The regular octagon in the ceiling of this cathedral has a radius of 10.5 feet and a perimeter of 64 feet.

What is the length of the apothem of the octagon? Round your answer to the nearest tenth of a foot.
feet

Using your answer for the length of the apothem, what is the area of the regular octagon? Round your answer to the nearest tenth of a square foot.
square feet

The area of a parallelogram can be found by multiplying the base by the height

The formula for the area of a parallelogram is shown:

A = b × h

where A is the area, b is the base, and h is the height of the parallelogram.

Note that the base and the height must be perpendicular to each other.

1) A = 1/2bh

= 0.5 * 13/6 * 24

= 26 ft^2

1)A = bh

= 15/4 * 14/5

10.5 ft^2

3) 8/3 * x = 24

x = 24 * 3/8

x = 9 ft

4) x * 4/5 = 10

x = 10 * 5/4

= 12.5 ft

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The area of this triangle is equal to 26 yd².

The area of this parallelogram is equal to 21 ft² or 10 1/2 ft².

The base of this parallelogram as a fraction is 72/8 feet.

The base of this rectangle is 25/2 cm or 12 1/2 cm.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following formula:

Area = 1/2 × base × height

Area = 1/2 × 24 × 2 1/6

Area = 12 × 13/6

Area = 156/6

Area = 26 yd²

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram = base × height

Area of a parallelogram = 2 4/5 × 3 3/4

Area of a parallelogram = 14/5 × 15/4

Area of a parallelogram = 7 × 3/2

Area of a parallelogram = 21/2 = 10 1/2 ft²

24 = base × 2 2/3

24 = base × 8/3

Base = 72/8

Base = 9 feet.

For the base of the rectangle, we have:

Area of rectangle = length × breadth

10 = 4/5 × breadth

Breadth = 50/4

Breadth = 25/2 = 12 1/2 cm.

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Answer:

h ≈ 19 m

Step-by-step explanation:

using the tangent ratio in the right triangle

tan43° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{20}[/tex] ( multiply both sides by 20 )

20 × tan43° = h , then

h ≈ 19 m ( to the nearest whole number )

Answer:

Large box = 50 pounds

Small box = 15 pounds

Step-by-step explanation:

Because there are 50 small boxes, the truck is carrying 50 combined large and small boxes. That means the area of those boxes are 50 * 65 = 3250 pounds. There are 10 large boxes left. 3750-3250 = 500. The weight of 10 large boxes is 500 pounds, which means 1 large box is 500/10 which is 50 pounds.

If a large box is 50 pounds, and the combined weight is 65 pounds, 65-50 = 15 pounds for a small box.

Answer:

Step-by-step explanation:

What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prismz is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.

How do I find the volume of a rectangular prism?

The rectangular prism volume formula is:

volume = h × w × l,

where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:

Find the box length. For example, it can be equal to 18 in.

Determine its width. Let's say you measured 12 in.

Find out the rectangular prism height. Assume it's 15 in.

Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².

Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To determine the diagonal of a rectangular prism, apply the formula:

diagonal = √(l² + h² + w²)

where h is prism height, w is its width, and l is its length.

Answer:

6.92 years

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount (in this case, $8800)

P = the initial investment (in this case, $4500)

r = the annual interest rate (in decimal form, so 6.8% = 0.068)

n = the number of times the interest is compounded per year (in this case, daily, so n = 365)

t = the number of years

We want to solve for t, so we can rearrange the formula as follows:

t = (ln(A/P)) / (n ln(1 + r/n))

where ln is the natural logarithm.

Plugging in the given values, we get:

t = (ln(8800/4500)) / (365 ln(1 + 0.068/365))

t ≈ 6.92

Therefore, it would take about 6.92 years (or about 7 years) for the investment to grow to $8800 at an annual interest rate of 6.8% compounded daily.

The number of National League players cards in the card collection in terms of the number of American League players cards can be expressed as 5x.

Let's start with the information given in the problem:

The baseball card collection contains five times as many National League players as American League players.

