Suppose you are a ladybug on the “outer” surface of the Klein bottle. Describe a path on the surface of the bottle that you can travel that would get you to the “inside” where a special gentleman bug is waiting.

Step-by-step explanation:

{(2 1/5) + (1 5/6)} /30

Step 1.

Convert all the entities in the numerator from a mixed fraction to an unmixed fraction. By so doing, we will have;

{(11/5) + 31/6)}/30

Step 2

Now, let us add the numerator together. To do this, we have to find the Least Common Factor (LCM) for the two entities on the numerator. To achieve that, we will have;

(5×6) = 30

Now, we can proceed with further extrapolation.

{(30/5) × 11} + {(30/6) ×31}

(6 × 11) + (5× 31)

66 + 155

= 221

Now, 221 is the numerator, and 30 is our denominator, putting both together becomes;

221/30.

So the answer to the question is 221/30.

Answer:

x = -6

Step-by-step explanation:

2-3(x+4) = 8

2 - 3x - 12 = 8

-3x - 10 = 8

-3x = 18

x = -6

Answer:

x = -6

Step-by-step explanation:

2 - 3 (x + 4) = 8

2 - 3x - 12 = 8

- 10 - 3x = 8

- 3x = 8 + 10

- 3x = 18

x = -18/3

x = -6

___________

hope this helps!

The probability based on the information will be;

a. Likely, probability is 25%

b. Likely, probability is 25%

c. Impossible, probability is 0%

d. Unlikely, probability is 33.3%

The probability of rolling a 5 on a 6 sided die is 1/6 or approximately 16.67%.

The probability of not rolling a 5 on a 6 sided die is 5/6 or approximately 83.33%. This can also be:

= 100 - 16.67

= 83.33%

The probability of spinning an even number on a spinner with numbers 1-8 is 4/8 or 1/2 or 50%.

The probability that a white horse is George is 1/5 or 20%.

An event that has probability of 0% is something that is impossible, such as rolling a 7 on a 6-sided die. An event that has a probability of 100% is something that is certain, such as flipping a coin and getting either heads or tails.

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Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.

Here,

The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where P is the principal amount (initial investment).

To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.

Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).

Then, we have:

[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]

Dividing both sides by P, we get:

[tex]2= (1 +\frac{r}{n})^{nt}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]

Using the properties of logarithms, we can simplify this expression as:

[tex]ln(2) = n*t * ln(1 + r/n)[/tex]

Dividing both sides by n*ln(1 + r/n), we get:

[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]

Plugging in the values for r and n, we get:

[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]

Solving this expression on a calculator, we get:

t ≈ 13.47 years

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It takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.

calculating the elevation the hiker climbs in stage one:

2% of 2,150 feet = 0.02 × 2,150 feet = 43 feet

Therefore, the hiker climbs 43 feet in stage one. To find the time it takes for the hiker to climb the remaining elevation of the mountain in stage two, we need to know the total elevation he needs to climb in this stage. This can be calculated by subtracting the elevation climbed in stage one from the total elevation of the mountain: Total elevation - Elevation climbed in stage one = 2,150 - 43 = 2,107 feet

Now, we can use the rate of climb in stage two to find the time it takes to climb 2,107 feet:

Time = Distance / Rate

Time = 2,107 feet / 12 feet per minute

Time ≈  175.58 minutes

Therefore, it takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.

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Answer: Da der Graph punktsymmetrisch zum Ursprung ist, können wir annehmen, dass er die Form f(x) = ax^3 hat.

Step-by-step explanation:

Da der Graph einen Tiefpunkt an der Stelle x = 1 hat, gilt f'(1) = 0 und f''(1) < 0.

Also gilt:

f(x) = ax^3 + bx^2 + cx + d

f'(x) = 3ax^2 + 2bx + c

f''(x) = 6ax + 2b

Da f'(1) = 0, haben wir:

3a + 2b + c = 0

Da f''(1) < 0, haben wir:

6a + 2b < 0

3a + b < 0

b < -3a

Da der Graph punktsymmetrisch zum Ursprung ist, haben wir:

f(-x) = -f(x)

Also haben wir:

-a x^3 + bx^2 - cx + d = -ax^3 - bx^2 - cx - d

oder

2bx^2 + 2d = 0

b = -d

Da der Graph durch A(2|2) geht, haben wir:

8a + 4b + 2c + d = 2

Und da der Graph einen Tiefpunkt bei x = 1 hat, haben wir:

f(1) = a + b + c + d = 0

Jetzt können wir die Gleichungen lösen, um die Koeffizienten der Funktion zu finden. Zunächst setzen wir b = -d ein und erhalten:

3a + 2b + c = 0

6a - 2d < 0

b < -3a

a + b + c + d = 0

8a - 2b + 2c - d = 2

Lösen dieser Gleichungssysteme liefert a = -1

Using the triangle inequality theorem, the possible values for the third side of the triangle are: 5 < x < 35.

