2. An academic senate has 15 members. A special committee of 5 members will be formed. In how many different ways can the committee be formed? 3. Suppose the academic senate is composed of 10 faculty representatives and 5 ex- officio members. The special committee must contain 4 faculty representatives and 1 ex-officio member. In how many different ways can the committee be formed?

Answer:

A

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Each time you divide or multiply by a negative number, you must change the direction of the inequality symbol.

(i) The set of boundary points of S is {1}.

(ii) There are no interior points in S.

(iii) S is not an open set because it does not contain any interior points.

(iv) S is a closed set because it contains all of its boundary points.

Let's analyze the set S step by step:

(i) Boundary points of S:

A boundary point of a set is a point that is neither an interior point nor an exterior point. In this case, since S consists of the elements x = 1 - 1/n for n = 1, 2, 3, ..., we can see that as n approaches infinity, x approaches 1. So, the set of boundary points of S is {1}.

(ii) Interior points of S:

An interior point of a set is a point that has an open neighborhood contained entirely within the set.

In this case, since S is defined as x = 1 - 1/n for n = 1, 2, 3, ..., we can see that as n increases, x approaches 1.

However, for any n, we can always find another n' greater than n such that 1 - 1/n' is closer to 1.

Therefore, there are no interior points in S.

(iii) S as an open set:

An open set is a set that contains all of its interior points.

Since S has no interior points (as discussed in part ii), it cannot contain all of its interior points.

Therefore, S is not an open set.

(iv) S as a closed set:

A closed set is a set that contains all of its boundary points.

In this case, the set of boundary points of S is {1}, and this set is contained within S itself.

Therefore, S contains all of its boundary points and is considered a closed set.

In summary, the set S has a single boundary point {1}, no interior points, is not an open set, and is a closed set.

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Answer:

a = (c - by) / x

Step-by-step explanation:

ax + by = c

ax = c - by

a = (c - by) / x

The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.

The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.

The three elements of the Project Triangle are:

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The volume of the basketball is approximately 1789. Rounding to the nearest tenth of an inch, the volume of the basketball is approximately 1789.1 cubic inches.

To find the volume of a basketball with a given radius, we can use the formula for the volume of a sphere. The formula tells us that the volume of a sphere is equal to four-thirds times pi times the radius cubed.

In this case, we are given that the radius of the basketball is 7.69 inches. So, we can plug this value into the formula to find the volume.

Using a calculator to perform the necessary calculations, we get:

V = (4/3) * pi * (7.69)^3

V ≈ 1789.1 cubic inches

Therefore, the volume of the basketball is approximately 1789.1 cubic inches, rounded to the nearest tenth of an inch. This tells us how much space the basketball takes up in three-dimensional space.

Knowing the volume of an object can be useful in various applications such as designing packaging, calculating the amount of material needed to manufacture the object, or estimating the amount of liquid or gas it can hold.

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Step-by-step explanation:

1/16 is ur ans.

\(2 ^{ - 4} \)

\(1 \div 2 ^{4} \)

\(1 \div 16\)

1 / 16 or 0.0625

you exponet using a^-n

= 1/ a^n

1/2^4

evaluate the power

1/16

or u can write 0.0625 whatever you want

Answer:  

x=5  

Step-by-step explanation:

x is the length of the line segment from the center to the boderline of circle. So x=5

Answer:

\(35\)

Step-by-step explanation:

One is given the following function (\(y=3x+5\)). The given problem asks one to find the output of the function when the input is (10). Keep in mind, a general rule for dealing with functions is that, when present, the variable (x) represents the input. Whereas the variable (y) represents the output. Thus, if one were to substitute (10) in place of (x), and simplify: the result one would get is the output. Apply this idea to the given scenario:

\(y=3x+5\)

\(y=3(10)+5\)

\(y=30+5\)

\(y=35\)

(7x-1)times(x-2)

Step-by-step explanation:

Hey there!

Let's simplify.

\(10x+2-7x^2\)

\(10x^2+10x+2\)

The answer we get is \(-7x^2+10x+2\).

Hope this helps! :)

\(\text{-TestedHyperr}\)

Answer:

15/40 and 28/40

Step-by-step explanation:

3/8 = 15/40

7/10 = 28/40

15+28=43

1 3/40

(I wasn't sure what the question really wanted)

xx

Answer:

D. 8.8

Step-by-step explanation:

As the pythagorean theorem.

