Carlos and his family left for the amsuement park at 8:35
a.M. The trip took 1 hour and 55 minutes. What time did they arrive

Answer:

32

Step-by-step explanation:

Answer:

\(\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}\)

Step-by-step explanation:

Given

\(\sin(105^o)\)

Required

Solve

Using sine rule, we have:

\(\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)\)

This gives:

\(\sin(105^o) = \sin(60 + 45)\)

So, we have:

\(\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)\)

In radical forms, we have:

\(\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}\)

\(\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}\)

Take LCM

\(\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}\)

Rewrite as:

\(\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}\)

Hence:

\(\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}\)

Answer:

\(\frac{13}{24}\)

Step-by-step explanation:

=> \(\frac{3}{8} +\frac{1}{6}\)

LCM = 24

=> \(\frac{9+4}{24}\)

=> \(\frac{13}{24}\)

Answer:

\(\frac{13}{24}\)

Step-by-step explanation:

\(\frac{3}{8} +\frac{1}{6}\)

\(\frac{3 \times 6}{8\times 6} +\frac{1\times8}{6\times8}\)

\(\frac{18}{48} +\frac{8}{48}\)

\(\frac{18+8}{48}\)

\(\frac{26}{48}\)

\(\frac{13}{24}=0.54166...\)

Answer:

Step-by-step explanation:

Corresponding angles: When two parallel lines are intersected by a transversal, the acute angles on the same side are congruent & the obtuse angles on the same side of the transversal are congruent and they are called corresponding angles.

Co-interior angles: The interior angles on the same side of the transversal are called co -interior angles and they are supplementary.

a) c + 123 =  180    {linear pair}

 c = 180 - 123

c = 57

a = 123 {Corresponding angles}

b = a   {Vertically opposite angles are congruent}

b = 123

b) f + 82 = 180   {Linear pair}

f  = 180 - 82

f = 98

d = f        {Corresponding angles}

d = 98

e = d   {Vertically opposite angles}

e = 98

c) h = 75   {Corresponding angles}

g = h {Vertically opposite anges}

g = 75

The probability that the digit that is received (after having been transmitted across the 4 channels) is 0.3645

In communication systems, it is common to face the challenge of transmitting information accurately over a noisy channel. In this scenario, errors can occur during transmission, and it is essential to quantify the probability of receiving the correct information at the end of the channel.

In this problem, we are asked to calculate the probability that the digit received after transmitting a 0 across four channels is also a 0. We know that each channel can either transmit the digit correctly with probability 0.9 or incorrectly with probability 0.1. Therefore, we can use the concept of conditional probability to solve this problem.

Using Bayes' theorem, we can rewrite this as:

P(CCCC | 0 received) x P(0 received) / P(CCCC)

Here, P(CCCC | 0 received) represents the probability that all four channels transmitted the 0 correctly, given that a 0 was received. This probability can be calculated as:

P(CCCC | 0 received) = P(C) x P(C | C) x P(C | C | C) x P(C | C | C | C)

Substituting the given probabilities, we get:

P(CCCC | 0 received) = 0.9 * 0.9 * 0.9 * 0.9 = 0.6561

Similarly, we can calculate the probability of receiving a 0 in general as:

P(0 received) = P(CCCC | 0 received) x P(0) + P(IIII | 0 received) x P(1)

where P(IIII | 0 received) represents the probability that all four channels transmitted the digit incorrectly, given that a 0 was received. This probability can be calculated similarly as:

P(IIII | 0 received) = P(I) * P(I | I) x P(I | I | I) x P(I | I | I | I) = 0.1 x 0.1 x 0.1 x 0.1 = 0.0001

Substituting the given probabilities, we get:

P(0 received) = 0.6561 x 0.5 + 0.0001 x 0.5 = 0.3281

Finally, we can calculate the denominator P(CCCC) as:

P(CCCC) = P(CCCC | 0 received) x P(0) + P(CCCC | 1 received) x P(1)

where P(CCCC | 1 received) represents the probability that all four channels transmitted the digit correctly, given that a 1 was received. This probability can be calculated similarly as:

P(CCCC | 1 received) = P(I) x P(I | C) x P(I | C | C) x P(I | C | C | C) = 0.1 x 0.9 x 0.9 x 0.9 = 0.0729

Substituting the given probabilities, we get:

P(CCCC) = 0.6561 * 0.5 + 0.0729 * 0.5 = 0.3645

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Answer:

The inverse Laplace transform of 1/(s-1)^2 (s+1) is e^t - te^t + e^(-t)

We start by applying partial fraction decomposition to the given expression:

1/(s-1)^2 (s+1) = A/(s-1) + B/(s-1)^2 + C/(s+1)

Multiplying both sides by the denominator, we get:

1 = A(s-1)(s+1) + B(s+1) + C(s-1)^2

Substituting s=1 gives:

1 = 4C

So, C=1/4.

