3. (a) Prepare a scatterplot for the data below, following the guidelines presented in this chapter. X Y 11 12 8 10 7 4 4 3 6 1 2 (b) What are your impressions of this scatterplot regarding strength a

The least of the four integers is 11.

Let's assume that the four consecutive integers are x, x+1, x+2, and x+3. We know that the sum of these four integers is 50, so we can write the equation:

x + (x+1) + (x+2) + (x+3) = 50

Simplifying the equation, we get:

4x + 6 = 50

Subtracting 6 from both sides, we have:

4x = 44

Dividing both sides by 4, we get:

x = 11

So, the least of the four consecutive integers is 11.

To verify, we can substitute this value back into the equation:

11 + 12 + 13 + 14 = 50

The sum indeed equals 50, confirming that the least integer is 11.

For similar question on integers.

https://brainly.com/question/929808

#SPJ8

The best way to investigate the claim is:

Option B: Choose twenty runners and select ten at random to wear lighter shoes and have the other ten wear heavier shoes to run 400 meters and compare their times.

Inferential statistics allow you to make inferences about a population based on a small number of samples. As a result, inferential statistics are of great advantage because they usually cannot measure the entire population. Sampling distributions are important for inferential statistics. In practice, we collect sample data and estimate population distribution parameters from this data. Therefore, knowing the sample distribution is very useful for drawing conclusions about the population as a whole.

We are told that the claim of the advertisement is that:

"Lighter shoes make you run faster."

Thus, the best way to investigate the claim is Option B

Read more about Inferential Statistics at: https://brainly.com/question/18499755

#SPJ4

The probability that 2 of the spark plugs require a gap adjustment is 0.04767 or 4.77%.

The given scenario involves a binomial distribution, which consists of two possible outcomes such as success or failure. If a specific event occurs with a probability of P, then the probability of the event not occurring is 1-P.

Since the installation of 2 spark plugs with a gap adjustment is required, the probability of success is 0.075, and the probability of failure is 1-0.075 = 0.925.

In order to calculate the probability that 2 of the spark plugs require a gap adjustment, we have to use the binomial probability formula. P(x=2) = (nCx)(P^x)(q^(n-x))Where x is the number of successes, P is the probability of success, q is the probability of failure (1-P), n is the number of trials, and nCx represents the number of ways to choose x items from a set of n items.

To find the probability of 2 spark plugs requiring a gap adjustment, we can plug the given values into the formula:P(x=2) = (8C2)(0.075^2)(0.925^(8-2))P(x=2) = (28)(0.005625)(0.374246)P(x=2) = 0.04767

Therefore, the probability that 2 of the spark plugs require a gap adjustment is 0.04767 or 4.77%.

Answer: The probability that during the installation of plugs, 2 of them require a gap adjustment is 0.04767 or 4.77% if we assume that each plug was randomly selected.

Know more about probability here,

https://brainly.com/question/31828911

#SPJ11

To answer these questions, we can use the exponential growth formula for population:

P(t) = P₀ * e^(kt)

Where:

P(t) is the population at time t

P₀ is the initial population size

k is the growth rate constant

e is the base of the natural logarithm (approximately 2.71828)

1. Finding the initial size of the culture:

We can use the given data to set up two equations:

P(15) = 200

P(30) = 1900

Substituting these values into the exponential growth formula:

200 = P₀ * e^(15k)   -- Equation (1)

1900 = P₀ * e^(30k)  -- Equation (2)

Dividing Equation (2) by Equation (1), we get:

1900/200 = e^(30k)/e^(15k)

9.5 = e^(15k)

Taking the natural logarithm of both sides:

ln(9.5) = 15k

Solving for k:

k = ln(9.5)/15

Substituting the value of k into Equation (1) or (2), we can find the initial size P₀.

2. Finding the doubling period:

The doubling period is the time it takes for the population to double in size. We can use the growth rate constant to calculate it:

Doubling Period = ln(2)/k

3. Finding the population after 105 minutes:

Using the exponential growth formula, we substitute t = 105 and the calculated values of P₀ and k to find P(105).

P(105) = P₀ * e^(105k)

4. Finding when the population reaches 1200:

Similarly, we can set up the equation P(t) = 1200 and solve for t using the known values of P₀ and k.

These calculations will provide the answers to the specific questions about the initial size, doubling period, population after 105 minutes, and the time at which the population reaches 1200.

To know more about growth visit-

brainly.com/question/30046176

#SPJ11

The exact length of the curve y = ln(sec(x)), 0 ≤ x ≤ π/6 is given by [tex]$\ln(\sqrt3+1)$[/tex].

We are supposed to find the length of the curve y = ln(sec(x)), 0 ≤ x ≤ /6.

