The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. Speed (MPH) Cars 30-39 5 40-49 18 50-59 50 60-69 17 70-79 10

For length of 50 yards , the width is 60 yards, for length of 40 yards , the width is 75 yards, for length of 48 yards, the width is 62.5 yards , for length of 36 yards, the width is 83.33 yards, they are inversely proportional.

The formula for the area of a rectangle is: Area = Length * Width.

So, for the given case, we have:

Area = 3000 square yards

Length = 50 yards, 40 yards, 48 yards, or 36 yards

Therefore, the width of the plot in each case can be calculated as:

For Length = 50 yards,

Width = Area / Length

= 3000 / 50

= 60 yards

For Length = 40 yards,

Width = Area / Length

= 3000 / 40

= 75 yards

For Length = 48 yards,

Width = Area / Length

= 3000 / 48

= 62.5 yards

For Length = 36 yards,

Width = Area / Length

= 3000 / 36

= 83.33 yards

Therefore, the width of the plot depends on the length chosen and they are inversely proportional. When the length increases, the width decreases, and when the length decreases, the width increases.

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Answer:

The first graph, the one your cursor is on

Step-by-step explanation:

This is the graph of f(x) = 4^x so the first one

neither, perpendicular,parallel, parallel

Question 22:
To determine if the lines are parallel, perpendicular, or neither, we need to compare their slopes. Let's find the slopes of the given lines.

First equation: 6x + 10y = 20
To find the slope, let's solve for y in terms of x:
10y = -6x + 20
y = (-6/10)x + 2
Slope of the first line: -6/10 = -3/5

Second equation: 5x - 3y = 21
To find the slope, let's solve for y in terms of x:
-3y = -5x + 21
y = (5/3)x - 7
Slope of the second line: 5/3

The slopes of the two lines are not equal, so they are not parallel. Additionally, the product of their slopes is not -1, so they are not perpendicular either. Therefore, the lines in question 22 are

neither parallel nor perpendicular

.

Question 23:
Let's find the slopes of the given lines.

First equation: x - y = 4
To find the slope, let's solve for y in terms of x:
-y = -x + 4
y = x - 4
Slope of the first line: 1

Second equation: x + y = 9
To find the slope, let's solve for y in terms of x:
y = -x + 9
Slope of the second line: -1

The slopes of the two lines are negative reciprocals of each other (-1 * 1 = -1), which means they are perpendicular. Therefore, the lines in question

23 are perpendicular

.

Question 24:
Let's find the slopes of the given lines.

First equation: x - 5y = 30
To find the slope, let's solve for y in terms of x:
-5y = -x + 30
y = (1/5)x - 6
Slope of the first line: 1/5

Second equation: 10y = 2x + 90
To find the slope, let's solve for y in terms of x:
y = (2/10)x + 9
y = (1/5)x + 9
Slope of the second line: 1/5

The slopes of the two lines are equal (1/5 = 1/5), so they are parallel. Therefore, the lines in question

24 are parallel.

Question 25:
The equations in question 25 are both in the form "x = constant." Since the slopes of these lines are undefined, we cannot determine by slope, but we can easily see that these lines are

parallel

To summarize:
- Question 22: The lines are neither parallel nor perpendicular.
- Question 23: The lines are perpendicular.
- Question 24: The lines are parallel.
- Question 25: The lines are parallel

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There are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same. We can solve this problem using Burnside's Lemma.

Burnside's Lemma states that for a group action on a set, the number of fixed points is given by the average over the group of the number of fixed points under a particular group element, where the average is taken over all group elements.

In this case, the group action is the action of rotating and reflecting the grid, and the set is the set of all possible bead arrangements in the grid. To use Burnside's Lemma, we need to find the number of fixed points (i.e., bead arrangements that are unchanged) under each group element, and then take the average over all group elements.

There are a total of $4$ rotations and $2$ reflections possible for a 2x3 grid.

