"Valeria and her family play the board game Parrots and Pirates on game night. Players who land on a cannon space roll a 6-sided weighted penalty die to determine how many gold doubloons they will lose. To see how the die is weighted, Valeria rolls it 15 times and records the results. Based on the data, what is the probability of rolling a 6 with this die.

The expression/equation as written in the question is ∠A ≈ ∠C

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

∠A ≈ ∠C

The above expression means that

The angles A and C are congruent

From the question, we understand that

The question is not to be solved; we only need to write out the expression

Hence, the expression/equation as written is ∠A ≈ ∠C

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Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

[tex]\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32[/tex]

Note that [tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of each base of the trapezoid, so it doesn't matter which is which.

The range of the rational function in this problem is given as follows:

All real values. (fourth option).

From the graph of the function given by the image presented at the end of the answer, it assumes all values of y, hence the range is all real values.

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The antiderivative of the function is f(x) = 2x + 5x³ + 2x⁶ - 9.

To find an antiderivative of f(x), we can integrate each term of f'(x) individually.

Given:

f'(x) = 2 + 15x² + 12x⁵

To integrate 2, we get:

∫2 dx = 2x + C₁, where C₁ is the constant of integration.

To integrate 15x², we get:

∫15x² dx = 5x³ + C₂, where C₂ is another constant of integration.

To integrate 12x⁵, we get:

∫12x⁵ dx = 2x⁶ + C₃, where C₃ is another constant of integration.

Putting it all together, the antiderivative of f(x) is:

f(x) = 2x + 5x³ + 2x⁶ + C,

where C = C₁ + C₂ + C₃ represents the constant of integration.

To find the specific value of C, we are given that f(1) = 0. Substituting x = 1 into the antiderivative equation:

0 = 2(1) + 5(1)³ + 2(1)⁶ + C,

0 = 2 + 5 + 2 + C,

0 = 9 + C.

Therefore, C = -9.

The final expression for f(x) is:

f(x) = 2x + 5x³ + 2x⁶ - 9.

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Answer:

b. 160°

d. 55°

Step-by-step explanation:

The Inscribed Angle Theorem states that an inscribed angle is half of the central angle that subtends the same arc.

In other words, if an angle is inscribed in a circle and it intercepts an arc, then the measure of the inscribed angle is equal to half the measure of the central angle that also intersects that arc.

For question:

b.

By using above theorem:

m arc XW=2* m arc XYW

m arc XW= 2*80=160°

d.

m arc WV=125°

The Inscribed Angle Diameter Right Angle Theorem states that any angle inscribed in a circle that intercepts a diameter is a right angle.

By using this theorem:

m arc WV+m arc XV =180°

Now

m arc XV =180°-m arc WV

m arc XV=180°-125°

n arc XV=55°

Answer:

[tex]\text{b.} \quad m\overset{\frown}{XW}=160^{\circ}[/tex]

[tex]\text{d.} \quad m\overset{\frown}{XV}=55^{\circ}[/tex]

Step-by-step explanation:

An inscribed angle is the angle formed (vertex) when two chords meet at one point on a circle.

An intercepted arc is the arc that is between the endpoints of the chords that form the inscribed angle.

[tex]\hrulefill[/tex]

From inspection of the given circle:

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:

[tex]m \angle WRX = \dfrac{1}{2}\overset{\frown}{XW}[/tex]

         [tex]80^{\circ}= \dfrac{1}{2}\overset{\frown}{XW}[/tex]

   [tex]\boxed{m\overset{\frown}{XW}=160^{\circ}}[/tex]

[tex]\hrulefill[/tex]

From inspection of the given circle:

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:

[tex]m \angle WVX= \dfrac{1}{2}\overset{\frown}{WX}[/tex]

         [tex]90^{\circ}= \dfrac{1}{2}\overset{\frown}{WX}[/tex]

    [tex]m\overset{\frown}{WX}=180^{\circ}[/tex]

The sum of the measures of the arcs in a circle is 360°.

[tex]m\overset{\frown}{VW}+m\overset{\frown}{WX}+m\overset{\frown}{XV}=360^{\circ}[/tex]

Therefore, so find the measure of arc XV, substitute the found measures of arcs VW and WX, and solve for arc XV:

[tex]125^{\circ}+180^{\circ}+m\overset{\frown}{XV}=360^{\circ}[/tex]

          [tex]305^{\circ}+m\overset{\frown}{XV}=360^{\circ}[/tex]

                    [tex]\boxed{m\overset{\frown}{XV}=55^{\circ}}[/tex]

The coordinate of the fourth vertex is (9,11)

Any of a set of numbers used in specifying the location of a point on a line, on a surface, or in space is called coordinate

For example (6,3) is a coordinate on a plane where 6 represent the value on x axis and 3 represent the value on y axis.

