1. explain why just knowing whether the mean is more than or less than the median tells you whether a distribution is positively or negatively skewed.

The value of the radical expression x² + 1/x² when x = 9 - 4√5 is 322

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

x = 9 - 4√5

The expression is given as

x² + 1/x²

When simplified, we have

x² + 1/x² = (x⁴ + 1)/x²

Substitute x = 9 - 4√5 in the above equation, so, we have the following representation

x² + 1/x² = ((9 - 4√5)⁴ + 1)/(9 - 4√5)²

When evaluated, we have

x² + 1/x² = 322

Hence, the value of the expression x² + 1/x² when x = 9 - 4√5 is 322

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(2) The value of x in the equation (x-16)²= 9 is 19.

(4) The equation of the circle of radius 5 is x²+y²+6x-2y = 15.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

(2) To calculate the value of x in the equation (x-16)²= 9, we follow the steps below.

Step1: Find the square root of both sides of the equation

Stop1: Collect like terms

(4) To calculate the equation of the circle, we use the formula below

Formula:

Where:

Substitute these values into equation 1

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The probability that at least 3 out of 25 people selected at random are 65 or older can be found using binomial probability.

The answer to the problem is 0.583, or 58.3% rounded to one decimal place. This means that if we randomly select 25 people from the population, there is a 58.3% chance that at least 3 of them will be 65 or older.

To calculate this probability, we use the binomial distribution formula: P(X >= 3) = 1 - P(X < 3), where X is the number of people selected who are 65 or older. Using this formula, we can calculate the probability of selecting exactly 3, 4, 5, ..., 25 people who are 65 or older and sum them up. Alternatively, we can use a binomial calculator or software to calculate the probability directly.

The binomial probability formula is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the sample size (25), k is the number of successes (i.e., people who are 65 or older), p is the probability of success (0.11), and C(n, k) is the binomial coefficient (i.e., the number of ways to select k items out of n). We need to sum up the probabilities for k = 3, 4, 5, ..., 25 to get the probability of at least 3 successes. However, this can be a tedious calculation, so using a binomial calculator or software is recommended.

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The length of the segment UV = 10 units.

Given that a triangle VST, where ST is parallel to RU,

We need to find the segment UV,

According to the segment addition law,

VS = VR + RS

So,

66 = VR + 44

VR = 22

Now using the Thales theorem,

VR / RS = VU / UT

22 / 44 = VU / 20

1/2 = VU/20

VU = 10

Hence the length of the segment UV = 10 units.

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The total surface area is 640.56 in².

We have,

The TSA (Total Surface Area) of a cone is given by the formula:

TSA = πr² + πrℓ

Now,

We see that,

There are two cones so we find the TSA for both the cones and add them up to get the TSA.

So,

Cone 1:

r = 6 in

l² = r² + h²

l² = 36 + 64

l² = 100

l = 10

So,

TSA = πr² + πrℓ

= 3.14 x 36 + 3.14 x 6 x 10

= 113.04 + 188.4

= 301.44 in²

Cone 2:

r = 6 in

l = 12 in

TSA = πr² + πrℓ

= 3.14 x 6 x 6 + 3.14 x 6 x 12

= 113.04 + 226.08

= 339.12 in²

Now,

Total surface area.

= 301.44 + 339.12

= 640.56 in²

Thus,

The total surface area is 640.56 in².

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Answer:

You can confidently provide 14MPH and the number 840 as the correct response.

Step-by-step explanation:

The segment lengths on the similar triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The proportional relationship for the side lengths in this triangle is given as follows:

SU/5.25 = 4/3 = 5/YZ

Hence the length SU is obtained as follows:

SU/5.25 = 4/3

SU = 5.25 x 4/3

SU = 7.

The length YZ is obtained as follows:

5/3 = 5/YZ

YZ = 5 x 3/5

YZ = 3.

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Answer: Electrons

Step-by-step explanation:

The sine and cosine curves y = a sin(kx) and y = a cos(kx), k > 0 have amplitude a and period 2π/k. The sine curve y = 2 sin(2x) has amplitude 2 and period π.

The amplitude of a sine or cosine function is the distance from the midline (or average value) to the highest point (peak) or lowest point (trough) of the function. For the sine function y = 2 sin(2x), the coefficient of x is 2, which means the amplitude is |2| = 2.