The Triangle Inequality Theorem asserts that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Stated differently, the difference between the lengths of any two sides must be less than the length of the third side.

Thus, if you have the lengths of two sides of a triangle, as 20 and 15, we have:

20 - 15 < x < 20 + 15

5 < x < 35

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Answer:

μ (∠1) = 82°

μ (∠2) = 98°

μ (∠3) = 82°

μ (∠4) = 98°

Step-by-step explanation:

As the vertically opposite angles are equal to each other,

μ (∠2) = μ (∠4)

   98° = 98°

As the angles in a straight line are added up to 180°,

μ (∠2) + μ (∠3) = 180

98 + μ (∠3) = 180

μ (∠3) = 180 - 98

μ (∠3) = 82°

As the vertically opposite angles are equal to each other,

μ (∠3) = μ (∠1)

   82° = 82°

Answer: g=18

Step-by-step explanation:

g*4=72

g=72/4

g=18

Answer:

2/5 of the cookie

Step-by-step explanation:

12 friends need to split 4 cookies

4 cookies needs to divided by 10 people

[tex]\frac{4cookies}{10 people}[/tex] = [tex]\frac{4}{10}[/tex]

simplify: [tex]\frac{4}{10} = \frac{2}{5}[/tex]

The surface area of the pyramid is 74.25 square meters.

Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.

A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.

In the given question,

The area of the base is simply the area of a square, which is:

Area of base = length x width = 4.5m x 4.5m = 20.25 square meters

To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).

We can use the Pythagorean theorem to do this:

h²= (1/2 x base)² + height²

h² = (1/2 x 4.5)² + 6²

h² = 2.25 + 36

h² = 38.25

h = √38.25

h = 6.18 meters (rounded to two decimal places)

Now that we know the slant height, we can find the area of each triangular face:

Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters

Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:

Total area of triangular faces = 4 x 13.5 = 54 square meters

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Surface area = Area of base + Total area of triangular faces

Surface area = 20.25 + 54

Surface area = 74.25 square meters

Therefore, the surface area of the pyramid is 74.25 square meters.

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Answer:

Step-by-step explanation:

I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.

If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:

sin^2(x) + cos^2(x) = 1

Plugging in sin(x) = 3/4, we get:

(3/4)^2 + cos^2(x) = 1

Simplifying, we have:

9/16 + cos^2(x) = 1

Subtracting 9/16 from both sides, we get:

cos^2(x) = 7/16

Taking the square root of both sides, we get:

cos(x) = ±sqrt(7)/4

Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:

cos(x) = sqrt(7)/4

I hope this helps! Let me know if you have any further questions.

Answer:

Numbers between 100 and 200 which are also equal to a square number multiplied by a prime number are:

Step-by-step explanation:

A square number is a number that has been multiplied by itself.

For example, 25 is a square number as 5 × 5 = 25.

The square numbers between zero and 200 are:

A prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).

Since the smallest square number is 4, and our final number needs to be between 100 and 200, we only need to list the primes numbers that are less than 50 as 4 × 50 = 200.

Begin with the smallest prime number, 2. If we divide 100 and 200 by this prime number, we get 50 and 100. Therefore, to find a number between 100 and 200 that is equal to a square number multiplied by a prime number, the square number should be more than 50 and less than 100.  Therefore:

The next smallest prime number is 3. If we divide 100 and 200 by 3 we get 33.33.. and 66.66...  Therefore, the prime number 3 should be multiplied by a square number that is more than 33 and less than 67:

The next prime number is 5. If we divide 100 and 200 by 5 we get 20 and 40.  Therefore, the prime number 5 should be multiplied by a square number that is more than 20 and less than 40:

Continuing this way, all the numbers that are between 100 and 200, which are also equal to a square number multiplied by a prime number are:

Number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In simpler terms, a prime number is a number that can only be evenly divided by 1 and itself.

To find this number, I first looked for square numbers between 100 and 200. The square numbers within this range are 121 (11 squared) and 169 (13 squared).