Let's use x to represent the number of American League players cards in the collection.

Since the collection contains five times as many National League players as American League players, we can express the number of National League players cards in terms of x as follows:

Number of National League players cards = 5 times the number of American League players cards

Number of National League players cards = 5x

So, if the number of American League players cards in the collection is x, then the number of National League players cards would be 5x, according to the problem statement.

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Answer:

[tex] {≈225.4 \: m}^{2} [/tex]

[tex] {≈248.2 \: m}^{2} [/tex]

Step-by-step explanation:

(My first few steps are in the photo I've added)

Now, we can find the area of the first cutout:

[tex]s(cutout1) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 114°}{360°} = \frac{36963\pi}{360°} = 102.6\pi[/tex]

We can also find the altitude of the first triangle using trigonometry:

[tex] \sin(∠obd) = \frac{od}{ob} [/tex]

We also need to find AB by using the Pythagorean theorem:

[tex] {ad}^{2} = {ao}^{2} - {od}^{2} = {18}^{2} - {5.56}^{2} = 293.0864[/tex]

[tex]ad > 0[/tex]

[tex]ad = \sqrt{293.0864} ≈ 17.12[/tex]

[tex]ab = 2 \times 17.12 = 34.24[/tex]

[tex]h1 = od = ob \times \sin(∠obd) = 18 \times \sin(18°)≈5.56[/tex]

Then, we can find the area of the 1st triangle:

[tex]s (1triangle)= \frac{1}{2} \times 5.56 \times 34.24 ≈95.19[/tex]

And we can also find the area 1:

[tex]area1 = s(cutout1) - s(triangle1) = 102.6\pi - 95.19≈225.25[/tex]

Now let's do the same thing with the second area:

[tex]s(cutout2) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 131°}{360°} = \frac{42444\pi}{360°} =117.9 \pi[/tex]

[tex] \sin(∠obe) = \frac{oe}{oc} [/tex]

[tex]h2 = oe = oc \times \sin(∠obe) = 18 \times \sin(24.5°)≈7.46[/tex]

[tex] {be}^{2} = {bo}^{2} - {oe}^{2} = {18}^{2} - {7.46}^{2} = 268.3484[/tex]

[tex]be > 0[/tex]

[tex]be = \sqrt{268.3484} ≈16.38[/tex]

[tex]bc = 2 \times 16.38 = 32.76[/tex]

[tex]s(triangle2) = \frac{1}{2} \times 7.46 \times 32.76 = 122.19[/tex]

[tex]area2 = s(cutout2) - s(triangle2) = 117.9\pi - 122.19≈248.2[/tex]

I don't know if I got this right, though...

The area of the shaded segments in the circle is 422.5 square meters

Given that

Radius = 18 meters

Angles = 114 degrees and 131 degrees

The area of the shaded segments is the sum of the area of the individual segments and this is calculated as

Segment area =  (½) × r² × [(π/180) θ – sin θ]

Using the above, we have

Shaded segments = (½) × 18² × [(114π/180) – sin (114)] + (½) × 18² × [(131π/180) – sin (131)]

Evaluate

Shaded segments = 422.5 square meters

Hence, the shaded segments is 422.5 square meters

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We can express this interval using set-builder notation as: {x | x > 4}

What is expression?

An expression consists of one or more numbers or variables along with one more operation.

The monthly costs of each plan as functions of the number of movies watched:

A(x) = 22 + x

B(x) = 14 + 3x

To graph these functions, we can plot several points for each one, as shown in follow fig.

A(x) - B(x) < 0

(22 + x) - (14 + 3x) < 0

22 + x - 14 - 3x < 0

-2x + 8 < 0

-2x < -8

x > 4

Therefore, Plan A is cheaper than Plan B for any number of movies watched greater than 4. We can express this interval using set-builder notation as: {x | x > 4}

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Answer:

A' (0, 0 )

Step-by-step explanation:

a translation of 5 units right adds 5 to the x- coordinate

a translation of 2 units down subtracts 2 from the y- coordinate

A (- 5, 2 ) → A' (- 5 + 5, 2 - 2 ) → A' (0, 0 )

The length of the missing leg of the triangle is 8 units. We have a right triangle ABC with angle BAC equal to 90 degrees. The length of one of the legs is 6 units, and the length of the hypotenuse is 10 units.

