The loudness measured in decibels (dB) is defined by loudness =10 log I₀, where I is the intensity and I₀=10⁻¹² W/m² .The human threshold for pain is 120 dB. Instant perforation of the eardrum occurs at 160dB.


(a) Find the intensity of the sound with the top up and with the top down.

The probability of drawing at least one heart in a series of five consecutive fair draws, with replacement and shuffling, is approximately 0.864, or 86.4%.

To calculate the probability of drawing at least one heart in a series of five consecutive fair draws from a standard deck of cards, where the card drawn is returned to the deck and the deck is shuffled between each draw, we can use the concept of complementary probability.

The probability of drawing at least one heart is equal to 1 minus the probability of drawing no hearts in the five draws. Let's break it down step by step:

The probability of drawing a card that is not a heart in a single draw is 39/52 since there are 39 cards that are not hearts out of the total 52 cards in the deck.

Since the draws are independent and the card is returned to the deck and shuffled between each draw, the probability of drawing no hearts in five consecutive draws is (39/52) * (39/52) * (39/52) * (39/52) * (39/52) = (39/52)^5.

Therefore, the probability of drawing at least one heart is 1 - (39/52)^5.

Calculating this probability:

1 - (39/52)^5 ≈ 1 - 0.136 ≈ 0.864.

So, the probability of drawing at least one heart in a series of five consecutive fair draws, with replacement and shuffling, is approximately 0.864, or 86.4%.

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The equation which must be true about the diagram which represents the construction of a line parallel to AB, passing through point P is IJ = PQ.

The correct answer choice is option C.

IJ = PQ

corresponding angles are equal

Corresponding angles are angles which occupy the same position at each intersection where a straight line crosses two other straight lines.

Corresponding angles are equal when two lines are parallel.

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Step-by-step explanation:

x = the number

3.5 % = .035 in decimal

.035 * x = 49

x = 49 / (.035 ) = 1400

The two-column proof shows that if CD ≅ EF, then y=8. This is because the definition of congruent segments states that if two segments are congruent, then they have the same length. In this case, CD ≅ EF, so CD and EF have the same length, which is 4. Since CD = 4, then y = 4, as shown in the proof.

The first step in the proof is to state the given information. In this case, we are given that CD ≅ EF. The second step is to use the definition of congruent segments to show that DE = EF. The third step is to use the Segment Addition Postulate to show that DE + EF = 8. The fourth step is to simplify the expression DE + EF = 8 to 2EF = 8. The fifth step is to divide both sides of the equation 2EF = 8 by 2 to get EF = 4. The sixth step is to substitute EF = 4 into the equation CD = EF to get CD = 4. The seventh and final step is to use the definition of congruent segments to show that y = 4.

As shown in the proof, if CD ≅ EF, then y=8. This is because the definition of congruent segments states that if two segments are congruent, then they have the same length. In this case, CD ≅ EF, so CD and EF have the same length, which is 4. Since CD = 4, then y = 4, as shown in the proof.

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The equation |x + 2| = x + 2 is sometimes true. It holds true for all values of x except for x = -2.

The absolute value inequality or equation |x + 2| = x + 2 is sometimes true.

To determine when it is true, we need to consider two cases:

1. When x + 2 is non-negative (x + 2 ≥ 0):

  In this case, the absolute value of x + 2 is equal to x + 2 itself. Therefore, the equation simplifies to x + 2 = x + 2. This equation is always true for any value of x since the left side is equal to the right side.

2. When x + 2 is negative (x + 2 < 0):

  In this case, the absolute value of x + 2 is the negation of x + 2. Therefore, the equation becomes -(x + 2) = x + 2. We can solve this equation by isolating x on one side:

     -(x + 2) = x + 2

     -x - 2 = x + 2

     -2x = 4

     x = -2

So, for x + 2 < 0, the equation |x + 2| = x + 2 is true only when x = -2.

In summary, the equation |x + 2| = x + 2 is sometimes true. It holds true for all x values except for x = -2.

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Answer:

400:600 (meters) or 0.4:0.6 (kilometers)

Explanation:

1km is equal to 1000m. Considering our ratio is 2:3, it can also be seen as 4:6 which is equal to 10.

[tex]10[/tex] × [tex]100 = 1000[/tex]
[tex]4[/tex] × [tex]100 = 400[/tex]
[tex]6[/tex] × [tex]100 = 600[/tex]
[tex]400:600[/tex]

So our answer is 400:600, which can also be converted back to kilometers.

