18) VISUALIZATION Is there an angle measure that is so small that any triangle with that angle measure will be an obtuse triangle? Explain.

The distance between the two metropolises on the chart is 9 elevation.

What's distance?

Distance refers to the quantum of space between two points or objects. It's a physical volume that can be measured and is generally expressed in units similar as measures, kilometers, long hauls, or bases.

According to question-

In this case, the scale of the chart is3/4 inch = 80 long hauls.

So, for every3/4 inch on the chart, the factual distance in real life is 80 long hauls.

To find the distance between metropolises on the chart, we need to convert the factual distance into a distance on the chart using the scale.

Let's suppose the factual distance between two metropolises is 240 long hauls. also, to find the distance between those metropolises on the chart, we can set up a proportion

/ 4 inch 80 long hauls = x elevation 240 long hauls

We cancross -multiply to break for x

inch * 240 long hauls = 80 long hauls * x elevation

720 = 80x

x = 9 elevation

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The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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(a) The likelihood of choosing at random a traveller who states that her decision to take a certain trip is affected by her opinion of the safety of the airline and that she is not interested in learning the aircraft's age is 0.742.

(b) The probability of randomly selecting a member of the traveling public  that she says that flight selection is neither influenced by perceptions of airline safety nor does she want to know the age of the aircraft is 0.31.

(c)The probability of randomly selecting a member of the traveling public  that he says that flight selection is not influenced by perceptions of airline safety and he wants to know the age of the aircraft is 0.273

According to the given information,

(a) We are aware that 30% of travellers claim that views of airline safety have an impact on their decision to book a ticket.

As a result, there is a 0.3 percent chance of picking a random traveler who has this attribute.

The 30% that are influenced by perceptions of airline safety,

we also know that 86% want to know the age of the aircraft.

Therefore, the likelihood of picking at random a traveller who is concerned about airline safety and requests information on the age of the aircraft is,

⇒ 0.3 x 0.86 = 0.258.

Now,

To find the probability of randomly selecting a member of the traveling public that is influenced by perceptions of airline safety but does not want to know the age of the aircraft,

We can subtract the probability of the previous scenario from 1.

The probability of randomly selecting a member of the traveling public that is influenced by perceptions of airline safety and does not want to know the age of the aircraft is therefore,

⇒ 1 - 0.258 = 0.742 or 74.2%.

(b) We know that 30% of the traveling public say that their flight selections are influenced by perceptions of airline safety and 39% want to know the age of the aircraft.

Therefore,

The likelihood of choosing at random a traveller who claims that airline safety perceptions impact their choice of trip or inquires about the aircraft's age is,

⇒ 0.3 + 0.39 = 0.69.

We may deduct the likelihood of the above scenario from 1 to get the likelihood of picking a randomly chosen traveller who claims that her decision on a trip is not impacted by her opinion of the airline's safety or her desire to know the age of the aircraft.

The probability of randomly selecting a member of the traveling public that says flight selection is neither influenced by perceptions of airline safety nor does she want to know the age of the aircraft is therefore,

⇒  1 - 0.69 = 0.31 or 31%.

(c) We know that 30% of the traveling public say that their flight selections are influenced by perceptions of airline safety.

Therefore, the probability of randomly selecting a member of the traveling public who says that flight selection is not influenced by perceptions of airline safety is,

⇒ 1 - 0.3 = 0.7

Of the traveling public, we also know that 39% want to know the age of the aircraft.

So the probability of randomly selecting a member of the traveling public who wants to know the age of the aircraft is 0.39.

To determine the likelihood of choosing at random a traveller who claims that views of airline safety have no impact on flight selection and requests information on the age of the aircraft,

we can multiply the probabilities of the two events,

The probability of randomly selecting a member of the traveling public who says that flight selection is not influenced by perceptions of airline safety and wants to know the age of the aircraft is therefore,

⇒  0.7 x 0.39 = 0.273 or 27.3%.

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the indentation diagonal length is approximately 0.0686 units.

What is Intention Diagonal Length?

The indentation diagonal d is determined by the mean value of the two diagonals d 1 and d 2 at right angles to each other: To avoid the risk of bulging of the material on the opposite side of the sample, the thickness should not fall below a certain minimum value. value. The minimum thickness depends on the expected hardness of the material and the test load.