Substituting s=-1 gives:

1 = -4A

So, A=-1/4.

Substituting s=1 and simplifying gives:

B = 1/2.

Thus, we have:

1/(s-1)^2 (s+1) = (-1/4)/(s-1) + (1/2)/(s-1)^2 + (1/4)/(s+1)

Taking the inverse Laplace transform of each term using the table of Laplace transforms, we get:

L^(-1){(-1/4)/(s-1)} = -e^t

L^(-1){(1/2)/(s-1)^2} = te^t

L^(-1){(1/4)/(s+1)} = (1/2)e^(-t)

Hence, the inverse Laplace transform of 1/(s-1)^2 (s+1) is e^t - te^t + e^(-t).

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Answer:(3,-1)

Step-by-step explanation:

slope intercept form:  y = -2x + 4

\(\sf slope \ intercept \ form: y = mx + b\)

where m is slope, b is y-intercept

=============================

\(\rightarrow \sf 2x + y = 4\)

\(\rightarrow \sf y = 4-2x\)

\(\rightarrow \sf y = -2x +4\)

Now, identify slope: -2, y-intercept: 4

Answer:

The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept.

Rewrite in slope-intercept form. Subtract 2 x from both sides of the equation. Multiply each term in −y=4−2x - y = 4 - 2 x by −1 - 1 .

Step-by-step explanation:

The interest earned on Option A is $2400 and Option B is $666.18.  Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.

To calculate the interest earned and total value for each option, we can use the following formulas:

For Option A:

- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400

- Total value = principal + interest earned = 3000 + 2400 = $5400

For Option B:

- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18

- Total value = principal + interest earned = 3000 + 666.18 = $3666.18

Therefore, the interest earned and total value for each option are as follows:

Option A:

- Interest earned = $2400

- Total value = $5400

Option B:

- Interest earned = $666.18

- Total value = $3666.18

To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.

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Answer:

Step-by-step explanation:

Divide 5 by 3

5 divided by 3 is 1 (in the set of integers). The remainder is 2.

5/3 is 1.666666666666666666666666666666666666666666666666666666666666667 (in the set of reals).

Solution for 5 divided by 3

✍️See below how to solve this division manually.

5 divided by 3 - Long Division Solution

The solution below uses the "Long Division With Remainders Method". It is one of two existing methods of doing long division.

Start by setting the divisor 3 on the left side and the dividend 5 on the right:

 1 ⇐ Quotient

 ―

3)5 ⇐ Dividend

 3

 -

 2 ⇐ Remainder

The result of the division of 5 divided by 3 is 1.6666666666666667, as a decimal number.

5/3 as a mixed number

5 divided by 3 equals to the mixed number 1 2

3

.

Note that the result of the division 5÷3 is not an exact value and is equivalent to a recurring decimal 1.66... (which has 6 as the period).

Answer:

y=1/2x

Step-by-step explanation:

It looks like it

Solution

The answer is

Absolute Value Function

Data triangulation is a research method that involves using multiple data sources or methods to gather and analyze information, enhancing the validity and comprehensiveness of findings.

Data triangulation is a research method that involves using multiple sources or methods to gather and analyze data on a particular topic or research question. By combining different data sources, researchers aim to enhance the validity, reliability, and comprehensiveness of their findings.

Two real-world examples of data triangulation are:

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The values of x and y are x = 6, y = 5.

First, we can identify that angle T is a right angle, as it is marked with a square symbol. We can use this information to set up the following equation: (4x - 3)² + (11y + 6)² = 41²

Next, we can use the fact that there are two pairs of congruent sides in a kite to find the values of x and y. Specifically, we can use the fact that BG and KT are congruent, as well as MT and WG.

Since angle T is a right angle, we know that angle MTG is also a right angle, and therefore triangle MTG is a right triangle. We can use the Pythagorean theorem to set up an equation: (4x - 3)² + (11y + 6)² = MG²

We can also use the fact that BG and KT are congruent to set up another equation: (4x - 3) = (11y + 6)

Solving this system of equations gives us: x = 6, y = 5

Substituting these values back into the original equation, we can verify that it holds true. Therefore, the values of x and y are 6 and 5, respectively.

