A surveyor wants to know the length of a tunnel built through a mountain. According to her equipment, she is located 243 meters from one entrance of the tunnel, at an angle of 47 degrees to the perpendicular. Also according to her equipment, she is 186 meters from the other entrance of the tunnel, at an angle of 27 degrees to the perpendicular. Based on these measurements, find the length of the entire tunnel.

Do not round any intermediate computations. Round your answer to the nearest tenth

The probability that all three selected students are boys is approximately 0.3929 or 39.29%.

To calculate the probability that all three selected students are boys, we need to consider the total number of possible outcomes and the number of favorable outcomes.

In this case, there are 12 boys and 4 girls in the class, making a total of 16 students. We want to select three students, and we want all three of them to be boys.

The total number of ways to select three students from the class is given by the combination formula, which can be represented as:

Total Possible Outcomes = nCr(16, 3) = (16!)/((16-3)! * 3!) = 560

Now, let's consider the number of favorable outcomes where all three selected students are boys. Since there are 12 boys, we can choose three of them using the combination formula:

Favorable Outcomes = nCr(12, 3) = (12!)/((12-3)! * 3!) = 220

Therefore, the probability that all three selected students are boys is:

Probability = Favorable Outcomes / Total Possible Outcomes = 220 / 560 ≈ 0.3929, or approximately 39.29%.

Hence, the probability that all three selected students are boys is approximately 0.3929 or 39.29%.

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Answer:

14

Step-by-step explanation:

3*7=21

2*7=14

Answer:

D. He answers the same number of questions correctly in both rounds and the same number of questions incorrectly in both rounds​.

Step-by-step explanation:

In the first equation he earns 5 points and loses 3 points. The value of one question is 5 points, and the value of losing one question is 3 points. The same goes for the second equation except the fact that its 10 points and 4 points lost instead.

The point, (5, -4), is the solution to the given system of equations because the lines intersect at the point.

From the question, we are to determine why the given point is a solution to the system of equations

The given system of equations is

4y = -3x - 1

2y = x - 13

When solving system of equations by the graphical method, the point where the lines intersect gives the solution to the system of equations.

From the given graph,

The two lines intersect at the point where x = 5 and y = -4.

That is,

The lines intersect at (5, -4), and thus, (5, -4) is the solution to the system of equations.

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Answer:

B , a segment

Step-by-step explanation:

A segment is the area between a chord and an arc, just like the shaded area

an arc does not include the area of the circle.

A sector has to include a central angle

The shaded part is an area of a circle so it cant be the an inscribed angle.

A

1. The 8th term of the arithmetic sequence is 315

2. The 8th term of the geometric sequence is 405329

3. The 8th term of the geometric sequence is 144999

1. The 8th term in the sequence 15, 24, 42, 78, 150;

The sequence is an arithmetic sequence, which means that the difference between any two consecutive terms is constant. In this case, the difference is 9. To find the 8th term, we can simply add 9 to the 7th term, which is 150.

8th term = 7th term + 9

= 150 + 9

= 315

2. The 8th term in the sequence 12, 59, 294, 1469, 7344

The sequence is a geometric sequence, which means that the ratio between any two consecutive terms is constant. In this case, the ratio is 5. To find the 8th term, we can simply raise the first term to the power of 8 and multiply it by the common ratio.

8th term = First term⁸ * Common ratio

= 12⁸ * 5

= 405329

3. The 8th term in the sequence 3, 19, 99, 499, 2499 is 144999.

The sequence is also a geometric sequence, but the common ratio is 6. To find the 8th term, we can simply raise the first term to the power of 8 and multiply it by the common ratio.

8th term = First term⁸ * Common ratio

= 3⁸ * 6

= 144999

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In a periodic review system when an order is placed  every 14 days, the uncertainty period is 22 days.

Lead time is the time that passes from the start to the conclusion.  It helps in measuring the time taken to complete a project. It varies from industry to industry.

It is normally calculated as:

Lead time = processing time + post-processing time.

Given,

lead time = 8 days

Order place date = 14 days

uncertainty period  = order date + lead time

uncertainty period = 14 + 8 = 22 days

So, we can say that in a periodic review system when an order is placed  every 14 days, the uncertainty period will be 22 days.