[tex]400[/tex] ÷ [tex]1000 = 0.4[/tex]
[tex]600[/tex] ÷ [tex]1000 = 0.6[/tex]
[tex]0.4:0.6[/tex]

Answer:

Step-by-step explanation:

First convert km to m

1km=1000m

then divide it into 5, because of 2+3

1000/5=200

2*200=400cm or 0.4km

3*200=600cm or 0.6km

The exact value of the given expression sin15° is 0.26.

Use the trigonometric identity cos 2a = 1-2sin²a

cos(30) = √3/2 = 1-2sin²(15)

2sin²(15) = 1-√3/2 = (2-√3)/2

sin²(15)=(2-√3)/2

sin(15)=±√(2-√3)/2

Since arc (15) deg is in Quadrant I, its sin is positive. Then,

sin(15)=√(2-√3)/2

Check by calculator.

√(2+√3)/2

= 0.52/2

=0.26

Therefore, the exact value of the given expression sin15° is 0.26.

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The graph representation of budget line is attached herewith.

To draw the budget line, we need to plot the different combinations of ATVs and snowmobiles that can be purchased within the given budget.

Given:

Budget for new vehicles: $375,000

Cost of ATVs: $7,500 each

Cost of snowmobiles: $12,500 each

We can use a graph with ATVs on the horizontal axis and snowmobiles on the vertical axis. The budget line will connect the points that represent the maximum number of vehicles that can be purchased within the budget.

To find the maximum number of ATVs that can be purchased, we divide the budget by the cost of ATVs:

Maximum number of ATVs = Budget / Cost of ATVs = $375,000 / $7,500 = 50 ATVs

To find the maximum number of snowmobiles that can be purchased, we divide the budget by the cost of snowmobiles:

Maximum number of snowmobiles = Budget / Cost of snowmobiles = $375,000 / $12,500 = 30 snowmobiles

Now, you can plot the budget line connecting the points (50, 0) and (0, 30) on the graph, representing the maximum combinations of ATVs and snowmobiles that can be purchased within the budget.

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The conditional "If there is no rain, then there is no rainbow" is equivalent to "Rain is a necessary condition for a rainbow."

The statement "Rain is a necessary condition for a rainbow" implies that if there is no rain, then there will be no rainbow. This is captured by the conditional "If there is no rain, then there is no rainbow." If the necessary condition of rain is not met, it follows that a rainbow cannot occur.

On the other hand, the remaining conditionals are not equivalent to the statement "Rain is a necessary condition for a rainbow."

The conditional "If there is no rainbow, then there is no rain" is the inverse of the original statement. It suggests that if there is no rainbow, it implies there is no rain. While it is true that rain is often associated with rainbows, the absence of a rainbow does not necessarily mean there is no rain. Therefore, the inverse is not equivalent.

The conditional "If there is a rainbow, then there is rain" is the converse of the original statement. It states that if there is a rainbow, it implies there is rain. While this is often the case, it does not capture the necessary condition aspect of the original statement. There can be other factors that contribute to the formation of a rainbow, such as water droplets in the atmosphere, without the presence of rain. Therefore, the converse is not equivalent.

The conditional "If there is rain, then there is a rainbow" is the contrapositive of the original statement. It suggests that if there is rain, it implies there is a rainbow. While rain is indeed a common condition for the formation of rainbows, it does not capture the necessary condition aspect of the original statement. There can be rain without the occurrence of a rainbow, such as in light drizzles or heavy downpours without sunlight. Therefore, the contrapositive is not equivalent.

In summary, the only conditional that is equivalent to "Rain is a necessary condition for a rainbow" is "If there is no rain, then there is no rainbow."

#Select which one(s) of the following conditionals are equivalent to Rain is a necessary condition for a rainbow. If there is no rainbow, then there is no rain If there is no rain, then there is no rainbow. If there is a rainbow, then there is rain If there is rain, then there is a rainbow.

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The mean of X+2W would be 110, The variance would be 1089 .The covariance of X and W can be calculated as  -45. The correlation coefficient of -0.25.