To calculate the indentation diagonal length using the Vickers hardness value, you need to know the applied load and the hardness number. The Vickers hardness test measures the resistance of a material to indentation using a diamond indenter.

In this case, you have the following information:

Load: 0.700 kg

Vickers HV: 650

The Vickers hardness number (HV) is defined as the applied load divided by the surface area of the indentation.

The formula to calculate the indentation diagonal length (d) is:

d = 1.854 * sqrt(L / HV)

Where:

d = indentation diagonal length

L = applied load in kg

HV = Vickers hardness number

Plugging in the values:

d = 1.854 * sqrt(0.700 / 650)

Calculating the square root and performing the division:

d ≈ 1.854 * 0.0370262

d ≈ 0.0686

Therefore, the indentation diagonal length is approximately 0.0686 units. Please note that the specific unit (e.g., millimeters) was not provided in the question, so the answer is given in relative units.

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Answer:

The range is 28

The variance is 90.855

The mean is 56.36

The median is 53

The sample standard deviation is 9.532

Step-by-step explanation:

The axis of symmetry for the quadratic function in this problem is given as follows:

x = 5.

The vertex is given as follows;

(5, 7).

The graph is given by the image presented at the end of the answer.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The function in this problem is given as follows:

g(x) = (x - 5)² - 7.

Hence the coordinates of the vertex are given as follows:

(5,7).

The axis of symmetry is the vertical line at the x-coordinate of the vertex, hence:

x = 5.

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The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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Answer:

The first option.

Explanation:

Since these numbers are given in scientific notation, we must first look at the exponent to determine whether or not it's big or small. Negative exponents are less, so we start with that. Immediately, that eliminates the second and third options as -8 is less than -6 and 3. The last two numbers given in the first and last options, however, both have 3 as the exponent. Now, we look at the number given in front. 2.5 is less than 7, so we know that the first option is in order from least to greatest.

Answer:

The answer is D

Step-by-step explanation:

When two finite populations are connected by migration , then (b) Fst decreases to 0 .

The Fixation Index denoted as Fst ,  is a measure of population differentiation, which is used to quantify the level of genetic differentiation between two populations.

The Fst ranges from 0 to 1, where 0 indicates complete gene flow between two populations and 1 indicates complete genetic isolation.

If the migration rate is 2% per organism per generation, over time this will lead to a reduction in genetic differentiation between the populations, and the Fst value will decrease towards 0.

This is because the exchange of genetic material will reduce the amount of variation that is unique to each population, which leads to an increase in the genetic similarities between the populations.

The given question is incomplete , the complete question is

What happens to Fst when two finite populations are connected by migration (say 2% chance of migration per organism per generation, and no selection) ?

(a) Fst increases to 1

(b) Fst decreases to 0

(c) Fst stays moderate, near 0.5

(d) Fst wanders around randomly between 0 and 1 forever  .

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Answer:

Step-by-step explanation:

The area of given circle is 28.27 sq.m. The circumference of given circle is 18.85 m (rounded to the nearest hundredth).

The circumference of a circle is the distance around the edge or boundary of the circle. It is also the perimeter of the circle. The circumference is calculated using the formula:

C = 2πr

where "C" is the circumference, "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle.

The circumference of a circle is proportional to its diameter, which is the distance across the circle passing through its center. Specifically, the circumference is equal to the diameter multiplied by π, or:

C = πd

where "d" is the diameter of the circle.

Given that the diameter of the circle is 6m.

We know that the radius (r) of the circle is half of the diameter (d), so:

r = d/2 = 6/2 = 3m

The area (A) of the circle is given by the formula:

A = πr²

Substituting the value of r, we get:

A = π(3)² = 9π ≈ 28.27 sq.m (rounded to the nearest hundredth)

The circumference (C) of the circle is given by the formula:

C = 2πr

Substituting the value of r, we get:

C = 2π(3) = 6π ≈ 18.85 m (rounded to the nearest hundredth)

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The complete question is:

The means of two or more populations being equal is determined by a statistical approach for the ANOVA procedure. Option B is correct.