The identity transformation keeps the grid in its original position, and thus there are

6!/(2!3!) = 60

The $90 rotation keeps $3 beads in the same place and switches the other $3, and similarly $180 and $270 rotation also keeps $3 beads in the same place and switches the other $3$, thus there are

3! = 6

The reflection on the horizontal axis keeps $3 beads in the same place and switches the other $3, and similarly the reflection on the vertical axis also keeps $3 beads in the same place and switches the other $3, thus there are

3! = 6

So the average number of fixed points is $(6+6+6+60)/8 = \(\frac{78}{8}\) = 9.75$

So, there are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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The estimates of the functions are x = 0.25 and 1.25 whe y = 0 and x = 0.5 and 1.5 when y = 2

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

y = 4x² - 4x– 1

Using the graph, we have the following readings

x = 0.25 and 1.25 when 4x² - 4x– 1 = 0

Similarly, we have the following readings

x = 0.5 and 1.5 when 4x² - 4x– 1 = 2

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Answer:y=8

Step-by-step explanation:

Answer:

\(\frac{1}{4}\)

Step-by-step explanation:

Using the rule of exponents / radicals

\(a^{\frac{m}{n} }\) = \((\sqrt[n]{a})^m\)

\(a^{-m}\) = \(\frac{1}{a^{m} }\) , then

\(-8^{-\frac{2}{3} }\)

= \(\frac{1}{-8^{\frac{2}{3} } }\)

= \(\frac{1}{(\sqrt[3]{-8})^2 }\)

= \(\frac{1}{-2)^{2} }\)

= \(\frac{1}{4}\)

The power of the lens is 2.5D

The focal length of 40 cm and a diameter of 5.0 cm.

Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device: P = 1/f.

Power of lens = 1 / focal length (in meters)

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive and is the distance at which a beam of collimated light will be focused to a single spot.

we have focal length 40cm (.4 m)

so

Converging lenses have positive optical power, while diverging lenses have negative power.

Power of lens = 1/0.4 m

=2.5 D  [The unit of Power of lens is Dioptre]

Therefore, the power of the lens that has a focal length and a diameter of 5.0 cm is 2.5D

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Answer:

your answer would be 9.4

Step-by-step explanation:

you'd have to plug in the numbers in the equation.

8^2 + 5^2 = c^2

64 + 25 = c^2

89 = c^2 then you'd do the square root of 89 which will give you 9.4 when rounded to the nearest tenth.

I apologize, but as a text-based AI model, I am unable to provide handwritten answers or show work in form of formulas. To determine annual interest rate of 4.5%, we can use compound interest formula.

To determine how long it will take to double your money with an annual interest rate of 4.5%, we can use the compound interest formula:

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

Where:

A = Final amount (double the initial amount)

P = Principal (initial amount)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Time (in years)

In this case, we want to find the value of t. Let's assume the initial amount is P, and the final amount is 2P (double the initial amount). Substituting these values into the formula, we have:

2P = P(1 + 0.045/n)^(nt)

To solve for t, we can divide both sides of the equation by P and simplify:

2 = (1 + 0.045/n)^(nt)

Taking the natural logarithm (ln) of both sides of the equation:

ln(2) = nt ln(1 + 0.045/n)

Now, we can solve for t:

t = ln(2) / (n ln(1 + 0.045/n))

The value of n will depend on how frequently the interest is compounded (e.g., annually, semi-annually, quarterly, etc.). By substituting the appropriate value for n and evaluating the expression, you can determine the time it will take to double your money.                                              Note: If you provide the specific compounding period, I can assist you in calculating the exact time it takes to double your money.

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Answer:

-1/2 π

Step-by-step explanation:

10sinA - 3sinA =9-16

7sinA = -7

sinA =-1

A= sin inverse of -1

Answer:

29/13

Step-by-step explanation:

The equation is a/b*13=29. So, if we divide the whole thing by 13m we get a/b=29/13. This means that a=29 and b=13. 29/13 is the maximum it can be simplified.

The limit of f(x) as x approaches any value in (0, 1) is 2 - 1 = 1. Hence, f(x) is continuous on (0, 1).

To show that the given functions are continuous on the interval (0, 1), we can make use of limit theorems.

(a) For the function f(x) = 2+1-2, we can use the sum rule of limits, which states that the limit of the sum of two functions is equal to the sum of their limits. We can evaluate the limits of each term separately. The limit of the constant function 2 is 2, and the limit of the function 1-2 as x approaches any value is -1. Therefore, the limit of f(x) as x approaches any value in (0, 1) is 2 - 1 = 1. Hence, f(x) is continuous on (0, 1).

(b) For the function f(x) = 3 I=1 CON +0 =0, we can use the product rule of limits, which states that the limit of the product of two functions is equal to the product of their limits. We can evaluate the limits of each term separately. The limit of the constant function 3 is 3, and the limit of the function I=1 CON +0 =0 as x approaches any value is 0. Therefore, the limit of f(x) as x approaches any value in (0, 1) is 3 * 0 = 0. Hence, f(x) is continuous on (0, 1).