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Answer: Cup-$14, Saucer-$6.5

Step-by-step explanation:

Given

Cup and saucer costs $20.5

A cup and two saucer costs $27

Assume the price of cup and saucer are x and y

So, we can write

\(\Rightarrow x+y=20.5\quad \ldots(i)\\\\\Rightarrow x+2y=27\quad \ldots(ii)\)

Solving \((i)\ \text{and}\ (ii)\) we get

\(x=\$\ 14, y=\$\ 6.5\)

Thus, the cost of the cup is $14 and that of the saucer is $6.5

Answer:

C. 12

Step-by-step explanation:

All rows must have the same number of cadets. If A company has 60 cadets and B company has 72 cadets

We find the factors of 60 and 70

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Then the greatest common factor is 12.

Therefore, the greatest number of cadets who can be in each row is 12 cadets.

Option C is the correct option.

Answer:

12 bro

Step-by-step explanation:

The value of width 'w' of rectangular prism with l = n/a, h = n/a, v = n/a is given by, w = a/n.

We know that the volume of rectangular prism with length L and width W and Height H is given by,

V = L*W*H

Given that the Height of the rectangular prism, h = n/a

Length of the rectangular prism, l = n/a

Volume of the rectangular prism, v = n/a

let the width of the rectangular prism be 'w'.

So from the volume formula we get,

v = lwh

n/a = (n/a)*w*(n/a)

n/a = (n/a)²*w

w = (n/a)/(n/a)² = (n/a)*(a/n)² = a/n

Hence the value of w is a/n.

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Answer:

93.33 miles

Step-by-step explanation:

60 min/ 20 min = 3

280/3 = 93.333333

Answer:

93.3 miles

Step-by-step explanation:

Since there are 60 minutes in an hour and 20/60 = 1/3, you can divide 280 by 3 to get the amount of miles travelled in 20 minutes.

Answer:

An isometry preserves all the following except orientation .

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

This question is asking you to write the algebraic expression for "five times the sum of a number and 8).  Basically it is saying take a number (x) and add 8 to it. When we add, the answer is the sum.  

So the first part of the expression is (x + 8)

Then multiply that sum by 5

So our answer is 5(x+8)

The solution of the expression (x + 1)³ will be;

(x + 1)³ = (x + 1) (x + 1)²

           = (x + 1) (x² + 2x + 1)

           = x³ + 3x² + 3x + 1

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The expression is;

⇒ (x + 1)³

Now, Solve the expression as;

The expression is;

⇒ (x + 1)³

Expand it as,

⇒  (x + 1)³ = = (x + 1) (x + 1)²

           = (x + 1) (x² + 2x + 1)

           = x³ + 2x² + x + x² + 2x + 1

           = x³ + 3x² + 3x + 1

Therefore,

The solution of the expression (x + 1)³ will be;

⇒ (x + 1)³ = (x + 1) (x + 1)²

              = (x + 1) (x² + 2x + 1)

              = x³ + 3x² + 3x + 1

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Answer:

3

3

1

Step-by-step explanation:

Answer:

12 inches

Step-by-step explanation:

Answer: 51

Step-by-step explanation:

We will use the Order of Operations, sometimes known as PEMDAS.

    Given:

5x² - x + 9

    Plug in the value of 3:

5(3)² - (3) + 9

    To the power of 2:

5(9) - 3 + 9

    Multiply:

45 - 3 + 9

   Subtract:

42 + 9

    Add:

51

Answer:

Step-by-step explanation:

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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The hypothesis test conducted by the quality control manager aims to determine if the average daily yield of the chemical plant has changed in recent months. The null hypothesis (H0) states that the population mean (μ) is equal to 880 tonnes, while the alternative hypothesis (H1) suggests that the population mean is not equal to 880 tonnes.

To test this hypothesis, the manager uses a significance level of 5%. If the computed test statistic falls within the critical region (the rejection region), the null hypothesis is rejected in favor of the alternative hypothesis.

In this case, the manager computes the sample mean of the 50 yields as 871 tonnes and the sample standard deviation as 21 tonnes. However, the answer does not provide the sample size (n) necessary for further calculations, such as determining the critical value or computing the test statistic.

To complete the analysis and reach a conclusion, the manager would need to calculate the appropriate test statistic (such as the t-test statistic) using the sample mean, sample standard deviation, sample size, and the assumed population mean of 880 tonnes. The test statistic can then be compared to the critical value corresponding to the 5% significance level.

If the test statistic falls within the critical region, the null hypothesis would be rejected, suggesting that the average daily yield has changed in recent months. Otherwise, if the test statistic falls outside the critical region, there would be insufficient evidence to reject the null hypothesis, indicating that the average daily yield has not changed significantly.

