When calculating the circumference of a circle, sometimes the radius is given instead of the diameter. What is the
relationship between radius and diameter?
a radius is twice the diameter
C.diameter is twice the radius
b. diameter is half the radius
d. no relationship, can't find circumference with
radius

Please select the best answer
from the choices provided

The braking distance is the distance the car travels before coming to a stop after the brakes are applied

a. The braking distances are as follows;

b. If the car takes 450 feet to brake, it was traveling with a speed of 98.211 ft./s

Reason:

The given function for the braking distance is D = 2.6 + v²/22

a. The braking distance if the car is going 25 mph is therefore;

25 mph = 36.66339 ft./s

\(D = 2.6 + \dfrac{36.66339^2}{22} = 63.7 \ ft.\)

At 25 mph, the braking distance is approximately 63.7 ft.

At 55 mph, the braking distance is given as follows;

55 mph = 80.65945  ft.s

\(D = 2.6 + \dfrac{80.65945^2}{22} \approx 298.35 \ ft.\)

At 55 mph, the braking distance is approximately 298.35 ft.

At 85 mph, the braking distance is given as follows;

85 mph = 124.6555 ft.s

\(D = 2.6 + \dfrac{124.6555^2}{22} \approx 708.92 \ ft.\)

At 85 mph, the braking distance is approximately 708.92 ft.

b. The speed of the car when the braking distance is 450 feet is given as follows;

\(450 = 2.6 + \dfrac{v^2}{22}\)

v² = (450 - 2.6) × 22 = 9842.8

v = √(9842.2) ≈ 98.211 ft./s

The car was moving at v ≈ 98.211 ft./s

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Answer:

5

Step-by-step explanation:

7^2 = (2(6)^1/2)^2 + BC^2 (Pyth. theorem)

BC = 5

Answer:

its supposed to be 6.08 but we can take of..08 so 6

Step-by-step explanation:

\(a + b = c \\ ( 2 \sqrt{6} ) {}^{2} + {b}^{2} = {7}^{2} \\ 2 \times 6 + {b}^{2} = 49 \\ {b}^{2} = 49 - 12 \\ {b }^{2} = 37 \\ \sqrt{b} {}^{2} = \sqrt{37} \\ b = 6.08 \: or \: 6\)

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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Answer:

i think that the answer is the first equation

Step-by-step explanation:

The equation of the line passing through the points (0, 3) and (6, 11) is:

y = (4/3)x + 3.

Option C is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

To find the equation of the line passing through the points (0, 3) and (6, 11).

We can use the slope-intercept form of a linear equation,

which is y = mx + b, where m is the slope of the line and b is the y-intercept.

First, we can find the slope of the line by using the formula:

\(m = (y_2 - y_1) / (x_2 - x_1)\)

where

\((x_1, y_1) = (0, 3)\\(x_2, y_2) = (6, 11).\)

So,

m = (11 - 3) / (6 - 0) = 8/6 = 4/3

The slope of the line is 4/3.

Next,

We can use the point-slope form of a linear equation to write the equation of the line in terms of one of the points and the slope:

\(y - y_1 = m(x - x_1)\)

Choosing the point (0, 3), we get:

y - 3 = (4/3)(x - 0)

Simplifying and solving for y, we get:

y = (4/3)x + 3

Therefore,

The equation of the line passing through the points (0, 3) and (6, 11) is:

y = (4/3)x + 3.

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The value of   Sin(a + b) =   \(-\frac{3+4\sqrt{15} }{20}\) and value of

Cos (a -b) = 119/400

Given,

In the question;

Sin(a) = 1/4 and cos(b) = -3/5

with a and b both in the interval [\(\frac{\pi }{2} ,\pi\))

To find the sin(a + b) and cos (a - b)

Now, According to the question:

We know that :

Sin (b) =   \(\sqrt{1-cos^2b}\) = 4/5

Cos (a) = - \(\sqrt{1-sin^2a} = - \frac{\sqrt{15} }{4}\)

∴ Sin(a + b) = Sin(a) Cos(b) + Cos(a) Sin(b)

  Sin(a + b) = 1/4. (-3/5) + \(-(\frac{\sqrt{15} }{4} )\) . 4/5

   Sin(a + b)  =   \(-\frac{3+4\sqrt{15} }{20}\)

∴ Cos (a -b) = \(cos^2a -sin^2b\)

Cos (a -b) = \((-\frac{\sqrt{15} }{4} )^2\) - \((\frac{4}{5} )^2\)

Cos (a -b) = 119/400

Hence, The value of   Sin(a + b) =   \(-\frac{3+4\sqrt{15} }{20}\) and value of

Cos (a -b) = 119/400 .

