emily can ride her scooter 18 miles in 50 minutes . how long would it take her 4 miles?

The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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CME 303 is a course offered at Stanford University that focuses on modeling, simulation, and optimization of complex systems.

It is an introduction to the fundamentals of mathematical optimization, which deals with the problem of finding the best solution to a given problem. The course covers basic optimization theory and algorithms, including linear programming, integer programming, nonlinear programming, dynamic programming, and stochastic programming. Furthermore, it introduces optimization software packages, such as MATLAB, GAMS, and CPLEX, and how to use them for solving real-world optimization problems. It also covers the application of optimization techniques to areas such as finance, engineering, economics, and computer science.CME 303 is a course offered at Stanford University that focuses on modeling, simulation, and optimization of complex systems.  The course is taught using lectures, tutorials, and computer lab assignments. In the final project, students apply the techniques learned in the course to solve a real-world problem.

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To find the probability that there will not be enough seats on any given flight, we need to calculate the probability of more than 200 passengers showing up.

The number of passengers that show up is approximately normally distributed with a mean of 185 and a standard deviation of 8.

To determine the 96th percentile of the number of people showing up, we can use the Z-score formula:

Z = (X - μ) / σ

where X is the number of people showing up, μ is the mean, and σ is the standard deviation.

To find the Z-score for the 96th percentile, we use the standard normal distribution table or a calculator to find the Z-value associated with a cumulative probability of 0.96. The Z-score for a cumulative probability of 0.96 is approximately 1.7507.

Next, we can calculate the number of people (X) corresponding to the 96th percentile using the formula:

X = Z * σ + μ

X = 1.7507 * 8 + 185

X ≈ 198.006

Therefore, the 96th percentile of the number of people showing up is approximately 198.

To find the probability that there will not be enough seats, we calculate the probability of more than 200 passengers showing up, which is equivalent to finding the probability that X is greater than 200.

Using the Z-score formula:

Z = (X - μ) / σ

Z = (200 - 185) / 8

Z ≈ 1.875

To find the probability corresponding to a Z-score of 1.875, we look up the value in the standard normal distribution table or use a calculator. The probability is approximately 0.0304.

Therefore, the probability that there will not be enough seats on any given flight is approximately 0.0304, or 3.04% (rounded to four decimal places).

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We can use the substitution $u=x^2+9$ to find the indefinite integral of the given expression. We have:

\(∫�2�2+9��=\)\(12∫2��2+9���∫ x 2 +9​\)

\(x 2\)

​

\(dx= 21​ ∫ x 2 +9​ 2x​ xdx\)

Let $u=x^2+9$, then $\frac{du}{dx}=2x$ and $dx=\frac{du}{2x}$, so we have:

\(12∫2��2+9���=12∫1���21​ ∫ x 2 +9​ 2x​ xdx= 21​ ∫ u​ 1​ du\)

Integrating with respect to $u$, we get:

\(12∫1���=�+�=�2+9+�21​ ∫ u​ 1​ du= u​ +C= x 2 +9​ +C\)

where $C$ is a constant of integration. Therefore, the indefinite integral of $\frac{x^2}{\sqrt{x^2+9}}$ is $\sqrt{x^2+9} + C$, where $C$ is a constant.

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1. The predicted trade for each pair using the gravity model is as follows:

  - Pair 1 (US-UK): Approximately $312.56 billion

  - Pair 2 (US-CAN): $700 billion

  - Pair 3 (US-MEX): $840 billion

  - Pair 4 (Vietnam-Thailand): $7.056 billion

Now, let's move on to the next questions.

2. The trade between the US and Mexico is predicted to be 20% higher than the trade between the US and Canada.

This is primarily due to the difference in GDP between Mexico and Canada. Despite the distance between the US and both countries being the same, Mexico's higher GDP leads to a higher predicted trade volume according to the gravity model. The gravity model suggests that larger economies tend to trade more with each other, all else being equal.

Now, let's move on to the third question.

