A small town is trying to establish a transportation system of large and small vans.
It can spend no more than $100,000 for purchasing both sizes of vehicles and no
more than $500 per month for maintenance. The town can purchase a small van for
$10,000 and maintain it for $100 per month. The large vans cost $20,000 each and
can be maintained for $75 per month. Each large van carries a maximum of 15
passengers and each small van carries a maximum of 7 passengers. Find the
maximum number of passengers the transportation system can handle given the
constraints. How many large and small vans will they need to maximize the
number of
passengers
it can service?

The limit of the sequence as n approaches infinity is ln(8). The sequence converges, and the limit is ln(8).

To determine whether the sequence given by an = ln(8n² + 9) − ln(n² + 9) converges or diverges, we can examine the behavior of the terms as n approaches infinity.

Taking the limit as n approaches infinity, we have:

lim(n→∞) ln(8n² + 9) − ln(n² + 9)

We can simplify this expression using logarithmic properties. The natural logarithm of a quotient is equal to the difference of the logarithms:

= lim(n→∞) ln[(8n² + 9)/(n² + 9)]

Now, let's analyze the behavior of the numerator and denominator as n approaches infinity:

As n becomes larger and larger, the higher-order terms dominate. In this case, the leading term in both the numerator and denominator is n².

In the numerator, 8n² dominates, and in the denominator, n² dominates. Therefore, as n approaches infinity, the ratio (8n² + 9)/(n² + 9) approaches 8.

Taking the natural logarithm of 8, we have ln(8).

Therefore, the limit of the sequence as n approaches infinity is ln(8).

Hence, the sequence converges, and the limit is ln(8).

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[tex]\left(x-2\right)^{2}+\left(y-4\right)^{2}=25[/tex]

Hope this helps!

The equation of circle is [tex](x-2)^{2}+(y-4)^{2} =25[/tex]

The equation of circle is given as,

                 [tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

Where [tex](h,k)[/tex] is the coordinate of center and r is radius.

From the given figure,

It is observed that, the center of circular pool is (2, 4)

and radius is 5.

substitute the value of center and radius in above equation.

                  [tex](x-2)^{2}+(y-4)^{2} =5^{2}\\\\(x-2)^{2}+(y-4)^{2} =25[/tex]  

The equation of circle is [tex](x-2)^{2}+(y-4)^{2} =25[/tex]

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Answer:

the solution to this equation is x = 9°

Step-by-step explanation:

9x + 3 = 84

9x = 84 - 3

9x = 81

x = 81 / 9

x = 9°

Answer:

D. Addition Property of Equality; Subtraction Property of Equality

Step-by-step explanation:

Answer:

Option C and B

Step-by-step explanation:

In the question step C is 23 + 11 = -11 +(-4x) + 11

which is in the form of a + b = c + a

In step C we have added 11 on both the sides to eliminate 11 from right side of the equation.

property which signifies this step is

Addition property of equality :

In step 'f' expression is

\frac{34}{-4}=\frac{-4x}{-4}

In this step equation has been divided by -4 on both the sides to eliminate 4 from the numerator.

In this step division property of equality has been applied.

Therefore Option C and B are the correct options.

Answer:

Look for 75% of 1 1/2, I got 1.125 or 1 1/8

Step-by-step explanation:

Answer:

24 inches

Step-by-step explanation:

Answer:

I think it's the first one

Answer:

to my knowledge I would pick A

The approximation of the integral ∫(x – 3)ex dx by the composite Trapezoidal rule with n = 4 is approximately: -5.1941.

To approximate the integral ∫(x – 3)ex dx using the composite Trapezoidal rule with n = 4, we divide the interval [a, b] into n subintervals of equal width. In this case, we don't have the limits of integration provided, so we'll assume the interval to be [a, b] = [a, a+4] for simplicity.