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Answer:

A The information in the table has a constant rate of change of 3.5.

Step-by-step explanation:

A linear equation is in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change (slope) and b is the value of y when x = 0.

Let y represent the cost of a corsage and x represent the number of flowers in the corsage

The table (x, y) has the points (2, 7) and (3, 10.5). The equation is given by:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-7=\frac{10.5-7}{3-2}(x-2)\\\\y-7=3.5(x-2)\\\\y-7=3.5x-7\\\\y=3.5x\)

Therefore the rate of change is 3.5

Answer:

Step-by-step explanation:

Are you after a solution for y?

quotient of y and 3 is a fancy word for division

y/3+9=10

To solve for y subtract 9 from both sides

y/3+9-9=10-9

y/3=1

To solve for y

multiply both sides by 3

3(y/3)=1*3

y=3

Answer: Wow, sorry it took me so long, but I believe your answer is 127.

Step-by-step explanation: When finding an angle for something like this, we need to find the angles of the triangle.  As you can see, 89 is provided already, but we need two more.  Let's say we make a guess of 127 as 14x + 1. The other side which is angle F has to add up with 127 to make 180, which is 53.  So angle F is 53.  That gives us 89 + 53 which equals 142.  180 - 142 equals 38.  To solve 5x - 7, you need to fill in 9 to make the equation true, which is 5 x 9 - 7 or 38.  So, angle H is 38.  38 + 89 + 53 equals 180.  So for 14x + 1, it's 127.

Hope this helps! :)

The probability that less than or equal to 5 of the 10 independent customers will take more than 3 minutes to check out their groceries is approximately 0.9245.

To calculate this probability, we can use the binomial probability formula. Let's denote X as the number of customers taking more than 3 minutes to check out. We want to find P(X ≤ 5) when n = 10 (number of trials) and p (probability of success) is not given explicitly.

Step 1: Determine the probability of success (p).

Since the probability of each customer taking more than 3 minutes is not provided, we need to make an assumption or use historical data. Let's assume that the probability of a customer taking more than 3 minutes is 0.2.

Step 2: Calculate the probability of X ≤ 5.

Using the binomial probability formula, we can calculate the cumulative probability:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = C(10, 0) * p^0 * (1 - p)^(10 - 0) + C(10, 1) * p^1 * (1 - p)^(10 - 1) + C(10, 2) * p^2 * (1 - p)^(10 - 2) + C(10, 3) * p^3 * (1 - p)^(10 - 3) + C(10, 4) * p^4 * (1 - p)^(10 - 4) + C(10, 5) * p^5 * (1 - p)^(10 - 5)

Substituting p = 0.2 into the formula and performing the calculations:

P(X ≤ 5) ≈ 0.1074 + 0.2686 + 0.3020 + 0.2013 + 0.0889 + 0.0246

P(X ≤ 5) ≈ 0.9928

Rounding this probability to the nearest hundredth/second decimal place, we get approximately 0.99. However, the question asks for the probability that less than or equal to 5 customers take more than 3 minutes, so we subtract the probability of all 10 customers taking more than 3 minutes from 1:

P(X ≤ 5) = 1 - P(X = 10)

P(X ≤ 5) ≈ 1 - 0.9928

P(X ≤ 5) ≈ 0.0072

Therefore, the probability that less than or equal to 5 customers out of 10 will take more than 3 minutes to check out their groceries is approximately 0.0072 or 0.72%.

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Answer:

y=12

Step-by-step explanation:

A card is drawn randomly from a standard 52-card deck. then the probabilities are a) 1/13 b) 3/13 and c) 10/13

There are four 3's in the deck. This means that, from 52 possible cards to drawn, we have 4 chances of drawing a 3. This means that the probability will be:

p = 4/52

p= 1/13

b.

For every suit, there are three face cards, J, Q and K. There are 4 suits, so, the total number of face cards its:

4*3 =12

The total possible cards are, still, 52, so, the probability will be

p= 12/52

p=3/13

c.

We know that the card drawn must be a face card, o not being a face card. There is no third choice here. So, the probability of drawing a face card OR not drawing a face card its:

p=52/52

p=1

so

p( the card is a face card ) + p( the card is not a face card) =1

but, we know that

p( the card is a face card ) =3/13

so

p( the card is not a face card) =1- 3/13

                                                 = 10/13

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68 68 70 61 67 71 63 67



Step 1: Write the formula of standard deviation

n = 8

Step 2: Find the mean

Step 3: find the standard deviation

Next, substitute to find the standard deviation

standard deviation = 3.14

Final answer

The number of data within the standard deviation of the mean = 5

The surface integral of f over the unit sphere is (4π/15) (3 k), where k is the unit vector in the z-direction. The answer is independent of the specific parameterization of the sphere and only depends on the surface itself.