3. For the trade between Vietnam and Thailand to double (i.e., increase by 100%), Vietnam's GDP would need to grow by approximately 100%.

  To increase its trade with Vietnam by $5 billion, Thailand's GDP would need to grow by approximately 70.86%.

  If both Vietnam and Thailand's GDPs fell by 5% in 2022 due to a resurgent pandemic, their trade would decrease by approximately 9.75%.

Answer:

Length of hypotenuse of given triangle

= sqrt(356)   (exact value)

= 18.87 (to 2 decimal places)

Step-by-step explanation:

Using the pythagorean Theorem,

The hypotenuse

c = sqrt(a^2+b^2)

= sqrt(16^2+10^2)

= sqrt(356)   (exact value)

= 18.87 (to 2 decimal places)

The length of the hypotenuse of the right triangle is approximately

18.9 cm.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (the base and the height in this case).

Plugging in the given values, we get:

c² = 16² + 10²

c² = 256 + 100

c² = 356

c ≈ 18.9

Rounding the answer to the nearest tenth of a centimeter, we get:

c ≈ 18.9 cm

Therefore,

The length of the hypotenuse of the right triangle is approximately

18.9 cm.

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The margin of error for a 95% confidence interval for the population mean is approximately 2.57. So, correct option is A.

To find the margin of error for a 95% confidence interval for the population mean (μ), we can use the formula:

Margin of Error = Z * (σ / √n),

where Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

For a 95% confidence interval, the corresponding z-score is approximately 1.96 (obtained from the standard normal distribution table).

Plugging in the values, we have:

Margin of Error = 1.96 * (8.5 / √42).

Calculating this expression, we find:

Margin of Error ≈ 2.57.

The correct answer is option a) 2.57.

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To find the vertical asymptotes of a rational function, we need to set the denominator equal to zero and solve for x.

To find the vertical asymptotes of a rational function, you need to determine the values of x that make the denominator of the function equal to zero.

Let's check the limit of our example function as x approaches each of the vertical asymptotes:

As x approaches 1 from the left side: f(x) approaches negative infinity

As x approaches 1 from the right side: f(x) approaches positive infinity

Therefore, x = 1 is a valid vertical asymptote.

As x approaches 3 from the left side: f(x) approaches positive infinity

As x approaches 3 from the right side: f(x) approaches negative infinity

Therefore, x = 3 is also a valid vertical asymptote.

The values of x that make the denominator zero are the vertical asymptotes of the function.

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Answer:

A parallelepiped has three sets of four parallel edges; the edges within each set are of equal length. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations).

Step-by-step explanation:

A parallelepiped focuses on three-dimensional figures formed by six parallelograms.

A parallelepiped shape has the following features

Think of a cube or a cuboid.

Notice that they contain squares and rectangles

A parallelepiped is to a parallelogram as a square is to a cube and a rectangle to a cuboid

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Answer:

None of the options are correct, the correct answer is 1,050 boys and 350 girls.

Step-by-step explanation:

A ratio of 3:4 can be turned into a percentage by dividing 3 by 4. This would give us 0.75 or 75%. This means that the remaining 25% (100-75 = 25) are girls in this ratio. If there are 12 boys we can find the total amount by dividing 12 by 0.75 and then multiplying that answer by 0.25 (25%) in order to find the amount of girls in that ratio, like so...

12 * 0.75 = 16 total

16 * 0.25 = 4 girls

If there are a total of 1,400 students we can find how many are boys and how many are girls by simply multiplying by the percentages.

1,400 * 0.75 = 1,050 boys

1,400 * 0.25 = 350 girls.

Apparently, none of the options are correct, the correct answer is 1,050 boys and 350 girls.

Answer:

iuvvvvvvvvvvvvvv

Step-by-step explanation:

uyfvfv

Answer:

0.7

Step-by-step explanation: (4/5)*7)/8

Hope this helps:)

Answer:

x=-4

Step-by-step explanation:

2(x-4)

2x-8

x=-4

Answer:

A

Step-by-step explanation:

The other values are lesser than 5.63

Answer:

5.658-A

Step-by-step explanation:

The amount of the 11% note is $110 and the amount of the 9% note is $90.

