A box contains 240 lumps of sugar. Five lumps are fitted across the box and there were three layers. How many lumps are fitted along the box?

The perimeter of the figure is 30 cm.

The perimeter of the figure is the sum of the whole sides of the figure. Therefore, the perimeter of the figure can be found as follows:

perimeter of the figure = sum of the whole sides

Therefore,

perimeter of the figure = 6 cm + 9 cm + 2 cm + 3cm + 2cm + 3cm + 2cm + 3cm

Hence,

perimeter of the figure = 15 cm + 5 cm + 5cm + 5 cm

perimeter of the figure = 30 cm

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The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.

To plot the line graph of the equation 2x - 6, we need to assign values to the variable x and calculate the corresponding values of y.

Let's choose a range of x-values and calculate the corresponding y-values:

For example, let's choose x = -3, -2, -1, 0, 1, 2, and 3.

Substituting these values into the equation 2x - 6, we get:

For x = -3: y = 2(-3) - 6 = -12

For x = -2: y = 2(-2) - 6 = -10

For x = -1: y = 2(-1) - 6 = -8

For x = 0: y = 2(0) - 6 = -6

For x = 1: y = 2(1) - 6 = -4

For x = 2: y = 2(2) - 6 = -2

For x = 3: y = 2(3) - 6 = 0

Now, we can plot these points on a graph with x as the horizontal axis and y as the vertical axis:

(-3, -12), (-2, -10), (-1, -8), (0, -6), (1, -4), (2, -2), (3, 0)

We can then connect these points with a straight line. Since the equation is in the form y = 2x - 6, the line will have a slope of 2 and a y-intercept of -6. The line will have a positive slope, meaning it will slant upwards from left to right.

The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.

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Answer:

AB is not tangent to the circle.

Step-by-step explanation:

A tangent is a straight line that touches a circle at only one point.

The tangent of a circle is always perpendicular to the radius.

Therefore, if AB is tangent to the circle, it will form a right angle with the radius, CA.

To determine if AB is tangent, we can use Pythagoras Theorem.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

If AB is tangent, then angle CAB will be a right angle. So AC and AB would be the legs of the right triangle, and BC would be the hypotenuse.

Therefore:

[tex]AC^2+AB^2=BC^2[/tex]

Substitute the values into the equation:

[tex]7^2+12^2=15^2[/tex]

[tex]49+144=225[/tex]

[tex]193 = 225 \; \leftarrow\; \sf not\;true[/tex]

As 193 ≠ 225, the equation does not hold, hence proving that AB is not tangent to the circle.

The given number 132 from base 6 to base 10 by expanding its digits using powers of 6. The number 132 in base 6 is equal to 211 in base 5.

To express the number 132 in base 6 as a number in base 5, we need to convert the given number from base 6 to base 10 and then from base 10 to base 5.

In base 6, the digits range from 0 to 5. The positional values of the digits increase from right to left by powers of 6. Let's break down the given number 132 in base 6:

1 * 6^2 + 3 * 6^1 + 2 * 6^0

= 1 * 36 + 3 * 6 + 2 * 1

= 36 + 18 + 2

= 56 in base 10

Now, we have the number 56 in base 10. To convert it to base 5, we divide the number by 5 and record the remainders from right to left until the quotient becomes 0.

56 divided by 5 is 11 with a remainder of 1.

11 divided by 5 is 2 with a remainder of 1.

2 divided by 5 is 0 with a remainder of 2.

The remainders in reverse order give us 211 in base 5.

Therefore, the number 132 in base 6 is equal to 211 in base 5.

In summary, we converted the given number 132 from base 6 to base 10 by expanding its digits using powers of 6. Then, we divided the resulting number in base 10 by 5 to obtain the equivalent number in base 5 by recording the remainders. The final result is 211 in base 5.

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From the graph, we can see that the parabola intersects the x-axis at two points, which are approximately (-0.5, 0) and (1, 0).

Therefore, the correct answer is: a. (1, 0) and (-0.5, 0)

To sketch the graph of the quadratic function y = -2x² + x + 1 and determine the x-intercepts, we can use a graphing calculator or analyze the equation directly.

Here's the visualization and explanation of the graph:

The graph of a quadratic function is a parabola.

The general form of a quadratic equation is y = ax² + bx + c,

where a, b, and c are constants.

In this case, we have y = -2x² + x + 1.

The coefficient of x², which is -2, tells us that the parabola opens downward.