A² + B² = C²,

5.4 × 5.4 + 7 × 7 = C²,

29.16 + 49 = C²,

78.16 = C²,

8.8 ≈ C

The confidence interval gives us an estimate of where the true population parameter θ likely falls, with a 95% probability. It does not mean that there is a 95% probability that θ is distributed within the interval [a, b].

A 95% confidence interval [a, b] for a parameter (let's call it θ) is a range of values within which the true value of θ is likely to fall with 95% probability. In other words, if we were to repeat the sampling process many times and calculate the confidence intervals, approximately 95% of those intervals would contain the true value of θ.

The correct description for a 95% confidence interval [a, b] is: "With 95% probability, the interval [a, b] covers the true value of θ."

Here's a step-by-step explanation:

1. Collect data: First, gather a random sample from the population of interest.

2. Calculate the sample statistic: Based on the data, calculate the sample statistic (e.g., mean, proportion, etc.) that will be used to estimate the population parameter θ.

3. Determine the standard error: Calculate the standard error of the sample statistic. The standard error measures the variability of the sample statistic across different samples.

4. Find the critical value: Determine the critical value that corresponds to a 95% confidence level. This value depends on the sampling distribution and can be found using a table or a calculator.

5. Calculate the margin of error: Multiply the standard error by the critical value. This gives you the margin of error, which represents the uncertainty in the estimate.

6. Construct the confidence interval: Add and subtract the margin of error from the sample statistic to obtain the lower and upper bounds of the 95% confidence interval, [a, b].

Remember, the confidence interval gives us an estimate of where the true population parameter θ likely falls, with a 95% probability. It does not mean that there is a 95% probability that θ is distributed within the interval [a, b].

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Answer:

Step-by-step explanation:

% to decimal

O.XY

The mean duration of one renewal interval in the given two-state Markov chain is 1/b.

In the given transition probability matrix, the probability of transitioning from state 1 to state 0 is represented by the element b. Since the process begins in state X₀ = 0, the first transition from state 1 to state 0 starts a renewal interval.

To calculate the mean duration of one renewal interval, we need to find the expected number of transitions from state 1 to state 0 before returning to state 1. This can be represented by the reciprocal of the transition probability from state 1 to state 0, denoted as 1/b.

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The fraction of the cabins that have windows is 29 / 80.

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a portion or section taken from a whole, which can be any number, a certain amount, or an object.

Given that there are 80 cabins on a ship. 29 of the cabins have windows. The ratios of the cabins that have windows will be calculated below.

Fraction = ( Number of windows) / ( Number of the cabins)

Fraction = 29 / 80

Hence, the proportion of cabins with windows is 29/80.

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The expected value of Alice's infinite decimal number is 0.45 or 9/2in reduced form.

To find the expected value of the infinite decimal generated by rolling the fair 6-sided die with the given numbers, we can consider the expected value of each digit's contribution and sum them up.

The possible digits are 1, 2, 3, 5, 7, and 9. The probability of rolling each digit is 1/6 since the die is fair.

Let's calculate the expected value for each digit:

Probability of rolling 1: 1/6

Expected contribution: 1 x (1/6) = 1/6

Probability of rolling 2: 1/6

Expected contribution: 2 x (1/6) = 1/3

Probability of rolling 3: 1/6

Expected contribution: 3 x (1/6) = 1/2

Probability of rolling 5: 1/6

Expected contribution: 5 x (1/6) = 5/6

Probability of rolling 7: 1/6

Expected contribution: 7 * (1/6) = 7/6

Probability of rolling 9: 1/6

Expected contribution: 9 x (1/6) = 3/2

Now, let's sum up the expected contributions for each digit:

(1/6) + (1/3) + (1/2) + (5/6) + (7/6) + (3/2)

Combine the fractions:

(1/6) + (2/6) + (3/6) + (5/6) + (7/6) + (9/6)

Now, simplify the fractions:

(27/6)

Reduce the fraction:

(9/2)

So, the expected value of the infinite decimal generated by Alice's rolling is 9/2.

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Answer:

B-)

Step-by-step explanation:

Answer:

$10.50 would be the cost for three bags

Step-by-step explanation:

17.50 divided by 5 gives you the cost for one bag which is $3.50. $3.50 multiplied by 3 gives you $10.50

Answer:

10.5$

Step-by-step explanation:

Cost of 1 bag=17.5$ ÷ 5 = 3.5$

Cost of 3 bags=3 x 3.5 = 10.5$

therefore he will spend 10.5 $

Closure is one of the Gestalt principles of grouping which states that elements are perceived as being grouped together if they are near each other and form a closure.