(e) For the function f(x) = 10 Svir sin, we can use the composition rule of limits, which states that the limit of the composition of two functions is equal to the composition of their limits. We can evaluate the limits of each function separately. The limit of the function 10 as x approaches any value is 10, and the limit of the function Svir sin as x approaches any value is sin(a), where a is a constant. Therefore, the limit of f(x) as x approaches any value in (0, 1) is 10 * sin(a), which is a constant. Hence, f(x) is continuous on (0, 1).

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The normal distribution that best approximates X is N(18, 3).To determine the normal distribution that best approximates the number of heads (X) when a fair coin is flipped 36 times, we can use the Central Limit Theorem.

According to the Central Limit Theorem, for a large enough sample size (in this case, 36 coin flips), the distribution of the sample mean will be approximately normal, regardless of the underlying distribution.

Since the coin is fair, the probability of getting a head (success) is 0.5, and the probability of getting a tail (failure) is also 0.5.

The mean of the binomial distribution is given by μ = n * p, where n is the number of trials and p is the probability of success. In this case, μ = 36 * 0.5 = 18.

The standard deviation of the binomial distribution is given by σ = sqrt(n * p * (1 - p)), where n is the number of trials and p is the probability of success. In this case, σ = sqrt(36 * 0.5 * (1 - 0.5)) = sqrt(9) = 3.

Since X represents the number of heads, which is a count, we can approximate it with a normal distribution with mean μ = 18 and standard deviation σ = 3.

Therefore, the normal distribution that best approximates X is N(18, 3).

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Answer:

oh srry ur not a scam

Step-by-step explanation:

Answer:

#1: (Problem 3² × 3³, Answer: 243) (Problem 3⁵, Answer: 243), yes the answer matches

#2: (Problem 2³ × 2⁴, Answer: 128) (Problem 2¹², Answer: 4096), No, the answer doesn't match.

#3: (Problem (-2)⁴ × (-2)², Answer: 64) (Problem (-2)⁸, Answer: 256), No the answer doesn't match.

#4: (Problem (-3)² × (-3)⁵, Answer: -2187) (Problem (-3)⁷, Answer: -2187), yes the answer matches

The pattern is: When 2 whole numbers raised to a power are multiplied together, the base stays the same and the exponent add up

Hope this helps!

In the given figure of Rhombus, Angle ∠BAD is 0°. In summary: angle ∠ABC = 135°

angle ∠ADC = 135°

angle ∠BAD = 0°

What is rhombus?

A rhombus is a quadrilateral (four-sided) geometric shape with equal-length sides. Since it has two sets of opposite equal acute angles and opposite equal obtuse angles, it is also known as a diamond form. In other words, the opposite angles and the neighbouring sides of a rhombus are congruent. A rhombus has two equal-length diagonals that are right angles to one another. A rhombus's area is equal to the product of its diagonal lengths.

by the question.

In a rhombus, opposite angles are equal, so we know that:

angle ∠ABC = angle ∠ADC (opposite angles of rhombus)

angle ∠BCD = angle ∠BAD (opposite angles of rhombus)

We are given that angle ∠ADC is 135°. Therefore, angle ∠ABC is also 135°.

To find angle ∠BAD, we can use the fact that the angles of a quadrilateral sum to 360°. Since we know three of the angles (∠ABC, ∠BCD, and ∠ADC), we can find the fourth angle (∠BAD) by subtracting their sum from 360°:

∠BAD = 360° - (∠ABC + ∠BCD + ∠ADC)

= 360° - (135° + 90° + 135°)

= 360° - 360°

= 0°

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

The equation of the function is y = 10 * sin(x/2pi) + 5.

What is the sinusoidal function?

The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.

The graph of a sinusoidal function can be represented by the equation:

y = A * sin(B(x - C)) + D

where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.

From the information given, we know that the maximum point is at (0,5) and the minimum point is at (2pi,-5). We can use this information to find the values of A, B, C, and D.

The amplitude is the distance between the maximum and minimum points. In this case, it is 5 - (-5) = 10. So A = 10.

The period of the function is the distance between two consecutive maximum or minimum points. In this case, it is 2π.

So the frequency is 1/2π.

The horizontal shift is the amount by which the function is shifted along the x-axis. In this case, the maximum point is at x = 0, so the function is not shifted horizontally. So C = 0.