Given the distributions of two variables, X and W, we will explore various aspects of their relationship. First, assuming they are uncorrelated, we will calculate the mean and variance of the sum X+2W. Then, considering a correlation coefficient of -0.25 between X and W, we will determine the covariance of the two variables. Finally, we will find the probabilities of X+2W exceeding 120 and the probability of X being less than 50.

a. If X and W are uncorrelated, their covariance is zero. Thus, the mean of X+2W would be

E(X+2W) = E(X) + 2E(W)

= 30 + 2(40)

= 110.

The variance would be

Var(X+2W) = Var(X) + 4Var(W)

= 144 + 4(225)

= 1089.

b. To find the probability that X+2W > 120, we can standardize the distribution by subtracting the mean and dividing by the square root of the variance. Then, we can use the standard normal distribution table to find the probability. Alternatively, we can use software or calculators to calculate the cumulative probability.

c. With a correlation coefficient of -0.25, the covariance of X and W can be calculated as

Cov(X, W) = ρσ(X)σ(W)

= -0.25(12)(15)

= -45.

d. Using the same approach as in part b, we can calculate the probability that X+2W > 120 considering the correlation coefficient of -0.25.

e. To find the probability that X < 50, we can again standardize the distribution of X and use the standard normal distribution table or appropriate tools for calculation.

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The remainder is equal to 13/8. The Remainder Theorem states that if a polynomial f(x) is divided by a linear polynomial of the form x - a, then the remainder is equal to f(a).

In this case, we have f(x) = x³ - 4x² + 8x + 2 and we want to divide it by the linear polynomial x - 1/2.

To find the remainder, we substitute 1/2 into the polynomial f(x) and evaluate it.

f(1/2) = (1/2)³ - 4(1/2)² + 8(1/2) + 2

      = 1/8 - 4/4 + 4 + 2

      = 1/8 - 1 + 4 + 2

      = 1/8 + 5

      = 13/8

Therefore, the remainder when f(x) is divided by x - 1/2 is 13/8.

The Remainder Theorem is a useful tool in polynomial division. It allows us to find the remainder when a polynomial is divided by a linear polynomial by simply evaluating the polynomial at the given value.

In this case, we are given the polynomial f(x) = x³ - 4x² + 8x + 2 and we want to divide it by the linear polynomial x - 1/2. According to the Remainder Theorem, the remainder will be equal to f(a) where a is the value inside the linear polynomial.

By substituting 1/2 into f(x), we evaluate the polynomial at that point. This involves replacing every instance of x in the polynomial with 1/2 and simplifying the expression. The result is 13/8, which represents the remainder when f(x) is divided by x - 1/2.

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Answer:

P(at least one hit) = 1 - .799⁴

= about .5924

= about 59.24%

The value of l is either 2 or 3, depending on whether the second letter drawn is b or not, respectively.The problem can be solved using the pigeonhole principle. We can draw letters one by one until we have seen any two of a, b, and c, but not all of them.

To minimize the number of letters drawn, we want to draw as few letters as possible before seeing any two of a, b, and c. We can start by assuming that the first letter drawn is a. Then, there are two cases to consider:

Case 1: The second letter drawn is b.

In this case, we have seen both a and b, so we stop drawing letters. The value of l is 2.

Case 2: The second letter drawn is not b (i.e., it is either a or c).

In this case, we need to draw one more letter to ensure that we have seen any two of a, b, and c. If the third letter is the same as the second letter, then we keep drawing letters until we see a different letter. Therefore, the maximum number of letters we need to draw in this case is 3.

Therefore, the value of l is either 2 or 3, depending on whether the second letter drawn is b or not, respectively.

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The final answer is:

f(x+h) = x² + 2xh + h² + 3x + 3h

To evaluate the function f(x) = x² + 3x for the given value of x+h, we substitute x+h into the function wherever we see x. This substitution allows us to find the value of the function at a specific point x+h.

In this case, when we substitute x+h into the function, we have:

f(x+h) = (x+h)² + 3(x+h)

Next, we expand and simplify the expression. For the first term (x+h)², we apply the binomial expansion formula:

(x+h)² = x² + 2xh + h²

For the second term 3(x+h), we distribute the 3 to both x and h:

3(x+h) = 3x + 3h

Combining these terms, we have:

f(x+h) = x² + 2xh + h² + 3x + 3h

This is the simplified expression for f(x+h) after substituting x+h into the function f(x). It represents the value of the function at the point x+h

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The function crosses the midline during the transition from a negative to a positive value or vice versa. The midline represents the horizontal line that divides the graph of the function into two equal halves.