We are asked to find the length of the other leg of the triangle.

[tex]That is, a^2 + b^2 = c^2[/tex]

In this case, we know that the length of one leg is 6 units, and the length of the hypotenuse is 10 units. We can substitute these values into the Pythagorean theorem and solve for the missing leg:

[tex]a^2 + b^2 = c^2[/tex]

[tex]6^2 + b^2 = 10^2[/tex]

[tex]36 + b^2 = 100[/tex]

[tex]b^2 = 100 - 36[/tex]

[tex]b^2 = 64[/tex]

Taking the square root of both sides, we get:

b = 8

Therefore, the length of the missing leg of the triangle is 8 units.

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Answer:

1. 33 foot

2. 6.2 foot

Step-by-step explanation:

1.

Let's denote the height of the tree by "h". We can use the tangent function to solve the problem:

tangent of the angle of elevation = opposite / adjacent

In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree to the point on the ground where the angle of elevation is measured. So we have:

tan(35) = h / 47

To solve for "h", we can multiply both sides by 47:

h = 47 tan(35)

Using a calculator, we get:

h ≈ 32.9 feet

So the height of the tree to the nearest foot is 33 feet.

2.

Let's call the distance we're trying to find "x". We can use trigonometry to relate the angle and the length of the guy wire to the distance "x". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the distance "x", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:

sin(51) = x / 8

To solve for "x", we can multiply both sides by 8:

x = 8 sin(51)

Using a calculator, we get:

x ≈ 6.2 feet

So the stake is about 6.2 feet from the foot of the stop sign, to the nearest tenth of a foot.

Answer:

Step-by-step explanation:

um

The equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.

A tangent is a straight line or plane that touches a curve or curved surface at a single point, but does not intersect it at that point. The tangent line can be thought of as the instantaneous rate of change of the curve at that point. In calculus, the slope of the tangent line at a point on a curve is defined as the derivative of the curve at that point. The tangent line is often used to approximate the behavior of the curve near the point of tangency.

To find the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2), we need to use the slope-point form of the equation of a line.

First, we find the slope of the tangent line by taking the derivative of the function y = xlnx:

y = xlnx

y' = ln(x) + 1

At x = 2, we have:

y' = ln(2) + 1

So the slope of the tangent line at (2,2ln2) is ln(2) + 1.

Next, we use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the given point, and m is the slope we just found.

Substituting x1 = 2, y1 = 2ln2, and m = ln(2) + 1, we get:

y - 2ln2 = (ln(2) + 1)(x - 2)

Expanding and simplifying, we get the equation of the tangent line:

y = (ln(2) + 1)x - 2ln2 - 2

So the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.

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On solving the provided question we can say that Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Therefore there are 15 bottles that match both requirements (well arranged and Plastic #4).

The sample has 100 bottles in total.

As a result, the likelihood that a randomly chosen bottle is appropriately put AND is a Plastic #4 bottle is:

P(properly positioned and Plastic #4) = the number of bottles that match both requirements. / The sample's total number of bottles

P(properly positioned and Plastic #4) = 15 / 100

P(properly positioned and Plastic #4) = 0.15 or 15%

Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.

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The height of the flagpole is approximately 68.53 feet.

Trigonometric equations are equations that involve trigonometric functions such as sine, cosine, tangent, and their reciprocals. These equations typically involve finding the values of the angles or sides of a right-angled triangle or periodic functions that repeat themselves after certain intervals.

This problem involves finding the height of a flagpole using trigonometry. The surveyor measures the angle of elevation from the tripod to the top of the pole and knows the distance from the base of the pole to the tripod. By using the tangent function and the given angle, we can set up an equation that relates the height of the pole to the distance and the angle. We simplify the equation and solve for the unknown height, which gives us an approximate value of 68.53 feet.

the height of the flagpole, we can use trigonometry. Let's call the height of the flagpole "h".