The vertical shift is the amount by which the function is shifted along the y-axis. In this case, the maximum point is at y = 5, so the function is shifted upward by 5. So D = 5.

So the equation of the function is:

y = 10 * sin(1/2pi (x - 0)) + 5

y = 10 * sin(x/2pi) + 5

where x is entered in radians.

Hence, the equation of the function is y = 10 * sin(x/2pi) + 5.

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Answer:

6,12,18,24,36,42,48,5,60,66,72,78,84,90,96

Step-by-step explanation:

got a friend help

The trend model that allows for one change in the direction of a series is:  A. linear trend model.

Here, we have,

The linear trend model is a commonly used technique in time series analysis, particularly when the data is expected to exhibit a consistent rate of growth or change over time.

First, Collect and organize your data, Before you can apply the linear trend model, you need to have a clear understanding of the data you're working with.

Then Plot your data on a graph, Once you have your data organized, the next step is to plot it on a graph. This will help you visualize any trends or patterns that may be present in the data.

Next, Calculate the slope of the line, To determine the rate of change in your data, you'll need to calculate the slope of the line. This is done using a formula called the least squares regression line.

And then determine the intercept of the line, by using the intercept of the line represents the starting point for the data. In other words, it's the value of the data at the beginning of the time series.

Finally, use the linear trend model to make predictions, Once you've calculated the slope and intercept of the line, you can use the linear trend model to make predictions about future values of the data.

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Answer:

2334

Step-by-step explanation:

hi

Answer:

Step-by-step explanation:

12 feet *12 inches per foot= 144 inches

144/4=36 stickers

The probability of AT LEAST TWELVE of the 14 randomly selected people having brown eyes is 0.147, rounded to three significant figures.

To find the probability of AT LEAST TWELVE of the 14 randomly selected people having brown eyes, we need to calculate the probability of twelve, thirteen, and fourteen successes, and then sum these probabilities together.

Using the binomial formula:

P(X ≥ x) = P(X = x) + P(X = x+1) + ... + P(X = n)

Where:

P(X ≥ x) is the probability of at least x successes

P(X = x) is the probability of exactly x successes

n is the number of trials (14 people)

x is the minimum number of successes (12 people)

p is the probability of success (0.40 for brown eyes)

(1 - p) is the probability of failure (not having brown eyes)

Using Excel, we can calculate the probability using the following formula:

=1 - BINOMDIST(11, 14, 0.40, TRUE)

The result is approximately 0.147.

Therefore, the probability of AT LEAST TWELVE of the 14 randomly selected people having brown eyes is 0.147, rounded to three significant figures.

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Answer:

6.4 miles

Step-by-step explanation:

Here we should notice that the distance that Brian runs and the spent time are two proportional variables.

Then

\(\frac{time}{distance } = k \ \ ;\text{where k is a constant}\)

\(k = \frac{30}{4} = 7.5\)

let ‘d’ be the number of miles thatBrian would run in 48 minutes

We can write this equation:

\(\frac{48}{d} = 7.5\)

Then

\(d = \frac{48}{7.5 } = 6.4\)

Roads that are well-maintained, dry, and free from hazards are generally less likely to result in traction loss.

The likelihood of losing traction depends on various factors such as road conditions, weather, vehicle type, and driver behavior. However, in general, roads that are well-maintained, dry, and free from debris or hazards are less likely to result in traction loss. Additionally, roads with good grip surfaces, such as asphalt or concrete, tend to provide better traction compared to unpaved or slippery surfaces. It's important to drive cautiously and adapt to the specific conditions of the road to minimize the risk of losing traction.

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Answer:

i think its D but not really sure

Step-by-step explanation:

105 lbs is approximately 47.628 kg. both are unit of measurement of weight.

To convert pounds (lbs) to kilograms (kg), you can use the conversion factor 1 kg = 2.20462 lbs. To convert 105 lbs to kg, you would divide 105 by 2.20462, which gives you 47.628 kg. The process of converting 105 lbs to kg is simple, one needs to divide it by 2.20462 .

The result is 47.628 kg.Pounds and kilograms are both units of measurement for weight, but they are not interchangeable. Pounds are commonly used in the United States and the United Kingdom, while kilograms are used in most other countries.

It's important to keep in mind that when converting between different units of measurements, one should be careful as the conversion factors are different for different units of measurements.

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