The vertex of the parabola can be found using the formula x = -b / (2a). Plugging in the values from our equation, we get x = -(1) / (2[tex]\times[/tex] (-2)) = 1/4.

So, the x-coordinate of the vertex is 1/4.

To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation: y = -2(1/4)² + (1/4) + 1 = -1/8 + 1/4 + 1 = 1 + 1/4 - 1/8 = 1 + 2/8 - 1/8 = 1 + 1/8 = 9/8.

Now that we have the vertex of the parabola, which is (1/4, 9/8), we can sketch the graph.

-1/2  1/4    1/2

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The volume of the gas after it is heated is approximately 0.0417 liters.

To find the volume of the gas after it is heated, we can use the combined gas law, which relates the initial and final conditions of a gas sample. The combined gas law is expressed as:

(P₁V₁) / T₁ = (P₂V₂) / T₂

Where:

P₁ and P₂ are the initial and final pressures of the gas (in kPa)

V₁ and V₂ are the initial and final volumes of the gas (in liters)

T₁ and T₂ are the initial and final temperatures of the gas (in Kelvin)

Given:

Initial volume (V₁) = 3.56 L

Initial temperature (T₁) = ST (which is typically 273.15 K)

Final temperature (T₂) = 400 K

Final pressure (P₂) = 125 kPa

Now we can plug these values into the combined gas law equation and solve for V₂:

(P₁V₁) / T₁ = (P₂V₂) / T₂

(1 * 3.56) / 273.15 = (125 * V₂) / 400

(3.56 / 273.15) = (125 * V₂) / 400

Cross-multiplying and solving for V₂:

3.56 * 400 = 273.15 * 125 * V₂

1424 = 34143.75 * V₂

V₂ = 1424 / 34143.75

V₂ ≈ 0.0417 L

As a result, the heated gas has a volume of approximately 0.0417 litres.

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Answer:she will actually need 1 dollar because all of that would be 31 dollars.

Step-by-step explanation:

3 pounds of lemons= $6

1 box of rice= $4

7 frozen diners= $21

6+4=10

10+21=31

[tex] \sf \hookrightarrow \: {8}^{2} + {b}^{2} = {17}^{2} [/tex]

[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 17 \times 17[/tex]

[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 289[/tex]

[tex] \sf \hookrightarrow \: 64 + {b}^{2} = 289[/tex]

[tex] \sf \hookrightarrow \: {b}^{2} = 289 - 64[/tex]

[tex] \sf \hookrightarrow \: {b}^{2} = 225[/tex]

[tex] \sf \hookrightarrow \: b = \sqrt{225} [/tex]

[tex] \sf \hookrightarrow \: b = \sqrt{15 \times 15} [/tex]

[tex] \sf \hookrightarrow \: b = 15[/tex]

Answer:

c=25

Step-by-step explanation:

Since you are given [tex]x^{2}[/tex]+10x+c

We know that in an equation of [tex]ax^{2}+bx+c[/tex], when a = 1, c can be found by [tex](\frac{b}{2})^{2}[/tex]

So c = [tex](10/2)^{2}[/tex]=[tex]5^{2}[/tex]=25

Answer:

d ≈ 8.1

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = R (5, 7 ) and (x₂, y₂ ) = S (- 2, 3 )

d = [tex]\sqrt{(-2-5)^2+(3-7)^2}[/tex]

  = [tex]\sqrt{(-7)^2+(-4)^2}[/tex]

  = [tex]\sqrt{49+16}[/tex]

  = [tex]\sqrt{65}[/tex]

  ≈ 8.1 ( to 1 decimal place )

The new required rate of return for Happy Corp. can be calculated using the Capital Asset Pricing Model (CAPM). The formula for CAPM is:

Required rate of return = Risk-free rate + Beta * Market risk premium

Since the analyst believes that the market risk premium will be unchanged, the only factor that will affect the new required return is the risk-free rate.

Given that the analyst predicts a 2.0% increase in inflation, the risk-free rate will also increase by that amount. Therefore, the new required rate of return for Happy Corp. will be the current risk-free rate plus the product of Happy Corp.'s beta and the market risk premium.

To plot the new Security Market Line (SML) on the graph, we would use the new required return calculated above and plot it against the corresponding beta values. The SML represents the relationship between risk (beta) and return (required rate of return).

By incorporating the new required return, we can determine the new expected returns for various levels of beta and create the updated SML.

