Juan read 300 pages in 5 days. Which reading rate is equivalent?
A.) 150 pages in 3 days
B. )120 pages in 2 days
C.) 105 pages in 1 day
D.) 100 pages in 3 days

A triangle is a three-sided polygon that consists of three sides and three angles. An extension of a side of a triangle is a line segment that is drawn from one of the endpoints of the side that extends beyond the side.

If we extend one side of the triangle and draw a line that passes through one of the adjacent vertices, the resulting shape is called a triangle's exterior angle. This exterior angle is formed by one side of the triangle and the extension of an adjacent side.

In other words, an exterior angle of a triangle is an angle that is formed by one side of a triangle and the extension of an adjacent side of the triangle.

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Answer:

B.traveling 18 meters in 3 hours

Step-by-step explanation:

distance/time

18/3

6

The daily report performed by the night auditor includes key operating ratios used by management, such as the previous evening's banquets, the total number of rooms in the hotel, the room occupancy percentage, and the front office schedule.

a) The previous evening's banquets refer to the events or functions held at the hotel's banquet facilities during the night.

This information is important for management to assess the revenue generated from banquets and evaluate the success of such events.

b) The total number of rooms in the hotel indicates the capacity of the property.

It helps management understand the size of the hotel and make decisions regarding room rates, marketing strategies, and overall operational planning.

c) The room occupancy percentage is a crucial operating ratio that reflects the percentage of occupied rooms out of the total available rooms.

It provides insights into the hotel's demand and utilization. Management uses this ratio to monitor performance, make pricing decisions, and optimize room inventory.

d) The front office schedule refers to the staffing schedule for the front desk and other guest service areas. It outlines the shift timings, employee assignments, and responsibilities.

This information is essential for effective management of guest services, ensuring adequate staffing levels, and maintaining smooth operations at the front desk.

Overall, the daily report performed by the night auditor includes these key operating ratios to provide management with valuable data and insights for decision-making and performance evaluation in various aspects of hotel operations.

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Hey there!

Assuming you meant….

(0.2)^3 * (0.3)^4

= 0.2^3 * 0.3^4

= 0.2 * 0.2 * 0.2 * 0.3 * 0.3 * 0.3 * 0.3

= 0.04 * 0.2 * 0.09 * 0.09

= 0.008 * 0.0081

= 0.0000648

≈ 0.000065

Therefore, your answer should be:

0.0000648

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

\( \tt{}(0.2 {)}^{3} \times (0.3 {)}^{4} \)

\(\tt{}0.3 \times 0.06 ^{3} \)

\(\tt{} \frac{3}{10} \times ( \frac{3}{50} {)}^{3} \)

\(\tt{} \frac{3}{10} \times \frac{ {3}^{3} }{ {50}^{3} } \)

\(\tt{} \frac{ {3}^{4} }{10 \times 50 ^3 } \)

\(\tt{} \frac{81}{10 \times 5 {0}^{3} } \)

\(\tt{}6.48\)

The estimated value of f(0.98,3.08) is  5.358

To find the differential of\(f(x,y) = \sqrt{(x^2 + y^3)}\), we can use the formula for the differential:

df = (∂f/∂x) dx + (∂f/∂y) dy

where dx and dy are small changes in x and y, respectively.

Taking the partial derivatives of f(x,y) with respect to x and y, we have:

∂f/∂x = \(x\sqrt{(x^2 + y^3)}\)

∂f/∂y = \((3/2)y^(1/3) / \sqrt{(x^2 + y^3)}\)

Substituting x = 1 and y = 3, we get:

∂f/∂x (1,3) = 1/√28

∂f/∂y (1,3) = (3/2)(3(1/3))/√28

So the differential of f(x,y) at (1,3) is:

df = (1/√28) dx + (3/2)(3(1/3))/√28 dy

To estimate f(0.98,3.08), we need to find the values of dx and dy that correspond to a small change in x and y from (1,3) to (0.98,3.08). We have:

dx = 0.98 - 1 = -0.02

dy = 3.08 - 3 = 0.08

Substituting these values into the differential, we get:

df ≈ (1/√28) (-0.02) + (3/2)(3(1/3))/√28 (0.08)

≈ 0.0187

f(0.98,3.08) ≈ f(1,3) + df

≈ √28 + 0.0187

≈ 5.358

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Answer:

3 and -3

Step-by-step explanation:

First, we need to split the equation into 2, based on the definition of absolute value.

Those 2 equations will be -2h = 6 and -2h = -6

Next, we divide by -2 on both sides of both equations.