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For this problem we can use the future value formula given by:

Where P= 4000 represent the initial amount

A= 8000 represent the amount doubled

t= 8 represent the number of years

n= 12 assuming that the interest is compounded each year

r= represent the rate of interest that we want to find

So then we need to solve for r

If we divide both sides by 4000 we got:

We apply exponentiation on both sides and we got:

The probability that a song selected by shuffle mode from the iPhone music library is not from Tool is 0.878.

To calculate the probability, we need to determine the number of songs that are not from Tool and divide it by the total number of songs in the library.

Total songs in the library = 500

Number of songs by Tool = 56

Number of songs not from Tool = Total songs in the library - Number of songs by Tool

                                 = 500 - 56

                                 = 444

Probability = Number of songs not from Tool / Total songs in the library

              = 444 / 500

              = 0.878

Therefore, the probability that a song selected by shuffle mode is not from Tool is 0.878 (or approximately 87.8%).

Out of the 500 songs in the iPhone music library, 56 are from Tool. By calculating the probability, we found that there is an approximately 87.8% chance that a song selected by shuffle mode will not be from Tool. This means that the majority of the songs played in shuffle mode will likely be from artists other than Tool.

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I hope this is the right answer.

Answer:

Step-by-step explanation:

The width of a rectangle is 4 meters less than twice the length. The area is 96 square meters. Find dimensions

The distance between points A and B is given as follows:

E. 54.4 feet.

The law of cosines states that we can find the length of the missing side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which the parameters of the equation are given as follows:

From the diagram given by the image presented at the end of the answer, the values of the parameters are given as follows:

a = 45, b = 69, C = 52º.

Hence the distance between points A and B is the missing length C obtained as follows:

c² = a² + b² - 2abcos(C)

c² = 45² + 69² - 2 x 45 x 69 x cos(52º)

c² = 2962.74223826

c = sqrt(2962.74223826)

c = 54.4 feet.

Meaning that option E is correct.

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Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.

The probability that a randomly selected fertilized chicken egg takes between 19 and 21 days to hatch depends on several factors such as the breed of the chicken, temperature, and humidity. However, on average, most chicken eggs take around 21 days to hatch. Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.
The probability that a randomly selected fertilized chicken egg takes between 19 and 21 days to hatch depends on several factors such as the breed of the chicken, temperature, and humidity. However, on average, most chicken eggs take around 21 days to hatch.

Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.

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Answer:

Step-by-step explanation:

You can't find an exact value, but you can find an simpler expression by using the distributive property.

a + 4bc + 2ab

And that is as much as it can be reduced.

Answer:

Uh yeah Its right...i think

Just make sure if its right

Answer:

132

Step-by-step explanation:

C=5

3c - 2 = 13

2c = 10

4c + 1 = 21

4c + 2 = 22

length = (3c- 2) + (4c + 1)

length = 13 + 21

length = 34

width = (4c + 2) + (2c)

width = 22 + 10

width = 32

Perimeter

p = 2l + 2w

p = 2*34 + 2*32

p = 68 + 64

p = 132

Answer:

Emily reads 32 pages a hour (192/6)  Maria reads 34 pages per hour (170/5) so Maria would read faster

Step-by-step explanation:

To determine which location yields the higher profit per year, we need the specific data for the annual profit in each location. Please provide the annual profit values for the locations in question, and I will be able to calculate and compare the profit per year.

Without the necessary information regarding the annual profits of the locations, it is not possible to determine which location yields the higher profit per year. To make a meaningful comparison, we need the specific profit figures for each location. Once the annual profit values are provided, we can calculate the profit per year by dividing the total profit by the number of years.