In a periodic function, such as a sine or cosine function, the midline is the horizontal line that represents the average value of the function. It is positioned halfway between the maximum and minimum values of the function. The midline corresponds to the x-axis or y-axis, depending on the orientation of the graph. When the function crosses the midline, it indicates a change in the direction of the function from positive to negative or vice versa.

For example, in a sine function, the midline is the x-axis, and the function oscillates above and below this line. The function crosses the midline at the highest and lowest points of its oscillation, representing the transition from positive to negative or vice versa. Similarly, in a cosine function, the midline is the y-axis, and the function transitions from positive to negative or vice versa when it crosses this line. The midline serves as a reference point for understanding the behavior and characteristics of the function's graph.

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The radius of the circle with a central angle of 261 degrees that intercepts an arc with a length of 5 miles is approximately 2.184 miles.

To find the radius of a circle with a central angle of 261 degrees that intercepts an arc with a length of 5 miles, we can use the formula relating the central angle, arc length, and radius of a circle.

The formula is given as: Arc Length = (Central Angle / 360 degrees) * (2π * Radius)

In this case, we are given the central angle (261 degrees) and the arc length (5 miles), and we need to solve for the radius.

Rearranging the formula, we have: Radius = (Arc Length / (Central Angle / 360 degrees)) * (1 / 2π)

Substituting the given values into the formula, we get: Radius = (5 miles / (261 degrees / 360 degrees)) * (1 / 2π)

Simplifying further, we have: Radius = (5 miles / 0.725) * (1 / 2π)

Finally, evaluating the expression, we find the radius of the circle to be approximately 2.184 miles.

Therefore, the radius of the circle with a central angle of 261 degrees that intercepts an arc with a length of 5 miles is approximately 2.184 miles.

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Answer:

65.1 degrees north of east

Step-by-step explanation:

The boat sails 285 miles south, which means it moves in the direction of south (S) on the diagram. Then it sails 132 miles west, which means it moves in the direction of west (W) on the diagram. We draw a vector diagram to represent the boat's motion (I attached a picture of the diagram)

The boat's motion can be represented by a resultant vector R, which is the vector that connects the starting point to the ending point of the boat's motion. We want to find the direction of this vector.

R^2 = (285 miles)^2 + (132 miles)^2

R = √((285 miles)^2 + (132 miles)^2)

R ≈ 316.2 miles

Now we can use trigonometry to find the angle θ between the resultant vector and the east direction.

tan θ = opposite/adjacent

tan θ = 285 miles / 132 miles

θ = atan(285 miles / 132 miles)

θ ≈ 65.1 degrees

So, the direction of the boat's resultant vector is 65.1 degrees north of east (NE).

The two constructions for determining the type of triangle are the construction of medians and the construction of perpendicular bisectors.

To construct the medians of a triangle, draw a line segment from each vertex of the triangle to the midpoint of the opposite side. The point where the medians intersect is called the centroid. By observing the lengths of the medians, you can determine the type of triangle. If all three medians are of equal length, the triangle is an equilateral triangle. If two medians are of equal length and one is shorter, it is an isosceles triangle. If all three medians have different lengths, it is a scalene triangle.

To construct the perpendicular bisectors of a triangle, draw a line segment perpendicular to each side of the triangle at its midpoint. The point where the perpendicular bisectors intersect is called the circumcenter. By analyzing the lengths of the perpendicular bisectors, you can determine the type of triangle. If all three perpendicular bisectors are of equal length, the triangle is an equilateral triangle. If two perpendicular bisectors are of equal length and one is shorter, it is an isosceles triangle. If all three perpendicular bisectors have different lengths, it is a scalene triangle. These constructions provide geometric methods for classifying triangles based on their side lengths and help identify their respective types.

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Answer:

first use 360 minis 62

Step-by-step explanation:

than find b to c than the remaining should be the anser letw know if whorng so i can help

Yes, the highlighter will fit in the 10 cm by 7 cm box as its area is smaller than the box's area.

According to the given data,

It states that each highlighter is an equilateral triangle with 9-centimeter sides, and we are asked if it will fit in a 10-centimeter by 7-centimeter rectangular box.

To solve this,

Determine the area of the highlighter and compare it to the area of the box.

The formula for the area of an equilateral triangle is,

A = (√(3)/4)s²,

Where s is the length of one side.