-6 divided by -2 is 3, and 6 divided by -2 is -3.

Therefore, our two answers are -3 and 3.

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

If the measures of the three angles of a triangle are x, x + 10, and 2x - 6, the triangle must be isosceles.

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the equation:

x + (x + 10) + (2x - 6) = 180

Combine the terms:

4x + 4 = 180

Subtract 4 from both sides:

4x = 176

Divide by 4:

x = 44

Now, we can find the measures of the other two angles:

x + 10 = 44 + 10 = 54
2x - 6 = 2(44) - 6 = 88 - 6 = 82

The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

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Answer:

BC ≈ 8.9 units

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos36° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{BC}{11}\) ( multiply both sides by 11 )

11 × cos36° = BC , then

BC ≈ 8.9 ( to the nearest tenth )

Answer:

8.9

Step-by-step explanation:

Option A is correct. The expression f(x)+g(x) is equal to \(x^3+x-204\).

The given two functions are f(x) and g(x):

\(f(x)=\sqrt{x^2+24x+144}\)

\(g(x)=x^3-216\)

We need to find f(x)+g(x).

Let us simplify f(x) function:

\(f(x)=\sqrt{x^2+24x+144}\)

\((x+12)^2=x^2+24x+144\) by using \((a+b)^2\) formula.

\(f(x)+g(x)=\sqrt{x^2+24x+144}+x^3-216\)

\(=\sqrt{(x+12)^2}+x^3-216\)

The square root gets cancelled.

\(=x+12+x^3-216\)

Combine like terms:

\(=x^3+x-204\)

Hence, the expression f(x)+g(x) is equal to \(x^3+x-204\). Option A is correct.

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Complete question:

Consider functions f and g.

f(X) =√(X^2 + 24x + 144)

g(x) = X^3 – 216

Which expression is equal to f(x) + g(x)?

(a) x^3+x-204

(b) x^3+x^2+24x-72

(c)x^4-204

(d) x^3+x-228

Answer:

C = -30

Step-by-step explanation:

C = 5/9 (F - 32)

C = 5/9 ( - 22 - 32)

C = 5/9 ( -54)

C = -30

There are 25 prime numbers between 1 and 100. There are 25 prime numbers between 1 and 100. Prime numbers are important in mathematics and have numerous applications, including cryptography, number theory, and computer science.

To find the prime numbers between 1 and 100, we can check each number in that range to see if it is divisible by any number other than 1 and itself. A more efficient approach is to use the Sieve of Eratosthenes algorithm. Using this method, we can eliminate multiples of each prime number starting from 2. The remaining numbers after the elimination process are prime.

Using this algorithm, we find that the prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

There are 25 prime numbers between 1 and 100. Prime numbers are important in mathematics and have numerous applications, including cryptography, number theory, and computer science.

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Problem 11: k = 1, Problem 12: y(x) = -3e^(-5x) and Problem 13: x(t) = 5t + 5, We can solve this differential equation using separation of variables.

Problem 11: We are given that x(t) = 5t is a solution of the differential equation -dx/dt = kx. We can substitute this into the differential equation to get -5 = kt. Solving for k, we find that k = -1/5.

Problem 12: We are given the differential equation dy/dx = 5y and the initial condition y(0) = -3. We can solve this differential equation using separation of variables.

The general solution is y = C*e^(5x), where C is an arbitrary constant. We can use the initial condition to find C = -3, so the specific solution is y(x) = -3e^(-5x).

Problem 13: We are given the differential equation dx/dt = 4 - x and the initial condition x(0) = 5. We can solve this differential equation using separation of variables.

The general solution is x = 4t + C, where C is an arbitrary constant. We can use the initial condition to find C = 5, so the specific solution is x(t) = 5t + 5.

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1. f(x) = √(25 - x²) represents a semicircle centered at (0,0) with radius 5. 2. f(x) = x² - x + 1 represents an upward-opening parabola with vertex at (0,1). 3. f(x) = e^x + 2 represents a rapidly increasing exponential function.

To predict a linear regression score, you first need to train a linear regression model using a set of training data.

Once the model is trained, you can use it to make predictions on new data points. The predicted score will be based on the linear relationship between the input variables and the target variable,

A higher regression score indicates a better fit, while a lower score indicates a poorer fit.

To predict a linear regression score, follow these steps:

1. Gather your data: Collect the data p

points (x, y) for the variable you want to predict (y) based on the input variable (x).

