What is the Mean for the given data: 2, 8, 7, 6, 6, 3, 4.4, 5.1, 9, 8

If in △ABC, A=27degree, a=37 and c=28, then the statements best describes the triangle is (B) △ABC is obtuse.

We can use the Law of Cosines to determine the length of side b:

b^2 = a^2 + c^2 - 2ac cos(A)

b^2 = 37^2 + 28^2 - 2(37)(28) cos(27°)

b ≈ 27.88

Now we can use the Law of Sines to determine the measure of angle B:

sin(B)/b = sin(A)/a

sin(B) = (b/a)sin(A)

sin(B) = (27.88/37)sin(27°)

B ≈ 46.18°

Finally, we can find the measure of angle C using the fact that the angles in a triangle sum to 180°:

C = 180° - A - B

C ≈ 106.82°

Since angle C is greater than 90°, we know that △ABC is obtuse triangle. Therefore, the best statement that describes the triangle is (B) △ABC is obtuse.

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The given question is incomplete, the complete question is:

In △ABC, A = 27 degree, a = 37 and c = 28. Which of these statements best describes the triangle? A) △ ABC is acute. B) △ABC is obtuse. C) △ABC can be either acute or obtuse. D) △ABC is a right triangle. E) △ABC cannot be constructed.

Given: Diameter of the cone = 18 cmHeight of the cone = 15 cmFormula used:The formula used to calculate the volume of a cone is given below: V = (1/3) πr²hWhere, V is the volume of the cone, r is the radius of the cone, h is the height of the cone and π = 3.14.

Radius of the cone = Diameter of the cone/2= 18/2= 9 cmVolume of the cone is given by: V = (1/3) πr²hSubstituting the given values, we get:V = (1/3) × 3.14 × (9)² × 15V = (1/3) × 3.14 × 81 × 15V = 113.1 cm³Therefore, the volume of the cone is 113.1 cm³.

Note: The calculation of the radius of the cone is important to calculate the volume of the cone. In this problem, the height of the cone and the diameter of the cone are given. Therefore, it is necessary to calculate the radius of the cone to solve the problem.

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Answer:

Step-by-step explanation:

4mx+2m

To determine the number of distinct ways two or more experiments can be performed, the multiplication principle can be used.

The multiplication principle is a fundamental counting technique in combinatorics that helps calculate the total number of outcomes for multiple experiments or events. When two or more independent events occur in a sequence, the total number of possible outcomes is the product of the individual outcomes of each event.


1. Identify the number of outcomes for each experiment or event.
2. Apply the multiplication principle by multiplying the number of outcomes for each event together.
For example, suppose you have two experiments: flipping a coin (2 outcomes - heads or tails) and rolling a die (6 outcomes - 1, 2, 3, 4, 5, or 6). To determine the number of distinct ways both experiments can be performed, simply multiply the outcomes of each experiment: 2 outcomes (coin) * 6 outcomes (die) = 12 distinct possible outcomes.

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The current value of the vending machine is $150,411.90, which is the sum of all discounted future payments.Vending machines are used to offer goods like snacks and beverages to consumers for sale without the need for a salesperson.  

These machines often necessitate cash or debit card payments to operate. Vending machines have become a preferred method of retailing due to their cost-effectiveness and ease of use. The current value of the vending machine can be determined using the present value formula.

The present value is the sum of the future payments, discounted back to their current value. In this case, we must discount the future payments to their present value using the given interest rate. The formula is as follows:PV = Pmt x ((1-(1/(1+r)n))/r).

Where, PV = Present Value Pmt = Payment per period n = Number of periods r = Interest rate per periodIn this scenario, Pmt = $750n = 30 periods (since the payments are made every six months for 15 years, which is 30 periods)r = 5% per period.

Present Value = $750 x ((1-(1/(1+0.05)^30))/0.05) Present Value = $150,411.90.

Therefore, the current value of the vending machine that is expected to pay out $750 every six months for 15 years at a 5% interest rate per annum, and the first payment is made four years after from today is $150,411.90.

In conclusion, the current value of the vending machine is $150,411.90, which is the sum of all discounted future payments.

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The reflection across x = -2 will be x = 2.

In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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The rate of discount for the CD radio cassette is 17.65%.

To calculate the rate of discount, we need to find the difference between the original price and the discounted price, and then divide that difference by the original price.

Original price: $16,999

Discounted price: $13,999

So, the Discount amount

= Original price - Discounted price

= $16,999 - $13,999

= $3,000

Rate of discount = (Discount amount / Original price) * 100%

= ($3,000 / $16,999) x 100%

≈ 17.65%

Therefore, the rate of discount for the CD radio cassette is 17.65%.

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The equation of the tangents that pass through the point (10, 8) is,

y = x - 2.