Proximity is another Gestalt principle of grouping which states that elements that are close together are perceived as being related. In the illustration below, the three squares appear to be grouped together because of their proximity to each other.

Continuity is another Gestalt principle of grouping which states that elements are perceived as being grouped together if they are arranged in a continuous line or curve. In the illustration below, the three triangles appear to be grouped together because they are arranged in a continuous line.

Illusory contours is another Gestalt principle of grouping which states that elements are perceived as being grouped together if they create an illusion of a contour or shape.

Similarity is another Gestalt principle of grouping which states that elements are perceived as being related if they have similar characteristics or features. In the illustration below, the two triangles appear to be grouped together because they are the same color and size.

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The equation of the line that has a slope of 4 and passes through (-5, 12) will be y = 4x - 8.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is 4. Then the equation of the line is given as,

y = 4x + c

The equation of the line is passing through (-5, 12), then the value of 'c' is calculated as,

12 = 4 (5) + c

c = - 8

Then the equation that represents the line will be y = 4x - 8.

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Answer: It's good to think about things before doing them because it is more thought out and you have a better chance of getting things correct whereas without thinking your most likely going to get it wrong. Without thinking through your options you are basically guessing the answer. I hope this helped you have a great day and god bless you :D

7h-15h+40=-72

40+72=15h-7h

112=8h

h=14

Hi there!

\(\large\boxed{2* 10^{2} \text{ or } 200 \text{ times greater} }\)

To solve, we can divide the two:

\(\frac{3.4*10^{10} }{1.7*10^{8} }\)

Divide the constants and the exponents. Use the division property of exponents:

\(\frac{3.4}{1.7} = 2 \\\\\frac{10^{10} }{10^{8} } = 10^{10-8} = 10^{2}\)

Combine the two:

2 × 10² or 200

Answer:

i think 20..

Step-by-step explanation:

Hope it helps

We plot the points `(0, π/2)` and `(0, 3π/2)`. Given the polar curve `r = 2(1 + sin θ)`. We have to find the values of θ for which the polar curve has horizontal tangents or vertical tangents and then graph the polar curve using those tangents as well by plotting the polar points corresponding to where these vertical and horizontal tangents occur.1.

To find the values of θ for which the polar curve has horizontal tangents, we differentiate the given curve with respect to θ. `r = 2(1 + sin θ)`

Differentiating w.r.t θ, `dr/dθ = 2cos θ`. The tangent is horizontal where `dr/dθ = 0`. Therefore, `2cos θ = 0` or `cos θ = 0`. This gives θ = π/2 and θ = 3π/2.2. To find the values of θ for which the polar curve has vertical tangents, we differentiate the given curve with respect to θ. `r = 2(1 + sin θ)`

Differentiating w.r.t θ, `dr/dθ = 2cos θ`The tangent is vertical where `dθ/dr = 0`. Therefore, `cos θ = 0`. This gives θ = π/2 and θ = 3π/2. Now, we graph the polar curve using the tangent points obtained above. We use the fact that at `θ = π/2` and `θ = 3π/2`, the curve intersects the x-axis (i.e., polar axis).

Hence, we plot the points `(0, π/2)` and `(0, 3π/2)`.

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Answer:

1) 20

2) 60

3) 10

4) 90

Step-by-step explanation:

1. first quartile is the beginning of the box

2. third quartile is the end of the box

3. lowest is the first point of the graph

4. vice versa of 3

Answer:

i. <DCB = \(53.13^{o}\)

ii. Sin of <DCB = 0.8

Step-by-step explanation:

Let <DCB be represented by θ, so that;

Sin θ = \(\frac{opposite}{hypotenuse}\)

Thus from the given diagram, we have;

Sin θ = \(\frac{4}{5}\)

        = 0.8

This implies that,

θ = \(Sin^{-1}\) 0.8

   = 53.1301

θ = \(53.13^{o}\)

Therefore, <DCB = \(53.13^{o}\).

So that,

Sin of <DCB = Sin \(53.13^{o}\)

                    = 0.8

Sin of <DCB = 0.8

Answer: 125lb < M < 155 lb

Step-by-step explanation:

The mean mass is 140 lb, and the deviation must be less than 15 pounds (exactly 15 is not accepted).

Then (140lb + 15lb) is not alowed, and (140lb - 15lb) is not alowed.

Then we can define M = mass.

We have the two equations:

M < 140lb + 15lb

M < 155lb

And

M > (140lb - 15lb)

M > 125lb

If we write these two relations togheter, we get:

125lb < M < 155 lb