The ANOVA (Analysis of Variance) procedure is a statistical method used to determine whether there is a significant difference between the means of two or more groups. To statistically test the equality of means ANOVA uses F-tests.

The repeated-measures ANOVA is a two-stage process that is described as an analysis of dependencies. This test is used to prove an assumed cause-effect relationship between variables. The conditions that must be met for the results of an ANOVA are Independence, Random Sampling, Large Sample Size, and Normality.

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The inequality representation can be expressed as: -4 < x < 5

An inequality is a mathematical connection that exists between two expressions and may be expressed by one of the following:

From the given expression, the conversion of °C to F is estimated by using the formula:

(°C × 9/5) + 32

For  -20°C , we have:

= (-20°C × 9/5) + 32

= -4 F

For -15°C, we have:

= (-15°C × 9/5) + 32

= 5 F

Therefore, this can be represented in inequality form as: -4 < x < 5.

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Answer:

To find the number of courts with doubles matches, we need to determine the total number of players playing doubles. If each court with a doubles match has 4 players, then the total number of players playing doubles would be 4 times the number of courts playing doubles.

Since there are 28 players in total, and each court with a singles match has 2 players, the number of players playing singles would be 28 - 4x, where x is the number of courts playing doubles.

Since each court with a singles match has 2 players, the number of courts playing singles would be 28/2 = 14.

So, 28 - 4x = 14, and solving for x, we get x = 7.

Therefore, there are 7 courts with doubles matches and 14 courts with singles matches.

Carl deposited 10,000 into the savings account.

We can use the formula for compound interest to solve this problem:

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

Where:

A = the final amount

P = the initial principal (what Carl deposited)

r = the annual interest rate (8%)

n = the number of times interest is compounded per year (2 for semiannual compounding)

t = the number of years (1)

Plugging in the given values and solving for P:

\(10,816 = P(1 + 0.08/2)^{(2\times 1)}\)

\(10,816 = P(1.04)^2\)

10,816 = 1.0816P

P = 10,000

Therefore, Carl deposited 10,000 into the savings account.

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Answer:

12.8

Step-by-step explanation:

they can dig at a rate of 1.25

Answer:

D

Step-by-step explanation:

Wkx2di2jd1nd1do jf2kd2ifj2dkdu2dj2d

Answer:

d

Step-by-step explanation:

Answer:

35% chance

Step-by-step explanation:

Carlos' speed, we cannot determine if the distance he cycled was greater than 6 miles based solely on the information that it took him half an hour.

The information provided states that Carlos took half an hour to cycle from his house to the library. However, the given information does not specify the speed at which Carlos was cycling.

Distance is determined by both speed and time. Without knowing Carlos' speed, we cannot accurately determine the distance he cycled.

For example, if Carlos cycled at a constant speed of 12 miles per hour, then the distance he traveled in half an hour would be 6 miles (12 miles/hour * 0.5 hours = 6 miles). In this case, the distance would be greater than 6 miles.

On the other hand, if Carlos cycled at a constant speed of 5 miles per hour, then the distance he traveled in half an hour would be 2.5 miles (5 miles/hour * 0.5 hours = 2.5 miles). In this case, the distance would be less than 6 miles.

Therefore, without knowing Carlos' speed or having additional information, we cannot determine whether the distance he cycled was greater than 6 miles based solely on the given information that it took him half an hour.

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a. The flow is physically possible, b. The flow is rotational, c. The velocity potential function is φ(x,y) = x^2y - xt^2 + yt^2, d. The stream function is ψ(x,y) = x^2 - y^2 + 10xyt, e. The flow is not permanent.

a. The flow is physically possible because the velocity field is defined everywhere and is continuous.

b. The flow is rotational because the curl of the velocity field is not zero. The curl of the velocity field is given by:

curl(u,v) = (-2y + 20t, 2x - 20t, 0)

The curl is not zero because the z-component is not zero. This means that the flow has vorticity, which is a measure of how much the fluid is rotating.

c. The velocity potential function is given by:

φ(x,y) = x^2y - xt^2 + yt^2

The velocity potential function is a scalar field that can be used to calculate the velocity field. The velocity field can be calculated using the following formula:

u = -grad(φ)

v = -grad(ψ)

where φ and ψ are the velocity potential functions.

d. The stream function is given by:

ψ(x,y) = x^2 - y^2 + 10xyt

The stream function is a scalar field that can be used to calculate the streamlines of the flow. The streamlines are the curves that are tangent to the velocity field.

e. The flow is not permanent because the velocity field is not time-independent. The velocity field depends on the time variable t. This means that the flow will change over time.