It is important to note that without specific values provided for the risk-free rate, market risk premium, and Happy Corp.'s beta, it is not possible to calculate the exact new required return or plot the new SML accurately.

These values are crucial in determining the precise position of the SML on the graph.

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The area of quadrilateral QUAD is 2.5 square units.

To find the area of quadrilateral QUAD with vertices Q (-4, 3), U (3, 6), 1 (6, 3), and D (1, -4), we can use the Shoelace formula (also known as Gauss's area formula or the surveyor's formula).

The Shoelace formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) can be calculated as:

[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (x2y1 + x3y2 + ... + x1yn)|[/tex]

Using this formula, we can calculate the area of quadrilateral QUAD as follows:

Area = [tex]1/2 * |(-46 + 33 + 6*(-4) + 13) - (33 + 6*(-4) + 1*(-4) + (-4)*3)|[/tex]

Simplifying the expression, we get:

[tex]Area = 1/2 * |(-24 + 9 - 24 + 3) - (9 - 24 - 4 - 12)|Area = 1/2 * |(-36) - (-31)|Area = 1/2 * |-36 + 31|Area = 1/2 * |-5|Area = 1/2 * 5Area = 5/2[/tex]

The area of quadrilateral QUAD is 2.5 square units.

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The area of quadrilateral QUAD is 17.5 square units.

The area of quadrilateral QUAD, we can use the Shoelace Formula, also known as the Gauss's Area Formula.

The formula states that if the coordinates of the vertices of a polygon are given in order, then the area of the polygon can be calculated using the following formula:

Area = 1/2 × |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|

Let's apply this formula to find the area of quadrilateral QUAD:

Q (-4, 3)

U (3, 6)

A (6, 3)

D (1, -4)

Area = 1/2 × |(-4 × 6 + 3 × 3 + 6 × (-4) + 3 × (-1)) - (3 × 3 + 6 × (-4) + (-4) × (-1) + (-1) × (-4))|

Area = 1/2 × |(-24 + 9 - 24 - 3) - (9 - 24 + 4 + 4)|

Area = 1/2 × |(-42) - (-7)|

Area = 1/2 × |-42 + 7|

Area = 1/2 × |-35|

Area = 1/2 × 35

Area = 17.5

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The distance around the shape after the smaller semicircle is removed is 29 cm.The correct answer is option D.

To find the distance around the shape after the smaller semicircle is removed, we need to calculate the circumference of the larger semicircle and subtract the circumference of the smaller semicircle.

The circumference of a semicircle is given by the formula:

Circumference = π * radius + diameter/2

For the larger semicircle:

Radius = diameter/2 = 28/2 = 14 cm

Circumference of the larger semicircle = π * 14 + 28/2 = 22/7 * 14 + 14 = 44 + 14 = 58 cm

For the smaller semicircle:

Radius = diameter/2 = 14/2 = 7 cm

Circumference of the smaller semicircle = π * 7 + 14/2 = 22/7 * 7 + 7 = 22 + 7 = 29 cm

Therefore, the distance around the shape after the smaller semicircle is removed is:

58 cm - 29 cm = 29 cm

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The Probable question may be:
A metalworker cuts out a large semicircle with a diameter of 28 centimeters. Then the metalworker cuts a smaller semicircle out of the larger one and removes it. The diameter of the semicircular piece that is removed is 14 centimeters. What will be the distance around the shape after the smaller semicircle is removed? Use 22/7​ as an approximation for π.

A. 80cm

B. 82cm

C. 85cm

D. 86cm

m∠BCD = 31.57° (approx). Hence, the answer of the angle is 31.57 degrees.

In the given diagram, BD is extended through point D to point E, m∠CDE = (9x - 12)°, m∠BCD = (2x + 3)°, and m∠DBC = (3x + 5)°. We need to find m∠BCD.

       We know that m∠BCD = (2x + 3)°

       Substituting x = 92/7, we get:

       m∠BCD = (2 × 92/7 + 3)° = (184/7 + 3)° = 221/7°

       Therefore, m∠BCD = 31.57° (approx). Hence, the answer is 31.57.

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A set S is T-finite if it satisfies Tarski's finite set condition, which states that for every nonempty subset X of P(S), there exists a maximal element u in X such that there is no v in X with u as a proper subset of v and u is distinct from v. If a set does not satisfy this condition, it is considered T-infinite.