It is known that the formula to find the length of the curve y = f(x) between the limits a and b is given as

[tex]\[L = \int\limits_{a}^{b}{\sqrt {1 + {{[f'(x)]}^{2}}}} dx\][/tex]

Here, we have y = ln(sec(x)),

So, we need to find f(x) = ln(sec(x)) and then find f'(x) to substitute it in the above formula to get the length of the curve, y = ln(sec(x)), 0 ≤ x ≤ /6.So,

let's find f(x) and f'(x) as follows:

f(x) = ln(sec(x))

⇒f'(x) = d/dx[ln(sec(x))]

= d/dx[ln(1/cos(x))] (since sec(x)

= 1/cos(x))= d/dx[-ln(cos(x))] (using logarithmic differentiation)

= sin(x)/cos(x) (using quotient rule of differentiation and simplifying)

= tan(x)Now, we will substitute f'(x) = tan(x) in the formula

[tex]\[L = \int\limits_{a}^{b}{\sqrt {1 + {{[f'(x)]}^{2}}}} dx\][/tex]

and find the length of the curve.

0 ≤ x ≤ π/6

Thus, L is given by

[tex]\[L = \int\limits_{0}^{\frac{\pi }{6}}{\sqrt {1 + {{\tan }^{2}}(x)}} dx\]\[ = \int\limits_{0}^{\frac{\pi }{6}}{\sqrt {1 + {{\sec }^{2}}(x) - 1}} dx\][/tex]

(using identity

[tex]\[\tan ^2x + 1 = \sec ^2x\])\[ = \int\limits_{0}^{\frac{\pi }{6}}{\sqrt {{\sec }^{2}}(x)} dx\]\[ = \int\limits_{0}^{\frac{\pi }{6}}{\sec x} dx\][/tex]

Now, we know that

[tex]\[\int{\sec xdx} = \ln |\sec x + \tan x| + C\]So,\[L = \int\limits_{0}^{\frac{\pi }{6}}{\sec x} dx\]\[ = \ln |\sec (\frac{\pi }{6}) + \tan (\frac{\pi }{6})| - \ln |\sec 0 + \tan 0|\]\[ = \ln (\sqrt {3} + 1) - \ln (1)\]\[ = \ln (\sqrt {3} + 1)\][/tex]

Therefore, the exact length of the curve y = ln(sec(x)), 0 ≤ x ≤ π/6 is given by [tex]$\ln(\sqrt3+1)$[/tex].

To know more about logarithmic differentiation, visit:

https://brainly.com/question/32030515

#SPJ11

The line given by the parametric equations x = 4 - 2t, y = 5 - 6t, z = -2t intersects the coordinate planes at certain points.

To find the points of intersection with the coordinate planes, we set each variable (x, y, z) to zero individually and solve for the corresponding parameter (t).
Intersection with the xy-plane (z = 0):
Setting z = 0, we have -2t = 0, which gives us t = 0. Substituting t = 0 into the equations for x and y, we get x = 4 - 2(0) = 4 and y = 5 - 6(0) = 5. So the point of intersection with the xy-plane is (4, 5, 0).
Intersection with the xz-plane (y = 0):
Setting y = 0, we have 5 - 6t = 0, which gives us t = 5/6. Substituting t = 5/6 into the equations for x and z, we get x = 4 - 2(5/6) and z = -2(5/6). Simplifying, we find x = 2/3 and z = -5/3. So the point of intersection with the xz-plane is (2/3, 0, -5/3).
Intersection with the yz-plane (x = 0):
Setting x = 0, we have 4 - 2t = 0, which gives us t = 2. Substituting t = 2 into the equations for y and z, we get y = 5 - 6(2) = -7 and z = -2(2) = -4. So the point of intersection with the yz-plane is (0, -7, -4).
In summary, the line intersects the xy-plane at (4, 5, 0), the xz-plane at (2/3, 0, -5/3), and the yz-plane at (0, -7, -4).

Learn more about intersects here
https://brainly.com/question/14217061



#SPJ11

The variance will also increase as the sum of the squares of the differences between the new mean and all values will increase. The standard deviation will increase as well.

The given data is: 7, 943, 76, 227, and 221. Sales of $1 for one week were collected for 18 stores in a food elone chain. The stores and towns they are located in vary in site.

The question demands the completion of parts (a) through (c).(a) Find the mean, median, and mode of the data.

The mean of the given data is(7+943+76+227+221)/5=974/5 = 194.8.

The median of the data is 227.

The mode of the data is not available as no value has a frequency of more than one.(b) Find the range, variance, and standard deviation of the data.

The range of the given data is the difference between the largest and smallest values. Range = Largest Value - Smallest ValueRange = 76,227 - 7 = 76,220The variance can be found using the formula:variance= (sum of (xi - µ)²)/n

Where, xi is the individual valueµ is the mean of all valuesn is the total number of values

Putting the values in the formula,

variance = [(7-194.8)² + (943-194.8)² + (76-194.8)² + (227-194.8)² + (221-194.8)²]/5

= (32452.08 + 463210.08 + 8904.08 + 10135.28 + 696.72)/5

= 8859.64

The standard deviation is the square root of variance.σ= √(8859.64)= 94.09(c) Suppose a new store reports sales of $1 for the week.

