Define a sample space and count the number of sample points in the sample space for each of the following experiments. a. Select at random a set of 5 questions from a set of 15 questions. b. Form by random selection a committee of 5 from a membership of 20.

The expression that will help to calculate the area of the figure is A = (n-6)² and the area will be 25 units² when n = 11.

A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these.

A single term or a collection of phrases can be used to create an algebraic expression.

For instance, 4x and y are the two terms in the formula 4x + y.

So, we have a square as a figure.

The side of the figure is (n - 6).

Now, the expression to find the area of the square will be:

A = (n-6)²

Now, evaluate when n = 11 as follows:

A = (n-6)²

A = (11-6)²

A = (5)²

A = 25 units²

Therefore, the expression that will help to calculate the area of the figure is A = (n-6)² and the area will be 25 units² when n = 11.

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Answer:

\(\sqrt{2}\)

The answer is \(\sqrt{2}\) because it equals an irrational number. ( \(1.41421356237\) )

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Answer:

I think the constraint of proportionality is 25 because each dot it increases buy 25.

I also believe that at 10 the total should be at 225.

Answer and Step-by-step explanation:

For this triangle, to find x, we will use the cosine trigonometric function.

cosine functions look like this:

\(cos(\theta) = \frac{adjacent}{hypotenuse}\)

(The weird looking symbol is called theta, and represents an angle measurement)

Plug in the values into the equation.

cos(42) = \(\frac{x}{15}\)

Multiply both sides by 15.

15(cos(42)) = x

Plug into a calculator.

11.1472 is the answer.

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Answer:

i think 315

Step-by-step explanation:

6*12/2

72/2

36

Ans:36

Your welcome

According to the question The estimated value of \(\( Y \)\) for an individual with an age of 25 and male gender is 327.

Let's assume we want to estimate the value of \(\( Y \)\) for a given age \((\( \times 1 \))\) and gender \((\( \times 2 \))\) using the provided regression equation:

\(\( E(Y) = 30 + 2(\times 1) - 3(\times 2) + 10(\times 1 \times 2) \)\)

Let's say we have an individual with an age of 25 and is male (gender \(\( \times 2 = 1 \))\). We can substitute these values into the equation and solve for \(\( E(Y) \):\)

\(\( E(Y) = 30 + 2(25) - 3(1) + 10(25)(1) \)\)

\(\( E(Y) = 30 + 50 - 3 + 250 \)\)

\(\( E(Y) = 327 \)\)

Therefore, the estimated value of \(\( Y \)\) for an individual with an age of 25 and male gender is 327.

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Answer:

 point slope form: y - y1 = m(x - x1)

m = slope, (x1, y1) is a point on the line

y - (-9) = 2(x - 1)

y + 9 = 2(x-1)

Step-by-step explanation:

Answer:

  82.4 mg/mm²

Step-by-step explanation:

You want to convert 8.24 g/cm² to units of mg/mm².

Multiply by the conversion factors that cancel the unwanted units, leaving the wanted units.

  \(\dfrac{8.24\text{ g}}{\text{cm}^2}=\dfrac{8.24\text{ g}}{\text{cm}^2}\cdot\dfrac{1000\text{ mg}}{\text{g}}\cdot\left(\dfrac{1\text{ cm}}{10\text{ mm}}\right)^2=\dfrac{8.24\cdot1000\text{ mg}}{100\text{ mm}^2}\\\\=\boxed{82.4\text{ mg/mm$^2$}}\)

The profit should be greater than or equal to $297 in order for Mr. Chan to make a profit by selling his shares.

To determine the profit Mr. Chan can make by selling his shares, we need to calculate the difference between the selling price and the purchase price of each share and then multiply it by the number of shares sold.

Let's denote the profit as 'p'. The selling price per share is $3.80, and the purchase price per share is $0.50. Mr. Chan has 90 shares.

