The sides of a right triangle form a three term geometric progression. If the shortest side has length 2, then what is the length of the hypotenuse?

The turning point (or vertex) of the quadratic equation y = x^2 + 14x - 3 is:

(-7, -52)

The turning point is also called the vertex. To find it we can complete squares, remember the perfect square trinomial:

(a + b)^2 = a^2 + 2ab + b^2

Here we have:

y = x^2 + 14x - 3

Completing squares we will get:

y = x^2 + 2*7*x - 3

Add in both sides 7^2 to get:

y + 7^2 = x^2 + 2*7*x + 7^2 - 3

y = (x + 7)^2 - 3 - 49

y = (x + 7)^2 - 52

Then the vertex is at (-7, -52), that is the turning point.

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In scientific notation, we write a number as a product of a number between 1 and 10 and a power of 10. The number before the multiplication sign is the significant figure, and the power of 10 indicates the magnitude of the number. To write a number to 3 significant figures, we only include one non-zero digit before the decimal point.

1. 2450: First, identify the non-zero digits (2, 4, and 5). Write the number as 2.45 and multiply it by 10 raised to the power of the number of places you moved the decimal point (3 in this case). So, the answer is 2.45 x 10^3.

2. 0.000326: Identify the non-zero digits (3, 2, and 6) and write the number as 3.26. Move the decimal point 4 places to the right, so multiply by 10 raised to the power of -4. The answer is 3.26 x 10^-4.

3. 0.000934: With non-zero digits 9, 3, and 4, write the number as 9.34. Move the decimal point 4 places to the right and multiply by 10^-4. The answer is 9.34 x 10^-4.

4. 685000: The non-zero digits are 6, 8, and 5, so write the number as 6.85. Move the decimal point 5 places to the left and multiply by 10^5. The answer is 6.85 x 10^5.

In summary:
2450 = 2.45 x 10^3
0.000326 = 3.26 x 10^-4
0.000934 = 9.34 x 10^-4
685000 = 6.85 x 10^5

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The row where three consecutive entries occur in the ratio 3:4:5 is row 7 in Pascal's Triangle.

To find the row in Pascal's Triangle where three consecutive entries occur in the ratio 3:4:5, we can use the property of Pascal's Triangle, where each entry is the sum of the two entries above it.
Let's denote the three consecutive entries in the ratio as 3x, 4x, and 5x. Since these are consecutive entries, we can use the following relationships from Pascal's Triangle:
1. 4x = C(n, k) = C(n-1, k-1) + C(n-1, k), where C(n, k) represents a binomial coefficient.
2. 3x = C(n-1, k-1) and 5x = C(n-1, k).
Now, we can write the equation:
4x = 3x + 5x => x = 3C(n-1, k-1) = 5C(n-1, k).
We can see that 3 divides C(n-1, k) and 5 divides C(n-1, k-1). Let's try different values of n until we find the smallest integer that fits this condition.
For n = 6:
C(5, 1) = 5, which is divisible by 5.
C(5, 2) = 10, which is not divisible by 3.
For n = 7:
C(6, 1) = 6, which is not divisible by 5.
C(6, 2) = 15, which is divisible by 3.

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The steps necessary to put he equation, x² - 3x + 27 = 8x - 3 in standard form is D. add 3 to both sides and subtract 8x from both sides

The standard form of quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number.

Hence, let's represent x² - 3x + 27 = 8x - 3 in standard form as follows:

x² - 3x + 27 = 8x - 3

Therefore, the two steps that are necessary to make the quadratic equation in standard form is add 3 to both sides and subtract 8x from both sides

Hence,

x² - 3x - 8x + 27 + 3 = 8x - 8x - 3 + 3

x² - 11x + 30 = 0

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Answer: 9.01 is the answer

Step-by-step explanation: Because when you add the number in the square you can split the number you add to the nearest sum to the number you get in the outcum.

Answer: the answer is 2 I believe

Step-by-step explanation:as you look at “stem” and go down to the number 4. You count below that. So 8, and 6. That’s 2 numbers :) hope this helps!

The stem and leaf plot shows the ages of people at the library. 2 people are under the age of 40.

The duration of a being's or thing's existence; the length of its existence or life up until the moment being discussed or alluded to age. A time frame for humans that begins at birth and is measured in years.