Since the shape is parallelogram;

√ -3-1)² + 8-0)² = √ x-5)² + y-3)²

= √4² +8² = √ x-5)² + y -3)²

therefore, relating the two values;

4 = x-5 and 8 = y -3

x = 4+5 = 9

y = 8+3 = 11

Therefore the coordinate of the fourth vertex = ( 9,11)

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Answer:

  x = 4

Step-by-step explanation:

You want the value of x in the figure of a circle with intersecting secants.

The product of lengths from the near and far circle intercepts to the point where the secants intersect is the same for both secants:

  6(6+10) = 8(8+x)

  6·16 = 8·(8+x)

  12 = 8 +x . . . . . . . divide by 8

  4 = x . . . . . . . . . . subtract 8

The length x is 4 units.

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Answer:

area = 8π/3

arc length = 4π/3

Step-by-step explanation:

θ = 60°

r = 4

Area of sector :

[tex]\frac{\theta}{360} \pi r^{2} \\\\=\frac{60}{360} \pi 4^{2} \\\\= \frac{1}{6} 16\pi \\\\= \frac{8}{3} \pi[/tex]

arc length:

[tex]\frac{\theta}{360} 2\pi r\\ \\= \frac{60}{360} 2(4)\pi \\\\= \frac{1}{6} 8\pi \\\\= \frac{4}{3} \pi[/tex]

Answer:

A ≈ 8.4 cm² , arc length ≈ 4.2 cm

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{60}{360}[/tex] ( r is the radius of the circle )

  = π × 4² × [tex]\frac{1}{6}[/tex]

  = [tex]\frac{16\pi }{6}[/tex]

  ≈ 8.4 cm² ( to 1 decimal place )

arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{60}{360}[/tex]

     = 2π × 4 × [tex]\frac{1}{6}[/tex]

     = [tex]\frac{8\pi }{6}[/tex]

     ≈ 4.2 cm ( to 1 decimal place )

Using the z-statistic relation given, the value of the z-statistic in the scenario would be 0.61

The Z-statistic relation is written thus:

phat = 140 / 200 = 0.7

p = 0.68

q = 1 - p = 0.32

n = 200

Inputting the values into our formula

z = (phat - p) / sqrt(p * q / n)

= (0.7 - 0.68) / sqrt(0.68 * 0.32 / 200)

= 0.02 / 0.0583

= 0.61

Therefore, Z-statistic is 0.61

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The measure of angle HFJ in the right triangle JFH is 43 degrees.

In the right triangle FGJ, first, we determine the hypotenuse FJ.

Angle GFJ = 43 degrees

Opposite of angle GFJ = 6

Hypotenuse FJ = ?

Using the trigonometric ratio, we can find the hypotenuse FJ:

sine = opposite / hypotenuse

sin( 43 ) = 6 / FJ

FJ = 6 / sin( 43 )

FJ = 8.7977

Now, we can find angle HFJ,

Angle HFJ = ?

opposite = 6

Hypotenuse FJ = 8.7977

Using the trigonometric ratio:

sin ( HFJ ) = 6 / 8.7977

sin ( HFJ ) = 6 / 8.7977

HFJ = sin⁻¹( 6 / 8.7977 )

HFJ = 43°

Therefore, angle HFJ measure 43 degrees.

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The values x = -5 and x = 3 make the second expression undefined. The correct answers are:

x = -5

x = 3

x= -3

To determine the values for which the given expressions are undefined, we need to find the values that make the denominators equal to zero.

First expression: [tex]\frac{3x}{(x^2 - 9)}[/tex]

For this expression, the denominator is (x^2 - 9). It will be undefined when the denominator equals zero:

x^2 - 9 = 0

Factoring the equation, we have:

(x - 3)(x + 3) = 0

Setting each factor equal to zero, we get:

x - 3 = 0 --> x = 3

x + 3 = 0 --> x = -3

So, the values x = 3 and x = -3 make the first expression undefined.

Second expression: [tex]\frac{(x + 4)}{(x^2 + 2x - 15)}[/tex]

For this expression, the denominator is (x^2 + 2x - 15). It will be undefined when the denominator equals zero:

x^2 + 2x - 15 = 0

Factoring the equation, we have:

(x + 5)(x - 3) = 0

Setting each factor equal to zero, we get:

x + 5 = 0 --> x = -5

x - 3 = 0 --> x = 3

So, The second expression is ambiguous because x = -5 and x = 3.

Consequently, the right responses are x = -5, x = 3 and x= -3.