Once the profit per year is calculated for each location, we can compare the values to determine which location has the higher profit per year. However, as the specific data regarding the annual profit in each location is missing, it is not feasible to provide a conclusive answer at this time. Please provide the annual profit figures for the locations in question, and I will be able to assist you further in determining which location yields the higher profit per year.

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Answer:

838 inches²

Step-by-step explanation:

Finding the area of the countertop including the hole

⇒ Area of countertop including hole: LB

⇒ Area of countertop including hole: (24)(48)

⇒ Area of countertop including hole: 1152 inches²

Finding the area of the hole (sink)

⇒ Area of hole: πr²

⇒ Area of hole: (π)(D/2)²

⇒ Area of hole: (π)(20/2)²

⇒ Area of hole: (π)(10)²

⇒ Area of hole: (π) x 100

⇒ Area of hole: 3.14 x 100 = 314 inches²

Finding the area excluding the hole

1152 - 314 = Area of countertop (excluding the hole)

838 inches² = Area of countertop (excluding the hole)

There is a 0.1818% chance that the production time will be between 11 and 12 minutes.

Each possible outcome is equally likely when there is a uniform probability.

We have an upper limit that we refer to as b and a lower limit that we refer to as a for this case.

The following formula gives the likelihood that we will discover a value X between c and d, where d is bigger than c.

P ( c ≤ X ≤ d ) = \(\frac{d-c}{b-a}\)           (Equation-1)

Production times are always within this range, which is evenly dispersed between 10 and 15.5 minutes.

This means that, a = 10 ; b = 15.5

The likelihood that a production time falls between 11 and 12 minutes is what.

d = 12 minutes ; c = 11 minutes

We can substitute in equation-1,

So,

We can write,

P ( c ≤ X ≤ d ) = \(\frac{d-c}{b-a}\)

P ( c ≤ X ≤ d ) = \(\frac{12-11}{15.5-10}\)

P ( c ≤ X ≤ d ) = \(\frac{1}{5.5}\)

P ( c ≤ X ≤ d ) = 0.1818

Therefore,

0.1818% probability that a production time is between 11 and 12 minutes.

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The simple interest rate on the account is 7.5%.

The simple interest rate can be calculated by dividing the interest earned by the principal balance and the time period. In this case, the interest earned is $56.25, the principal balance is $300, and the time period is two and one-half years.

To find the interest rate, we use the formula:

Simple Interest = Principal × Rate × Time

Substituting the given values:

$56.25 = $300 × Rate × 2.5

To solve for the interest rate, divide both sides of the equation by $750:

Rate = $56.25 / ($300 × 2.5)

Simplifying the calculation:

Rate = $56.25 / $750

Rate = 0.075

Therefore, the simple interest rate on the account is 7.5%.

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To find the possible lengths of the legs of a right triangle with a hypotenuse of √265, solve the equation a^2 + b^2 = 265 for positive integer pairs (a, b).

To determine the possible lengths of the legs (a, b) of a right triangle with a hypotenuse of √265, we apply the Pythagorean theorem, which states that a^2 + b^2 = c^2, where c represents the hypotenuse. In this case, we have a^2 + b^2 = 265.

To find valid solutions, we search for positive integer pairs (a, b) that satisfy this equation. By trying different values of a and solving for b using the equation, we can identify potential combinations of leg lengths.

It is important to note that there may be multiple valid solutions, as there are various pairs of positive integers that fulfill the Pythagorean theorem for this specific hypotenuse length.

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Answer:

X ≤ 0

Step-by-step explanation:

Trust

Step-by-step explanation:

first, distribute 7 to 6m (this means 7 • 6m)

7 • 6m = 42m

then distribute 7 to 7 (which is 7 • 7)

7 • 7 = 49

your simplified expression is 42m + 49. i hope this helps! have a great day <3

Therefore, the mean salary paid to the office assistants in this company is $24,000.Answer: B. $24,000

A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. The mean salary paid to the office assistants in this company can be calculated by taking the weighted average of the mean salaries of the two offices.
Here's the formula to calculate the weighted average:
Weighted average = (weight1 × value1 + weight2 × value2) / (weight1 + weight2)
Where weight represents the number of data points, and value represents the mean salary of office assistants.
In this question, the weight of the New Jersey office is 128, and the weight of the Utah office is 32. The value of the New Jersey office is $28,500, and the value of the Utah office is $22,500.
Now let's plug in the values:
Weighted average = (128 × 28,500 + 32 × 22,500) / (128 + 32)
= (3,648,000 + 720,000) / 160
= 24,000

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You have to pay $3,233 in property taxes.