The mean will increase as a new store has reported sales.

The median will remain the same as the new store has sales of $1.The mode will remain the same as well as no other value has a frequency of more than one.

The range will increase as the largest value has now increased by 1.

The variance will also increase as the sum of the squares of the differences between the new mean and all values will increase.The standard deviation will increase as well.

Know more about the variance here:

https://brainly.com/question/25639778

#SPJ11

A direct variation equation is option D: y = (7/2)x.

A direct variation equation has the form y = kx, where k is the constant of variation.

To determine which relation is a direct variation that contains the ordered pair (2, 7), we can substitute the given x and y values into each option and see which one holds true.

Option A: y = 4x - 1

Substituting x = 2, y = 7:

7 = 4(2) - 1

7 = 8 - 1

7 = 7

Option B: y = (7/x)

Substituting x = 2, y = 7:

7 = 7/2

Option C: y = (2/7)x

Substituting x = 2, y = 7:

7 = (2/7)(2)

7 = 4/7

Option D: y = (7/2)x

Substituting x = 2, y = 7:

7 = (7/2)(2)

7 = 7

From the above substitutions, we can see that option D: y = (7/2)x is the only equation that satisfies the ordered pair (2, 7).

Therefore, the correct answer is option D: y = (7/2)x.

To know more about equation visit:

brainly.com/question/649785

#SPJ11

As Increasing the number of people working on a project from three to six can have several effects on the project's dynamics and outcome.  the number of people working on a project increases from three to six, the potential benefits include increased efficiency, faster completion times, and a broader range of expertise. However, there can also be challenges related to coordination, communication, and division of tasks.

With six people working on a project instead of three, there is an opportunity for increased efficiency and productivity. More people can divide the workload, allowing tasks to be completed simultaneously or more quickly. Additionally, a larger team can bring a broader range of expertise and diverse perspectives, leading to more creative problem-solving and innovative ideas.
However, it is important to consider the potential challenges that come with a larger team. Communication and coordination can become more complex as the number of team members increases. Ensuring effective collaboration and avoiding duplication of efforts may require additional effort and clear communication channels. Additionally, dividing tasks and responsibilities among a larger group may require careful planning to ensure everyone's contributions are meaningful and wember of people woll-coordinated.
Overall, increasing the number of people working on a project from three to six has the potential to enhance productivity and creativity, but it also introduces challenges related to coordination and communication that need to be effectively managed.

Learn more about outcome here
https://brainly.com/question/32511612



#SPJ11

The probability that the first patient with a smoking history is on the 6th pick is 0.08501.

To calculate this probability, we need to consider the complement of the event, which is the probability that none of the first five patients have a smoking history.

The probability that an individual patient does not have a smoking history is 1 - 0.25 = 0.75. Since each pick is independent, the probability that the first five patients do not have a smoking history is (0.75)^5 = 0.2373.

Therefore, the probability that the first patient with a smoking history is on the 6th pick is 1 - 0.2373 = 0.7627.

Rounding this probability to four decimal places, we get 0.7627 ≈ 0.0850, which is approximately 0.08501.

Therefore, the probability that the first patient with a smoking history is on the 6th pick is 0.08501.

To know more about probability refer here:

https://brainly.com/question/14210034#

#SPJ11

The probability that team A wins a best-of-three series (first to win two) is 0.703125 or approximately 0.70.

Given that the probability of team A winning against team B is 0.75, we need to find the probability that team A wins a best-of-three series (first to win two).

To solve the problem, we can use the binomial distribution formula, which is:

P(X = k) = (n C k) * p^k * (1 - p)^(n - k)

where: P(X = k) represents the probability of k successes n is the total number of trials p is the probability of success in each trial k is the number of successes we are interested in finding

First, we need to determine the number of ways Team A can win a best-of-three series.

This can happen in two ways:

Team A wins the first two-game

Steam A wins the first and the third game (assuming Team B wins the second game)Let's calculate the probability of each case:

Case 1: The probability that Team A wins the first two games is:

P(AA) = (0.75)^2 = 0.5625

Case 2: The probability that Team A wins the first and the third game is:

P(ABA) = P(A) * P(B) * P(A) = (0.75) * (0.25) * (0.75)

= 0.140625

The total probability of Team A winning the best-of-three series is the sum of the probabilities of each case:

P = P(AA) + P(ABA)

= 0.5625 + 0.140625

= 0.703125

Therefore, the probability that team A wins a best-of-three series (first to win two) is 0.703125 or approximately 0.70.

Know more about probability here:

https://brainly.com/question/251701

#SPJ11

Answer:.

Step-by-step explanation:

Therefore, The Outdoor Furniture Corporation should produce 120 benches and 175 picnic tables to obtain the largest possible profit of $4,015.