This time frame is typically characterised by a specific stage or level of physical or mental development as well as the potential for legal responsibility. The stem and leaf plot shows the ages of people at the library. 2 people are under the age of 40.

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The sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is [tex]$-164$[/tex].

To find the sum of all the perfect squares between $15$ and $25$, we need to list them out: $16$, $25$. The sum of these perfect squares is $16+25=41$.

To find the sum of all the other integers between $15$ and $25$, we can use the formula for the sum of an arithmetic series. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. In this case, the first term is $16$ and the last term is $25$, so there are $10$ terms. The average of the first and last term is [tex]$\frac{16+25}{2}=20.5$[/tex]. Therefore, the sum of all the other integers between $15$ and $25$ is $20.5\times 10 = 205$.

Now we can subtract the sum of all the other integers from the sum of the perfect squares to get our final answer: $41-205 = -164$.

Therefore, the sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is $-164$.

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The null and alternative hypotheses are H₀ = μ ≥ 6 and H₁ = μ < 6.

Given that, the mean GPA of students in colleges is different from 2.0 (out of 4.0).

H₀: μ = 2.0 and H₁: μ ≠ 2.0

So,

We test the likelihood of the statement being true in order to decide whether to accept or reject our alternative hypothesis. Since, the question wants to test if the college student take less than six years to graduate on average, then we take, H₀ = μ ≥ 6.

And,

WE determine whether to accept or reject based on the likelihood of the null hypotheses being true, so we then take H₁ = μ < 6.

Hence, the null and alternative hypotheses are H₀ = μ ≥ 6 and H₁ = μ < 6.

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(i) To calculate the probability that the time between buses will be at least 20 minutes,

we need to find the area under the exponential distribution curve for values greater than or equal to 20.

Using the formula for the exponential distribution, we have: P(X ≥ 20) = 1 - P(X < 20) = 1 - e^(-20/20) = 1 - e^(-1) ≈ 0.632, Therefore, the probability that the time between buses will be at least 20 minutes is approximately 0.632.

(ii) To calculate the probability that the time between buses will exceed 20 minutes but will be less than 30 minutes,

we need to find the area under the exponential distribution curve between 20 and 30. Using the formula for the exponential distribution, we have:

P(20 < X < 30) = ∫[from 20 to 30] λe^(-λx) dx
               = [-e^(-λx)] from 20 to 30
               = [-e^(-30/20) + e^(-20/20)]
               ≈ 0.117

Here, T represents the inter-arrival time, λ is the rate parameter (1/mean), and t is the time we want to calculate the probability for. In this case, λ = 1/20 and t = 20 minutes.

P(T >= 20) = e^(-1/20 * 20) = e^(-1) ≈ 0.368

We want to find P(20 < T < 30), which can be calculated as P(T <= 30) - P(T <= 20).

P(T <= 30) = 1 - e^(-1/20 * 30) ≈ 0.776
P(T <= 20) = 1 - e^(-1/20 * 20) ≈ 0.632

P(20 < T < 30) = 0.776 - 0.632 ≈ 0.144

So, the probability that the time between buses will exceed 20 minutes but be less than 30 minutes is approximately 0.144 or 14.4%.

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Note that where the above qualities of a right triangle are given the value of BC in it's simples radical is 11√2.

Here we simply applied the trigonometric rule.

BC = a / Sin (Ф)

Where a = 11 and
Ф = 45

So

BC = 15.55635 = 11√2

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A planning phase for an engineering component generated 80 engineering drawings. The QA team randomly selected 8 drawings for inspection. This exercise can BEST be described as example of random sampling.

The exercise can be described as an example of random sampling, which is a statistical technique used to select a subset of individuals or items from a larger population, in a way that each member of the population has an equal chance of being selected. In this case, the 80 engineering drawings represent the population, and the QA team randomly selecting 8 of them for inspection is a form of random sampling.

By selecting the drawings randomly, the QA team can get an unbiased representation of the population and make inferences about the quality of the engineering component as a whole based on the inspection results of the selected subset.

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The probability that in a randomly selected hour, the number of calls is 2 is approximately 0.133 or 13.3%.

The number of calls received by a car towing service follows a Poisson distribution with an average of 18 calls per day (per 24-hour period). To find the mean number of calls per hour, divide the daily average by the number of hours in a day: 18 calls/day ÷ 24 hours/day = 0.75 calls/hour.