Let's denote h as the width of each subinterval, given by

[tex]h = (b - a) / n \\= 4 / 4 = 1[/tex]

Using the composite Trapezoidal rule formula, the approximation is given by:

[tex]Approximation = h/2 * [f(a) + 2*f(a + h) + 2*f(a + 2h) + ... + 2*f(a + (n-1)h) + f(b)][/tex]

Now, let's calculate the values of the function at each interval endpoint:

[tex]f(a) = (a - 3)*e^a\\f(a + h) = (a + h - 3)*e^{a + h}\\f(a + 2h) = (a + 2h - 3)*e^{a + 2h}\\f(a + 3h) = (a + 3h - 3)*e^{a + 3h}\\f(b) = (b - 3)*e^b[/tex]

[tex]Approximation = (1/2) * [(a - 3)*e^a + 2*(a + h - 3)*e^{a + h} + 2*(a + 2h - 3)*e^{a + 2h} + 2*(a + 3h - 3)*e^{a + 3h} + (b - 3)*e^b][/tex]

[tex]= -5.1941[/tex]

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Answer:

b. 12

Step-by-step explanation:

Answer:

either a or d because they are both correct.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The required surface area is multiplied by a factor of 25 or 5 to 2. Option C is correct.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,

The lateral surface area of a pyramid is given by the formula:

L = (1/2) * P * l

where P is the perimeter of the base and l is the slant height.
In this case, the perimeter of the base is 5 * 5 = 25 centimeters.

So the lateral surface area of the original pyramid is
L = (1/2) * 5 * 8 = 20 square centimeters.

Total area = 4[20] + 25 = 105

When the sides of the base and the slant height are each multiplied by 5, the new perimeter of the base is 5 * 5 * 5 = 125 centimeters and the new slant height is 8 * 5 = 40 centimeters.

So the lateral surface area of the new pyramid is
L = (1/2) * 25 * 40 = 500 square centimeters.

Total area = 4{500} + 125 = 2125

Therefore, the surface area is multiplied by a factor of 2125/105 = 25.

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Answer:

8.4 I think

Step-by-step explanation:

Please don't hate me if I am wrong

Answer:

135

Step-by-step explanation:

Well 3 friends and 45 dollars each

45*3=135

The five number summary for the percent of the population that is obese among the SOUS states are Minimum: 23.0, First Quartile (Q1): 28.6, Median: 30.9, Third Quartile (Q3): 34.4, Maximum: 39.5

The five number summary provides a concise summary of the distribution of a dataset, consisting of five key values: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Let's explain each part using the given information:

Minimum: The minimum value represents the smallest observed value in the dataset. In this case, the minimum value is 23.0. It indicates that the lowest recorded percentage of obesity among the SOUS states is 23.0%.

First Quartile (Q1): The first quartile is the value that divides the dataset into the lower 25% of the data. It represents the 25th percentile of the data. In the table, the first quartile (Q1) is given as 28.6. This means that 25% of the SOUS states have a percentage of obesity lower than or equal to 28.6%.

Median: The median, also known as the second quartile or the 50th percentile, is the middle value of the dataset when it is sorted in ascending order. It represents the point that splits the data into two equal halves. In the table, the median is given as 30.9. This implies that 50% of the SOUS states have a percentage of obesity lower than or equal to 30.9%.

Third Quartile (Q3): The third quartile is the value that divides the dataset into the upper 25% of the data. It represents the 75th percentile of the data. In the table, the third quartile (Q3) is provided as 34.4. This means that 75% of the SOUS states have a percentage of obesity lower than or equal to 34.4%.

Maximum: The maximum value represents the largest observed value in the dataset. In this case, the maximum value is 39.5. It indicates that the highest recorded percentage of obesity among the SOUS states is 39.5%.

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Answer:

12

Step-by-step explanation:

put the numbers in least to greatest. so that would be 0,0,1,1,1,1,2,3,3,6,7,8, then find the one or two. in this case it is two. the medians in the one in the middle

Answer:b

Step-by-step explanation:

Question:

2 people A and B travel from X to Y along different routes. Their journeys take the same amount of time. B's route is 100km at an average speed of 40km/hour A's route is 60km. What is A's average speed?

Answer:

Person A's average speed is 24km/hr

Step-by-step explanation:

Given

Person B

[tex]Distance = 100km[/tex]

[tex]Speed = 40km/hr[/tex]

Person A

[tex]Distance = 60km[/tex]

Required

Average speed of person A

Speed is calculated as:

[tex]Speed = \frac{Distance}{Time}[/tex]

For person B

[tex]40 = \frac{100}{Time}[/tex]

Make Time the subject

[tex]Time= \frac{100}{40}[/tex]

[tex]Time= 2.5hr[/tex]

For person A

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]Speed = \frac{60}{Time}[/tex]

The journeys last for the same duration.