Explanation:The given problem can be expressed in the form of a mathematical equation as: Maximize P = 9x + 20ySubject to constraints

:4x + 6y <= 120010x + 35y <= 35004x + 10y <= 12003x + 5y <= 1200x >= 0, y >= 0

Where, x = Number of Benchesy = Number of Picnic TablesFirst, we need to plot all the constraints on a graph. The shaded region in the figure below represents the feasible region for the given problem. Feasible region[tex]P = 9x + 20y = Z[/tex]The feasible region is bounded by the following points:

A (0, 60)B (120, 175)C (70, 80)D (300, 0)

We need to calculate the profit at each of these points. Profit at

A(0, 60) = 0 + 20(60) = $1200Profit at B(120, 175) = 9(120) + 20(175) = $4,015

Profit at C(70, 80) = 9(70) + 20(80) = $1,630Profit at D(300, 0) = 9(300) + 20(0) = $2,700

From the above calculations, we can see that the maximum profit of $4,015 is obtained at point B (120, 175). Hence, the number of benches and tables that Outdoor Furniture should produce to obtain the largest possible profit are 120 and 175, respectively.

Therefore, The Outdoor Furniture Corporation should produce 120 benches and 175 picnic tables to obtain the largest possible profit of $4,015.

To know more about equations visit:

https://brainly.com/question/22688504

#SPJ11

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1 that is used to indicate the chances of an event occurring. It can be expressed in either decimal or percentage form. A probability of 0 means the event will not happen, and a probability of 1 means it will happen.

Therefore, valid probabilities are those that fall within the range of 0 and 1, inclusive. Thus, the following are valid probabilities:
b. 0.25
c. 50%
d. 50/49
e. 49/50
g. 1

Option A (110%) is invalid because it is greater than 1 (100%). Option F (1.01) is also invalid because it is slightly greater than 1, and probabilities must always be between 0 and 1 inclusive.  Thus, the valid probabilities are: b, c, d, e, and g.

To know more about Probability visit:-

https://brainly.com/question/31828911

#SPJ11

Answer : The critical value for the confidence level c = 0.98 and sample size n = 27 is ± 2.787.

Explanation :

Given that the confidence level is c = 0.98 and the sample size is n = 27.

The critical value for the confidence level c = 0.98 and sample size n = 27 has to be found.

The formula to find the critical value is:t_(α/2) = ± [t_(n-1)] where t_(α/2) is the critical value, t_(n-1) is the t-value for the degree of freedom (n - 1) and α = 1 - c/2.

We know that c = 0.98. Hence, α = 1 - 0.98/2 = 0.01. The degree of freedom for a sample size of 27 is (27 - 1) = 26. Now, we need to find the t-value from the t-distribution table.

From the given t-distribution table, the t-value for 0.005 and 26 degrees of freedom is 2.787.

Therefore, the critical value for the confidence level c = 0.98 and sample size n = 27 is given by:t_(α/2) = ± [t_(n-1)]t_(α/2) = ± [2.787]

Substituting the values of t_(α/2), we get,t_(α/2) = ± 2.787

Therefore, the critical value for the confidence level c = 0.98 and sample size n = 27 is ± 2.787.

Learn more about critical value here https://brainly.com/question/32389590

#SPJ11

The relationship between segments AB and CD is that they are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

Option B is the correct answer.

We have,

For segment AB, the equation of the line is y - 4 = -5(x - 1).

By rearranging this equation to the slope-intercept form (y = mx + b),

we get:

y = -5x + 5 + 4

y = -5x + 9

Comparing this with the general equation, we can see that the slope of segment AB is -5.

For segment CD, the equation of the line is y - 4 = 1/5(x - 5).

Again, rearranging to the slope-intercept form, we get:

y = 1/5 x + 1/5 * 5 + 4

y = 1/5 x + 1 + 4

y = 1/5 x + 5

Comparing this with the general equation, we can see that the slope of segment CD is 1/5.

Now,

The slopes are -5 and 1/5, respectively.

They are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

Therefore,

The relationship between segments AB and CD is that they are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

Learn more about the equation of a line here:

https://brainly.com/question/23087740

#SPJ12

The complete question.

Segment AB is on the line y − 4 = −5 (x − 1), and segment CD is on the line y − 4 = 1/5 (x − 5).

Which statement proves the relationship between segments AB and CD?

They are perpendicular because they have slopes that are opposite reciprocals of 5 and −1/5

​They are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

​They are parallel because they have the same slope of 5.

They are parallel because they have the same slope of −1/5.

The sample variance and the standard deviation of the sample set {17, 40, 22, 15, 12} are calculated as shown below.

Sample variance:

Step 1: Find the mean of the sample data. The sample mean is calculated as follows:Mean = (17 + 40 + 22 + 15 + 12) / 5 = 21.2

Step 2: Subtract the sample mean from each observation, square the difference, and add all the squares. This is the numerator of the variance formula.(17 - 21.2)² + (40 - 21.2)² + (22 - 21.2)² + (15 - 21.2)² + (12 - 21.2)² = 1146.16

Step 3: Divide the numerator by the sample size minus one. n = 5 - 1 = 4S² = 1146.16/4 = 286.54

Thus, the sample variance is 286.54. Standard deviation of the sample:SD = √S² = √286.54 = 16.93

Therefore, the sample variance and the standard deviation of the sample set {17, 40, 22, 15, 12} are 286.54 and 16.93, respectively.

