cubic meters.

                                                             = 180 cubic meters.

Hence, the volume of the container is 180 cubic meters.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{4}\\ o=\stackrel{opposite}{5.4} \end{cases} \\\\\\ x=\sqrt{ 4^2 + 5.4^2}\implies x=\sqrt{ 16 + 29.16 } \implies x=\sqrt{ 45.16 }\implies x\approx 6.7[/tex]

The values of x we found are x = 14 and x = 0.

To find the value of x in the given set of equations and expressions, we need to solve each equation individually and substitute the value of x into subsequent expressions. Let's solve each equation step by step:

Equation 21: 21 = B + 2 + 3x

To isolate 3x, we subtract 2 from both sides: 21 - 2 = B + 3x

19 = B + 3x

Equation 25: 25 = 2x - 3

To isolate 2x, we add 3 to both sides: 25 + 3 = 2x

28 = 2x

Divide both sides by 2: x = 14

Equation 24: 24 = G + LL + F

We don't have enough information to solve this equation since we don't know the values of G, LL, and F.

Equation 22: 22 = 5x + H + 10

To isolate 5x, we subtract H and 10 from both sides: 22 - H - 10 = 5x

12 - H = 5x

Equation 23: 23 = x + 8 + x + 3 + 12

Combining like terms: 23 = 2x + 23

Subtracting 23 from both sides: 0 = 2x

Divide both sides by 2: x = 0

Therefore, the values of x we found are x = 14 and x = 0.

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Answer:

x = 8

Step-by-step explanation:

Intersecting tangent and secant theorem:

If a tangent and a secant are drawn to the circle from a point from outside, the square of the measure of the tangent is equal to the product of the measures of the secant segment and its external secant segment.

         x² = (4+12)*4

         x² = 16 * 4

         x² = 64

        x = √64

         x = 8

Answer: Pretty sure it should be 2.

Step-by-step explanation:

maybe -2 but i dont think so

By translation, the images of the vertices Q and S are Q'(x, y) = (- 1, 4) and S'(x, y) = (- 3, 2).

In this problem we find the representation of a parallelogram, which is formed by four vertices. The images of the vertices can be found by means of translation, whose formula is introduced below:

C'(x, y) = C(x, y) + T(x, y)

Where:

If we know that Q(x, y) = (4, 1), S(x, y) = (2, - 1) and T(x, y) = (- 5, 3), then the images of the points are:

Q'(x, y) = (4, 1) + (- 5, 3)

Q'(x, y) = (- 1, 4)

S'(x, y) = (2, - 1) + (- 5, 3)

S'(x, y) = (- 3, 2)

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Hello !

Answer:

[tex]\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]

Step-by-step explanation:

The volume of a sphere is given by the following formula : [tex]\sf V_{sphere}=\frac{4}{3}\pi r^3[/tex] where r is the radius.

Moreover, we know that the volume of a hemisphere is half the volume of a sphere : [tex]\sf V_{hemisphere}=\frac{1}{2} V_{sphere}[/tex]

We obtain : [tex]\sf V_{hemisphere}=\frac{2}{3}\pi r^3[/tex]

Given :

[tex]\sf r=\frac{1}{2} d=\frac{12}{2} \\\underline{\sf r=6mm}[/tex]

Let's substitue r with it value in the previous formula :

[tex]\sf V_{hemisphere}=\frac{2}{3} \pi\times 6^3\\\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]

Have a nice day ;)

In the given expression, 2x³-4x²+2x-x-3, there are five terms. An expression is a mathematical phrase that can be constructed using variables, constants, and operators.

It can include any mathematical operations such as addition, subtraction, multiplication, and division. Additionally, an expression can be made up of one or more terms.In the given expression, 2x³-4x²+2x-x-3, there are five terms. The terms are:2x³: This is the first term in the expression.

It is a cubic term, which means it has an exponent of 3.4x²: This is the second term in the expression. It is a quadratic term, which means it has an exponent of 2.2x: This is the third term in the expression. It is a linear term, which means it has an exponent of 1.-x:

This is the fourth term in the expression. It is also a linear term, but it has a negative coefficient.-3: This is the fifth term in the expression. It is a constant term since it does not have any variable attached to it.In summary, the given expression has five terms, which are 2x³, -4x², 2x, -x, and -3.

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(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).

Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).

Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:

1. (f x g)(x):

We start by substituting g(x) into f(x) wherever we see an x in f(x):

(f x g)(x) = f(g(x)) = f(1/x)

Substitute 1/x into f(x):

(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)

2. (g x f)(x):

We start by substituting f(x) into g(x) wherever we see an x in g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2))

Substitute √(x + 2) into g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))

Therefore, we have:

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

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The volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

To find the volume of the solid obtained by rotating the region enclosed by the given graphs about the y-axis, we can use the method of cylindrical shells.