Using the tangent function, we can set up the following equation:

tan(26) = h / (150 + 3)

The 3 feet is added to the distance because the tripod is 3 feet tall.

Simplifying this equation, we get:

tan(26) = h / 153

To solve for "h", we can multiply both sides by 153:

h = tan(26) * 153

Using a calculator, we can evaluate the right side of the equation to get:

h ≈ 68.53

Therefore, the height of the flagpole is approximately 68.53 feet.

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X=-10 when the points (-5, 6) and (x, 3) are elements of an inverse variation.

A relationship between two variables known as an inverse variation occurs when one variable increases while the other decreases, resulting in a constant product. Y = k/x, where k is a constant of variation, can be used to explain the relationship between two variables x and y if they are inversely proportional in mathematics.

The fact that their product must be constant allows us to determine the value of x because the points (-5, 6) and (x, 3) are components of an inverse variation.

As a result, x must be 10 to provide the elements of an inverse variation (-5, 6) and (x, 3).

x * 3 = -5 * 6

x = -30/3

x = -10

In conclusion, an inverse variation is a mathematical connection where the product of two variables stays constant.

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Answer:

180 cubic centimeters

Step-by-step explanation:

We can find the volume of a box by multiplying the dimensions of the box together.
In other words

Volume = length × width × height

Given dimensions

By plugging these given dimensions into the formula we acquire

Volume = 6 × 10 × 3

==> multiply 10 and 6

Volume = 60 × 3

==> multiply 60 and 3

Volume = 180

The volume of the box is 180 cubic centimeters.

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The correct equation to find the measure of ∠CMD is C. 15° + 30° = a; 90° – a = m.

It is formed when two straight lines intersect at a single point, creating two equal and opposite angles.

This is because the angles in a triangle must add up to 180°.

In this case, ∠FMD and ∠BMC are the two angles of the triangle, and the third angle is a right angle.

Therefore, the measure of ∠CMD must be 90°.

To find the measure of ∠CMD, we must first find the sum of ∠FMD and ∠BMC.

This can be done by setting up the equation 15° + 30° = a.

We then subtract this sum from 90° to get the measure of ∠CMD, which gives us the equation 90° – a = m.

Therefore, the correct equation to find the measure of ∠CMD is

15° + 30° = a; 90° – a = m.

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The solutions to the quadratic equation  [tex]5x^2 + 20x - 7 = 0[/tex] are[tex]x = -2 + \sqrt{(23/5)[/tex] and [tex]x = -2 - \sqrt{(23/5)[/tex].

A quadratic equation is a second-degree polynomial equation of the form [tex]ax^2 + bx + c = 0[/tex], where x is the variable, and a, b, and c are coefficients, where a is non-zero.

The square root is an important mathematical concept that arises in many areas of mathematics and science, such as geometry, algebra, and physics. It is used to calculate the length of sides of a right triangle, to solve quadratic equations, and to model the behavior of physical systems

The three steps Sergey could use to solve the quadratic equation by completing the square are:

Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex].

Add and subtract [tex](b/2a)^2[/tex] to complete the square:

[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]

Simplify the left side and solve for x by taking the square root:

[tex]5(x + 2)^2 = 11[/tex]

[tex](x + 2)^2 = 11/5[/tex]

[tex]x + 2 = \pm \sqrt{(11/5)[/tex]

[tex]x = -2 \pm \sqrt{(11/5)[/tex]

Therefore, the three correct options are:

[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]

[tex]5(x + 2)^2 = 11[/tex]

[tex](x + 2)^2 = 11/5, x = -2 \pm \sqrt{(11/5)[/tex]

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Answer: The common difference of the arithmetic sequence 10, 8, 6, 4, 2,… is -2. Note: By considering the formula of arithmetic sequence we verify the common difference which we obtained.