Now, to calculate the probability that in a randomly selected hour, the number of calls is 2, we can use the formula for the Poisson distribution:

P(X=k) = (e^(-λ) * λ^k) / k!

where P(X=k) is the probability of having k calls, λ is the mean number of calls per hour (0.75 in this case), k is the desired number of calls (2), e is the base of the natural logarithm (approximately 2.718), and k! is the factorial of k.

Plugging in the values, we get:

P(X=2) = (e^(-0.75) * 0.75^2) / 2!

P(X=2) ≈ (0.472 * 0.5625) / 2 ≈ 0.133

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To find P(AC), we need to remember that the probability of an event and its complement always adds up to 1. So, P(AC) = 1 - P(A) = 1 - 0.7 = 0.3.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

P(A or AC) is the probability that either event A occurs or its complement occurs. Since these two events are mutually exclusive (they cannot both happen at the same time), we can use the addition rule of probability to find P(A or AC) = P(A) + P(AC) = 0.7 + 0.3 = 1.

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The equation to represent the relationship is x - 3y + 9 = 0.

We have the table

Input (x)     Output (y)

      3              4

      6              5

      9              6

     12              7

     15              8

So, the equation can be formed as

(y - 4) = (5-4)/ (6-3) (x-3)

y - 4 = 1/3 (x -3)

3y - 12 = x - 3

x - 3y - 3 + 12 =0

x - 3y + 9 = 0

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Sin-1(0) is equivalent to either 0 radians or π radians, depending on the context of the problem.The sine function is defined as the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

It ranges from -1 to 1 and is zero at 0 radians and at every multiple of π radians (π, 2π, 3π, etc.). The inverse sine function or sin-1, also known as arcsine, gives the angle whose sine is equal to a given value.In this case, sin-1(0) represents the angle whose sine is zero. Since the sine function is zero at 0 radians and at every multiple of π radians, sin-1(0) is equivalent to either 0 radians or π radians. These are the only two possible solutions for sin-1(0), as the sine function is positive in the first and second quadrants and negative in the third and fourth quadrants, where it takes on nonzero values. In summary, sin-1(0) is equivalent to either 0 radians or π radians, depending on the context of the problem.

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To determine if a series is convergent or divergent, we need to analyze the behavior of the sequence of its partial sums. If the sequence approaches a finite limit as we add more and more terms, then the series is convergent. Otherwise, if the sequence either grows without bound or oscillates, then the series is divergent.

Without any specific series to consider, it's hard to give a definitive answer. However, in general, there are various techniques and tests we can use to evaluate the convergence or divergence of a series. Some common ones include the comparison test, the ratio test, the root test, the integral test, and the alternating series test.

If the series is convergent, we can also try to find its sum by using formulas or manipulations that express the series in a simpler form. For example, if the series is a geometric series, then we can use the formula for its sum. If the series is a telescoping series, then we can use partial fraction decomposition or other algebraic tricks to cancel out most of the terms.

Overall, the analysis of series convergence and divergence is an important topic in calculus and mathematical analysis, with many applications in physics, engineering, finance, and other fields.

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The probability of both the socks and the t-shirt being white is 21/44.

The probability of selecting a white pair of socks from the drawer is 6/11. The probability of selecting a white t-shirt from the drawer is 7/8. To find the probability of both events occurring together, we multiply the two probabilities:
P(white socks and white t-shirt) = (6/11) * (7/8) = 0.4773
Therefore, the probability of randomly selecting one pair of white socks and one white t-shirt from the drawer is approximately 0.4773 or 47.73%.
Hi there! To find the probability that both the socks and the t-shirt you randomly select are white, you'll need to multiply the individual probabilities for each item being white.
For the socks, there are 6 white pairs out of a total of 11 pairs. So, the probability of selecting a white pair is 6/11.
For the t-shirts, there are 7 white ones out of a total of 8. So, the probability of selecting a white t-shirt is 7/8.
Now, multiply these probabilities together: (6/11) * (7/8) = 42/88. Simplify the fraction to get 21/44.
So, the probability of both the socks and the t-shirt being white is 21/44.

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The  determinant of this matrix is -67/16.

To find the determinant of a matrix by row reduction to echelon form, we perform elementary row operations until the matrix is in echelon form, and then take the product of the diagonal entries. The determinant is the product of the pivots, with a factor of -1 for each row exchange.