First, let's sketch the region to visualize it better.

The region is enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0.

Let's find the intersection points of these curves by setting them equal to each other:

18 - x = 3x - 6

Simplifying the equation, we have:

4x = 24

x = 6

So, the intersection point is (6, 12).

Now, we can integrate to find the volume of the solid.

The radius of each cylindrical shell is the distance from the y-axis to the curve y = 18 - x.

This can be expressed as x.

The height of each cylindrical shell is the difference between the two curves, which is (18 - x) - (3x - 6).

The volume of each cylindrical shell is given by the formula:

V = 2πrhΔx, where r is the radius, h is the height, and Δx is the width of each shell.

Integrating from x = 0 to x = 6, we can find the total volume:

V = ∫[0,6] 2πx[(18 - x) - (3x - 6)] dx

V = ∫[0,6] 2πx(24 - 4x) dx

V = 2π ∫[0,6] (24x - 4x²) dx

V = 2π [12x² - (4/3)x³] | [0,6]

V = 2π [(12(6)² - (4/3)(6)³) - (12(0)^2 - (4/3)(0)^3)]

V = 2π [(12(36) - (4/3)(216)) - (0 - 0)]

V = 2π [(432 - 288) - (0 - 0)]

V = 2π (432 - 288)

V = 2π (144)

V = 288π

Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

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Answer:

156yd²

Step-by-step explanation:

area of parallelogram = base X vertical height

= 12 X 13

= 156yd²

Answer:

Step-by-step explanation:

To solve this problem, we can use the following formula:

(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture

Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.

We know that:

The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.

The store owner wants to sell the final mixture for $2.10 per pound.

The black tea is worth $1.80 per pound.

Using the formula above, we can write:

(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10

Simplifying this equation, we get:

84 + 1.8x = 73.5 + 2.1x

0.3x = 10.5

x = 35

Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.

The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:

Cost of oolong tea = 35 pounds × $2.40/pound = $84

The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:

Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x

Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:

$73.5 + $2.10x = $84

Now, let's solve for x to find the amount of black tea needed:

$2.10x = $84 - $73.5

$2.10x = $10.5

x = $10.5 / $2.10

x ≈ 5

Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.

The quantities in the two columns cannot be compared due to the absence of specific point values. D.

The given question presents two columns, Column A and Column B, representing the slopes of lines through different sets of points.

The actual points themselves are not provided in the question.

Without the specific point values, it is not possible to determine the slope values or compare the quantities in Column A and Column B.

The slope of a line is determined by the change in the y-coordinate divided by the change in the x-coordinate between two points.

Since the coordinates of the points are missing, it is impossible to calculate the slopes accurately or make any comparison between the quantities in Column A and Column B.

Without the points, it is not possible to determine the slopes or establish any relationship between the quantities in Column A and Column B.

To draw any conclusions or comparisons, the coordinates of the points through which the lines pass are crucial.

Without that information, we lack the necessary data to assess the slopes and make any meaningful comparison.

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The dimensions (length and breadth) of the box are 10r x 8r.

We are given that;

π = 3,142

Number of tins=4,5

Now,

To calculate the area of sheet metal needed to make a soup tin, we can use the formula for surface area of a cylinder which is given by:

Surface Area = 2πrh + 2πr^2

where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we can calculate the surface area of the soup tin as follows:

Surface Area = 2π(4.5)(8) + 2π(4.5)^2 Surface Area = 226.08 cm^2

To calculate the total surface area of the label, we can use the formula for surface area of a cylinder which is given by:

Surface Area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we can calculate the surface area of the label as follows:

Surface Area = 2π(4.5)(8) Surface Area = 226.08 cm^2

To find out the dimensions (length and breadth) of the box in which tins are packed, we can use the given information that 4 tins fit in the width of the box and 5 tins fit in the length of the box. Let’s assume that each tin has a diameter of d cm.

4d = width of box 5d = length of box

We know that diameter (d) = 2r where r is radius.

So, width of box = 4d = 8r length of box = 5d = 10r

Therefore, by the area the answer will be 10r x 8r.

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Given statement solution is :- 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

To find the percentage of pupils who passed the final examination, you can use the following formula:

Percentage = (Number of pupils passed / Total number of pupils) * 100

Given that 90 pupils passed the final examination out of a total of 150 pupils, we can substitute these values into the formula:

Percentage = (90 / 150) * 100

Percentage = 0.6 * 100

Percentage = 60%

Therefore, 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

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