The profit made from selling the shares can be calculated as:

Profit (p) = Selling Price per Share - Purchase Price per Share

Since Mr. Chan can sell any number of shares (from 0 to 90), we need to multiply the profit per share by the number of shares sold.

The inequality describing the profit Mr. Chan can make by selling his shares is:

p >= (Selling Price per Share - Purchase Price per Share) * Number of Shares

Substituting the given values:

p >= ($3.80 - $0.50) * 90

Simplifying the expression:

\(p\ ^ > _- $ 3.30 * 90\\p\ ^ > _- $297\)

Therefore, the inequality describing the profit Mr. Chan can make by selling his shares is p >= $297. This means that the profit should be greater than or equal to $297 in order for Mr. Chan to make a profit by selling his shares.

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Answer: No, because they are not the same in slope - intercept form

Step-by-step explanation:

    First, we will distribute and simplify into slope-intercept form.

   Equation 1:

y - 3 = 4(x - 2)

y = 4(x - 2) + 3

y = 4x - 8 + 3

y = 4x - 5

   Equation 2:

y + 2 = 4(x + 7)

y = 4(x + 7) - 2

y = 4x + 28 - 2

y = 4x + 26

      We see that the answer to this question is "No, because they are not the same in slope - intercept form" as they have different y-intercepts, one being -5 and one being 26.

When reading a buret with graduated markings at every 0.1 ml, your recorded volume should read to a) hundredths place.

A burette is a long tube-shaped glass instrument with scale lines like a measuring pipette or measuring cup with the same cross section from top to bottom. At the bottom of this tool is equipped with a faucet as a place for the solution to come out at the mouth of the burette.

The function of the burette is as a tool to measure the solution based on the volume released. The burette size usually has a volume of 25 / 50 ml.

If the burette is being used, it must be supported firmly with a stand equipped with clamps to clamp the burette. Make sure that when clamping the burette in the stand and clamp the position of the burette must be perpendicular so that the scale reading is correct and does not cause paralax errors.

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Answer:

r=60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

3-r/8=-9/2

r/8=3-(-9/2)

r/8=3+9/2

r/8=6/2+9/2

r/8=15/2

r=(15/2)*(8/1)

r=120/2

r=60

Answer:

x ≥ -1

Step-by-step explanation:

The domain is all the possible x-values of the function.

Reading from left to right, the first x-value is x = -1 (which is included because the dot is filled in.) From there, the graph goes to the right, towards infinity.

So x is greater than or equal to -1.

x ≥ -1

From the given diagram we get that:

Subtracting 4x from the above equation we get:

Adding 1 to the above equation we get:

Dividing the above equation by 6 we get:

Therefore, the length of the given rectangle is:

Now, since the area of a rectangle is the length times the width, we can set the following equation:

Dividing the above result by 4cm we get:

Answer: The width of the given rectangle is 5cm.

Solution :

Given : \($T(x)=7-9(x-2)^2-3(x-2)^3$\)

a). f(2) = T(2) = 7

    \($\frac{f""(2)}{2!} =-9$\)  , so f''(2) = \($-18$\)

b).  Yes, since f'(2) = T'(2) \($=$\) 0, \($f$\) does have the critical point at \($x=2.$\)

   Since f''(2) = \($-18$\) < 0, \($f(2)$\) is relative maximum value.

c).  \($f(0)=T(0)=-5$\)

   It is also not possible for determining if \($f$\) has a critical point at x = 0 because \($T(x)$\)   gives exact information only at \($x=2.$\)

d). The Lagrange \($\text{error}$\) bound \($=\frac{6}{4!}|0-2|^4= 4$\)

     \($f(0) \leq T(0)+4 = -1$\)

     Therefore, \($f(0)$\) is negative.

we know the 100% or total is 50 hours, and walking was only 10 hours.