Let's start with Exercise 5:

-1 -3  1
1  4  9
-1  0  5

We can start by adding the first row to the third row to eliminate the -1 in the (3,1) position:

-1 -3  1
1  4  9
0 -3  6

Next, we can multiply the third row by -1/3 to get a pivot in the (3,3) position:

-1 -3  1
1  4  9
0  1 -2

Then we add 3 times the second row to the third row to eliminate the 3 in the (3,2) position:

-1 -3  1
1  4  9
0  0  3

We now have an upper triangular matrix, which is in echelon form. The product of the diagonal entries is -1*4*3 = -12. Since we did not perform any row exchanges, there is no factor of -1. Therefore, the determinant of this matrix is -12.

Now let's move on to Exercise 6:

-1  0  5
3 -32  3
3  3  -1

We can start by adding 3 times the first row to the second row to eliminate the 3 in the (2,1) position:

-1  0   5
0 -32  18
3  3  -1

Then we can add the first row to the third row to eliminate the 3 in the (3,1) position:

-1  0   5
0 -32  18
0  3  4

Next, we can multiply the second row by -1/32 to get a pivot in the (2,2) position:

-1  0   5
0  1  -9/16
0  3   4

Then we add 9/16 times the second row to the third row to eliminate the -9/16 in the (3,2) position:

-1  0  5
0  1  -9/16
0  0  67/16

We now have an upper triangular matrix, which is in echelon form. The product of the diagonal entries is -1*1*67/16 = -67/16. Since we performed two row exchanges, there is a factor of (-1)^2 = 1. Therefore, the determinant of this matrix is -67/16.

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To solve this problem, we can use the law of total probability and the definition of conditional probability. Let's start by calculating the probabilities of the first ball being red or green:

Pr(R1) = (31)/(31+16+12) = 31/59

Pr(G1) = (16+20+24)/(31+16+12) = 28/59

(a) Pr(R2) = Pr(R2|R1)Pr(R1) + Pr(R2|G1)Pr(G1)

To calculate the conditional probabilities, we need to consider two cases:

If the first ball is red (R1), we pick the second ball from box B, which has 12 red balls and 20 green balls:

Pr(R2|R1) = 12/32

Pr(G2|R1) = 20/32

If the first ball is green (G1), we pick the second ball from box C, which has 24 red balls and 16 green balls:

Pr(R2|G1) = 24/40

Pr(G2|G1) = 16/40

Plugging these values into the formula, we get:

Pr(R2) = (12/32)(31/59) + (24/40)(28/59) = 65957/173420

(b) Pr(G2) = 1 - Pr(R2) = 107463/173420

(c) Pr[R2|R1] = 12/32 (as calculated above)

(d) Pr[R2|G1] = 24/40 (as calculated above)

(e) Pr[G2|G1] = 16/40 (as calculated above)

(f) Pr[G2|R1] = 20/32 = 5/8 (complementary to Pr[R2|R1])

Therefore, the answers are:

(a) Pr(R2) = 65957/173420

(b) Pr(G2) = 107463/173420

(c) Pr[R2|R1] = 12/32

(d) Pr[R2|G1] = 24/40

(e) Pr[G2|G1] = 16/40

(f) Pr[G2|R1] = 5/8

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To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3. Thus, the 75th term of the sequence is $111$.

To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3, we can use the base-3 (ternary) numeral system. The 75th term can be represented as the 74th number in base-3 without a digit 2 (as it will require subtraction to form distinct powers of 3).

The 74th number in base-10 is represented as $74_{10}$, which when converted to base-3 is $2202_3$. Since we need to avoid the digit 2, we can carry out the operation similar to addition with carry-over: $2202_3 + 1111_3 = 10310_3$.

Now, we can convert $10310_3$ back to base-10: $(1 \times 3^4) + (0 \times 3^3) + (3 \times 3^2) + (1 \times 3^1) + (0 \times 3^0) = 81 + 0 + 27 + 3 + 0 = 111$.

Thus, the 75th term of the sequence is $111$.

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The probability of getting a multiple of 4 or a multiple of 7 is 0.267

There are three multiples of 4 (4, 8, 12) and two multiples of 7 (7, 14) on the spinner.

However, 8 is a common multiple of 4 and 7, so it is counted twice. Thus, there are 4 outcomes that are either a multiple of 4 or a multiple of 7: 4, 7, 8, and 12.