Given that,

The curves are x = 6t² and y = 4t³ + 4

Now, Differentiate both the x and y equations with respect to t to find the slopes of the tangent lines.

dx/dt = 12t

dy/dt = 12t²

Substitute the x and y equations into the equation of a line,

y - y₁ = m(x - x₁)

where (x₁, y₁) is the point (10, 8) and m is the slope obtained from step 1.

y - 8 = m(x - 10)

Substitute the x and y equations into the equation above to eliminate t and obtain an equation in terms of x and y.

4t³ + 4 - 8 = t(6t² + 4 - 10)

Simplifying the equation, we get:

4t³ - 4 = 6t³ + 4t - 10t

6t³ - 4t³ - 6t + 4 = 0

2t³ - 6t + 4 = 0

Solve the above equation for t to find the values of t that correspond to the points of tangency.

After solving the equation, we get one value of t:

t = 1

Substitute the values of t into the x and y equations to find the corresponding points of tangency.

When t = 1,

x = 6(1)² + 4

x = 10

And , y = 4(1)³ + 4

y = 8.

This gives us the point (10, 8).

Finally, use the point-slope form of the equation of a line to write the equations of the tangents.

For the point (10, 8), the equations of the tangents are:

y - 8 = (1)(x - 10),

y - 8 = x - 10

y = x - 10 + 8

y = x - 2

Therefore, the equation of the tangents that pass through the point (10, 8) is y = x - 2.

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Answer:

AB ≈ 6.53

Step-by-step explanation:

using the cosine ratio in the right triangle

cos40° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{5}{AB}\) ( multiply both sides by AB )

AB × cos40° = 5 ( divide both sides by cos40° )

AB = \(\frac{5}{cos40}\) ≈ 6.53 ( to the nearest hundredth )

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

The probability of drawing 2 yellow markers and 2 red markers is approximately 0.2697.

To find the probability of drawing 2 yellow markers and 2 red markers, we need to calculate the total number of ways to draw 4 markers from the bag, as well as the number of ways to draw 2 yellow and 2 red markers.

The total number of ways to draw 4 markers from the bag is:

¹⁴C₄ = (14!)/(4!*(14-4)!) = 1001

This is because there are 14 markers in total, and we are choosing 4 of them.

To find the number of ways to draw 2 yellow and 2 red markers, we can use the combination formula again. The number of ways to choose 2 yellow markers from 4 yellow markers is:

⁴C₂ = (4!)/(2!*(4-2)!) = 6

Similarly, the number of ways to choose 2 red markers from 10 red markers is:

¹⁰C₂ = (10!)/(2!*(10-2)!) = 45

Therefore, the number of ways to draw 2 yellow and 2 red markers is:

6 * 45 = 270

Now we can find the probability of drawing 2 yellow and 2 red markers by dividing the number of ways to draw 2 yellow and 2 red markers by the total number of ways to draw 4 markers:

P(2 yellow and 2 red) = 270/1001 = 0.2697 (rounded to four decimal places)

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The probability of drawing 2 yellow marker and 2 red markers 15/1078

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty an event will occur is 1 which is equivalent to 100%.

Probability = sample space / total outcome

for the first draw ;

probability of picking yellow = 2/14 = 1/7

second draw;

probability of picking yellow = 1/13

third draw;

probability of picking red = 10/12 = 5/6

fourth draw;

probability of picking red = 9/11

Probability of picking two yellow = 2/14 × 1/7 = 2/98 = 1/49

probability of picking two reds = 5/6 × 9/11 = 45/66 = 15/22

probability of picking 2 yellow and 2 red = 1/49 × 15/22 = 15/1078

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Answer:

Step-by-step explanation:

looking at all the stress you're in I knew I had to help so all your lists are bunched up, so I went of the picture C is correct because B 4 and 7 aren't even a part of the question itself and A has 16 and 49 but it doesn't have sqrt so it's not = to the question and D is not correct either because it doesn't have one sqrt it has two on top of each other. HOPE THIS HELPED!

Answer:

4x = 20

x = 5

Step-by-step explanation:

Have a nice day!

The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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Answer: 4 days, more below

Step-by-step explanation:

40.50x + 0.15y < 210

(0.15)(125)=18.75

40.50x + 18.75 < 210

40.50x < 191.25

x < 4.7222222...

She can afford to rent the car for 4 days if she drives 125 miles and has 210$ to spend.

The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.

The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.

We have,

The absolute value function f(x) = |x – 2| is a piecewise function that returns the positive distance between the input value x and the number 2.

Geometrically,

It represents the distance of a point on the number line from point 2.

On the coordinate plane,

The graph of the absolute value function is V-shaped, with its vertex at the point (2, 0).

The two arms of the V extend indefinitely in opposite directions, passing through the points (-∞, 2) and (2, +∞) on the positive and negative sides of the x-axis, respectively.

Thus,

The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.