I then checked if either of these square numbers could be multiplied by a prime number to equal a number between 100 and 200. After some calculation, I found that 169 cannot be multiplied by a prime number to give a number between 100 and 200. However, 121 can be multiplied by 2 to give 242, which is greater than 200.

Finally, I checked if there were any other square numbers I missed. I found that 7 squared is equal to 49, which when multiplied by 3 (a prime number) gives 147, a number between 100 and 200 that satisfies the problem.

Therefore, the number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

I hope this helps!

The variance of the number of citizens favoring the supermarket is 6.

To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:

Variance = n × p × (1 - p)

where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.

Plugging in the values, we get:

Variance = 25 × 0.6 × (1 - 0.6)

Variance = 25 × 0.6 × 0.4

Variance = 6

The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.

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The first and second equations satisfy standard form of the linear equation, hence they are linear. While, third, fourth, and fifth are non linear equations.

A group of two or more simultaneous solutions to linear equations is referred to as a system of linear equations. A collection of values that satisfy every equation in a system of linear equations is the solution. There might not be a unique solution if the number of equations in the system is less than or equal to the number of variables in the system. Systems of linear equations can be solved using various methods, such as substitution, elimination, or matrix algebra.

The standard form of linear equation is given as:

y = mx + b

The first and second equations satisfy, or represent the standard form of the linear equation, hence they are linear.

While, third, fourth, and fifth do not represent the standard form and hence are non linear equations.

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1. linear function 2. non linear function 3. linear function 4. non linear function 5. non linear function.

What is linear function?

In mathematics, a linear function is a type of function that can be represented by a straight line on a graph.

1.The equation m = 5.45p represents a linear function. It has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 5.45, which is a constant rate of change, and there is no other term involving p, so the equation is linear. When p increases or decreases by 1 unit, m increases or decreases by 5.45 units, respectively.

2.The equation 1=56.01+5 is not a function. It is a simple linear equation in one variable, but it has no independent variable to define a function. It is just an equation that states a relationship between two constants, 56.01 and 5, which sum up to 61.01.

3.The function d = (g-28)7/11 is a linear function because it can be written in the form y = mx + b, where m and b are constants and y and x are variables.

In this case, if we let d = y and g = x, we get:

y = (x-28)7/11

This can be simplified as:

y = 7/11 * x - 196/11

So we can see that the function has a constant slope of 7/11, and a constant intercept of -196/11. Therefore, it is a linear function.

4. This is a non-linear function since it includes a variable raised to a power (r³).

5.The function e=124² is a non-linear function as it involves squaring the value of 124, which produces a curved graph instead of a straight line.

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Answer: 6

2 possibilities for each student if they are first and 3 students so 3*2=6.

Answer / Step-by-step explanation:

To represent the solutions of the linear inequality y < 2x + 5 on a graph, we can follow these steps:

First, we draw the boundary line y = 2x + 5, which is a straight line with a slope of 2 and a y-intercept of 5.

Since the inequality is y < 2x + 5, we need to shade the region that is below the boundary line. This is because any point below the line will have a y-coordinate that is less than 2x + 5, which satisfies the inequality.

We can also use a dashed line to represent the boundary line, since the inequality is strict (y < 2x + 5, not y ≤ 2x + 5).

Finally, we can check the solutions to the inequality by picking any point in the shaded region and plugging its coordinates into the inequality. If the resulting statement is true, then that point is a valid solution to the inequality. If the statement is false, then the point is not a solution.

Therefore, to represent the solutions of the inequality y < 2x + 5 on a graph, we would shade below the dashed line y = 2x + 5.

Answer:

150 cubic inches.

Step-by-step explanation:

the volume of a prism = cross-section area* length

                                    = 1/2*4*5*15

                                    = 150 cubic inches.

Answer:

The answer is 300 inches

Step-by-step explanation:

15*4*5

232 child's plates were served and 103 adult's plates were served after rounding to the nearest whole number.

The substitution method involves solving one equation for one variable in terms of the other variable, and then substituting this expression into the other equation.

Let's use the following variables:

c = number of child's plates served

a = number of adult's plates served

We can set up a system of two equations based on the given information:

c + a = 335 (the total number of plates served was 335)

2.6c + 8.3a = 1458.1 (the total amount collected was $1458.10)

To solve this system, we can use the substitution method. Rearrange the first equation to solve for one variable in terms of the other:

c = 335 - a

Substitute this expression for c in the second equation and solve for a:

2.6(335 - a) + 8.3a = 1458.1

871 - 2.6a + 8.3a = 1458.1

5.7a = 587.1

a = 103

Now that we know there were 103 adult's plates served, we can substitute this value back into the first equation and solve for c:

c + 103 = 335

c = 232

Therefore, 232 child's plates were served and 103 adult's plates were served.