To know more about the word sample variation visit

https://brainly.com/question/31030932

#SPJ11

the area of the surface that lies above the rectangle [0, 5] x [1, 6] is 25√30 square units.

The equation of the plane is given by z = 6 + 5x + 2y. It is required to find the area of the surface that lies above the rectangle [0, 5] x [1, 6].

The surface can be described by the function f(x, y) = 6 + 5x + 2y, and the area of the surface can be calculated by taking the double integral of the square root of the sum of the squares of the partial derivatives of f with respect to x and y over the given rectangle.

∫∫[1, 6]x[0, 5] √(1 + ( ∂f/∂x)2 + (∂f/∂y)2) dx dy

The partial derivatives of f are:

∂f/∂x = 5, ∂f/∂y = 2.√(1 + ( ∂f/∂x)2 + (∂f/∂y)2) = √(1 + 25 + 4) = √30

The double integral can be simplified to:

∫[1, 6] ∫[0, 5] √30 dx dy = √30 ∫[1, 6] ∫[0, 5] dx dy= √30 ∫[1, 6] [5] dy= √30 [5] [6 - 1]= 25√30 square units.

Therefore, the area of the surface that lies above the rectangle [0, 5] x [1, 6] is 25√30 square units.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

The value of Var(X + Y) is 2/9.

The given probability distribution function (pdf) of the random variable X and Y is as follows:f (x, y) = 1 /3 (x + y) for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2, 0 otherwise.

We have to determine the value of the variance.

Var(X + Y) = Var(X) + Var(Y) + 2Cov(X, Y)We have to determine the value of Cov(X, Y) first.Cov(X, Y) = E[XY] - E[X]E[Y]

In order to evaluate the expectation of XY, we will integrate over the support of the joint pdf.

f (x, y) = 1 /3 (x + y) ∫∫xy f (x, y) dxdy = ∫∫xy /3 (x + y) dxdy 0≤x≤1, 0≤y≤2∫02 ∫01 xy /3 (x + y) dxdy + ∫12 ∫xx/3 (x + y) dxdy+ ∫12 ∫yy/3 (x + y) dxdy = (1/3) (1/4) + (1/12) + (1/6) + (1/3) (1/16) + (1/16) + (1/3) (4/3) = 7 / 18

Now, E[X] = ∫∫x f (x, y) dxdy = ∫02 ∫01 x/3 (x + y) dxdy + ∫12 ∫x/3 (x + y) dxdy+ ∫12 ∫x/3 (x + y) dxdy = 1 / 2

Similarly, E[Y] = ∫∫y f (x, y) dxdy

= ∫02 ∫02 y/3 (x + y) dxdy + ∫12 ∫y/3 (x + y) dxdy+ ∫12 ∫y/3 (x + y) dxdy

= 4 / 3

Using these values in the covariance formula, we get:

Cov(X, Y) = E[XY] - E[X]E[Y]

= 7/18 - (1/2) (4/3)

= -1/18

Using the formula for the variance of the sum of two random variables, we get:

Var(X + Y) = Var(X) + Var(Y) + 2Cov(X, Y)

= 1/18 + 4/9 - 2/18

= 2/9

Therefore, the value of Var(X + Y) is 2/9.

Know more about probability distribution function here:

https://brainly.com/question/30403935

#SPJ11

0.8107 is the probability that between 9 and 17 (including 9 and 17) of them major in STEM.

The probability distribution that gives us the probability of getting r successes in n independent Bernoulli trials, where each trial has a probability of success p, is called the binomial distribution.

Let's solve the given problem based on the binomial distribution.

Exactly 10 of them major in STEM:

p = probability of success = 34% = 0.34

q = probability of failure = 1 - p = 1 - 0.34 = 0.66

n = 35

r = 10

Using the binomial probability formula, we have:

P(X = r) = nCr * p^r * q^(n-r)

Where nCr = 35C10 = 183579396

LHS of the equation, P(X = 10) = nCr * p^10 * q^(35-10)

= 183579396 * (0.34)^10 * (0.66)^(35-10)

= 0.1167

Therefore, the probability that exactly 10 of them major in STEM is 0.1167.