To evaluate the surface integral of f over the unit sphere, we need to use the formula:

∫∫S f · dS = ∫∫R f(φ,θ) · ||r(φ,θ)|| sin(φ) dφdθ

Where S is the surface of the unit sphere, R is the region in the parameter domain (φ,θ) that corresponds to S, ||r(φ,θ)|| is the magnitude of the partial derivative of the position vector r(φ,θ), and sin(φ) is the Jacobian factor.

For the unit sphere, we have:

x = sin(φ) cos(θ)
y = sin(φ) sin(θ)
z = cos(φ)

So, we can find the partial derivatives:

r_φ = cos(φ) cos(θ) i + cos(φ) sin(θ) j - sin(φ) k
r_θ = -sin(φ) sin(θ) i + sin(φ) cos(θ) j

Then, we can compute the magnitude:

||r_φ x r_θ|| = ||sin(φ) cos(φ) cos(θ) j + sin(φ) cos(φ) sin(θ) (-i) + sin^2(φ) k|| = sin(φ)

Now, we can substitute into the formula and evaluate the integral:

∫∫S f · dS = ∫0^π ∫0^2π (sin^3(φ) cos^3(θ) i + sin^3(φ) sin^3(θ) j + sin^3(φ) cos^3(φ) k) · sin(φ) dφdθ
= ∫0^π ∫0^2π sin^4(φ) (cos^3(θ) i + sin^3(θ) j + cos^3(φ) k) dφdθ

To integrate over θ, we can use the fact that cos^3(θ) and sin^3(θ) are odd functions, so their integral over a full period is zero. Thus, we get:

∫∫S f · dS = ∫0^π (1/5) sin^5(φ) (3 cos^3(φ) k + 2 sin^3(φ) i + 2 cos^3(φ) j) dφ
= (4π/15) (3 k)

Therefore, the surface integral of f over the unit sphere is (4π/15) (3 k), where k is the unit vector in the z-direction. The answer is independent of the specific parameterization of the sphere and only depends on the surface itself.

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The ascending order of the expressions are π/3 , √8/3 , √4/2

Given data ,

Let the expression be represented as A

Now , the value of A is

A = π/3 , √8/3 , √4/2

On simplifying , we get

Now , π > √8

So , the value of π/3 is greater than √8/4 since they have the same denominator

And , the value of √4/2 = 1

Hence , the ascending order is √4/2 , √8/3 , π/3

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The code initializes the variable `count` to 0. Then, it enters a while loop that continues as long as `count` is less than 11. The value printed by the code is: 1

The value printed by the code is:

1

2

3

4

5

6

7

8

9

10

11

The code initializes the variable `count` to 0. Then, it enters a while loop that continues as long as `count` is less than 11. Inside the loop, `count` is incremented by 1, and then the current value of `count` is printed. This process repeats until `count` reaches 11.
Therefore, the numbers from 1 to 11 (inclusive) are printed.

The value printed by the code is:

1

In the second code, after initializing `count` to 0, the if statement checks if `count` is less than 11. Since the condition is true (`count` is 0), the code enters the if block. Inside the block, `count` is incremented by 1 and then printed. After executing the if block once, the code exits, and only the value 1 is printed.

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The complete question is:

What value is printed by the code below? count = 0 while count < 11: count = count + 1 print(count) What value is printed by the code below? count = 0 if count < 11: count = count + 1 print(count)?

Answer:

5(n-7)

Step-by-step explanation:

Answer:

The correct answer:

The data are continuous because the data can take on any value in an interval. (A)

Step-by-step explanation:

There are two categories of data:

Discrete data: These are data that have specific values that they can take on. There are limits to what values can be assigned to such categories. for example, The number of countries in a continent, there can either be 15 countries, 50 countries 30 countries, etc. There is not a possibility of having 40.56 countries on this kind of list. hence it is a discrete dataset.

Continuous data are data that can take on any value within an interval or on a particular scale of measurement. In this example, the height of the elephant in meters can be 1.5m, 2m, 1.06m, etc. There is no limit to the possibility of the height of an elephant on a meter scale.

Answer:

567 ft

Step-by-step explanation:

1 yd = 3 ft

1 yd is to 3 ft as 189 yd is to x ft

1/3 = 189/x

1 × x = 3 × 189

x = 567

567 ft