Answer:

-2

Step-by-step explanation:

In the sequence we have three kinds of sequence namely, arithmetic sequence, geometric sequence and harmonic sequence. In arithmetic sequence we the common difference between the two terms, In geometric sequence we the common ratio between the two terms, In harmonic sequence it is a ratio of arithmetic sequence to geometric sequence.

Answer:

White

Step-by-step explanation:

Number of favorable outcomes/Number of trails =4/20 or 1/5

The dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.

What is Rectangular prism ?

A rectangular prism is a three-dimensional geometric shape that has six faces, all of which are rectangles.

To label the dimensions of the net for the current cereal box, you need to identify the six faces of the rectangular prism that makes up the cereal box.

Start by drawing a rectangular prism with the given dimensions (12 inches high, 8 inches wide, and 2 inches deep).

Then, label each face with its dimensions, as follows:

The top face (which will be the same size as the bottom face) has dimensions 8 inches by 2 inches.

The front and back faces have dimensions 12 inches by 8 inches.

The left and right faces have dimensions 12 inches by 2 inches.

Top face: 8 in. x 2 in.

Front and back faces: 12 in. x 8 in.

Left and right faces: 12 in. x 2 in.

Therefore, Note that the dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.

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Answer: The square root of 10 is 3.162

147

$3 x 147 cookies = (approximately) $440

$440 x 2 = 880

Step-by-step explanation:

The number line is GREATER than but does not INCLUDE -4 ( due to the hollow dot)  and is less than or EQUAL to 5  (solid dot)

-4 < n ≤ 5

So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros

Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.

Here,

To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:

120 + 72 + 68 = 260

The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:

0.4615 x 1600 = 738.40 euros

Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:

0.2769 x 1600 = 443.04 euros

The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:

0.2615 x 1600 = 418.56 euros

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Complete question:

The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?

To approximate the value of log(3)15309 using log(3)7 = 1.7712, we can use the following steps:

Express 15309 as a power of 3:

15309 = 3^x

Take the logarithm base 3 of both sides:

log(3)15309 = x

Use log rules to simplify the expression:

log(3)15309 = log(3)(3^x)

log(3)15309 = x * log(3)3

log(3)15309 = x * 1

log(3)15309 = x

Substitute the value of x by using log(3)7 = 1.7712:

log(3)15309 ≈ 1.7712 * log(3)81 (since 81 is the largest power of 3 that is less than 15309)

log(3)15309 ≈ 1.7712 * 4

log(3)15309 ≈ 7.0848

Therefore, log(3)15309 ≈ 7.0848.

Answer:

$47.7

Step-by-step explanation:

You first have to find how much of 53 is 10%:  53/10 = 5.3  53-5.3= 47.7

The probability of winning the minimum award in the lottery is 0.00185%.

The possibility of an event occurring is expressed in terms of probability and odds. Probability is often stated as a decimal or percentage and represents the ratio of the number of likely outcomes to all conceivable possibilities. Conversely, odds are often stated as a ratio or fraction and are the ratio of the number of favourable events to the number of negative outcomes.

The probability of correctly matching two out of five white balls is given by the combination formula:

C(5,2) = 5! / (2! * (5-2)!) = 10

The probability of matching the gold ball is = 1/44.

Multiplying we have:

P(win minimum award) = (10 / C(54,5)) * (1 / 44) = 0.0000185, or approximately 0.00185%

Hence, the probability of winning the minimum award in the lottery is 0.00185%.

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Answer:

3 km

Step-by-step explanation:

3000 m = x km

1000 m = 1 km

Form a proportion to represent the situtation based on a conversion.

[tex]\frac{3000}{x} = \frac{1000}{1}[/tex]

Cross multiply.

1000x = 3000

x = 3 km

To calculate 3000 Meters to the corresponding value in Kilometers, multiply the quantity in Meters by 0.001 (conversion factor). In this case we should multiply 3000 Meters by 0.001 to get the equivalent result in Kilometers:

3000 Meters x 0.001 = 3 Kilometers

Therefore, 3000 Meters is equivalent to 3 Kilometers.