2. Calculate the means: Find the mean of the x values (x) and the mean of the y values (y).

3. Calculate the slope (b1): Use the formula b1 = Σ[(xi - x)(yi - y)]  Σ(xi - x)^2, where xi and yi are the individual data points, and x and y are the means of x and y, respectively.

4. Calculate the intercept (b0): Use the formula b0 = y - b1 * x, where y is the mean of the y values and x is the mean of the x values.

5. Form the linear equation: The linear equation will be in the form y = b0 + b1 * x, where y is the predicted value, x is the input variable, and b0 and b1 are the intercept and slope, respectively.

6. Predict the linear regression score: Use the linear equation to predict the value of y for any given value of x by plugging the x value into the equation. The resulting y value is your predicted linear regression score.

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Answer:B

Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer

Answer:

(-1,-3)

Step-by-step explaintion:

hope this helps!!

btw i just chnaged the x and y sign coordinates, thats all u needa do !!

Answer:

126

Step-by-step explanation:

6 (14 + 7)

6 (21)

126

A positive third charge can be placed at 0.55 m on the x-axis such that it experiences a net electric force equal to zero when the charges q1 and q2 are 0.50 nC and 10 nC respectively, and are separated by a distance of 3m. So, the correct answer is D).

Find the distance between the two charges

r = 3 m

Use Coulomb's law to find the force exerted by q1 on a positive charge q3 at a distance x from q1:

F1 = k * q1 * q3 / (x²)

Use Coulomb's law to find the force exerted by q2 on a positive charge q3 at a distance (r-x) from q2:

F2 = k * q2 * q3 / ((r-x)²)

Set the net force equal to zero

F1 + F2 = 0

Substitute the values for k, q1, q2, and r:

(9 x 10⁹) * (0.50 x 10⁻⁹) * q3 / x² + (9 x 10⁹) * (10 x 10⁻⁹) * q3 / (3-x)² = 0

Solve for x

(0.45 / x²) + (30 / (3-x)²) = 0

0.45(3-x)² + 30x² = 0

1.35 - 0.9x + 30x² = 0

30x² - 0.9x + 1.35 = 0

x = 0.019 m or x = 0.55 m

Since the problem asks for a point on the x-axis to the right of the two charges, the answer is x = 0.55 m. So, the correct option is D).

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--The given question is incomplete, the complete question is given below "  Two particles having charges of qı = 0.50 nC and q2 = 10 nC are separated by a distance of r = 3 m along the x- axis as shown in the figure below. At what point on the x-axis (pointing to the right) can a positive third charge be placed such that it experiences a net electric force on it equal to zero? Image size: s ML Max Select the correct answer Saved 1 of 3 attempts used CHECK ANSWER O 0.38m  O 0.19 m  O 0.14m O 0.55m o 1.50 m "--

Answer:

x=5, y=2

Step-by-step explanation:

solve the system of equations w/ substitution

5x+6y=37    

2x-3y=4           -> manipulate equation to get 3y=2x-4 -> 6y=4x-8

plug in: 5x+(4x-8)=37

9x=45, x=5

plug x in for y: 37-25=6y, y=2

The largest possible angle measure opposite the smallest side in the triangle is 42°.

We know that the sum of the three angles in a triangle is 180°. And one of the angles is 116°.
Therefore, the sum of the other two angles = 180 - 116 = 64°
Let A be the largest angle measure opposite the smallest side in the triangle.
Let's assume that the smallest angle is x. Then the second angle will be (64 - x).By the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
This implies that 116 + x > (64 - x) + x
116 + x > 64
or x > -52
This means that the smallest angle x can take is 53°.
Therefore, the other angle is 11°.Also, A + 53° + 11° = 180°A = 116°

Hence, the largest possible angle measure opposite the smallest side in the triangle is 42°.

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Compute P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.

Compute P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.

Compute E(x): The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15

Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.

The probability density function is as follows: As the random variable x is uniformly distributed between 10 and 20. Thus, f(x) = 1/(20-10) = 1/10 for 10 ≤ x ≤ 20.Compute P(x ≤ 15):Thus, P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.Compute P(12 ≤ x ≤ 18):Thus, P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.Compute E(x):The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15.Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.

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The solution matrix of the matrix equation \(\left[\begin{array}{ccc}-3&2\\5&-1\end{array}\right]\) = \(\left[\begin{array}{ccc}4&5\\-1&3\end{array}\right]\) - (1/2) X is given by X = \(\left[\begin{array}{ccc}14&6\\-12&8\end{array}\right]\).