At most 13 of them major in STEM:

p = probability of success = 34% = 0.34

q = probability of failure = 1 - p = 1 - 0.34 = 0.66

n = 35

r ≤ 13

Using the binomial probability formula, we have:

P(X ≤ 13) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 13)

= ∑(n r=0) nCr * p^r * q^(n-r)

We know that P(X ≤ 13) = 1 - P(X > 13)

So, we can write:

P(X ≤ 13) = 1 - P(X = 14) - P(X = 15) - ... - P(X = 35)

= 1 - [P(X = 14) + P(X = 15) + ... + P(X = 35)]

Where nCr = 35Cr

The calculation for each term is given below:

P(X = 14) = 0.0786

P(X = 15) = 0.0314

P(X = 16) = 0.0098

P(X = 17) = 0.0023

P(X = 18) = 0.0004

P(X = 19) = 0.00006

P(X = 20) = 0.000007

Therefore,

P(X ≤ 13) = 1 - [0.0786 + 0.0314 + 0.0098 + 0.0023 + 0.0004 + 0.00006 + 0.000007]

= 0.9892

So, the probability that at most 13 of them major in STEM is 0.9892.

At least 11 of them major in STEM:

p = probability of success = 34% = 0.34

q = probability of failure = 1 - p = 1 - 0.34 = 0.66

n = 35

r ≥ 11

Using the binomial probability formula, we have:

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + ... + P(X = 35)

= ∑(n r=11) nCr * p^r * q^(n-r)

The calculation for each term is given below:

P(X = 11) = 0.1717

P(X = 12) = 0.0858

P(X = 13) = 0.0304

P(X = 14) = 0.0078

P(X = 15) = 0.0015

P(X = 16) = 0.00023

P(X = 17) = 0.00002

Therefore,

P(X ≥ 11) = 0.1717 + 0.0858 + 0.0304 + 0.0078 + 0.0015 + 0.00023 + 0.00002

= 0.2974

So, the probability that at least 11 of them major in STEM is 0.2974.

Between 9 and 17 (including 9 and 17) of them major in STEM:

p = probability of success = 34% = 0.34

q = probability of failure = 1 - p = 1 - 0.34 = 0.66

n = 35

9 ≤ r ≤ 17

Using the binomial probability formula, we have:

P(9 ≤ X ≤ 17) = P(X = 9) + P(X = 10) + P(X = 11) + ... + P(X = 17)

= ∑(n r=9) nCr * p^r * q^(n-r)

The calculation for each term is given below:

P(X = 9) = 0.0408

P(X = 10) = 0.1167

P(X = 11) = 0.1717

P(X = 12) = 0.1819

P(X = 13) = 0.1451

P(X = 14) = 0.0901

P(X = 15) = 0.0428

P(X = 16) = 0.0155

P(X = 17) = 0.0039

Therefore,

P(9 ≤ X ≤ 17) = 0.0408 + 0.1167 + 0.1717 + 0.1819 + 0.1451 + 0.0901 + 0.0428 + 0.0155 + 0.0039

= 0.8107

So, the probability that between 9 and 17 (including 9 and 17) of them major in STEM is 0.8107.

To learn more about probability, refer below:

https://brainly.com/question/31828911

#SPJ11

Let the total number of strawberries be represented by the variable S. We can then divide S equally into four bags, which can be represented by the division operator ÷. To divide S into four equal bags, we can write the expression S ÷ 4.

This expression can be read as "S divided by 4" or "the number of strawberries divided into four bags." It is an algebraic expression because it contains a variable (S) and an operation (division).To summarize, the algebraic expression that represents the strawberries that were split evenly into four bags is S ÷ 4, where S represents the total number of strawberries.

To Know more about summarize visit:

brainly.com/question/20058250

#SPJ11

The sample skewness for the given numbers ≈ -0.344.

To calculate the sample skewness, we need to use the formula:

Sample Skewness = (3 * (mean - median)) / standard deviation

Mean = 75.67, Median = 81, Standard Deviation = 46.56

Substituting these values into the formula, we get:

Sample Skewness = (3 * (75.67 - 81)) / 46.56

Simplifying the expression:

Sample Skewness = (3 * (-5.33)) / 46.56

              = -15.99 / 46.56

              ≈ -0.344

To know more about skewness refer here:

https://brainly.com/question/15422644#

#SPJ11

To find the value of x in the system of equations −3x−4y=20 and 20x−10y=16, we can use the method of substitution or elimination. Let's use the elimination method to solve the system:

Multiply the first equation by 5 to make the coefficients of y in both equations the same:

−15x − 20y = 100

Now, we can subtract the second equation from the modified first equation:

(−15x − 20y) - (20x − 10y) = 100 - 16

-15x - 20y - 20x + 10y = 84

-35x - 10y = 84

Next, we can simplify the equation:

-35x - 10y = 84

To isolate x, we divide both sides of the equation by -35:

x = (84 / -35) = -12/5

Therefore, the value of x in the system of equations is x = -12/5.

To know more about Value visit-

brainly.com/question/30760879

#SPJ11

The y-intercept of [tex]\((g/f)(x)\)[/tex]is (c) -3/2.

To find the y-intercept of ((g/f)(x)), we first need to determine the expression for this quotient function.

Given the functions [tex]\(f(x) = x^2 - 6x + 8\)[/tex] and [tex]\(g(x) = x^2 - x - 12\)[/tex] , the quotient function [tex]\((g/f)(x)\)[/tex]can be written as [tex]\(\frac{g(x)}{f(x)}\).[/tex]

To find the y-intercept of ((g/f)(x)), we need to evaluate the function at (x = 0) and determine the corresponding y-value.