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Answer: Choice C

Step-by-step explanation:

First, flip the triangle ABC. After you flipped it you would find that AB=DE

The area of the triangle is 3/4 units.

What is area of the triangle?

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.

Suppose

x is the shorter leg of the triangle.

As the longer leg of a right triangle is three times as long as the shorter leg.

⇒ 3x is the longer leg of the triangle.

The hypotenuse of the triangle is, √5.

By using Pythagorean theorem,

\(x^2 + (3x)^2 = (\sqrt{5} )^2\\x^2 + 9x^2 = 5\\10x^2 = 5\\x^2 = \frac{5}{10}\\ x^2 = \frac{1}{2} \\x = \frac{1}{\sqrt{2} }\)

⇒ Shorter leg of the triangle is 1/√2.

⇒ Longer leg of the triangle is 3/√2.

Now to find the area of the triangle.

Area of triangle = \(\frac{1}{2}(\frac{1}{\sqrt{2} })(\frac{3}{\sqrt{2} } )\)

\(A = \frac{3}{4}\)

Hence, the area of the triangle is 3/4 units.

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(a) 77+21(6) = $203

(b) 329 = 77 + 21h means 252 = 21h, and thus h = 12 hours

Based on the above analysis, the set W = {(a₁, a₂, a₃) ∈ ℝ³ : a₁ - 5a₂ + a₃ = 2} does not satisfy all the conditions to be considered a subspace of ℝ³. Therefore, W is not a subspace of ℝ³.

To determine whether the set W = {(a₁, a₂, a₃) ∈ ℝ³ : a₁ - 5a₂ + a₃ = 2} is a subspace of ℝ³, we need to verify three conditions:

1. The zero vector is in W.

2. W is closed under vector addition.

3. W is closed under scalar multiplication.

Let's check each condition:

1. Zero vector: The zero vector in ℝ³ is (0, 0, 0). We need to check if this vector satisfies the equation a₁ - 5a₂ + a₃ = 2 when substituted into the equation.

When we substitute a₁ = 0, a₂ = 0, and a₃ = 0 into the equation, we get 0 - 0 + 0 = 2, which is not true. Therefore, the zero vector is not in W.

2. Vector addition: Let's take two vectors (a₁, a₂, a₃) and (b₁, b₂, b₃) that satisfy the equation a₁ - 5a₂ + a₃ = 2 and b₁ - 5b₂ + b₃ = 2. We need to check if their sum, (a₁ + b₁, a₂ + b₂, a₃ + b₃), also satisfies the equation.

(a₁ + b₁) - 5(a₂ + b₂) + (a₃ + b₃) = (a₁ - 5a₂ + a₃) + (b₁ - 5b₂ + b₃) = 2 + 2 = 4

Since the sum of the two vectors satisfies the equation, W is closed under vector addition.

3. Scalar multiplication: Let's take a vector (a₁, a₂, a₃) that satisfies the equation a₁ - 5a₂ + a₃ = 2 and multiply it by a scalar c. We need to check if the resulting vector, (ca₁, ca₂, ca₃), also satisfies the equation.

(ca₁) - 5(ca₂) + (ca₃) = c(a₁ - 5a₂ + a₃) = c(2) = 2c

Since 2c is not equal to 2 for all values of c, we can conclude that W is not closed under scalar multiplication.

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Answer: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.

Step-by-step explanation:

You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!

You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54

If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.

Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

When combining like terms with exponents, you add the exponents only if the terms have the same base.

For example,

3x² + 9x²

= (3 + 9)x²

= 12x²

And,

2² x 2³

= \(2^{2 + 3}\)

= \(2^5\)

Thus,

Yes, we add the exponents.

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