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Answer:

Davis has a loss of $19

i.e -19

Step-by-step explanation:

On day 1, David lost 5.4 * 10 = $54

On day 2, David gained 5 * 7 = $35

Overall, his loss is greater than the profit

Total loss is $54 - $35 = $19

Answer:

[tex]m = \frac{1 - ( - 7)}{9 - ( - 3)} = \frac{8}{12} = \frac{2}{3} [/tex]

B is the correct answer.

The measure of an arc in a circle is determined by the central angle that subtends it. Let's analyze each given measure of the indicated arcs:

90°: A 90° arc spans one-fourth of the entire circle since a full circle has 360°.

80°: An 80° arc is smaller than a quarter of the circle but larger than a sixth since 360° divided by 4 is 90°, and by 6 is 60°. Therefore, it lies between these two values.

100°: A 100° arc is slightly larger than a quarter of the circle but smaller than a third, as 360° divided by 4 is 90°, and by 3 is 120°.

70°: A 70° arc is smaller than both a quarter and a sixth of the circle, falling between 60° and 90°.

H: The measure of an arc denoted by "H" is not provided, so it cannot be determined without further information.

40°: A 40° arc is smaller than a sixth of the circle but larger than a twelfth, as 360° divided by 6 is 60°, and by 12 is 30°.

F: Similarly, the measure of the arc denoted by "F" is not provided, so it remains unknown without additional data.

Thus, the measures of the indicated arcs are as follows: 90°, between 60° and 90°, between 90° and 120°, between 60° and 90°, unknown (H), between 30° and 60°, and unknown (F).

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11. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB.

12. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because C is equidistant from AB.

In Mathematics and Geometry, a perpendicular bisector can be used for bisecting or dividing a line segment exactly into two (2) equal halves, in order to form a right angle with a magnitude of 90° at the point of intersection.

Question 11.

By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB:

AC ≅ BC

CD ≅ CD

AE ⊥ EC

Question 12.

By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector because C is equidistant from line segment AB.

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Answer:

The correct answer is A. As x increases, the rate of change of f(x) exceeds the rate of change of g(x)

Step-by-step explanation:

The missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form simply refers to a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

       x           12

2      2x         24

Note: 2x/2 = x.

        24/2 = 12.

Next, we would write the expression 2x + 24 as a product as follows;

(2x + 24) = 2(x + 12).

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Answer:

She willl be $1.40 under budget

Step-by-step explanation:

8% = 8/100 = 0.08

Adding this to 100% of the price of the shoes, we get 108% = 108/100 = 1.08.

We multiply the price of the shoes by this:

45*1.08 = 48.60

Subtract this from 50:

50 - 48.60 = 1.40

Answer:

Step-by-step explanation:To calculate the value of x, we can use the formula for the area of a trapezoid:

Area = (1/2) * (sum of the parallel sides) * height

Given that the area of the trapezoid ABCD is 70 square units, we can set up the equation as follows:

70 = (1/2) * (AB + DC) * Height

Substituting the given values:

70 = (1/2) * ((2x + 4) + (x - 2)) * 4

Simplifying the equation:

70 = (1/2) * (3x + 2) * 4

Multiplying both sides by 2 to remove the fraction:

140 = (3x + 2) * 4

Dividing both sides by 4:

35 = 3x + 2

Subtracting 2 from both sides:

33 = 3x

Dividing both sides by 3:

x = 11

Therefore, the value of x is 11.

The interval notation (-3, 4) represents the set of real numbers r that are greater than -3 and less than 4, excluding -3 and 4.

The set builder notation {r | -3 < r < 4} can be expressed in interval notation as (-3, 4).

In interval notation, the parentheses indicate that the endpoints, -3 and 4, are not included in the set.

The interval (-3, 4) represents all the real numbers r that are greater than -3 and less than 4, but not including -3 and 4.

It can also be visualized on a number line as an open interval between -3 and 4, where the endpoints are not filled in.

The interval (-3, 4) can be interpreted as a range of values for r. Any real number between -3 and 4, excluding the endpoints, would satisfy the given set builder notations.

For example, -2, 0, and 3 are all included in the interval (-3, 4), but -3 and 4 themselves are not part of the set.

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Answer:

47 cents or $0.47

Step-by-step explanation:

1 dime = 10 cents (or $0.1)

1 quarter = 25 cents or ($0.25)

12 cents + 1 dime + 1 quarter = 12 + 10 + 25 = 47 cents

Answer:

Assuming options are independent or not independent/dependent, it would be not independent

Step-by-Step:

Probability of (A given B) = Probability(A)

P(A & B) divided by P(B) = P(A)

(1/9)/(1/15) = 2/5

5/3 = 2/5

Since 5/3 doesn't equal 2/5, the events if A and B are not independent

Answer: substitute the given number for the variable in the expression and then simplify the expression using the order of operations

Step-by-step explanation:3a2 - 4b2 for a = -3/4 and b = 1/2

The cube root of 30 would be between 3 and 4, but closer to 3.