In set theory, a set S is said to be T-finite if it satisfies a particular property called Tarski's finite set condition. This condition states that for every nonempty subset X of the power set of S (denoted as P(S)), there exists a maximal element u in X such that there is no element v in X that properly contains u (i.e., u is not a proper subset of v) and u is distinct from v.

To understand this concept, let's break it down further:

T-finite set: A set S is T-finite if, for any nonempty subset X of P(S), there exists an element u in X that is maximal. This means that u is not properly contained in any other element in X.

Maximal element: In the context of Tarski's finite set condition, a maximal element refers to an element u in X that is not a proper subset of any other element in X. In other words, there is no v in X such that u is a proper subset of v.

Distinct elements: This means that u and v are not the same element. In the context of Tarski's finite set condition, u and v cannot be equal to each other.

T-infinite set: A set S is T-infinite if it does not satisfy Tarski's finite set condition. This means that there exists a nonempty subset X of P(S) for which no maximal element u can be found, or there exists an element v in X that properly contains another element u.

In conclusion, a set S is T-finite if it meets Tarski's finite set condition, which asserts that there exists a maximal element u in X such that there is no v in X with v as a proper subset of u and u is different from v. A set is regarded as T-infinite if it does not meet this requirement.

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Due to the presence of spheres X and Y, the electric field strength at point B is [tex]1.01 * 10^6 N/C[/tex] and [tex]-4.05 * 10^6 N/C[/tex], respectively.

Given that two spheres X and Y are carrying charges of 72mC and -72mC respectively, and they are located 4.0 m apart from each other. The electric field strength at points A and B due to the presence of each sphere is to be determined.

Let's begin by calculating the electric field strength at point A due to sphere X. Electric field strength is given by E=kq/r², where k is Coulomb's constant, q is the charge and r is the distance between the two charges. The electric field strength at point A due to sphere X, E₁=kq₁/r₁² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (4.0m)^2 = 4.05 * 10^6 N/C[/tex] (approx.)

Similarly, the electric field strength at point A due to sphere Y can be calculated as follows, E₂=kq₂/r₂² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (4.0m)^2 = 4.05 * 10^6 N/C[/tex] (approx.). Here, the negative sign indicates that the electric field due to sphere Y is in the opposite direction to the electric field due to sphere X. Now, let's calculate the electric field strength at point B. The electric field strength at point B due to sphere X, E₁=kq₁/r₁² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (8.0m)^2 = 1.01 * 10^6 N/C[/tex] (approx.)

Similarly, the electric field strength at point B due to sphere Y can be calculated as follows, E₂=kq₂/r₂² [tex]= (9*10^9Nm^2/C^2) * (-72mC) / (4.0m)^2 = -4.05 * 10^6 N/C[/tex] (approx.). Therefore, the electric field strength at point A due to the presence of sphere X is [tex]4.05 * 10^6 N/C[/tex] and due to the presence of sphere Y is [tex]-4.05 * 10^6 N/C[/tex]. The electric field strength at point B due to the presence of sphere X is [tex]1.01 * 10^6 N/C[/tex] and due to the presence of sphere Y is [tex]-4.05 * 10^6 N/C[/tex].

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The break-even sales (units) when the variable costs are decreased by $4 is approximately 47,714 units.

To find the break-even sales (units) when the variable costs are decreased by $4, we need to calculate the new unit variable costs and then use the break-even formula.

Fixed costs (F) = $334,000

Unit selling price (P) = $22

Unit variable costs (V) = $19

Change in unit variable costs = $4

New unit variable costs (V') = V - Change in unit variable costs

= $19 - $4

= $15

Now, let's calculate the break-even sales (units) using the formula:

Break-even sales (units) = Fixed costs / (Unit selling price - Unit variable costs)

Break-even sales (units) = $334,000 / ($22 - $15)

= $334,000 / $7

= 47,714.29

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Answer:

There were 126 student tickets sold and 252 adult ticket sold.

Step-by-step explanation:

Let x be the number of adult tickets sold

y be the number of students tickets sold

Twice as many student tickets as adult tickets were sold

a.

x = 2y  ---equation 1

6x + 4y = 2016   ---equation 2

b.

Substitute equation 1 to equation 2

6(2y) + 4y = 2016

12y + 4y = 2016

16y = 2016

Divide both sides of the equation by 16

16y/16 = 2016/16

y = 126

Substitute y = 126 to equation 1

x = 2y

x = 2(126)

x = 252

The system of inequalities shown in this problem is defined as follows:

d) y < 1 and y ≥ x.