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 50&100\\ 10&x \end{array}\implies \cfrac{50}{10}=\cfrac{100}{x}\implies 5=\cfrac{100}{x}\implies 5x=100 \\\\\\ x=\cfrac{100}{5}\implies x=20\)

Minimum value of Z = 395.84, x = 5.5, y = 28.67 (rounded to 2 decimal places).

In order to minimize Z=8x+12y subject to the constraints 4x+6y≥214, 4x+5y > 9, x>0, y20, we need to graph the constraints to get the feasible region. The graph is shown below:

To find the minimum value of Z, we need to find the point in the feasible region where Z is minimized. We can use the corner point method to do this. The corner points of the feasible region are (0,35.67), (2.25,33), (5.5,28.67), and (53.5,0).

We can substitute each of these points into the objective function

Z=8x+12y to find the minimum value.

Z at (0,35.67) is 428.04, Z at (2.25,33) is 416.5, Z at (5.5,28.67) is 395.84, and Z at (53.5,0) is 428.

We see that the minimum value of Z is 395.84, which occurs at the point (5.5,28.67).

Therefore, the solution is x=5.5 and y=28.67 (rounded to 2 decimal places).

Minimum value of Z = 395.84, x = 5.5, y = 28.67 (rounded to 2 decimal places).

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I. After 10 tosses: The results can vary, as it is a random process.

II. After 50 tosses: Again, the results can vary, but on average, we would expect to have around 25 heads and 25 tails.

III. After 100 tosses: Similarly, the results can vary, but on average, we would expect to have around 50 heads and 50 tails.

IV. After 200 tosses: Once more, the results can vary, but on average, we would expect to have around 100 heads and 100 tails.

For a fair coin, the probability of getting heads or tails is 1/2 or 0.5. Using this probability, we can simulate the coin tosses and record the results.

I. After 10 tosses:

The number of heads could vary, but it is likely to be around 5. However, there is a possibility of it being slightly higher or lower due to randomness.

II. After 50 tosses:

Again, the number of heads is expected to be around 25, but there can be some deviation. It is possible to have results like 23 or 27 heads.

III. After 100 tosses:

The number of heads is likely to be close to 50, but some variance can occur. Results such as 48 or 52 heads are within the realm of possibility.

IV. After 200 tosses:

Here, the number of heads should converge closer to 100. However, there can still be some fluctuation due to chance. The actual number of heads can be in the range of 95 to 105.

It is important to note that these results are based on the assumption of a fair coin. However, due to the inherent randomness in the process, there can be slight deviations from these expected values in any individual trial.

If you actually conduct a series of 200 coin tosses, the results could differ from the expected averages due to random variation. To obtain accurate results, it is necessary to conduct a large number of coin tosses and calculate the relative frequencies of heads and tails.

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To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, we need to consider the time taken by each person to complete each job. Using the given Table 50, we can analyze the data and identify the optimal assignment.

By examining Table 50, we can identify the minimum time taken by each person for each job. Starting with Job 1, we see that Person 4 takes the least time of 16 hours. Moving to Job 2, Person 2 takes the least time of 18 hours. For Job 3, Person 1 takes the least time of 25 hours. Lastly, for Job 4, Person 4 takes the least time of 14 hours.

Therefore, the optimal assignment would be:

- Person 4 for Job 1 (16 hours)

- Person 2 for Job 2 (18 hours)

- Person 1 for Job 3 (25 hours)

- Person 4 for Job 4 (14 hours)

This assignment ensures that the minimum total time is required to perform the four jobs, resulting in a total time of 16 + 18 + 25 + 14 = 73 hours.

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If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.

Let h represent hard cover

Let p represent paperbacks

Formulate an equation

h + p= 8.......(1)

4h + 2p= 26......(2)

Multiply equation (1) by -2

-2h + -2p = -16

4h  +  2p   = 26

2h  +   0p =10

2h = 10

Divide both side by 2h

h=10/2

h =5 hard covers

Paper backs

P=5-2

P=3 paper backs

Therefore If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.

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A. 130.4 pounds shows an appropriate level of precision for the scale

The quantity 0.2 pound represents readability of the digital scale. It is also known by the terms division size or resolution. The number indicates the division in digital scale. The scale division will be 20 in case 0.2 readability. Another example of readability can be understood by more simple divisions. For instance, 1 gram readability can be divided into divisions like 5 or 25 etc.

Capacity, is another term related to digital scale. It refers to the highest amount that can be weighed safely by the digital scale. Precision is defined as the total number of digits in any given number. Among the given options, the option with 4 digits will be the correct option. This is represented in option A. 130.4 pounds. Hence, it shows an appropriate level of precision.

The complete question is -

A digital scale measures weight to the nearest 0.2 pound. Which

measurement shows an appropriate level of precision for the scale?

A.130.4 pounds

B.124.75 pounds

C.125 pounds

D.120 pounds

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Answer:

6 i think

Step-by-step explanation:

Answer:

negative one third

Step-by-step explanation:

So you go to the 1 and half

The proportion that contains CD and NK is CD/NK, which is a comparison between the lengths of the two corresponding sides of the two similar shapes.

The proportion that contains CD and NK is a comparison between the lengths of the two corresponding sides of the two shapes. Since Figure ABCD and Figure MNKL are similar shapes, the lengths of their corresponding sides are in proportion. Therefore, the proportion that contains CD and NK is CD/NK.

The proportion that contains CD and NK is CD/NK, which is a comparison between the lengths of the two corresponding sides of the two similar shapes.

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The probability that at least one sensor detects the pollutant is 0.9.The probability that either only S1 or only S2 detects the pollutant is 0.5.The probability that S1 does not detect the pollutant, and S2 detects the pollutant is 0.2.The probability that S2 fails to detect the pollutant is 0.3.

The event "at least one sensor detects the pollutant" refers to the scenario where either S1 or S2 (or both) detect the excessive pollution. This can be visualized as the union of the two events: S1 detecting the pollutant (event A) and S2 detecting the pollutant (event B). The probability of event A is 0.7, the probability of event B is 0.8, and the probability of both events A and B occurring together is 0.6. By applying the principle of inclusion-exclusion, we can calculate the probability of the union as P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.7 + 0.8 - 0.6 = 0.9.

The event "either only S1 or only S2 detects the pollutant" can be represented as the exclusive OR (XOR) of the two events: S1 detecting the pollutant without S2 detecting it (event A) and S2 detecting the pollutant without S1 detecting it (event B). Since the probabilities of events A and B are not explicitly given, we assume that they are equal. Let's denote this probability as p. Therefore, the probability of either event A or event B occurring is 2p. Given that the sum of probabilities of all possible outcomes is equal to 1, we have 2p + P(A ∩ B) = 1. We are also given that P(A ∩ B) = 0.6. Solving these equations simultaneously, we find that p = 0.2. Hence, the probability of the event "either only S1 or only S2 detects the pollutant" is 2p = 2 × 0.2 = 0.4.

The event "S1 does not detect, and S2 detects the pollutant" is the complement of S1 detecting the pollutant (event A) intersected with S2 detecting the pollutant (event B). The probability of event A is 1 - P(S1 detects) = 1 - 0.7 = 0.3. The probability of event B is P(S2 detects) = 0.8. The probability of both events A and B occurring together is given as P(A ∩ B) = 0.6. Therefore, the probability of the event "S1 does not detect, and S2 detects the pollutant" is P(A' ∩ B) = P(A ∩ B') = P(A) - P(A ∩ B) = 0.3 - 0.6 = 0.2.

The event "S2 fails to detect the pollutant" is the complement of S2 detecting the pollutant. Therefore, the probability of this event is 1 - P(S2 detects) = 1 - 0.8 = 0.2.

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Answer:

Go back to -1

Step-by-step explanation:

4 - -5 = -1