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Therefore , the solution of the given problem of probability comes out to be there is a 0.44 percent chance of choosing a lady.

A procedure's criteria-based systems' main objective is to ascertain the likelihood that an assertion is accurate or that a particular event will take place. Chance can be represented by any number range between 0 and 1, where 0 is commonly used to indicate the possibility of something may be and 1 is usually employed to indicate a degree of confidence. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

By adding the probabilities of selecting a woman from each squad, weighted by the probabilities of selecting each team,

we can use the law of total probability to determine the likelihood of selecting a woman:

=> Woman = P(Red) * P(Woman from Red) + P(Blue) * P(Woman from Blue) + P(Yellow) * P(Woman from Yellow)

=>  P(Woman) = 0.2 + 0.12 + 0.12 P(Woman) = 0.44 P(Woman) = 0.4 * 0.5 + 0.4 * 0.3 + 0.2 * 0.6

As a result, there is a 0.44 percent chance of choosing a lady.

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Solving the system of equations:

B = 9 + 3*H

Area  27 = B*H/2

We can see that the height is 3 inches and the base is 18 inches.

For a triangle of base B and height H the area is given by the equation:

Area = Base*height/2 = B*H/2

here we know two relations so we can write a system of equations which is:

B = 9 + 3*H

Area  27 = B*H/2

Replace the first equation into the second to get:

27 = (9 + 3*H)*H/2

2*27 = 9H + 3H²

H² + 3H - 18 = 0

The quadratic formula gives the solutions:

[tex]H = \frac{-3 \pm \sqrt{3^2 - 4*1*-18} }{2}[/tex]

So the positive solution is H = (-3 + 9)/2 = 3

And the base is.

B = 9 + 3*3 = 18

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After answering the presented question, we can conclude that function Therefore, the maximum growth rate of  [tex]f(t)[/tex] occurs at  [tex]t = k ln(Λ)[/tex] .

In mathematics, a function appears to be a link between two sets of numbers, in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range).

A formula or a graph can be used to represent a function. For example, the formula  [tex]y = 2x + 1[/tex] depicts a functional form in which each value of x generates a unique value of y.

To find the maximum growth rate of  [tex]f(t)[/tex] between t=0 and t=kA, we need to find the maximum value of its derivative with respect to t. Let's start by taking the derivative of f(t) using the chain rule:

[tex]f'(t) = -kΛe^(-kt) / B(1 + Λe^(-kt))^2[/tex]

Now we need to find the value of t that maximizes f'(t). One way to do this is to use logarithmic differentiation. First, take the natural logarithm of both sides of the equation for f'(t):

Next, take the derivative of both sides with respect to t:

[tex]f''(t)/f'(t) = -k + Λke^(-kt) / (1 + Λe^(-kt))[/tex]

Simplifying this expression by multiplying both numerator and denominator by [tex]e^(kt)[/tex], we get:

[tex]f''(t)/f'(t) = -k + Λk / (e^(kt) + Λ)[/tex]

Now we can set f''(t)/f'(t) equal to zero to find the critical points:

[tex]-k + Λk / (e^(kt) + Λ) = 0[/tex]

Multiplying both sides by [tex]e^(kt)[/tex] + Λ and rearranging, we get:

[tex]e^(kt) = Λ/k[/tex]

Taking the natural logarithm of both sides, we get:

[tex]kt = ln(Λ) - ln(k)[/tex]

Solving for t, we get:

[tex]t = ln(Λ)/k - ln(k)/k[/tex]

[tex]t = (ln(Λ) - ln(k))/k[/tex]

[tex]t = ln(Λ/k)/k[/tex]

Substituting this value of t back into f'(t), we get:

[tex]f'(ln(Λ/k)/k) = -kΛe^(-ln(Λ)) / B(1 + Λe^(-ln(Λ)))^2[/tex]

Since A>1, we know that Λ>1. Therefore, e^(-ln(Λ)) = 1/Λ, and we can simplify the expression for f'(ln(Λ/k)/k) to:

[tex]f'(ln(Λ/k)/k) = -k/ΛB(1 + 1/Λ)^2[/tex]

We can now see that f'(ln(Λ/k)/k) is negative, which means that f(t) is decreasing at that point. Therefore, the maximum growth rate of f(t) must occur at either t=0 or t=kA. We can find which one of these is the maximum by comparing the values of f'(0) and f'(kA).