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¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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probability of picking a red candy = Probability of picking a red candy from the large bottle + Probability of picking a red candy from the mid-size bottle + Probability of picking a red candy from the small bottle.

Based on the information provided, we have three bottles of different sizes with different compositions of red and blue candy. The largest bottle contains 8 red and 2 blue pieces, the mid-size bottle has 5 red and 7 blue, and the small bottle holds 4 red and 2 blue.

The probability of the large bottle being picked is 0.5, and the probability of the mid-size bottle being chosen is 0.4. Once a bottle is selected, the probability of picking any candy inside is equal, regardless of its color.

To find the probability of selecting a red candy, we can calculate the overall probability by considering the probabilities of each bottle being chosen and the number of red candies in each bottle.

Let's calculate:

Probability of picking a red candy from the large bottle = (Probability of picking the large bottle) * (Probability of picking a red candy from the large bottle)
= 0.5 * (8 red candies / (8 red candies + 2 blue candies))

Probability of picking a red candy from the mid-size bottle = (Probability of picking the mid-size bottle) * (Probability of picking a red candy from the mid-size bottle)
= 0.4 * (5 red candies / (5 red candies + 7 blue candies))

Probability of picking a red candy from the small bottle = (Probability of picking the small bottle) * (Probability of picking a red candy from the small bottle)
= (1 - (Probability of picking the large bottle) - (Probability of picking the mid-size bottle)) * (4 red candies / (4 red candies + 2 blue candies))

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The number of rows required in a truth table to evaluate a logical statement with four variables is 16. The logical equivalence between "p → (q→ r)" and "(p —— q) → r" is True.

The statement that DeMorgan's laws are invalid if the negation operator distributes over conjunction and disjunction operators is False.

A truth table is a useful tool to evaluate the truth values of logical statements for different combinations of variables. In this case, since there are four variables involved, we need to consider all possible combinations of truth values for these variables.

Since each variable can take two possible values (True or False), we have 2^4 = 16 possible combinations. Therefore, we require 16 rows in the truth table to evaluate the logical statement.

Moving on to the logical equivalence between "p → (q→ r)" and "(p —— q) → r", we can determine if they are equivalent by constructing a truth table. Both expressions have three variables (p, q, and r). By evaluating the truth values for all possible combinations of these variables, we can observe that the truth values of the two expressions are identical in all cases.

Hence, the logical equivalence between "p → (q→ r)" and "(p —— q) → r" is True.

Regarding the statement about DeMorgan's laws, it states that if the negation operator distributes over the conjunction and disjunction operators in propositional logic, then DeMorgan's laws are invalid. However, this statement is false.

DeMorgan's laws state that the negation of a conjunction (AND) or disjunction (OR) is equivalent to the disjunction (OR) or conjunction (AND), respectively, of the negations of the individual propositions. These laws hold true irrespective of whether the negation operator distributes over the conjunction and disjunction operators.

Therefore, the statement about DeMorgan's laws being invalid in such cases is false.

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SOLUTION:

Case: Probability

Given:

20% of cars travelling in a certain diamond lane have fewer than three passengers.

Fifty cars are selected at random.

If 20% have less than 3 passengers. p= 0.20

Then 80% have greater than or equal to 3 passengers, q= 0.80

Total sample,

n= 50

sample, x= 15.

Answer: linear combo of terms involving x & y, with respective numbers determining their contribution to the expression

The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

a) The probability of winning after tossing the die once is 1/3 or approximately 0.333.

b) The probability of winning after tossing the die twice is 5/18 or approximately 0.278.

a) To calculate the probability of winning after tossing the die once, we need to consider the possible outcomes. There are six equally likely outcomes corresponding to the numbers on the die. Out of these, two outcomes (1 and 2) result in staying put, which means the player does not win. The remaining four outcomes (3, 4, 5, and 6) move the game piece, increasing the chances of winning. As the game piece can only reach or pass the winning box W by moving two boxes to the right, there are two favorable outcomes out of six possibilities. Thus, the probability of winning after one toss is 2/6 or simplifying further, 1/3.

b) To find the probability of winning after tossing the die twice, we need to consider the possible combinations of outcomes. Each toss of the die has six equally likely outcomes, resulting in a total of 36 possible combinations for two tosses. Out of these combinations, there are three scenarios in which the game piece can win: (3, 3), (4, 4), and (5, 6). Therefore, the probability of winning after two tosses is 3/36, which simplifies to 1/12.

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Answer:

whats the question love?

Step-by-step explanation:

Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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