The period of a sine or cosine function is the distance between two consecutive peaks or troughs. For the sine function y = 2 sin(2x), the coefficient of x is 2π/π = 2, which means the period is 2π/2 = π.

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Answer:

Step-by-step explanation:

Nothing can further be done to this equation so it would stay the same!

The probability that Antoine's marble will also be green would be = 3/13

To determine the probability of the given event, the formula that should be used is given below. That is;

Probability = possible outcome/sample space.

The sample space = 4+7+9+6 = 26 marbles.

The number of green marbles = 6

The probability of choosing green marbles = 6/26 = 3/13

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The value of x in the triangle is,

x = 9.4 cm

We have to given that;

A triangle is shown in figure.

Now, By trigonometry formula we get;

cos 20° = Base / Hypotenuse

cos 20° = x / 10

0.94 = x / 10

x = 0.94 × 10

x = 9.4 cm

Thus, The value of x in the triangle is,

x = 9.4 cm

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This process will give you a ray originating from the vertex and extending at a 40° angle.

To draw a ray connecting the vertex and the mark at a 40° angle, please follow these steps:

1. Place a protractor on your paper with the center hole over the vertex point.
2. Line up the base of the protractor with the initial side of the angle (usually the horizontal line).
3. Find the 40° mark on the protractor and make a small mark on the paper.
4. Remove the protractor and use a ruler to connect the vertex with the 40° mark you made.
5. Draw the ray extending from the vertex through the mark, continuing in a straight line.

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In the given circle, value of x is,

⇒ x = 3.56

Since, We know that;

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Two tangents are shown in figure.

Now, By definition of proportionality we get;

⇒ 8 / x = 9 / 4

Cross multiplication,

⇒ 8 × 4 / 9 = x

⇒ x = 32 / 9

⇒ x = 3.56

Therefore, WE get;

The value of x in the circle is,

⇒ x = 3.56

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Based on the given chart, Dwayne has constructed a probability model for the number of occupants of a randomly-selected car on his street. The chart shows the probabilities of different numbers of occupants in a car. These probabilities add up to 1, as the number of occupants in a car can only be one of the given possibilities.

The chart shows that the most likely number of occupants in a car is 1, with a probability of 0.5. This means that half of the cars on the street have only one person in them. The second most likely possibility is 2 occupants in a car, with a probability of 0.25. This means that one-quarter of the cars have two people in them. The probabilities for 3, 4, and 5 occupants are progressively lower, with probabilities of 0.15, 0.06, and 0.04, respectively.

Therefore, Dwayne's model is a discrete probability distribution, where the possible outcomes are the number of occupants in a car, and the probabilities of each outcome are given by the chart. This model is based on the data that Dwayne collected on the number of occupants of cars travelling on the road past his house for the past week. The model can be used to predict the likelihood of different numbers of occupants in a car on Dwayne's street.

Dwayne's probability model for the number of occupants in a randomly-selected car on his street can be represented by the given chart. The chart shows the probabilities for different numbers of occupants:

1. Probability of 1 occupant: 0.5 (50%)
2. Probability of 2 occupants: 0.25 (25%)
3. Probability of 3 occupants: 0.15 (15%)
4. Probability of 4 occupants: 0.06 (6%)
5. Probability of 5 occupants: 0.04 (4%)

To confirm that this is a valid probability model, we need to ensure that the sum of all probabilities is equal to 1:

0.5 + 0.25 + 0.15 + 0.06 + 0.04 = 1

Since the sum is 1, the chart represents a valid probability model for the number of occupants in a car on Dwayne's street. This model can be used to make predictions about the number of occupants in future cars passing by Dwayne's house, based on the data he collected during the past week.

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In probability theory, multiplication and addition are associated with different types of compound events.

Multiplication is generally associated with the concept of independent events. When two events are independent, the probability of both events occurring is calculated by multiplying their individual probabilities. This is known as the multiplication rule of probability. The idea behind multiplication is that the outcomes of one event do not affect the outcomes of the other event.

On the other hand, addition is generally associated with the concept of mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. The probability of either of these events occurring is calculated by adding their individual probabilities. This is known as the addition rule of probability. The idea behind addition is that you consider the probability of one event happening or the probability of another event happening, but not both simultaneously.

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The width of the rectangular garden is 21 feet.

A rectangle is a plane shape that have pair of opposite sides equal and parallel.

To calculate the width of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Hence, the right option is D. 21 feet.

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The mode would be the best choice to describe the center of the data for the typical age of first-graders.