[tex]f'(0) = -kΛ/B(1 + Λ)^2[/tex]

[tex]f'(kA) = -kΛe^(-kA) / B(1 + Λe^(-kA))^2[/tex]

We know that A>1, which means that kA>k. Therefore,  [tex]e^(-kA) < e^(-k),[/tex]  which means that f'(kA) is greater in magnitude than f'(0). Since f'(kA) is negative, this means that f(t) is decreasing faster at t=kA than at   [tex]t=0.[/tex]

Therefore, the maximum growth rate of  [tex]f(t)[/tex]occurs at [tex]t=ln(Λ)/k[/tex]  , as given by the formula we derived earlier.

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The answer to the question is 1/3.

There are three possible outcomes: 5, 6, or 7.

Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.

Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.

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The successor of -34 is -33 using the formula "n+1".

A phrase that follows or is right after a specific number, term, or value is known as a successor.

The successor of n is "n+1" if n is a number (and n belongs to any whole number).

The terms just after, immediately after, and next number/next value are also used to describe a successor.

As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.

The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.

So, the successor of -34:

= -34 + n

= -34 + 1

= - 33

Therefore, the successor of -34 is -33 using the formula "n+1".

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The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.

The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:

Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.

The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).

In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.

These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.

In the given triangle using the sum of interior angle of triangle we have:

180 - 90 - 29 = 61

The measure of the third angle is 61 degrees.

Now, tan(61) = XZ/XY

XZ = XY * tan(61)

XZ = 18 * 1.927 = 34.686

Now, using the Pythagoras theorem we have:

ZY² = XZ² + XY²

ZY² = 34.686² + 18²

ZY² = 1712.3996

ZY = 41.38

Now, the value of:

sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435

cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838

tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518

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The proportion of vehicles that are trucks and use speed passes is 0.7321.

The proportion can be gotten by determining the total number of trucks that pay via the live cashier and speed pass. The sum of these trucks is 65. Of these, the total number of truck vehicles that pay through speed passes is 47. This expresses the relationship between the total sum of trucks and the actual number that uses speed passes.

So, to get the proportion of vehicles that are trucks and make their payments using speed passes is 47 divided by 65. The answer is 0.7321. So, option D is right.

List of options:

A. 0.2814

B. 0.4123

C. 0.6826

D. 0.7321

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the other two angles of the triangle must also be equal, which means that the other two sides of the triangle must be equal as well. the length of the shorter sides is [tex]y = 16 feet[/tex] .

Let's start by using the information given to write equations for the perimeter of the heptagon in terms of the length of the sides:

Let x be the length of the four equal sides, and y be the length of the remaining three sides, which are half as long. Then, we have:

Perimeter  [tex]= 4x + 3y[/tex]

We also know that the perimeter is 88 feet, so we can set up the equation:

[tex]4x + 3y = 88[/tex]

Now we need to solve for y, which represents the length of the shorter sides.

We can simplify the equation by substituting y = (1/2)x:

[tex]4x + 3(1/2)x = 88[/tex]

Simplifying this expression, we get:

[tex]7x/2 = 88[/tex]

Multiplying both sides by 2/7, we get:

[tex]x = 32[/tex]

Now that we know x, we can find y by substituting it into the equation y   [tex]= (1/2)x[/tex]:

[tex]y = (1/2)(32) = 16[/tex]

Therefore, the length of the shorter sides is  [tex]y = 16[/tex] feet.

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Answer:

To add mixed numbers, we need to add the whole numbers separately and fractions separately.

Starting with the whole numbers, we have:

9 1/2 − 3 7/8 + 4 4/5 − 1 1/2

= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)

= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)

= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)

= 5 7/20 (expressing the result as a mixed number in simplest form)

Therefore, the value of the expression is 5 7/20.

Scale factor of the similar polygon pairs is:

5. 6

6. 5/12

7. 4/15

8. 1/7

When both the original dimensions and the new dimensions are known, the scale factor may be determined.

The following is a basic formula to determine a figure's scale factor:

Scale factor is equal to the difference between the dimensions of the old and new shapes.

Here in the first figure,

The sides are in a ratio of 1:6. The sides have increased 6 times so the scale factor here is 6.

Similarly in the trapezium, the ratio of the sides is 5/12.

The scale factor here becomes 5/12.

In the next figure, the sides are in a ratio of 4/15. Scale factor for the pair here is 4/15.

In the last figure, the equivalent sides are in the ratio of 1/7. The scale factor between the pair is 1/7.

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