The line in the image has an intercept of zero and slope of 1, hence it is given as follows:

y = x.

Points above the solid line are plotted, hence the first condition is:

y ≥ x.

The upper bound, represented by the dashed horizontal line, is y = 1, hence the second condition is:

y < 1.

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The x-axis represents the values of x, and the y-axis represents the values of y. The first point (0, 11/2) lies on the y-axis, at a height of 11/2. The second point (2, 17/2) lies to the right of the y-axis, at a height of 17/2. The third point (-3, 1) lies to the left of the y-axis, at a height of 1.

To find three points that satisfy the equation -3x + 2y = 11, we can arbitrarily assign values to either x or y and solve for the other variable. Let's choose to assign values to x and solve for y:

Let x = 0:

-3(0) + 2y = 11

2y = 11

y = 11/2

The first point is (0, 11/2).

Let x = 2:

-3(2) + 2y = 11

-6 + 2y = 11

2y = 11 + 6

2y = 17

y = 17/2

The second point is (2, 17/2).

Let x = -3:

-3(-3) + 2y = 11

9 + 2y = 11

2y = 11 - 9

2y = 2

y = 1

The third point is (-3, 1).

Now let's plot these points on a graph:

The x-axis represents the values of x, and the y-axis represents the values of y. The first point (0, 11/2) lies on the y-axis, at a height of 11/2. The second point (2, 17/2) lies to the right of the y-axis, at a height of 17/2. The third point (-3, 1) lies to the left of the y-axis, at a height of 1.

By plotting these three points on the graph, you will have a visual representation of the solutions to the equation -3x + 2y = 11.

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The z - score z = (x - μ)/σ equals z = (p' - p)/[√(pq/n)]

The z-score is the statical value used to determine probability in a normal distribution

Given the z-score z = (x - μ)/σ where

We need to show that

z = (p' - p)/√(pq/n)

We proceed as follows

Now, the z-score

z = (x - μ)/σ

Substituting in the values of μ and σ into the equation, we have that

So, z = (x - μ)/σ

z = (x - np)/[√(npq)]

Now, dividing both the numerator and denominator by n, we have that

z = (x - np)/[√(npq)]

z = (x - np) ÷ n/[√(npq)] ÷ n

z = (x/n - np/n)/[√(npq)/n]

z = (x/n - p)/[√(npq/n²)]

z = (x/n - p)/[√(pq/n)]

Now p' = x/n

So, z = (x/n - p)/[√(pq/n)]

z = (p' - p)/[√(pq/n)]

So, the z - score is z = (p' - p)/[√(pq/n)]

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The solution for k in the equation 10 - 10|-8k + 4| = 10, expressed in set notation, is {1/2}.

1. Start with the equation: 10 - 10|-8k + 4| = 10.

2. Simplify the expression inside the absolute value brackets: -8k + 4.

3. Remove the absolute value brackets by considering two cases:

  Case 1: -8k + 4 ≥ 0 (positive case):

    -8k + 4 = -(-8k + 4)  [Removing the absolute value]

    -8k + 4 = 8k - 4     [Distributive property]

    -8k - 8k = -4 + 4    [Group like terms]

    -16k = 0             [Combine like terms]

    k = 0               [Divide both sides by -16]

  Case 2: -8k + 4 < 0 (negative case):

    -8k + 4 = -(-8k + 4)  [Removing the absolute value and changing the sign]

    -8k + 4 = -8k + 4     [Simplifying the expression]

    0 = 0                [True statement]

4. Combine the solutions from both cases: {0}.

5. Check if the solution satisfies the original equation:

  For k = 0: 10 - 10|-8(0) + 4| = 10

             10 - 10|4| = 10

             10 - 10(4) = 10

             10 - 40 = 10

             -30 = 10 [False statement]

6. Since k = 0 does not satisfy the equation, it is not a valid solution.

7. Therefore, the final solution expressed in set notation is {1/2}.

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Answer:

x = - 2 , x = 4

Step-by-step explanation:

the x- intercepts are the points on the x- axis where the graph crosses

the graph crosses the x - axis at - 2 and 4 , then

x- intercepts are x = - 2 , x = 4

Answer: 18.84

Step-by-step explanation : To find the circumference you use the formula:

2πr

Since we have the diameter (6), divide by 2 to find the radius, or r.

So (2)(3.14)(3)