Code snippet

Note Type | Principal | Interest | Interest Rate

------- | -------- | -------- | --------

11% | $100 | $11 | 11%

9% | $100 | $9 | 9%

Use code with caution. Learn more

The interest for the 11% note is calculated as $100 * 0.11 = $11. The interest for the 9% note is calculated as $100 * 0.09 = $9.

Therefore, the total interest for the two notes is $11 + $9 = $20. The principal for the two notes is $100 + $100 = $200.

So the answer is $110 and $90

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The value of the line integral ∫_c x sin(y) ds is approximately 3.633.

To evaluate the line integral ∫_c x sin(y) ds, where c is the line segment from (0, 3) to (4, 6), we need to parameterize the curve in terms of a single variable, say t.

Let P₁ = (0, 3) and P₂ = (4, 6) be the endpoints of the line segment. Then, the direction vector for the line segment is given by

d = P₂ - P₁ = (4 - 0, 6 - 3) = (4, 3)

So, we can parameterize the curve as

x = 0 + 4t = 4t

y = 3 + 3t

where 0 ≤ t ≤ 1.

Now, we need to find ds, which is the differential arc length along the curve. We can use the formula

ds = sqrt(dx/dt)^2 + (dy/dt)^2 dt

= sqrt(16 + 9) dt

= 5 dt

Therefore, the line integral becomes

∫_c x sin(y) ds = ∫₀¹ (4t) sin(3 + 3t) (5 dt)

= 20 ∫₀¹ t sin(3 + 3t) dt

This integral can be evaluated using integration by substitution. Let u = 3 + 3t, then du/dt = 3 and dt = du/3. Substituting these into the integral, we get

= 20 ∫₃⁶ [(u - 3)/3] sin(u) du/3

= (20/9) ∫₃⁶ (u - 3) sin(u) du

= (20/9) [(-3 cos(3) + sin(3)) + (6 cos(6) + sin(6))]

≈ 3.633

Therefore, the value of the line integral ∫_c x sin(y) ds is approximately 3.633.

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Answer:

1. Since you have to square the number of units to use the Pythagorean theorem, the dashes represent the number you would use in the equation(without squaring afterwards) . So if its 3 units long, there are 9 dashes. (3^2=9)

2. You can't use the number of boxes because that wouldn't give you the correct answer for C, since all of the variables have to be squared first for the formula to work.

Step-by-step explanation:

A possible set of scores for the students is: 4, 4, 6, 6, 6

We are given that five students took the quiz. If the lowest score is 4 and the highest score is 6, we can say that the set of values ​​can be expressed as:

4, x, y, z, 6

Here we can see that the mode is 6 and the mean is 5.2. Therefore, at least one other student of hers has scored her 6, which could result in:

4, x, y, 6, 6

Therefore:

(4 + x + y + 6 + 6)/5 = 5.2

16+x+y=26

x + y = 10

So the other two numbers are probably 6 and 4, because 6 is the mode, so they can't both be 5.

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On calculating, the 40% of 84 is found to be 33.6.

Given is that to find the 40% of 84.

Assume that the 40% of 84 is equivalent to [x]. Then, we can write -

x = (40/100) x 84

x = 4/10 x 84

x = 8.4 x 4

x = 33.6

Therefore, on calculation, the 40% of 84 is equivalent to 33.6.

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Hey there!

1/2 * 1/2

= 1(1) / 2(2)

= 1 / 4 ≈ 0.25

Therefore, your answer is: 1/4

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

segment IG ≅ segment LJ

Step-by-step explanation:

Please refer to the attached image as per the triangles as given in the question statement.

\(\triangle HGI, \triangle JKL\)

\(G\left(-3,1\right),\ H\left(-1,1\right),\ I\left(-2,3\right)\)

\(J\left(3,3\right),K\left(1,3\right),L\left(2,1\right)\)

Given that:

\(HI\cong KL\) and

\(\angle I \cong \angle L\)

SAS congruence between two triangles states that two triangles are congruent if two corresponding sides and the angle between the two sides are congruent.