The total number of possible outcomes is 15, since there are 15 sectors on the spinner.

Therefore, the probability of getting a multiple of 4 or a multiple of 7 is:

P(multiple of 4 or multiple of 7) = number of favorable outcomes / total number of possible outcomes

= 4 / 15

≈ 0.267

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Answer:

the answer is 1/3

Strengths Finder 2.0 is a valuable tool that can help individuals identify and develop their unique strengths. By leveraging these strengths, individuals can achieve greater success in their personal and professional lives, and organizations can create a more positive and productive work environment.

Strengths Finder 2.0 is a popular survey tool that helps individuals identify their unique strengths and talents. The survey has been completed by 10 million people to date and has been adopted by many universities and organizations to assist individuals in identifying their strengths.

The survey consists of a series of questions designed to assess an individual's natural talents and abilities. The results are then used to provide personalized feedback and coaching on how to leverage those strengths in their personal and professional lives.

The use of Strengths Finder 2.0 has become increasingly popular in recent years as individuals and organizations recognize the importance of focusing on strengths rather than weaknesses. By identifying and developing their strengths, individuals can improve their performance, increase their engagement and job satisfaction, and achieve greater success in their careers.

Organizations that use Strengths Finder 2.0 have reported increased productivity, employee engagement, and retention rates. By providing employees with the tools and resources to develop their strengths, organizations can create a more positive and fulfilling work environment.

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Answer:

The answer to your problem is, B. Player B is the most consistent, with an IQR of 1.5.

Step-by-step explanation:

Steps in which we need to answer

We know the first table be represented as A.

A = { 2 , 1 , 3 , 8 , 2 , 1 , 4 , 3 , 1 }

mean of A = 25/9 = 2.778

We know the second table be represented as B.

B = { 2 , 3 , 1 , 3 , 2 , 2 , 1 , 3 , 6 }

mean of B = 23/9 = 2.5556

The standard deviation of B = 1.5

Which can conclude to the answer.

Thus the answer to your problem is, B. Player B is the most consistent, with an IQR of 1.5.

Therefore, there were 75 downloads of the standard version with total size downloaded is 75 MB + 3(25 MB) = 150 MB.

To solve this problem, we can use a system of equations. Let x be the number of downloads for the standard version and y be the number of downloads for the high-quality version.

From the problem, we know that:
- The size of the standard version is x MB
- The size of the high-quality version is 3y MB
- The total size downloaded for the two versions was x + 3y MB

Putting these equations together, we get:

x + 3y = 150

We also know that the size of the standard version is smaller than the high-quality version, so we can assume that the standard version was downloaded more times than the high-quality version:

x > y

Now we have two equations and two unknowns. We can solve for x and y by substitution or elimination.

Let's use substitution:

From the second equation, we can isolate y:

y = x/3

Substitute this into the first equation:

x + 3(x/3) = 150

Simplify:

x + x = 150

2x = 150

x = 75

So there were 75 downloads of the standard version.

To check our answer, we can find the number of downloads for the high-quality version:

y = x/3 = 75/3 = 25

And verify that the total size downloaded is 75 MB + 3(25 MB) = 150 MB.

Therefore, there were 75 downloads of the standard version.

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The complex number (cos π/4 + i sin π/4)³ can be written in a trigonometric form as (cos π³/64 + i sin π³/64).

We have,

De Moivre's theorem states that for any non-zero complex number

z = r(cosθ + i sinθ) and any positive integer n.

z^n = r^n (cos nθ + i sin nθ)

In this case,

We have z = cos π/4 + i sin π/4 and n = 3.

So we can apply de Moivre's theorem as follows:

z³ = (cos π/4 + i sin π/4)³

= cos³ π/4 + 3i cos² π/4 sin π/4 - 3 cos π/4 sin² π/4 - i sin³ π/4

= (cos³ π/4 - 3 cos π/4 sin² π/4) + i (3 cos² π/4 sin π/4 - sin³ π/4)

We can simplify the real and imaginary parts using the trigonometric identities:

cos³ θ - 3 cos θ sin² θ = cos 3θ

3 cos² θ sin θ - sin³ θ = sin 3θ

So we get:

z³ = cos 3π/4 + i sin 3π/4

= cos π³/4 + i sin π³/4

Therefore,

The complex number (cos π/4 + i sin π/4)³ can be written in a trigonometric form as (cos π³/64 + i sin π³/64).

