A plane flies 240 miles due north, then 320 miles due west. How
many miles must it fly to return to its starting point by the shortest
route? (Enter your answer without units.)

Answer:

[tex]\boxed{\sf \ \ \ 49a^8b^6c^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex](-7a^4b^3c)^2=(-1)^27^2a^{4*2}b^{3*2}c^2=49a^8b^6c^2[/tex]

as

[tex](-1)^2=1[/tex]

Answer:

a) P(x > 43) = 0.9599

b) P(x < 42) = 0.0228

c) P(x > 57.5) = 0.03

d) P(x = 42) = 0.

e) P(x<40 or x>55) = 0.1118

f) 43.42

g) Between 46.64 and 53.36.

h) Above 45.852.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 50, \sigma = 4[/tex]

a) x>43

This is 1 subtracted by the pvalue of Z when X = 43. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{43 - 50}{4}[/tex]

[tex]Z = -1.75[/tex]

[tex]Z = -1.75[/tex] has a pvalue of 0.0401

1 - 0.0401 = 0.9599

P(x > 43) = 0.9599

b) x<42

This is the pvalue of Z when X = 42.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{42 - 50}{4}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

P(x < 42) = 0.0228

c) x>57.5

This is 1 subtracted by the pvalue of Z when X = 57.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{57.5 - 50}{4}[/tex]

[tex]Z = 1.88[/tex]

[tex]Z = 1.88[/tex] has a pvalue of 0.97

1 - 0.97 = 0.03

P(x > 57.5) = 0.03

d) P(x = 42)

In the normal distribution, the probability of an exact value is 0. So

P(x = 42) = 0.

e) x<40 or x>55

x < 40 is the pvalue of Z when X = 40. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{40 - 50}{4}[/tex]

[tex]Z = -2.5[/tex]

[tex]Z = -2.5[/tex] has a pvalue of 0.0062

x > 55 is 1 subtracted by the pvalue of Z when X = 55. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 50}{4}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.0062 + 0.1056 = 0.1118

P(x<40 or x>55) = 0.1118

f) 5% of the values are less than what X value?

X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.645 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -1.645*4[/tex]

[tex]X = 43.42[/tex]

43.42 is the answer.

g) 60% of the values are between what two X values (symmetrically distributed around the mean)?

Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.

20th percentile:

X when Z has a pvalue of 0.2. So X when Z = -0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.84 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -0.84*4[/tex]

[tex]X = 46.64[/tex]

80th percentile:

X when Z has a pvalue of 0.8. So X when Z = 0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.84 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = 0.84*4[/tex]

[tex]X = 53.36[/tex]

Between 46.64 and 53.36.

h) 85% of the values will be above what X value?

Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.037 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -1.037*4[/tex]

[tex]X = 45.852[/tex]

Above 45.852.

Answer:

Step-by-step explanation:

Given that;

the following procedure for accomplishing our task are:

1. Flip the coin.

2. Flip the coin again.

From here will know that the coin is first flipped twice

3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails

But if the outcomes of the two flip are different i.e they did not land on both heads or both did not land on tails , then we will consider such an outcome.

Let the probability of head = p

so P(head) = p

the probability of tail be = (1 - p)

This kind of probability follows a conditional distribution and the probability  of getting heads is :

[tex]P( \{Tails, Heads\})|\{Tails, Heads,( Heads ,Tails)\})[/tex]

[tex]= \dfrac{P( \{Tails, Heads\}) \cap \{Tails, Heads,( Heads ,Tails)\})}{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]

[tex]= \dfrac{P( \{Tails, Heads\}) }{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]

[tex]= \dfrac{P( \{Tails, Heads\}) } { {P( Tails, Heads) +P( Heads ,Tails)}}[/tex]

[tex]=\dfrac{(1-p)*p}{(1-p)*p+p*(1-p)}[/tex]

[tex]=\dfrac{(1-p)*p}{2(1-p)*p}[/tex]

[tex]=\dfrac{1}{2}[/tex]

Thus; the probability of getting heads is [tex]\dfrac{1}{2}[/tex] which typically implies that the coin is fair

(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?

For a fair coin (0<p<1) , it's certain that both heads and tails at the end of the flip.

The procedure that is talked about in (b) illustrates that the procedure gives head if and only if the first flip comes out tail with probability 1 - p.

Likewise , the procedure gives tail if and and only if the first flip comes out head with probability of  p.

In essence, NO, procedure (b) does not give a fair coin flip outcome.

Answer:

17x +7y

Step-by-step explanation:

8x + 10y + 9x - 3y

Combine like terms

8x+ 9x          + 10y - 3y

17x                   +7y

8x+9x are like terms    and 10y -3y are like terms

Answer:

17x + 7y

Step-by-step explanation:

8x + 10y + 9x - 3y

Rearrange.