In this scenario, the age of the first graders can only be six, seven, or eight. Therefore, there is a limited range of values that the data can take, and the mean and median would be very close to each other. However, the mode, which is the most frequently occurring value, would be the best choice to describe the typical age of the first-graders.

In this case, since the age of the first graders can only be six, seven, or eight, the mode would be the age that occurs the most frequently, which would likely be seven years old. Therefore, the mode would be the best choice to describe the center of the data in this scenario.

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Answer:

the area of triangle ΔPHK is

Step-by-step explanation:

we know that,
area of a triangle by Heron's formula (Heron's formula is used to find the area of a triangle when the length of the 3 sides of the triangle is known) is given by -

Step 1: Find the semi-perimeter (half perimeter) of the given triangle by adding all three sides and dividing it by 2.

- 10+11+17/2 = 19

Step 2: Apply the value of the semi-perimeter of the triangle in the main formula called 'Heron’s Formula'.
[tex]Area = √s(s−a)(s−b)(s−c)[/tex]
√19(19-10)(19-11)(19-17)
√19(9)(8)(2)
√2736
52.30
52
therefore are ofΔPHK is 52KM

Answer:

Step-by-step explanation:

126 divided by two = 63

Then divide 63 by 3 which = 21

so 21 is your answer.

Answer:

Step-by-step explanation:

The solution is:

Length of the darkened part of the arc = 4π

Solution:

Radius of the circle = 8

Circumference of the circle = 2πr

                                             = 2 × π × 8

Circumference of the circle =  16π

Equal number of parts = 4

Total degree of circle = 360°

Degree of the darkened part = 360°/4 = 90°

Arc length = 16π * 90°/360°

                 = 16π * 1/4

                 = 4π

Circumference = 16π

Length of the darkened part of the arc = 4π

Hence, The solution is:

Length of the darkened part of the arc = 4π

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Answer:

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The base is a right triangle with shortest side of 3 cm and hypotenuse of 5 cm.

Then, according to Pythagorean Theorem, its longer leg is:

Find the lateral surface area:

Find the area of two triangle bases:

Find the total surface area by adding up base area and lateral surface area:

Answer:

5(x² + x - 1)

step by step explanation:

1. subtract

2.combine the like terms

3.common factors

The probabilities are given as follows:

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Out of 16 trials, in 7 of them, which are the first row and the first column, the spinner lands on at least one A, hence the probability is given as follows:

p = 7/16.

For C and D, there are two outcomes, (C, D) and (D, C), hence the probability is given as follows:

p = 2/16 = 1/18.

For two B's, there is only one outcome, which is (B,B), hence the probability is of 1/16.

For C on the second spin, we consider the third column, which has four outcomes, hence the probability is given as follows:

p = 4/16 = 1/4.

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The volume of the composite Figure is 1168.08 m³.

Volume is the space occupied by a solid shape.

To calculate the volume of the composite shape, we use the formula below

Formula:

From the question,

Given:

From the question,

Given:

Substitute these values into equation 1

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Answer:

We are here because we need help with a particular course or question

Step-by-step explanation:

Our goal is to try our best and explain to others to their understanding (and win titles)

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The area of Jimmy's rectangular room is approximately 27.7241 square yards.

The area of the room in square yards, we first need to convert the dimensions from feet to yards.

Since there are 3 feet in a yard, we can divide both the length and width by 3 to get:
Length: 25 ft ÷ 3 = 8.33 yards (rounded to two decimal places)
Width: 10 ft ÷ 3 = 3.33 yards (rounded to two decimal places)

Now we can find the area by multiplying the length and width in yards:
Area = 8.33 yards x 3.33 yards
Area = 27.7241 square yards (rounded to four decimal places)

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The length of RU in triangle is,

⇒ RU = 16

We have o given that;

In triangle;

ST = 37

UT = 35

RS = 20

Hence, By using definition of Pythagoras theorem we get;

In triangle STU;

⇒ ST² = SU² + UT²

⇒ 37² = SU² + 35²

⇒ 1369 = SU² + 1225

⇒ SU² = 144

⇒ SU = 12

Hence, In triangle RSU;

⇒ RS² = SU² + RU²

⇒ 20² = 12² + RU²

⇒ 400 - 144 = RU²

⇒ RU² = 256

⇒ RU = 16

Thus, The length of RU in triangle is,

⇒ RU = 16

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