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The complete question:

Use de Moivre's theorem to write the complex number in trigonometric form (cos π/4 + i sin π/4)³

(cos π³/64 + i sin π³/64)

Each team member should run 9073.6 miles in the race on Course B.

Let's break down the problem step by step:

1. First, we need to find the length of Course B. We know that Course B is 212 times as long as Course A, and Course A is 214 miles. So, to find the length of Course B, we multiply:
  Course B length = 212 × 214 miles

2. Calculate the length of Course B:
  Course B length = 45368 miles

3. Now, we need to determine the distance each team member should run. There are 5 members on the team, and they need to run an equal distance on Course B. To find the distance for each member, we divide the total length of Course B by the number of team members:
  Distance per member = Course B length / number of members

4. Calculate the distance per team member:
  Distance per member = 45368 miles / 5

5. Finally, we find the distance each team member should run:
  Distance per member = 9073.6 miles

So, each team member should run 9073.6 miles in the race on Course B.

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The revolutions the wheel will have to make before the car comes to a complete stop are approximately 25.5 revolutions.

To find out how many revolutions the wheel will have to make before the car comes to a complete stop, we need to use the information provided about the distance and diameter of the wheel.

First, we need to convert the diameter from centimeters to meters: 61 centimeters = 0.61 meters.

Next, we can use the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter.

So the circumference of the wheel is: C = π(0.61m) = 1.92m.

Now we can use the distance the car can stop in, 49 meters, to calculate the number of revolutions of the wheel:

49m ÷ 1.92m/rev ≈ 25.5 revolutions.

Therefore, the wheel will have to make approximately 25.5 revolutions before the car comes to a complete stop.

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The probability of choosing 6 people at random from the group and having all of them be left-handed is approximately 0.00002599 or 0.0026%.

We can approach this problem using the binomial distribution, which models the probability of a certain number of successes (in this case, choosing left-handed people) in a fixed number of trials (choosing 6 people).

Let p be the probability of choosing a left-handed person, which is given as 15% or 0.15. Then, the probability of choosing all 6 people to be left-handed can be calculated as:

P(6 left-handed) = (0.15[tex])^6[/tex] * (1 - 0.15)[tex]^(6 - 6) * C(6, 6)[/tex]

where C(6, 6) represents the number of ways to choose 6 items from a set of 6, which is equal to 1.

Plugging in the values, we get:

P(6 left-handed) = (0.15[tex])^6[/tex] * (0.85)^0 * 1

= 0.00002599

Therefore, the probability of choosing 6 people at random from the group and having all of them be left-handed is approximately 0.00002599 or 0.0026%.

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The measure of length of x from the similar triangles is x = 10

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔACD

Now , AC is the common side of the triangle

And , they are similar triangles

So , the corresponding sides are in the same ratio

And , x / 5 = 20 / x

On cross multiplying , we get

x² = 100

Taking square roots on both sides , we get

x = 10

Hence , the length of side is x = 10

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The distance that you will travel if you will drive at given speed for the following situations are 120 km, 330km, 69km, 60km, and 234km respectively.

Calculating distance involves using the formula:

distance = rate x time

Where "rate" is the speed at which you're traveling, measured in units of distance per unit of time (such as kilometers per hour or miles per minute), and "time" is the duration of your travel in those units of time (such as hours or minutes).

To find the distance, simply multiply the rate by the time. For example, if you're traveling at 60 kilometers per hour for 2 hours, your distance would be:

distance = 60 km/h x 2 h = 120 km

So in this case, you would travel 120 kilometers.

Similarly,

Distance = (Speed) x (Time) = 55 km/h x 6 h = 330 km

Distance = (Speed) x (Time) = 46 km/h x 1.5 h = 69 km

Distance = (Speed) x (Time) = 80 km/h x (45 min/60 min) = 60 km

Distance = (Speed) x (Time) = 78 km/h x 3 h = 234 km

Thus, the distances are 120 km, 330km, 69km, 60km, and 234km respectively.

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Calculate the distance that you will travel is you will

drive for the following situations. Write your answers on a separate sheet of

paper.

1. 3 hours at 40km/h

2. 6 hours at 55km/h

3. 1.5 hours at 46km/h

4. 45 minutes at 80km/h

5. 3 hours at 78km/h​