The polygons above are similar. Write a similarity statement and solve for x. The images are not drawn to scale.

To solve such problems, we need to know about Units conversion.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm,

though the real measurement is still the same the units and numerical values have been changed.

1 yard = 36 inches,

1 foot = 12 inches,

Given to us,

6 feet, 15 yards, 45 feet, 600 inches, 12 feet, 640 inches

Converting the units to inches,

1 foot = 12 inches,

6 feet = 6 x 12 = 72 inches,

45 feet = 45 x 12 = 540 inches,

12 feet = 12 x 12 = 144 inches,

1 yard = 36 inches,

15 yards = 15 x 36 = 540 inches,

As we can see above the value of 15 yards and 45 feet are equal to 540 inches, therefore, equal to each other.

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To determine which set is more variable, calculate their measures of variability such as range and standard deviation. Sets with larger range and standard deviation are considered more variable.

To determine which set is more variable, you need to calculate the measures of variability for both sets. The measures of variability commonly used are the range and standard deviation. The set with a larger range and standard deviation is considered to be more variable.

For example, if we have two sets of data: Set A (2, 4, 6, 8, 10) and Set B (3, 5, 7, 9, 11), we can calculate the range for both sets. The range of Set A is 10 - 2 = 8, while the range of Set B is 11 - 3 = 8. Both sets have the same range, so we need to calculate the standard deviation to determine which set is more variable.

By calculating the standard deviation, we find that Set A has a standard deviation of 2.83, while Set B has a standard deviation of 2.83 as well. Again, both sets have the same standard deviation, so in this example, both sets are equally variable.

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The odds against the next car leaving the parking lot being black are calculated by finding the number of black cars (6) and using the formula (Total cars - Black cars) : Black cars, which results in odds of 14:3.

To answer the question regarding the odds against the next car leaving the parking lot being black, we need to calculate the number of black cars and then the odds.

There are a total of 34 cars in the lot, with 20 green and 8 gold, so the rest are black.

To find the number of black cars, subtract the number of green and gold cars from the total:
34 (total cars) - 20 (green cars) - 8 (gold cars) = 6 (black cars).

The odds in favor of an event are the ratio of the probability of the event happening to the probability of it not happening. Therefore, the odds against an event are just the opposite -- the ratio of the probability of the event not happening to the probability of it happening.

To calculate the odds against picking a black car, we use this ratio:
Odds against a black car = (Total cars - Black cars) : Black cars
Odds against a black car = (34 - 6) : 6
Odds against a black car = 28 : 6
Odds against a black car = 14 : 3.

So, the odds against the next car leaving the lot being black are 14:3.

Based on the information given the total number of shapes on bretts paper is 24 shapes.

Using this formula

Total number of shapes=Number of shapes/Percentage of total sales

Where:

Number of shapes=6

Percentage of total sales=25% or .25

Let plug in the formula

Total number of shapes=6/.25

Total number of shapes=24 shapes

Inconclusion the total number of shapes on bretts paper is 24 shapes.

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To determine after how many years only 5 grams of radium will be present, we use the decay equation [tex]R = 100e^{-0.00043t}[/tex] to solve for t when R equals 5 grams, yielding approximately 1,605 years.

To determine after how many years only 5 grams of radium will be present, we can use the provided equation for radioactive decay: R = [tex]100e^{-0.00043t}[/tex]. We need to solve for when R equals 5 grams. Here are the steps:

After approximately 1,605 years, only 5 grams of radium will be present.

To find the time after which only 5 grams of radium remain, the exponential decay equation [tex]R = 10e^{-0.00043t[/tex] is solved using natural logarithms, yielding an approximate time of 1608 years.

To determine after how many years only 5 grams of radium will be present, we need to solve the exponential decay equation provided, R = [tex]10e^{-0.00043t[/tex], for t when R = 5 grams. We can do this using logarithms.

Set up the equation with R = 5: 5 = [tex]10e^{-0.00043t[/tex]

Divide both sides by 10 to isolate the exponential term: 0.5 = [tex]e^{-0.00043t[/tex]

Take the natural logarithm (ln) of both sides: ln(0.5) = ln([tex]e^{-0.00043t[/tex]), which simplifies to ln(0.5) = -0.00043t because the natural logarithm and the exponential function are inverses of each other.

Divide by -0.00043 to solve for t: t = ln(0.5) / -0.00043

Use a calculator to find the value of t: t ≈ 1608 years (rounded to the nearest whole year)

After approximately 1608 years, there will only be 5 grams of radium present in the container.

Answer:

The slopes of these other two segments would be 2.

Step-by-step explanation:

In order to find these slopes, you need to know that rectangles have right angles. Given this fact, we know these segments are perpendicular to the given segment. This means that we take the current slope (-1/2), we flip it, (-2) and negate it (2) to get the new slope.

Final answer:

The division of 4 1/4 by 1 1/2, when converted to improper fractions, results in 17/6, or 2 5/6 as a mixed number.

Explanation:

The question asks us to find the result of the division 4 1/4 divided by 1 1/2. To tackle this problem, we need to convert the mixed numbers into improper fractions and then perform the division by multiplying by the reciprocal. Here's how it is done step-by-step:

Convert mixed numbers to improper fractions:
4 1/4 = (4×4 + 1)/4 = 17/4 and
1 1/2 = (1×2 + 1)/2 = 3/2.

Divide the fractions by multiplying by the reciprocal of the divisor:
(17/4) × (2/3) = 34/12.

Simplify the result:
34/12 can be simplified to 17/6, or as a mixed number, 2 5/6.

Therefore, the answer to 4 1/4 divided by 1 1/2 is 2 5/6.

Answer:

What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?

Answer is B or # 2

The graph touches, but does not cross, the x–axis at x =    ⇒ 4.

The graph of the function crosses the x–axis at x =  ⇒ 0

Step-by-step explanation:

Answer:

The velocity of sound in air is 369 meters per second at 67 degrees Celcius.

Step-by-step explanation:

The veloctiy of sound in air is given by the equation

[tex]v=20\sqrt{273+t}[/tex]

where v is the velocity in meters per second and t is the temperature in degrees Celcius.

We need find the temperature when the velocity of sound in air is 369 meters per second.

Substitute v=369 in the give equation.

[tex]369=20\sqrt{273+t}[/tex]

Divide both sides by 20.

[tex]\frac{369}{20}=\sqrt{273+t}[/tex]

[tex]18.45=\sqrt{273+t}[/tex]

Taking square both the sides.

[tex](18.45)^2=273+t[/tex]

[tex]340.4025=273+t[/tex]

Subtract 273 from both the sides.

[tex]340.4025-273=t[/tex]

[tex]67.4025=t[/tex]

[tex]t\approx 67[/tex]

Therefore the velocity of sound in air is 369 meters per second at 67 degrees Celcius.

The other dimension of the rectangular lot is 120 feet.

In a rectangular lot, the diagonal forms a right triangle with the two sides of the rectangle. We can use the Pythagorean theorem to find the length of the other dimension of the lot.

Let's assume that the other dimension of the lot is x feet. The diagonal, which is 130 feet, is the hypotenuse of the right triangle. The two sides of the rectangle are 50 feet and x feet.

Using the Pythagorean theorem, we have:

x2 + 502 = 1302

x2 + 2500 = 16900

x2 = 14400

x = √14400 = 120

Therefore, the other dimension of the lot is 120 feet.