We are given that one angle and one sides are congruent in the given triangles.

We need to prove that other sides that makes this angle are also congruent.

To show the triangles are congruent i.e. \(\triangle GHI \cong \triangle JKL\) by SAS congruence we need to prove that

segment IG ≅ segment LJ

Let us use Distance formula  to find IG and LJ:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(IG =\sqrt{(-2+3)^2+(3-1)^2} =\sqrt5\ units\)

\(LJ =\sqrt{(2-3)^2+(1-3)^2} =\sqrt5\ units\)

Hence, segment IG ≅ segment LJ

\(\therefore\) ΔGHI ≅ ΔJKL by SAS

The integral ∫t S(r(t)) dt calculates the total amount of water that has been filled into the hot tub from the initial time (t = 0) up to time t. It represents the accumulated water volume over the interval [0, t].

The expression ∫t S(r(t)) dt = 3 represents the definite integral of the rate function r(t) over a specific time interval [t1, t2], where t1 and t2 are the limits of integration. In this case, the limits are not provided, so we'll consider it as a general integral.

To understand the meaning of this expression, let's break it down:

r(t): This represents the rate at which water is being filled into the hot tub at time t. The rate function r(t) gives the instantaneous rate of change of the water level with respect to time. It is measured in gallons per minute.

S(r(t)): This indicates the amount of water being filled into the hot tub per unit of time. It is obtained by multiplying the rate r(t) by a small time increment Δt. As Δt approaches zero, S(r(t)) represents the infinitesimal amount of water being filled in during that very small time interval.

dt: This represents the infinitesimal change in time. It is the differential of the independent variable t.

∫: This symbol denotes the integral operation, which is used to find the accumulated or total amount of something over a given interval.

t: This variable represents the time.

In this case, the given expression ∫t S(r(t)) dt = 3 indicates that after a certain amount of time t, the total volume of water in the hot tub is 3 gallons. This means that the integral of the rate function r(t) from the initial time to the given time t has resulted in a total volume of 3 gallons in the hot tub.

It's important to note that the specific limits of integration are not provided in the given expression. Therefore, the exact meaning of this expression may vary depending on the specific time interval considered.

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Answer:

ajasjzaallxaxxzaobzab

The vector parametric equation for the line passing through points P and Q with r(6) = P and r(10) = Q is r(t) = (-3,-1,1) + t(-1,-1,1).

To find the vector parametric equation of the line passing through points P and Q, we need to first find the direction vector d. We can find this by subtracting the coordinates of P from Q, i.e., d = Q - P = (-8,-4,5) - (-3,-1,1) = (-5,-3,4).  Now, we need to find the equation of the line in vector parametric form, which can be written as r(t) = P + td, where t is a scalar parameter. We are given that r(6) = P and r(10) = Q, which means that r(6) = (-3,-1,1) + 6d and r(10) = (-3,-1,1) + 10d.

We can now set these two equations equal to each other to solve for d:

(-3,-1,1) + 6d = (-3,-1,1) + 10d

4d = (-3,-1,1) - (-3,-1,1)

4d = (0,0,0)

d = (0,0,0)

This means that the line passing through P and Q is actually a point, which is not possible. However, we know that the direction vector is not zero, so there must be an error somewhere. Looking back at our calculations, we realize that we made a mistake when finding d. The correct value of d is actually (-5,-3,4), which means that the vector parametric equation of the line is r(t) = (-3,-1,1) + t(-5,-3,4), or equivalently, r(t) = (-3 - 5t, -1 - 3t, 1 + 4t).

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tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

B. 1/4

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

13+11=24

Answer: D. m∠x+m∠y=180°

Step-by-step explanation:

m∠x and m∠y creates a linear pair (two angles formed one line)

a line is 180°, this means:

m∠x+m∠y=linear pair

m∠x+m∠y=180°

Hope this helps!! :)

Please let me know if you have any question