Plugging in s = 9,

We get

A = (√(3)/4)(9)²,

Which simplifies to

A = 81(√(3))/4

  ≈ 37.07 cm².

Next, we need to find the area of the box, which is simply length times width.

Multiplying 10 cm by 7 cm gives us an area of 70 cm².

Comparing the two areas, we see that the highlighter's area is smaller than the box's area.

Therefore, the highlighter should fit inside the box without any issues.

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The number 8.49 × 10⁻⁷ in decimal form is 0.000000849.

When a number is expressed in scientific notation, such as 8.49 × 10⁻⁷, it means that we need to multiply the first part (8.49) by the power of 10 raised to the exponent (-7). In this case, the exponent is negative, indicating that the decimal point needs to be shifted to the left.

To convert the number into decimal form, we move the decimal point 7 places to the left since the exponent is -7. This gives us the decimal representation of 0.000000849.

So, the correct answer is 0.000000849.

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To determine the volume of the metal, we can use the formula. The height of the metal is approximately 7.545 meters.

Volume = Length × Width × Height

We need to convert the volume from cubic centimeters (cm³) to cubic meters (m³) since the given dimensions are in meters.

1 cm³ = 0.000001 m³

Converting the volume to cubic meters:

Volume = 869.0 cm³ × 0.000001 m³/cm³

Volume = 0.000869 m³

Now, we can find the height of the metal by rearranging the volume formula:

Height = Volume / (Length × Width)

Height = 0.000869 m³ / (0.06519 meters × 0.1881 meters)

Height ≈ 7.545 meters

Therefore, the height of the metal is approximately 7.545 meters.

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The probability that exactly 10 are yellow out of 9 random selections is 0.

To calculate the probability of exactly 10 jelly beans being yellow out of 9 selected at random, we need to consider the total number of favorable outcomes (selecting exactly 10 yellow jelly beans) divided by the total number of possible outcomes (selecting any 9 jelly beans).

The total number of jelly beans in the box is 23 (yellow) + 33 (green) + 37 (red) = 93.

The number of ways to select exactly 10 yellow jelly beans out of 9 is 0, as we have fewer yellow jelly beans than the required number.

Therefore, the probability of exactly 10 yellow jelly beans is 0.

In this case, it is not possible to have exactly 10 yellow jelly beans out of the 9 selected because there are not enough yellow jelly beans available in the box.

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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that: exactly 10 are yellow?

The equation for the indifference curve using the values A=4, alpha=2/5, and beta=3/5 is [tex]Y=4*(X^(2/5))*(Z^(3/5)).[/tex]

The equation for the indifference curve represents combinations of two goods, X and Z, that provide the same level of utility or satisfaction to an individual. In this case, the values provided are A=4, alpha=2/5, and beta=3/5.

The general form of the equation for the indifference curve is given by [tex]Y=A*(X^alpha)*(Z^beta)[/tex], where Y represents the level of utility, X represents the quantity of good X consumed, and Z represents the quantity of good Z consumed.

By substituting the given values, the equation for the indifference curve becomes [tex]Y=4*(X^(2/5))*(Z^(3/5))[/tex]. This equation shows that the level of utility, Y, is determined by the quantities of goods X and Z, with X raised to the power of 2/5 and Z raised to the power of 3/5, and multiplied by the scaling factor A=4.

Therefore, the equation for the indifference curve is [tex]Y=4*(X^(2/5))*(Z^(3/5))[/tex] based on the provided values of A, alpha, and beta.

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The sum and product of the roots of a given quadratic equation,

2x²+3x-2 =0, are -3 and -1 respectively.

The given quadratic equation is,

2x²+3 x-2=0

Since we know that,

if ax² + bx + c have roots x and y then

Sum of roots: x+y = -b/a

Product of roots: xy = c/a

Here we have,

a = 2, b = 3, c = -2

Therefore,

Sum of roots = -3/2

                     = -3

Product of roots = -2/2

                           = -1

Hence the sum and product of roots are -3 and -1 respectively.

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To determine the number of gold atoms in the coin, we need to use the molar mass of gold and Avogadro's number. The number of gold atoms in the coin is approximately 1.068 × 10^22 atoms. None of the provided options matches this value.

1. Find the molar mass of gold (Au):

The molar mass of gold is the atomic mass of gold, which can be found on the periodic table. The atomic mass of gold is approximately 197 g/mol.