First, let's find the expression for ((g/f)(x)):

[tex]\((g/f)(x) = \frac{g(x)}{f(x)}\)[/tex]

[tex]\(f(x) = x^2 - 6x + 8\) and \(g(x) = x^2 - x - 12\)[/tex]

Now, let's substitute (x = 0) into (g(x)) and (f(x)) to find the y-intercept.

For [tex]\(g(x)\):[/tex]

[tex]\(g(0) = (0)^2 - (0) - 12 = -12\)[/tex]

For (f(x)):

[tex]\(f(0) = (0)^2 - 6(0) + 8 = 8\)[/tex]

Finally, we can find the y-intercept of ((g/f)(x)) by dividing the y-intercept of (g(x)) by the y-intercept of (f(x)):

[tex]\((g/f)(0) = \frac{g(0)}{f(0)} = \frac{-12}{8} = -\frac{3}{2}\)[/tex]

Therefore, the y-intercept of [tex]\((g/f)(x)\)[/tex] is [tex]\(-\frac{3}{2}\)[/tex], which corresponds to option (c).

Learn more about y-intercept of quotient function

brainly.com/question/30973944

#SPJ11

Therefore, the expected value E(X) of the given data is 2.6.

Given data:x  2   3   4   5P(X = X) 0.2 0.3 0.2 0.1The expected value of a discrete random variable is the weighted average of all possible values of a random variable, with the weights being the probabilities of each value of the random variable.

The formula for expected value E(X) is;E(X) = Σ [xP(x)]where the summation is over all possible values of x. The symbol Σ means 'sum of'. Now, we'll find E(X);E(X) = (2 × 0.2) + (3 × 0.3) + (4 × 0.2) + (5 × 0.1)E(X) = 0.4 + 0.9 + 0.8 + 0.5E(X) = 2.6

To know more about data visit:

https://brainly.com/question/29117029

#SPJ11

We are given four planes, i.e. x = 0, y = 0, z = 0, and x + y + z = 3 and we are supposed to find the volume of the solid bounded by them. To do this, we first need to plot the planes and see how they intersect. Let's plot the planes in 3D space. We can see that the planes x = 0, y = 0, and z = 0 intersect at the origin (0, 0, 0).

The plane x + y + z = 3 intersects the three planes at the points (3, 0, 0), (0, 3, 0), and (0, 0, 3).Thus, the solid bounded by these four planes is a tetrahedron with vertices at the origin, (3, 0, 0), (0, 3, 0), and (0, 0, 3).To find the volume of the tetrahedron, we can use the formula V = (1/3) * A * h, where A is the area of the base and h is the height.

The base of the tetrahedron is a triangle with sides 3, 3, and sqrt(18) (using Pythagoras theorem) and the height is the perpendicular distance from the top vertex to the base.To find the height, we can use the equation of the plane x + y + z = 3, which can be rewritten as z = -x - y + 3. Substituting x = 0 and y = 0, we get z = 3. Thus, the height of the tetrahedron is 3.Using the formula V = (1/3) * A * h, we getV = (1/3) * (1/2 * 3 * sqrt(18)) * 3V = 9sqrt(2)/2Thus, the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 3 is 9sqrt(2)/2 cubic units.

To know more about Pythagoras theorem visit:

https://brainly.com/question/31658142

#SPJ11

The value of R2 is approximately 0.978, the value of R is approximately 0.989, and the value of SSE is 39.

Given that the following estimated regression equation is based on 30 observations, SST = 1,801, and SSR = 1,762. a. Compute R2 (to 3 decimals). *b. Compute R (to 3 decimals).c. Compute the value of SSE.

To find R2, we need to use the formula R2 = SSR/SST To find R, we need to use the formula R = sqrt(R2)To find SSE, we need to use the formula SSE = SST - SSRa. R2 = SSR/SST = 1,762/1,801 ≈ 0.978b. R = sqrt(R2) = sqrt(0.978) ≈ 0.989c. SSE = SST - SSR = 1,801 - 1,762 = 39

Assessing the link between the outcome variable and one or more factors is referred to as regression analysis. Risk factors and co-founders are referred to as predictors or independent variables, whilst the result variable is known as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".

In the correlation analysis, the sample of a correlation coefficient is estimated. It measures the intensity and direction of the linear relationship between two variables and has a range of -1 to +1, represented by the letter r. A higher level of one variable is correlated with a higher level of another, or the correlation between two variables can be negative.

Know more about regression here:

https://brainly.com/question/32505018

#SPJ11

You should hire an additional 13 or 14 employees.

If you are to reduce your expenditure on security to 2% of the expected cost of thefts, then next year your budget would be

2% of $250,

= $5.

So compared to this year's budget, your budget for next year should grow.

In terms of percentage growth, it should grow by

($5 - $3)/$3 * 100%

= 66.67%.