So;

[tex]Speed = \frac{60}{2.5}[/tex]

[tex]Speed = 24[/tex]

Person A's average speed is 24km/hr

Answer:

This question is clearly incomplete, so i will answer it in a really general way.

Suppose that for a quadratic function, we know that the x-intercepts are a and b.

And we also know that this function passes through the point (c, d).

First a definition, for a n-degree polynomial with the x-intercepts {x₁, x₂, ...,xₙ}  and a leading coefficient K, we can write this polynomial in the factorized form as:

p(x) = K*(x - x₁)*(x - x₂)*...*(x - xₙ)

Now let's do the same for our quadratic function, we can write it as:

f(x) = K*(x - a)*(x - b)

(where a and b are known numbers)

Now we also know that this function passes through the point (c, d)

This means that:

f(c) = d

then:

d = K*(c - a)*(c - b)

With this equation we can find the value of K,

K = d/( (c-a)*(c - b))

Then the quadratic function is:

[tex]f(x) = d\frac{(x-a)}{(c-a)} \frac{(x-b)}{(c-b)}[/tex]

Where again, it is supposed that you know the values of a and b, and also the point (c, d)

im not smart enough lol

Answer:

I could be any number.

But it couldn't just be a 'b' it could be other letters. The letters is just a grown up way of saying a missing number. Its like saying:

10+b=11..

11-b=10..

therefore b=1

Does that make sense

It can also mean in the quadratic formula b

Step-by-step explanation:

In algebra, the variable "b" represents an unknown or variable number.

It is used to denote a quantity that can vary or take on different values. The purpose of using variables in algebraic equations is to generalize mathematical relationships and solve problems with unknown quantities. By assigning the letter "b" to a variable, we can manipulate and solve equations using algebraic operations, such as addition, subtraction, multiplication, and division.

The value of "b" can be determined through various methods, such as solving equations, simplifying expressions, or applying mathematical principles. The flexibility of variables like "b" allows us to solve a wide range of problems and analyze mathematical relationships without relying on specific numerical values.

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It is because the moon revolves around Earth.

Hope it helps you...

The largest possible error you could make in the given approximation is [tex]1 / (10^11 * 11!)[/tex]

To approximate the value of [tex]e^x[/tex] using the series expansion, we can use the formula:

[tex]e^x[/tex] ≈ ∑ [tex](x^n)/n![/tex]

In this case, we have:

x = -1/10

To find the largest possible error in the approximation, we can consider the next term in the series that we are neglecting:

1 / (10^11 * 11!) = [tex]|x^(n+1) / (n+1)!|[/tex]

For the given approximation, n = 10 (since we are using terms up to n = 10).

Substituting the values, we have:

[tex]|Error|[/tex] = [tex]|(-1/10)^(10+1) / (10+1)!|[/tex]

|Error| =[tex]|(-1/10)^11 / 11!|[/tex]

|Error| =[tex]1 / (10^11 * 11!)[/tex]

Since the value of n is fixed at 10, the largest possible error occurs when x is at its maximum value within the given range (0 ≤ x ≤ 100).

In this case, the maximum value of |Error| would be obtained by using the maximum value of x = 100 in the formula.

|Error| = [tex]1 / (10^11 * 11!)[/tex]

Therefore, the largest possible error you could make in the given approximation is [tex]1 / (10^11 * 11!)[/tex].

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(i) the polar coordinates of the point are (6, π/6).

(ii) the polar coordinates of the point are (-6, π/6).

The Cartesian coordinates of the point are given as (3√3, 3). We need to find the polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π and also where r < 0 and 0 ≤ θ < 2π.

To find the polar coordinates (r, θ) of the point, we use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where x and y are the Cartesian coordinates of the point.