2. Convert the mass of the coin to moles:

Number of moles = Mass / Molar mass

Number of moles = 3.5 g / 197 g/mol ≈ 0.01777 mol

3. Calculate the number of atoms:

Number of atoms = Number of moles × Avogadro's number

Number of atoms = 0.01777 mol × 6.022 × 10^23 atoms/mol ≈ 1.068 × 10^22 atoms

Therefore, the number of gold atoms in the coin is approximately 1.068 × 10^22 atoms. None of the provided options matches this value.

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The best description of the population of interest in Pew's stricter gun laws survey is B. All adults in the United States."

The survey aimed to gather information and insights from a representative sample of the entire adult population in the United States regarding their support for stricter gun laws. Therefore, the results and conclusions drawn from the survey were intended to represent the broader population of all adults in the country.

The population of interest in Pew's stricter gun laws survey is all adults in the United States. This is because the survey was designed to collect data on the opinions of all adults in the United States, not just adults with US addresses, adults in households with the next birthday, or adults who responded to the survey.

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In May, 2021, the Pew Research Center reported the results from one its surveys about whether US adults support stricter gun laws. To obtain a random sample of US adults, Pew mailed invitations via the US Postal Service to randomly selected address-based households in the United States. The adult member of the household with the next birthday was invited to participate in the survey. Of the 5,970 households who received invitations, 5,109 completed the survey in April, 2021. Of those who were interviewed, 53% supported stricter guns laws than currently exist in the United States.

Which of the following best describes the population of interest in Pew's stricter gun laws survey?

Adults with US addresses

All adults in the United States

Adults in each household with the next birthday

O 5.109 U.S. adults

53% who favored stricter gun laws in the United States

The cost of the delivery truck between 1 mile and 2 miles is constant.

According to the given information, the delivery truck driver charges a fixed base price of $6 for 2 miles. This means that irrespective of whether the distance traveled is 1 mile or 2 miles, the cost remains the same.

The additional charges of $2 per mile or $4 per mile mentioned in the subsequent statements are applicable only after the initial 2 miles. Since we are specifically looking at the cost between 1 mile and 2 miles, these additional charges do not come into play.

Therefore, the cost during this range remains constant at $6.

In this scenario, the driver charges a fixed base price for the first 2 miles, which is $6. The additional charges per mile mentioned after the 2-mile mark are irrelevant when considering the range between 1 mile and 2 miles.

Therefore, the cost of the delivery truck within this range is constant at $6. The additional charges mentioned for distances beyond 2 miles, such as $2 per mile or $4 per mile, are not applicable within the 1-2 mile range.

It is essential to consider the specific information given in the question and focus on the relevant range to determine the correct answer.

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The measure of -225° in radians is -5π/4 or approximately -3.93 radians. To convert degrees to radians, we use the conversion factor that states 180° is equal to π radians.

In this case, we have -225°. To convert this to radians, we divide -225° by 180° and multiply by π. This gives us (-225/180) * π, which simplifies to -5π/4. As a decimal approximation, we can evaluate -5π/4. Using the approximate value of π as 3.14, we get (-5 * 3.14)/4 = -15.7/4 ≈ -3.93 radians rounded to the nearest hundredth.

Therefore, the measure of -225° in radians is -5π/4 or approximately -3.93 radians.

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The equation of a line perpendicular to y=-2 x+6 containing (3,2) in slope-intercept form: y = 0.5 x - 0.5

Two lines are perpendicular if their slopes are negative reciprocals of each other. The slope of y=-2 x+6 is -2, so the slope of the perpendicular line will be 1/2.

We can plug the point (3,2) into the slope-intercept form of a line, y = mx + b, to solve for b, the y-intercept.

```

2 = (1/2) * 3 + b

```

```

2 = 1.5 + b

```

```

b = 2 - 1.5 = 0.5

```

Therefore, the equation of the perpendicular line is y = 0.5 x + 0.5.

Here is a graph of the two lines:

```

[asy]

unitsize(1 cm);

draw((-1,0)--(6,0));

draw((0,-1)--(0,4));

draw((3,2)--(3,0.5));

draw((-0.5,4)--(5.5,-0.5),dashed);

label("y = -2 x + 6", (6,4), E);

label("y = 0.5 x + 0.5", (3,0.5), NE);

dot("(3,2)", (3,2), SW);

[/asy]

```

As you can see, the two lines intersect at the point (3,2), and their slopes are negative reciprocals of each other.

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