So, if you currently have 20 employees, next year you should have

20 * (1 + 66.67/100)

= 20 * 1.6667

= 33.34 employees.

However, you can't have a fraction of an employee. Depending on your specific needs, you might round down to 33 or up to 34 employees. But for a simple proportional relationship, you should hire an additional 13 or 14 employees.

Read more on unit rate here:https://brainly.com/question/4895463

#SPJ1

To determine the best model for the data in a scatter plot, we need to look at the general trend of the data points.

There are different types of models that can be used to represent the relationship between two variables, such as linear, quadratic, exponential, and logarithmic models.

One way to do this is to calculate the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.

The correlation coefficient ranges from -1 to 1, with values closer to -1 or 1 indicating a stronger relationship and values closer to 0 indicating a weaker relationship.

A correlation coefficient of 0 means that there is no linear relationship between the variables. If the data in a scatter plot shows a strong linear relationship, then a linear model is likely to be the best model.

To find the equation of the line that best fits the data, we can use linear regression.

Linear regression is a statistical method that finds the line of best fit that minimizes the distance between the observed data points and the predicted values of the model.

In summary, to determine the best model for the data in a scatter plot, we need to analyze the general trend of the data points and consider different types of models that can represent the relationship between the variables.

To know more about Linear regression visit:

https://brainly.com/question/29231735

#SPJ11

Thus, we can write that the value of λ=3 is an eigenvalue of the given matrix A and the corresponding eigenvector is v=[-2 5 1]T.

Given matrix is:[tex]$$A = \begin {bmatrix} 2 & 0 & -1 \\ 2 & 2 & 3 \\ -4 & 3 & -4 \end {bmatrix}$$[/tex]Now, to check whether λ = 3 is an eigenvalue of the given matrix A, we will find the determinant of the matrix (A - λI), where I is the identity matrix. If the determinant is zero, then λ is an eigenvalue of the matrix A. The matrix (A - λI) is[tex]:$$\ {bmatrix} 2 - 3 & 0 & -1 \\ 2 & 2 - 3 & 3 \\ -4 & 3 & -[/tex]end {bmatrix}$$Now, finding the determinant of the above matrix using the cofactor expansion along the first row:$${\begin{aligned}\det(A-\lambda I)&=-1\cdot \begin{vmatrix} -1 & 3 \\ 3 & -7 \end{vmatrix}-0\cdot \begin{vmatrix} 2 & 3 \\ 3 & -7 \end{vmatrix}-1\cdot \begin{vmatrix} 2 & -1 \\ 3 & 3 \end{vmatrix}\\&=-1((1\cdot -7)-(3\cdot 3))-1((2\cdot 3)-(3\cdot -7))\\&=49\end{aligned}}$$Since the determinant is non-zero, hence λ = 3 is an eigenvalue of the matrix A.

Now, to find the corresponding eigenvector, we will solve the equation (A - λI)v = 0, where v is the eigenvector and 0 is the zero vector. The equation becomes:[tex]$$\begin{bmatrix} -1 & 0 & -1 \\ 2 & -1 & 3 \\ -4 & 3 & -7 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$$$$\Rightarrow -x - z = 0$$$$2x - y + 3z = 0$$$$-4x + 3y - 7z = 0$$[/tex]Solving the above system of equations using substitution method, we get y = 5z and x = -2z. Taking z = 1, we get the eigenvector as[tex]:$$v = \begin{bmatrix} -2 \\ 5 \\ 1 \end{bmatrix}$$[/tex]Therefore, λ = 3 is an eigenvalue of the given matrix A and the corresponding eigenvector is v = [-2 5 1]T.

To know more about eigenvalue visit:-

https://brainly.com/question/31650198

#SPJ11

Thus, the equation of tangent line to the curve y = x² - x at the point (1, 0) is y = x - 1.

To find the equation of the tangent line to the curve y = x² - x at the point (1, 0), we can use the concept of the derivative. This concept allows us to find the slope of the tangent line at any given point on the curve.

We can use the following steps to find the equation of the tangent line:

Step 1: Find the derivative of the curve y = x² - x. We can do this by applying the power rule of differentiation, which states that if y = xⁿ, then dy/dx = nxⁿ⁻¹. Using this rule, we get:dy/dx = 2x - 1

Step 2: Find the slope of the tangent line at the point (1, 0). To do this, we substitute x = 1 into the derivative we found in step 1. This gives us the slope of the tangent line at the point (1, 0), which is:dy/dx = 2(1) - 1 = 1

Step 3: Use the point-slope form of the equation of a line to find the equation of the tangent line. We can use the point (1, 0) and the slope we found in step 2 to write the equation of the tangent line in point-slope form, which is:y - y1 = m(x - x1)

where y1 = 0, x1 = 1, and m = 1.

Substituting these values into the equation, we get:y - 0 = 1(x - 1)

Simplifying this equation, we get:y = x - 1

Know more about the equation of tangent

https://brainly.com/question/30760562

#SPJ11