Cube root is the number that needs to be multiplied three times to get the original number.

The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:

Step 1: Start with the prime factorization of the given number.

Step 2: Then, divide the factors obtained into groups containing three same factors.

Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.

We have to find the cube root of 30.

Prime factorization of 30 = [tex]2\times3\times5[/tex].

Therefore the cube root of 30 = [tex]\sqrt[3]{ (2\times3\times5)}= \sqrt[3]{30}[/tex].

As [tex]\sqrt[3]{30}[/tex] cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.

So here we will use approximation method to find the cube root of 30 using Halley's approach:

Halley’s Cube Root Formula:

[tex]{\sqrt[3]{\text{a}} = \dfrac{\text{x}[(\text{x}^3 + 2\text{a})}{(2\text{x}^3 + \text{a})]}}[/tex]

The letter “a” stands in for the required cube root computation.

Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.

Here we have a = 30

and we will substitute x = 3 because 3³ = 27 < 30 is the nearest perfect cube.

Substituting a and x in Halley's formula,

[tex]\sqrt[3]{30} = \dfrac{3[(3^3 + 2\times30)}{(2\times3^3 + 30)]}[/tex]

      [tex]= \dfrac{3[(27+60)}{(54+30)]}[/tex]

      [tex]= 3\huge \text(\dfrac{87}{84} \huge \text)[/tex]

      [tex]= 3\times1.0357[/tex]

[tex]\bold{\sqrt[3]{30} = 3.107}[/tex].

Hence, the cube root of 30 is 3.107.

Therefore, we can conclude that the cube root of 30 would be between 3 and 4, but closer to 3.

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Complete question:

Describe in words where cube root of 30 would be plotted on a number line.

A. Between 3 and 4, but closer to 3

B. Between 3 and 4, but closer to 4

C. Between 2 and 3, but closer to 2

D. Between 2 and 3, but closer to 3

Answer:

[tex]\text{a.} \quad m\angle NLM=93^{\circ}[/tex]

[tex]\text{c.} \quad m\angle FHG=31^{\circ}[/tex]

Step-by-step explanation:

The inscribed angle in the given circle is ∠NLM.

The intercepted arc in the given circle is arc NM = 186°.

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc.

Therefore:

[tex]m\angle NLM=\dfrac{1}{2}\overset{\frown}{NM}[/tex]

[tex]m\angle NLM=\dfrac{1}{2} \cdot 186^{\circ}[/tex]

[tex]\boxed{m\angle NLM=93^{\circ}}[/tex]

[tex]\hrulefill[/tex]

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:

[tex]m\angle HFG=\dfrac{1}{2}\overset{\frown}{HG}[/tex]

[tex]m\angle HFG=\dfrac{1}{2}\cdot 118^{\circ}[/tex]

[tex]m\angle HFG=59^{\circ}[/tex]

As line segment FH passes through the center of the circle, FH is the diameter of the circle. Since the angle at the circumference in a semicircle is a right angle, then:

[tex]m\angle FGH = 90^{\circ}[/tex]

The interior angles of a triangle sum to 180°. Therefore:

[tex]m\angle FHG + m\angle HFG + m\angle FGH =180^{\circ}[/tex]

[tex]m\angle FHG + 59^{\circ} + 90^{\circ} =180^{\circ}[/tex]

[tex]m\angle FHG +149^{\circ} =180^{\circ}[/tex]

[tex]\boxed{m\angle FHG =31^{\circ}}[/tex]

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are options 1 (x < 5) and 3 (–6x + 15 < 10 – 5x).

To determine the correct representations of the inequality –3(2x – 5) < 5(2 – x), let's simplify the expression and analyze the options:

First, we simplify the inequality:

–3(2x – 5) < 5(2 – x)

–6x + 15 < 10 – 5x

Now let's analyze the options:

x < 5: This option represents the solution to the inequality. It indicates that x must be less than 5 for the inequality to hold true.

–6x – 5 < 10 – x: This is not a correct representation of the inequality. The sign of the x-term on the right side of the inequality is incorrect.

–6x + 15 < 10 – 5x: This option represents the solution to the inequality. It correctly represents the simplified inequality we obtained earlier.

A number line from negative 3 to 3 in increments of 1, with an open circle at 5 and a bold line starting at 5 and pointing to the right: This representation does not accurately represent the solution to the inequality. The inequality is not satisfied at x = 5, so the circle should be closed.

A number line from negative 3 to 3 in increments of 1, with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left: This representation is not correct as it does not represent the solution to the inequality.

Therefore, choices 1 (x 5) and 3 (-6x + 15 10 - 5x) are the proper expressions of the inequality -3(2x - 5) 5(2 - x).

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