To calculate the property taxes you have to pay, we need to first find the assessed value of your home after the homestead exemption.

Assessed value = Appraised value - Homestead exemption

Assessed value = $315,000 - $50,000

Assessed value = $265,000

Now, we can calculate the amount of property taxes you have to pay using the tax rate of 1.22%:

Property taxes = Assessed value x Tax rate

Property taxes = $265,000 x 0.0122

Property taxes = $3,233

Therefore, you have to pay $3,233 in property taxes.

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Here are the vectors **t**, **n**, and **b** at the given point:

* **t** = (-3 sin t, 3 cos t, 0)

* **n** = (-3 cos t, -3 sin t, 3 / cos^2 t)

* **b** = (3 cos^2 t, -3 sin^2 t, -3)

The vector **t** is the unit tangent vector, which points in the direction of the curve at the given point. The vector **n** is the unit normal vector, which points in the direction perpendicular to the curve at the given point. The vector **b** is the binormal vector, which points in the direction that is perpendicular to both **t** and **n**.

To find the vectors **t**, **n**, and **b**, we can use the following formulas:

```

t(t) = r'(t) / |r'(t)|

n(t) = (t(t) x r(t)) / |t(t) x r(t)|

b(t) = t(t) x n(t)

```

In this case, we have:

```

r(t) = (3 cos t, 3 sin t, 3 ln cos t)

r'(t) = (-3 sin t, 3 cos t, 3 / cos^2 t)

```

Substituting these into the formulas above, we can find the vectors **t**, **n**, and **b** as shown.

The vectors **t**, **n**, and **b** are all orthogonal to each other at the given point. This is because the curve is a smooth curve, and the vectors are defined in such a way that they are always orthogonal to each other.

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The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.

To find the vectors t, n, and b at the given point, we need to calculate the first derivative, second derivative, and third derivative of the position vector r(t).
Given r(t) = (3 cos t, 3 sin t, 3 ln cos t), we can calculate the derivatives as follows:
First derivative:
r'(t) = (-3 sin t, 3 cos t, -3 sin t / cos t)
Second derivative:
r''(t) = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 sin^2 t / cos t)
       = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 tan^2 t)
Third derivative:
r'''(t) = (3 sin t, -3 cos t, 6 cos t / cos^3 t - 6 sin t / cos t)
        = (3 sin t, -3 cos t, 6 sec^3 t - 6 tan t sec t)
At the given point (3, 0, 0), substitute t = 0 into the derivatives to find the vectors:
r'(0) = (0, 3, 0)
r''(0) = (-3, 0, 3)
r'''(0) = (0, -3, 6)
Therefore, at the given point, the vectors t, n, and b are:
t = r'(0) = (0, 3, 0)
n = r''(0) = (-3, 0, 3)
b = r'''(0) = (0, -3, 6)
These vectors represent the tangent, normal, and binormal vectors, respectively, at the given point.
The tangent vector (t) represents the direction of motion of the curve at that point. The normal vector (n) is perpendicular to the tangent vector and points towards the center of curvature.

The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.
Remember to check your calculations and units when applying this method to different functions.

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The appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.

Given:

The t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14.

It is the 97.5%-quantile of the t-distribution with 14 degrees of freedom.

In the figure the dashed line shows the value such that the yellow shaded area has size 0.975: the 97.5%-quantile is the value such that 97.5% of the probability mass is to the left of it and the rest to the right.

so t - multiplier = 2.15.

Therefore the appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.

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Answer:

338

Step-by-step explanation:

ok

Answer:

(4/7,2)

Step-by-step explanation:

x= 4/7

y= 2