Matrix is an array or arrangement of numbers.

Addition or subtraction of two matrices is given by the addition and subtraction of corresponding numeric value respectively.

Given the matrix equation is,

\(\left[\begin{array}{ccc}-3&2\\5&-1\end{array}\right]\) = \(\left[\begin{array}{ccc}4&5\\-1&3\end{array}\right]\) - (1/2) X

We have to find the matrix X.

Now,

(1/2) X = \(\left[\begin{array}{ccc}4&5\\-1&3\end{array}\right] -\left[\begin{array}{ccc}-3&2\\5&-1\end{array}\right]\) , arranging the matrices of the given equation in one side

(1/2) X = \(\left[\begin{array}{ccc}4-(-3)&5-2\\-1-5&3-(-1)\end{array}\right]\)

(1/2) X = \(\left[\begin{array}{ccc}4+3&3\\-6&3+1\end{array}\right]\)

(1/2) X = \(\left[\begin{array}{ccc}7&3\\-6&4\end{array}\right]\)

X = \(2\left[\begin{array}{ccc}7&3\\-6&4\end{array}\right]\) , multiplying 2 with both sides of the equation

X = \(\left[\begin{array}{ccc}14&6\\-12&8\end{array}\right]\)

Hence the solution matrix is given by X = \(\left[\begin{array}{ccc}14&6\\-12&8\end{array}\right]\).

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To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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The grams of antimony present in the alloy is 80 grams

To find the grams of antimony present in the alloy we have use the formula:

\(Weight = (\frac{Mass\: Compound}{Mass \:alloy}) \times100\)

Here Weight = 16

Mass alloy = 500

Mass Compound = ?

\(16 = \frac{Mass compound}{5}\)

Mass compound = 16 * 5 = 80 grams

The grams of antimony present in the alloy is 80 grams

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Answer:

m = 2

Step-by-step explanation:

6m = 12

6 × m = 12

m = 12 ÷ 6

m = 2

If it helps, then pls like and mark as brainliest!

Answer:

m = 2

Step-by-step explanation:

6m = 12

6m = 6^2

• get rid of common element which is 6. Devide both side by six.

6m ÷ 6 = 6^2 ÷ 6

m = 2

The solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

To solve the given differential equation y''(t) = 1 - t^17 with the initial condition y(1) = 12, we can integrate the equation twice.

Integrating the equation once will give us y'(t):

y'(t) = ∫(1 - t^17) dt

y'(t) = t - (1/18)t^18 + C₁

Now, we need to apply the initial condition y(1) = 12 to determine the value of the constant C₁:

12 = 1 - (1/18) + C₁

C₁ = 12 + (1/18) - 1

C₁ = 217/18

Next, we integrate y'(t) to find y(t):

y(t) = ∫(t - (1/18)t^18 + 217/18) dt

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + C₂

Finally, we apply the initial condition y(1) = 12 to determine the value of the constant C₂:

12 = (1/2) - (1/342) + (217/18) + C₂

C₂ = 12 - (1/2) + (1/342) - (217/18)

C₂ = (20619 - 1 + 6 - 819)/(342)

C₂ = 19805/342

Therefore, the solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

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Answer:

36 times

Step-by-step explanation:

Given

\(Red = 4\)

\(Total = 7\)

\(n = 63\)

See attachment

Required

Predicted number of times to land on red

First, we calculate the probability of landing on red

\(Pr = \frac{Red}{Total}\)

\(Pr = \frac{4}{7}\)

The predicted number of red is the =n calculated as:

\(Red = Pr * n\)

\(Red = \frac{4}{7}*63\)

\(Red = 4 * 9\)

\(Red = 36\)

The values of x where the tangent line to the function is horizontal are x=4+√37/3 and x=4-√37/3.

We need to find the values of x where the tangent line to the function f(x)=x³-4x²-7x+13 is horizontal, we need to find the points where the derivative of the function is equal to zero.

First, let's find the derivative of f(x):

f'(x)=3x²-8x-7

Now, let's set the derivative equal to zero and solve for x:

3x²-8x-7=0

a=3, b=-8 and c=-7.

We can solve this quadratic equation by factoring or using the quadratic formula.

x=-(-8)±√64-4(3)(-7)/2(3)

x=+8±√64+84/6

x=8±2√37/6

x=4±√37/3

Therefore, the values of x where the tangent line to the function is horizontal are x=4+√37/3 and x=4-√37/3.

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Answer:

An)  is a value that does not change​?  yes