(i). For r > 0 and 0 ≤ θ < 2π, we have:

x = 3√3

y = 3

Using the above formulas, we get:

r = √((3√3)² + 3²) = √(27 + 9) = √36 = 6

θ = tan⁻¹(3/3√3) = tan⁻¹(1/√3) = π/6

Therefore, the polar coordinates of the point are (6, π/6).

b. For r < 0 and 0 ≤ θ < 2π, we have:

x = 3√3

y = 3

Using the above formulas, we get:

r = -√((3√3)² + 3²) = -√(27 + 9) = -√36 = -6

θ = tan⁻¹(3/3√3) = tan⁻¹(1/√3) = π/6

Therefore, the polar coordinates of the point are (-6, π/6).

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Given question is incomplete the complete question is incomplete

The Cartesian Coordinates Of A Point Are Given.

(3√3,3)

(i) Find Polar Coordinates (r, θ) Of The Point, Where r>0 And 0≤θ<2π.

(ii) Find Polar Coordinates (r, θ) Of The Point, Where r<0 And 0≤θ<2π.

The matrix norm for an n x n real matrix B is  ||B||M = max{|Bij|}

First, we will prove that ||B||M ≤ max{|Bij|}. Let's assume k is the index that achieves the maximum value, i.e., max{|Bij|} = |Bkj|. Consider the vector x = (0, 0, ..., 0, 1, 0, ..., 0)T, where the 1 is in the k-th position. Then, ||x||2 = 1. Now, let's calculate ||Bx||M:

||Bx||M = sup{||Bx||2 : ||x||2 = 1}

= sup{√((Bx)T(Bx)) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1, xk = 1}

≤ √((BTB)kk) (using the fact that xTBTBx is a scalar and sup{scalar} = scalar)

= √(|Bkj|²)

= |Bkj|

= max{|Bij|}

Therefore, we have shown that ||B||M ≤ max{|Bij|}.

Now, let's prove the reverse inequality: max{|Bij|} ≤ ||B||M. Consider the vector x = (x1, x2, ..., xn)T, where xi = 1 for the index i that achieves the maximum absolute value of Bij, and xi = 0 for all other indices. Then, ||x||2 = 1. Now, let's calculate ||Bx||M:

||Bx||M = sup{||Bx||2 : ||x||2 = 1}

= sup{√((Bx)T(Bx)) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1, xi = 1 for some i}

≥ √((BTB)ii) (using the fact that xTBTBx is a scalar and sup{scalar} = scalar)

= sqrt(|Bij|²)

= |Bij|

= max{|Bij|}

Therefore, we have shown that max{|Bij|} ≤ ||B||M.

Combining both inequalities, we conclude that ||B||M = max{|Bij|}.

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Answer:

b. 4m+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

(b − 7)(b + 3). SOLUTION: 4. (4n + 3)(n + 9). SOLUTION: 5. (8h − 1)(2h − 3) ... (m. 2. − 5m + 4)(m. 2. + 7m − 3). SOLUTION: 28. (x. 2. + 5x − 1)(5x. 2. − 6x + 1) ... The value of x must be greater than 4. If x = 4 ... c. SYMBOLIC For a sum of the form a + b, write an expression for the square of the sum. ... Then, for five days,.

Rewrite equations:

y=2;y=

−4

3

x+6

Step: Solvey=2for y:

y=2

Step: Substitute2foryiny=

−4

3

x+6:

y=

−4

3

x+6

2=

−4

3

x+6

2+

4

3

x=

−4

3

x+6+

4

3

x(Add 4/3x to both sides)

4

3

x+2=6

4

3

x+2+−2=6+−2(Add -2 to both sides)

4

3

x=4

4

3

x

4

3

=

4

4

3

(Divide both sides by 4/3)

x=3

Answer:

x=3 and y=2

An isosceles trapezoid LMNO has the side LO is congruent to side MN, the diagonal LN is congruent to diagonal MO, and the angle L is congruent to angle M. Hence correct options are a), c), and e)

Given :

Trapezoid LMNO.

The following are the conditions that show any trapezoid is an isosceles trapezoid:

Condition 1 -- Both the legs are of the same length.

Condition 2 -- The base angles are of the same measure.

Condition 3 -- Diagonals are of the same length.

So, the given trapezoid LMNO is an isosceles trapezoid when:

The side LO is congruent to side MN.

The diagonal LN is congruent to diagonal MO.

The angle L is congruent to angle M.

Therefore, the correct option is a), c), and e).

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Answer:

The answer is B

Step-by-step explanation:

Answer: its B i did the quiz lol

Step-by-step explanation: