A hypothesis is _____ Question 20 options: a proven scientific fact an instrument that is used to examine environmental conditions a testable proposition that explains an observed phenomenon or answers a question the design of an experiment that can be used in scientific inquiry a prediction about something that has not yet been observed

Answer:

c = 6*e^(-10) -  e^(-5)  ( ≈ -e⁻⁵ = -6.74*10⁻³)

Step-by-step explanation:

for the function

y=c*e^(−2x)+e^(−x)

as a solution of y'+2y=e^(−x)

then for  y(x=−5)=6

6 =c*e^(−2(-5))+e^(−(-5)) = c*e^10 + e^5

6 = c*e^10 + e^5

c = (6 -  e^5)/*e^10 = 6*e^(-10) -  e^(-5)

c = 6*e^(-10) -  e^(-5)  ( ≈ -e⁻⁵ = -6.74*10⁻³)

Answer:

mi/hr • min does not equal mi. You must convert 30 minutes to hours.

Step-by-step explanation:

I got it correct on TTM

Answer:

a) [tex] P(X \leq 100) = 1- e^{-0.01342*100} =0.7387[/tex]

[tex] P(X \leq 200) = 1- e^{-0.01342*200} =0.9317[/tex]

[tex] P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930[/tex]

b) [tex] P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498[/tex]

c) [tex] m = \frac{ln(0.5)}{-0.01342}=51.65[/tex]

d) [tex] a = \frac{ln(0.05)}{-0.01342}=223.23[/tex]

Step-by-step explanation:

Previous  concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

[tex]P(X=x)=\lambda e^{-\lambda x}[/tex]

Solution to the problem

For this case we have that X is represented by the following distribution:

[tex] X\sim Exp (\lambda=0.01342)[/tex]

Is important to remember that th cumulative distribution for X is given by:

[tex] F(X) =P(X \leq x) = 1-e^{-\lambda x}[/tex]

Part a

For this case we want this probability:

[tex] P(X \leq 100)[/tex]

And using the cumulative distribution function we have this:

[tex] P(X \leq 100) = 1- e^{-0.01342*100} =0.7387[/tex]

[tex] P(X \leq 200) = 1- e^{-0.01342*200} =0.9317[/tex]

[tex] P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930[/tex]

Part b

Since we want the probability that the man exceeds the mean by more than 2 deviations

For this case the mean is given by:

[tex] \mu = \frac{1}{\lambda}=\frac{1}{0.01342}= 74.516[/tex]

And by properties the deviation is the same value [tex] \sigma = 74.516[/tex]

So then 2 deviations correspond to 2*74.516=149.03

And the want this probability:

[tex] P(X > 74.516+149.03) = P(X>223.547)[/tex]

And we can find this probability using the complement rule:

[tex] P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498[/tex]

Part c

For the median we need to find a value of m such that:

[tex] P(X \leq m) = 0.5[/tex]

If we use the cumulative distribution function we got:

[tex] 1-e^{-0.01342 m} =0.5[/tex]

And if we solve for m we got this:

[tex] 0.5 = e^{-0.01342 m}[/tex]

If we apply natural log on both sides we got:

[tex] ln(0.5) = -0.01342 m[/tex]

[tex] m = \frac{ln(0.5)}{-0.01342}=51.65[/tex]

Part d

For this case we have this equation:

[tex] P(X\leq a) = 0.95[/tex]

If we apply the cumulative distribution function we got:

[tex] 1-e^{-0.01342*a} =0.95[/tex]

If w solve for a we can do this:

[tex] 0.05= e^{-0.01342 a}[/tex]

Using natural log on btoh sides we got:

[tex] ln(0.05) = -0.01342 a[/tex]

[tex] a = \frac{ln(0.05)}{-0.01342}=223.23[/tex]

The question involves applying the exponential distribution formula to calculate certain probabilities and expectations involving the distances travelled by kangaroo rats. You need to calculate these by using the formula, P(X≤x) = 1 - e^(-λx), and using that the standard deviation of an exponential distribution is the reciprocal of the parameter. Median and the distance that only 5% will exceed can be calculated by setting the P(X≤a) = 0.50 and 0.95, respectively.

This question surrounds the concepts within probability theory and specifically the exponential distribution.

Firstly, understand that an exponential distribution can be described by the formula: P(X≤x) = 1 - e^(-λx). Given λ = 0.01342, you can solve for Part (a), calculate the probabilities for distances at most 100m, 200m, and between 100 and 200m. Plug the distances into the formula and calculate.

For part (b), you need to know that the standard deviation of an exponential distribution is the reciprocal of the parameter (1/λ). Calculate the mean and standard deviation and use these values to find the required probability.

For Part (c), set P(X≤ a) = 0.50 and solve for 'a', this will give you the median.

For Part (d), set P(X≤ a) = 0.95 and solve for 'a', this will give you the distance that only 5% of animals will exceed.

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Answer:

[tex]P(junior)=\frac{9}{35}[/tex]

[tex]P(freshmen)=\frac{5}{35}=\frac{1}{7}[/tex]

Step-by-step explanation:

In a class there are 13 seniors, 9 juniors, 8 sophomores and 5 freshmen

Total number of students= [tex]13+9+8+5=35[/tex]

one student is selected at random from this class, selected student is Junior

there 9 juniors in the class

[tex]P(junior)= \frac{juniors}{total} =\frac{9}{35}[/tex]

there 5 freshmen in the class

[tex]P(freshmen)= \frac{freshmen}{total} =\frac{5}{35}=\frac{1}{7}[/tex]

Answer: 13 outcomes

Step-by-step explanation:

Given:

She wants to get a gift from the following choices;

- one of five books

- one of four ties

- one of four X-box

Since, the three groups of choices are joined with "OR" but not "AND" that means she is getting just one gift from any of the 3 groups.

Total number of gift she needed = 1

Total number of choices = 3 groups with total of 13 options

N = 13P1 = 13!/(13-1)! = 13!/12! =13

N = 13 outcomes.

Answer:

[tex]\frac{a(450-8a^2)}{4}[/tex]

is the volume in terms of side a

Step-by-step explanation:

Given that you I built a storage shed in the shape of a rectangular box on a square base. The material that I used for the base cost $4 per square foot, the material for the roof cost $2 per square foot, and the material for the sides cost $2.50 per square foot; and I spent $450 altogether on material for the shed.

Let a be the side of square and h be the height

Total cost of materials = cost for floor + cost for roof + cost for sides

= area of floor (4) + lateral area (2.50)+roof area (2)

[tex]=4a^2+4ah+4a^2\\=8a^2+4ah = 450[/tex][tex]h = \frac{450-8a^2}{4a}[/tex]

Now coming to volume

Volume = V = lbh = [tex]a^2 h\\= a^2*\frac{450-8a^2}{4a} \\=\frac{a(450-8a^2)}{4}[/tex]

Answer:

not

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}-2&4\\1&3\end{array}\right] *\left[\begin{array}{ccc}-2&1\\3&7\end{array}\right]=[/tex]

First is A and Second is B

Let's find A*B

[tex]\left[\begin{array}{ccc}-2(-2)+4*3&-2*1+4*7\\1(-2)+3*3&1*1+3*7\end{array}\right] =\left[\begin{array}{ccc}16&26\\7&22\end{array}\right][/tex]

b)

[tex]\left[\begin{array}{ccc}-2&1\\3&7\end{array}\right] \left[\begin{array}{ccc}-2&4\\1&3\end{array}\right] =[/tex]

Now let's find B*A

[tex]\left[\begin{array}{ccc}-2(-2)+1*1&-2*4+1*3\\3(-2)+7*1&3*4+7*3\end{array}\right] =\left[\begin{array}{ccc}5&-5\\1&23\end{array}\right][/tex]

c) They are not

Answer:

The x-coordinate of the solution is 3.

The ordered pair that is the solution to the system lies in Quadrant I

The y-coordinate of the solution is 4

The graph in the attached figure

Step-by-step explanation:

we have

[tex]8x+6y=48[/tex] ----> equation A

[tex]2x-3y=-6[/tex] ----> equation B

To graph the system of equations , find the intercepts of each line

Line A

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

[tex]8(0)+6y=48\\y=8[/tex]

The y-intercept is the point is (0,8)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

[tex]8x+6(0)=48\\x=6[/tex]

The x-intercept is the point is (6,0)

Plot the points (0,8) and (6,0), and connect them to graph the line A

Line B

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

[tex]2(0)-3y=-6\\y=2[/tex]

The y-intercept is the point is (0,2)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

[tex]2x-3(0)=-6\\x=-3[/tex]

The x-intercept is the point is (-3,0)

Plot the points (0,2) and (-3,0), and connect them to graph the line B

Remember that the solution of the system of equations is the intersection point both graphs

The solution of the system is the point (3,4)

The graph in the attached figure

Verify each statement

case 1) The x-coordinate of the solution is −3

The statement is false

Because the x-coordinate of the solution is 3

case 2) The x-coordinate of the solution is 3.

The statement is true (see the explanation)

case 3) The ordered pair that is the solution to the system lies in Quadrant I

The statement is true

Because, the x-coordinate and the y-coordinate of the solution are positive values

case 4) The y-coordinate of the solution is 4

The statement is true (see the explanation)

case 5) The ordered pair that is the solution to the system lies in Quadrant II

The statement is false

Because, the ordered pair that is the solution to the system lies in Quadrant I

case 6) The y-coordinate of the solution is 3

The statement is false

Because, the y-coordinate of the solution is 4

Answer:

We conclude that there is not enough evidence to support the claim  compute technique performs differently than the traditional method.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101 hours

Sample mean, [tex]\bar{x}[/tex] =100 hours

Sample size, n = 140

Alpha, α = 0.01

Population standard deviation, σ = 6 hours

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 101\text{ hours}\\H_A: \mu \neq 101\text{ hours}[/tex]

We use Two-tailed z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{100 - 101}{\frac{6}{\sqrt{140}} } = -1.972[/tex]

Now, [tex]z_{critical} \text{ at 0.01 level of significance } = \pm 2.58[/tex]

Since,  

The calculated z statistic lies in the acceptance region, we fail to reject the null hypothesis and accept it.

We conclude that there is not enough evidence to support the claim that compute technique performs differently than the traditional method.

To determine if the technique performs differently than the traditional method, a hypothesis test is performed by comparing the test statistic to the critical value(s) from the t-distribution.

To determine if there is sufficient evidence to support the claim that the CAI technique performs differently than the traditional method, we can perform a hypothesis test. First, we state our null hypothesis (H0) and alternative hypothesis (Ha). H0: The mean time for obtaining a flying license using CAI is equal to 101 hours. Ha: The mean time for obtaining a flying license using CAI is different from 101 hours.

Next, we calculate the test statistic using the formula z = (X - µ) / (σ / √n), where X is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values: X = 100, µ = 101, σ = 6, and n = 140, we can calculate the test statistic.

Using a significance level of 0.01, we compare the test statistic to the critical value(s) from the t-distribution. If the test statistic falls outside the critical region, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the technique performs differently than the traditional method.

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Answer:

a) s = 8.81

b) Q1 = 43.4, Q2 = 49.4, Q3 = 57.35

c) See below

Step-by-step explanation:

(a) Find the standard deviation of the reflectance for these smolts. (Round your answer to two decimal places.)

In order to find the standard deviation, we need the mean first. The mean is defined as

[tex]\bar x=\displaystyle\frac{\displaystyle\sum_{i=1}^{n}x_i}{n}[/tex]

where the [tex]x_i[/tex] are the values of the data collected and n=50 the size of the sample.

So, the mean is

[tex]\bar x=50.882[/tex]

Now, the standard deviation of the sample is defined as  

[tex]s=\sqrt{\displaystyle\frac{\displaystyle\sum_{i=1}^n(x_i-\bar x)^2}{n-1}}[/tex]

and we have that our standard deviation is

s = 8.81

(b) Find the quartiles of the reflectance for these smolts

To find the quartiles, we must sort the data from lowest to largest:  

33.6,  37.7,  38.3,  38.7,  42,  42,  42.2,  42.4,  42.7,  42.8,  42.9,  43.1,  43.7,  43.8,  44.2,  44.6,  45.5,  45.7,  46.3,  46.6,  47.4,  47.6,  47.7,  47.9,  49.2,  49.6,  50.5,  50.9,  51.3,  53,  53.9,  54.8,  54.9,  55.5,  56,  56,  56.2,  57.1,  57.6,  58.3,  59,  59.5,  60.4,  63.2,  63.4,  63.5,  64.6,  68,  69.1,  69.2

The first quartile is the number between the 12th and the 13th data (so 25% of the data are below it and 75% above it)

So the 1st quartile is

[tex]Q_1=\displaystyle\frac{43.1+43.7}{2}=43.4[/tex]

The 2nd quartile is the median, the point between the 25th and 26th data, it splits the data in two halves.

[tex]Q_2=\displaystyle\frac{49.2+49.6}{2}=49.4[/tex]

The 3rd quartile is the point between the 38th and 39th data (so 75% of the data are below it and 25% above it)

[tex]Q_3=\displaystyle\frac{57.1+57.6}{2}=57.35[/tex]

(c) Do you prefer the standard deviation or the quartiles as a measure of spread for these data? Give reasons for your preference.

In this case, we prefer the quartiles as a measure of spread since the data are very scattered around the mean and there is no a central tendency.

Answer:

Reword the question so that is balanced or increase the sample size so that more people respond to the question.

Step-by-step explanation:

Given that the owner of a shopping  mall wishes to expand the number of shops available in the food court. He has a market researcher survey the first 120 customers who come into the food court during weekend morning to determine what types of food the shoppers would like to see added to the food court.

This has sample bias.

Because first 120 customers may not represent the entire population of all customers. There may be bias in selecting the weekend morning.

So this is sampling bias.

Remedy would be

Reword the question so that is balanced or increase the sample size so that more people respond to the question.

Final answer:

The cause of bias is sampling bias. The best remedy is to increase the sample size.

Explanation:

The cause of bias in the given scenario is sampling bias.

The best remedy to this problem would be to increase the sample size so that more people respond to the question. This will help in making the sample more representative of the population and reduce the bias.

Other possible remedies could include asking customers throughout the day on both weekdays and weekends, or rewording the question so that it is balanced.

Answer:

Step-by-step explanation:

Given that two random variables X and Y are independent. Each has a binomial distribution with success probability 0.4 and 2 trials.

When x and y are independent joint probability would be product of individual probabilities

pdf of X

X is Binom (2,0.4)

and Y is Binomi (2,0.4)

Hence joint distribution of XY would be

P(X=x, Y=y) =[tex]2Cx (0.4)^x (0.6)^{2-x} *2Cy (0.4)^y (0.6)^{2-y}[/tex]

for x=0,1,2 and y =0,1,2

b) Joint probability using table

PDF of X is

X        0            1           2

p       0.36    0.48      0.16

and same for Y also

Joint prob would be

X  Y       0            1              2

0      0.1296     0.1728      0.0576

1       0.1728      0.2304     0.0768

2      0.0576     0.0768     0.0256

Joint probability distribution function are used to represent the probability of multiply variables

The joint probability distribution function is [tex]f(x,y) = ^2C_x *0.4^x * 0.6^{2- x} *^2C_y * 0.4^y * 0.6^{2- y}[/tex]

The given parameters are:

[tex]p = 0.4[/tex] --- the probability of success

[tex]n = 2[/tex] ----the number of trials

The joint probability distribution function f(x,y) is calculated as:

[tex]f(x,y) = ^nC_x * p^x * (1 -p)^{n- x} *^nC_y * p^y * (1 -p)^{n- y}\\[/tex]

So, we have:

[tex]f(x,y) = ^2C_x *0.4^x * (1 -0.4)^{2- x} *^2C_y * 0.4^y * (1 -0.4)^{2- y}[/tex]

Evaluate the differences

[tex]f(x,y) = ^2C_x *0.4^x * 0.6^{2- x} *^2C_y * 0.4^y * 0.6^{2- y}[/tex]

The above represents the joint probability distribution function f(x,y)

When x = 0, y = 0;

We have:

[tex]f(0,0) = 0.130[/tex]

When x = 0, y = 1;

We have:

[tex]f(0,1) = 0.173[/tex]

When x = 0, y = 2;

We have:

[tex]f(0,2) = 0.058[/tex]

When x = 1, y = 0;

We have:

[tex]f(1,0) = 0.173[/tex]

When x = 1, y = 1;

We have:

[tex]f(1,1) = 0.230[/tex]

When x = 1, y = 2;

We have:

[tex]f(1,2) = 0.077[/tex]

When x = 2, y = 0;

We have:

[tex]f(2,0) = 0.058[/tex]

When x = 2, y = 1;

We have:

[tex]f(2,1) = 0.077[/tex]

When x = 2, y = 2;

We have:

[tex]f(2,2) = 0.026[/tex]

So, the joint probability as a table is:

X /Y       0            1              2

0      0.1296     0.1728      0.0576

1       0.1728      0.2304     0.0768

2      0.0576     0.0768     0.0256

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Answer:

36

Step-by-step explanation: thats what i got

Answer:the speed of postman from A to B is 6 km/hr

Step-by-step explanation:

Let x represent the speed of the postman when moving from A to B.

From point A, the postman delivered a letter to point B in half hour.

Distance = speed × time

It means that

Distance from A to B = 0.5 × x = 0.5x

In back way he reduced speed by 1km/h and gets back in 36 min. It means that his speed on returning back would be (x - 1)km/h

Converting 36 minutes to hour, it becomes

36/60 = 0.6 hours

Distance from B to A = 0.6(x - 1)

Since distance from A to B = distance from B to A, then

0.5x = 0.6(x - 1) = 0.6x - 0.6

0.6x - 0.5x = 0.6

0.1x = 0.6

x = 0.6/0.1 = 6

Answer:b. 0.22

Step-by-step explanation:

Since the lengths of adult walleye fishes are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = lengths of walleye fishes.

µ = mean length

σ = standard deviation

From the information given,

µ = 44 cm

σ = 4 cm

We want to find the probability or fraction of fishes that are greater than 41 cm in length. It is expressed as

P(x > 41) = 1 - P(x ≤ 41)

For x = 41,

z = (41 - 44)/4 = - 0.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.22

To find the fraction of fish that are greater than 41 cm in length, calculate the z-score with the mean and standard deviation.

To find the fraction of fish that are greater than 41 cm in length, we need to calculate the z-score of 41 cm using the mean and standard deviation. The z-score formula is z = (x - μ) / σ. Plugging in the values, we have z = (41 - 44) / 4 = -0.75. We can then look up the corresponding value on the z-table to find the fraction of fish with a length greater than 41 cm, which is approximately 0.7734. Therefore, the answer is option d, 0.75.

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Answer:

D

Step-by-step explanation:

The correlation coefficient r=-0.84 denotes that there is inverse relationship between x and y. It means that as the x values increase the y values decrease whereas as the x values decreases the y-values increases. Also, r=-0.84 denotes the strong relationship between  x and y because it is close to 1. So, r=-0.84 denotes that there is strong linear relationship between x and y with smaller x values tending to be associated with larger y values.

The correlation coefficient of -0.84 indicates a strong inverse relationship between x and y, with smaller x values generally corresponding to larger y values.

Based on the given correlation coefficient of -0.84, the correct answer is option d. This option states that there is a strong linear relationship between variables x and y, with smaller x values tending to be associated with larger values of the y variable.

A correlation coefficient communicates both the strength and direction of a linear relationship between two variables. In this context, a coefficient of -0.84 indicates a strong relationship (values close to -1 or 1 denote strong relationships), and because the value is negative, it reflects an inverse or negative correlation, meaning y tends to decrease as x increases, and vice versa.

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Answer:

24

Step-by-step explanation:

A 2024-T4 aluminum tube with an outside diameter of 3.6 in. will be used to support a 24-kip load. If the axial stress in the member must be limited to 6.4 ksi, determine the wall thickness required for the tube.

Answer: 0.025

Step-by-step explanation: we reject null hypothesis if p<0.05

Answer:

I also gave aadded the complete question for the expressions of the function f(x)

a) Exact value of the net signed area = 1/2 or 0.5

b) Exact average value of f = 53/30 = 1.7667

Step-by-step explanation:

The step by step explanation and calculation is attached below.

I think the answer is D. hours because its variation does not depend on another variable

Answer:

cannot say

Step-by-step explanation:

Given that Kari owns 28 golf balls. Some are green, some are blue and several are orange. One fourth are red.

With the available information we know that 7 balls are red (1/4 of 28)

No mention is made about any of the other colour.

With the available information we cannot say whether 7 gold balls are definitely green.

We are given only some are green, some blue and several other are organe.

Nothing mentioned about red in that but given 1/4 are red.

The term some is a relative term and mathematically we cannot define whether this equals 7 or not

Cannot say.

Answer:

Definitely

Step-by-step explanation:

In order to completely surround a circle, you need six circles to do that while here in the question it is mentioned that currently there are only five circles surrounding the circle, hence there is enough room to easily fit one more circle.

I just hope that you are satisfied with the answer, Best of Luck.

Final answer:

To answer the student's combinatorics question, there are a total of 8008 potential delegations, 84 of which are all men and 7924 that include at least one woman.

Explanation:

The question involves combinatorics, which is a branch of mathematics. In particular, we are dealing with combinations since the order of selection does not matter for the delegation.

Number of possible delegations:

To find the total number of delegations possible, we must select 6 individuals out of 16 (7 women + 9 men) without regard to order. This is done using the combination formula:

C(n, k) = n! / (k!(n-k)!)

So, C(16, 6) = 16! / (6!(16-6)!) = 8008

Delegations with all men:

To find the number of delegations with all men, we select 6 men out of the 9 available. Using the combination formula again:

C(9, 6) = 9! / (6!(9-6)!) = 84

Delegations with at least one woman:

To find this, we subtract the number of all-male delegations from the total number of delegations:

8008 - 84 = 7924

So, there are 7924 delegations that include at least one woman.

Final answer:

To answer the student's question about the total number of possible delegations, all male delegations, and delegations with at least one woman, combinations are used. There are 8008 total possible delegations, 84 all-male delegations, and 7924 delegations with at least one woman.

Explanation:

To solve this problem, we will use combinatorics, specifically the concept of combinations as the order in which the delegation members are selected does not matter.

a) Total number of delegations possible

The total number of ways to choose 6 members from a board of 16 (7 women + 9 men) is calculated using the combination formula C(n, k) = n!/(k!(n-k)!), where n is the total number of items, and k is the number of items to choose.

Therefore, C(16, 6) = 16!/(6!*(16-6)!) = 8008 different delegations are possible.

b) Delegations with all men

To find the number of all-male delegations, we choose 6 men from a group of 9, which is C(9, 6) = 9!/(6!*(9-6)!) = 84 delegations.

c) Delegations with at least one woman

Instead of calculating this directly, we use the complement principle. We subtract the number of all-male delegations from the total number of delegations. Thus, the number of delegations with at least one woman is 8008 - 84 = 7924 delegations.

The radius of the circumscribed circle is [tex]\( 3.2\sqrt{3} \)[/tex] centimeters.
The length of a side of the hexagon is [tex]\( 3.2\sqrt{3} \)[/tex] centimeters.
The perimeter of the hexagon is [tex]\( 19.2\sqrt{3} \)[/tex] centimeters.

Let's solve each part of the problem step by step:

a. **Find the radius of the circumscribed circle:**

The apothem of a regular polygon and the radius of the circumscribed circle are related by the formula:

[tex]\[ \text{Radius} = \frac{\text{Apothem}}{\cos(180^\circ / \text{number of sides})} \][/tex]

For a regular hexagon (6 sides), the formula becomes:

[tex]\[ \text{Radius} = \frac{4.8}{\cos(180^\circ / 6)} \][/tex]

[tex]\[ \text{Radius} = \frac{4.8}{\cos(30^\circ)} \][/tex]

[tex]\[ \text{Radius} = \frac{4.8}{\frac{\sqrt{3}}{2}} \][/tex]

[tex]\[ \text{Radius} = \frac{4.8 \times 2}{\sqrt{3}} \][/tex]

[tex]\[ \text{Radius} = \frac{9.6}{\sqrt{3}} \][/tex]

[tex]\[ \text{Radius} = \frac{9.6\sqrt{3}}{3} \][/tex]

[tex]\[ \text{Radius} = 3.2\sqrt{3} \][/tex]

b. **What is the length of a side of the hexagon?**

The length of a side of a regular hexagon can be found using the formula:

[tex]\[ \text{Side Length} = 2 \times \text{Apothem} \times \tan(180^\circ / \text{number of sides}) \]\\[/tex]

For a regular hexagon with apothem 4.8 cm:

[tex]\[ \text{Side Length} = 2 \times 4.8 \times \tan(30^\circ) \][/tex]

[tex]\[ \text{Side Length} = 2 \times 4.8 \times \frac{1}{\sqrt{3}} \][/tex]

[tex]\[ \text{Side Length} = \frac{9.6}{\sqrt{3}} \][/tex]

[tex]\[ \text{Side Length} = \frac{9.6\sqrt{3}}{3} \][/tex]

[tex]\[ \text{Side Length} = 3.2\sqrt{3} \][/tex]

c. **What is the perimeter of the hexagon?**

Since a regular hexagon has six equal sides, its perimeter is simply:

[tex]\[ \text{Perimeter} = 6 \times \text{Side Length} \][/tex]

[tex]\[ \text{Perimeter} = 6 \times 3.2\sqrt{3} \][/tex]

[tex]\[ \text{Perimeter} = 19.2\sqrt{3} \][/tex]

Answer:

Option B

Step-by-step explanation:

The data constitutes nominal scale of measurement when the observations can be classified into groups. For example, students are classified into groups on the basis of eye color. The numerical values can also be use in nominal scale for grouping. For example, the students can be categorize into 1,2 and 3  if they have brown, black and green eye color. But they have no numerical significance. Thus, data obtained from a nominal scale can be either numeric or non-numeric.

Answer: C.  [tex]0.75^4[/tex]

Step-by-step explanation:

Let x be the binomial variable that denotes the number of makes.

Since each throw is independent from the other throw , so we can say it follows Binomial distribution .

So [tex]X\sim Bin(n=4 , p=0.75)[/tex]

Binomial distribution formula: The probability of getting x success in n trials :

[tex]P(X=x)=^nC_xp^n(1-p)^{n-x}[/tex] , where p = probability of getting success in each trial.

Then, the probability of Michael Beasley making all of his next 4 free throw attempts will be :

[tex]P(X=4)=^4C_4(0.75)^4(1-0.75)^{0}[/tex]

[tex]=(1)(0.75)^4(1)\ \ [\because\ ^nC_n=1]\\\\=(0.75)^4[/tex]

Thus, the probability of Michael Beasley making all of his next 4 free throw attempts is [tex]=0.75^4[/tex]

Hence, the correct answer is C.  [tex]0.75^4[/tex].

Answer:

we CANNOT DIVIDE 3 with 6.

Step-by-step explanation:

Here,as given in the question:

Starting value = 6

Constant ratio = 1/3

Now, exponential function is obtained by the product of starting value and the constant ratio repeatedly.

⇒ f(x) = (Starting value) x (ratio)... x times

[tex]\implies f(x) = 6 (\frac{1}{3} )^x = 6 (\frac{1}{3} ) (\frac{1}{3} ) (\frac{1}{3} ) .... x[/tex]  

Now, we CANNOT DIVIDE 3 with 6 as it is in the power of x.

Hence, [tex]\implies f(x) = 6 (\frac{1}{3} )^x[/tex] and [tex]f(x) \neq 2^x[/tex]

Answer:

The student made an error by applying the exponent to the product of a and b instead of just b. The final answer should be ​f(x)=6(1/3)^x

Step-by-step explanation:

U can't multiply 6 by 1/3

Answer:

1

Step-by-step explanation:

For a quadratic equation, the roots are expressed by the quadratic formula.

x=(-b+/- Sqrt[b^2-4ac])/2a

In this case a=6, b=-7 and c=k

 So,

x=(7 +/- √[(-7)^2-4(6)(k)]/2(6))

Simplifying gives:

x=(7 +/- √[49-24k])/12

For k=0 the square root simplifies to √[49]=7 which yields roots of 7/6 and 0

For k=1 the square root simplifies to √[49-24]=√[25]=5 which yields roots of 1 and 1/6

For k=2 the square root simplifies to √[49-48]=√[1]=1 which yields roots of 2/3 and 1/2

k= 1 as other roots are fractions

Answer:

k=-5

Step-by-step explanation:

6x^2+7x+k=0 is a quadratic equation.

a= 6; b=7; c=k

Let the roots of the equation be R1 and R2

R1+R2 = -b/a = -7/6 ---------1

R1xR2 = c/a =k/6 or (R1xR2)6=k------------2

From Equation 1:

R1=-7/6-R2

We know 2R1+3R2=-4 Substituting for R1, we get

3 (-7/6-R2)+3R2=-4

R2=-5/3

R1=-7/6-(-5/3)= 1/2

Substituting these values in Eq2,

k= (-5/3 x 1/2) 6

k=-5

Answer:

The solution is (6.2,6.2)

Step-by-step explanation:

we have

[tex]0.4x+0.6y=6.2[/tex] ----> equation A

For variable x and y equal

[tex]x=y[/tex] ----> equation B

Solve the system by substitution

substitute equation B in equation A

[tex]0.4y+0.6y=6.2[/tex]

solve for y

combine like terms

[tex]y=6.2[/tex]

so

[tex]x=6.2[/tex]

therefore

The solution is (6.2,6.2)

Answer:

The coefficient is 3 and the constant is 4 in

relation to the equation mx + c where m is the coefficient of x and c is the constant.

Answer:

13

Step-by-step explanation:

The given expression is (3-2i)(3-2i)

This is of the form (a-b)(a+b)

This is equivalent to [tex]\[a^{2}-b^{2}\][/tex], where a = 3 and b=2i

= [tex]\[3^{2}-(2i)^{2}\][/tex]

= [tex]\[9-4i^{2}\][/tex]

But [tex]\[i^{2} = -1\][/tex]

= [tex]\[9-4*(-1)\][/tex]

= [tex]\[9+4\][/tex]

= [tex]\[13\][/tex]

Hence the value of the expression (3-2i)(3-2i)  is 13.