The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.

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When x = 11, the value of y is approximately 8.276. We are given that the relationship between x and y is given by \(y = Ax^n\)where A and n are constants.

We are also given the values of A and n:

\(A = e^0.5\)

n = 3/8

We can substitute these values into the equation to get:

\(y = e^0.5 x^(3/8)\)

Now, we are asked to find the value of y when x = 11. To do this, we substitute x = 11 into the equation:

\(y = e^0.5 x^(3/8)\)

\(y = e^0.5 (11)^(3/8)\)

We can use a calculator to evaluate this

First, we evaluate the exponent (3/8) using the exponent rules:

\((11)^(3/8) = (11^(1/8))^3 = 1.706\)

Next, we substitute this value back into the equation:

\(y = e^0.5 x^(3/8)\)

\(y = e^0.5 (11)^(3/8)\)

\(y = e^0.5 (1.706)\)

Using a calculator, we can evaluate this expression to get:

y ≈ 8.276

Therefore, when x = 11, the value of y is approximately 8.276.

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Answer:

the answer is 8

Step-by-step explanation:

cube root of 512 is 8

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Answer:

Well, I'm not the smartest person, nor do I exactly know what you mean, but I have a wild guess that the least you could rotate it is 100 degrees.

Step-by-step explanation:

Considering the fact that it's sides are all equal, you could compare this to a square, which also has equal sides. Its angles are equal, too, so you could measure it's angles (100 degrees) and turn it that exact amount,

I hope this helps you, like I said, I don't exactly know what you are talking about, I am not studying that sort of thing yet.

Answer:

I don't know if you want to find this answer using the quadratic formula or not, the question is no the greatest but i will solve it the best that i can. Or

Step-by-step explanation:

I used the discriminant which is √-4ac

Then I filled the numbers in, and found that 9 gets plug in for b and this becomes 9 squared, and that becomes 81. 4 is multiplied to 4 and 1 and becomes 16. Then 81 and 16 are subtracted and we get 65. We then find the square root, and will find that the answer is C.

Let be x the amount the owner withdrew. Then, we can write and solve the following equation:

Answer

The owner withdraws $2,000.

Answer:

38.5 mm^2

Have a nice day!

Step-by-step explanation:

Area = πr^2

Area = π(3.5^2)

Area = π(12.25)

Area = 38.48451...

Area = 38.5

To determine the exposure from a radioactive substance at a different distance, we can use the inverse square law. The exposure at a distance of 20 cm is 11,250 mR.

The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source. In this case, we have the initial distance of 100 cm and the corresponding exposure of 450 mR.

Using the inverse square law equation, we can set up a proportion to find the new exposure at a distance of 20 cm. The equation can be written as:

(Exposure at initial distance) / (Exposure at new distance) = (Square of new distance) / (Square of initial distance)

Substituting the given values, we have:

450 mR / X = \((20 cm)^2 / (100 cm)^2\)

Simplifying the equation, we get:

450 mR / X = 1/25

Cross-multiplying, we have:

X = (450 mR) * (25)

Calculating the value, we find:

X = 11,250 mR

Therefore, the exposure at a distance of 20 cm is 11,250 mR.

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Sarah completed reading for x = 18 minutes.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question

The number of pages Sarah will read in an hour is x. (this is "pages per hour" rate).

(10 minutes) / (3 pages) = (x pages) / (60 minutes)

cross-multiply:

10x = 3*60

x = 18

Hence, Sarah completed reading for x = 18 minutes.

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a. The z-score for a blood pressure reading of 140 is 1.22.

b. The proportion of the population suffering from high blood pressure (reading above 140) is 0.1112.

c. The proportion of the population with systolic blood pressure in the range from 104 to 140 is 0.7185.

To solve the problem, we need to use the standard normal distribution since we know the mean and standard deviation of the population.

a. The z-score for a blood pressure reading of 140 is calculated as:

z = (140 - 118) / 18 = 1.22

Therefore, the z-score for a blood pressure reading of 140 is 1.22 (rounded to two decimal places).

b. To find the proportion of the population suffering from high blood pressure, we need to calculate the area under the standard normal distribution curve to the right of z = 1.22 (since we are interested in readings above 140). Using a standard normal distribution table or calculator, we find that the area to the right of 1.22 is 0.1112.

Therefore, the proportion of the population suffering from high blood pressure (reading above 140) is 0.1112.

c. To find the proportion of the population with systolic blood pressure in the range from 104 to 140, we need to calculate the area under the standard normal distribution curve between z = (104 - 118) / 18 = -0.78 and z = (140 - 118) / 18 = 1.22. Using a standard normal distribution table or calculator, we find that the area between -0.78 and 1.22 is 0.7185.

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Answer: 105 or b

Step-by-step explanation: inner 256 and outer is 361 making the difference 105