8x + 9x + 10y - 3y

Factor out x and y.

x (8 + 9) + y (10 - 3)

Add or subtract.

x (17) + y (7)

17x + 7y

Answer:

[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-1.35)=0.0885[/tex]  

For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409

Step-by-step explanation:

Information given

[tex]\bar X=404[/tex] represent the sample mean

[tex]\sigma=24[/tex] represent the population standard deviation

[tex]n=42[/tex] sample size  

[tex]\mu_o =409[/tex] represent the value to verify

[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true mean is less than 409, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 409[/tex]  

Alternative hypothesis:[tex]\mu < 409[/tex]  

The statistic for this case is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-1.35)=0.0885[/tex]  

For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409

Answer: b

Explanation:

The -2 outside of the parentheses means it’s at y=-2 and the -4 inside the parentheses means it’s at x= 4 because it’s always the opposite

Answer:

2

Step-by-step explanation:

Since there are four negative signs, we have -1 multiplying each other 4 times,  multiplying by positive 2. This is then 1 * 2, which is 2.

Answer:

+2

Step-by-step explanation:

=> -(-(-(-2))))

=> -(-(+2))

=> -(-2)

=> +2

Answer:

A. The E(Y) is 0.80

B. The expected amount of the surcharges is $165

Step-by-step explanation:

A. In order to calculate the E(Y), we would have to calculate the following formula:

E(Y)=∑yp(y)

E(Y)=(0*0.5)+(1*0.25)+(2*0.20)+(3*0.05)

E(Y)=0+0.25+0.40+0.15

E(Y)=0.80

B. In order to calculate the expected amount of the surcharges we would have to calculate the following formula:

E($110Y∧2)=110E(Y∧2)

=110∑y∧2p(y)

=110((0∧2*0.5)+(1∧2*0.25)+(2∧2*0.20)+(3∧2*0.05))

110(0+0.25+0.80+0.45)

=$165

Answer:

The full name of the place is the "Danat Jebel Dhanna".  The Jebel Dhanna is currently located in the Abu Dhabi.  It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.

hope this helps ;)

best regards,

`FL°°F~` (floof)

Answer:

it’s C

Step-by-step explanation:

No, the vertices of the image and pre-image do not correspond

No, the vertices of the image and pre-image do not correspond, Micaela tried to rotate the square 180° about the origin. Hence, option C is correct.

A figure can be rotated by 90 degrees clockwise by rotating each vertex of the figure 90 degrees clockwise about the origin.

Let's take the vertices of a square with points at (+1,+1), (-1,+1), (-1,-1), and (+1,-1), centered at the origin, can be found in the following positions after rotation:

Micaela's rotation must be accurate if it led to the same points. Her rotation is incorrect if the points are different, though.

It is impossible to tell if Micaela's rotation is accurate without more details or a diagram.

Thus, option C is correct.

For more information about rotation about the origin, click here:

https://brainly.com/question/30198965

#SPJ7

Answer:

B) 92.03 < μ < 97.97

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Step-by-step explanation:

Step(i):-

Given sample mean (x⁻) = 95

standard deviation of the sample (s) = 6.6

Random sample size 'n' = 30

99% confidence interval for the mean score of all students.

[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]

step(ii):-

Degrees of freedom

ν =   n-1 = 30-1 =29

[tex]t_{0.01} = 2.462[/tex]

99% confidence interval for the mean score of all students.

[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]

( 95 - 2.966 , 95 + 2.966)

(92.03 , 97.97)

Final answer:-

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Answer:

  193.77 < p < 1806.23

Step-by-step explanation:

You want R(p) > 2,100,000, so ...

  -6p^2 +12000p > 2100000

  p^2 -2000p < -350000 . . . . divide by -6

Adding (2000/2)^2 = 1000000 will "complete the square".

  p^2 -2000p +1000000 < 650000 . . . . complete the square

  (p -1000)^2 < 650000

  -√650000 < p -1000 < √650000 . . . . take the square root

  1000 -806.23 < p < 1000 +806.23 . . . .add 1000

  193.77 < p < 1806.23 . . . . range of prices for desired revenue

Answer:

5.12 x 10¹¹ bit

Step-by-step explanation:

1GB = 8 x 10⁹ bits

so 64gb = 64 x 8 x 10⁹

= 512 x 10⁹

= 5.12 x 10¹¹ bits

scientific notation = 5.12 x 10¹¹ bits

standard Notation = 512 ,000,000,000 bits.

Answer:8.2 x 10^5

Step-by-step explanation:

Answer:

Option C (-4,-1) (In Quadrant III)

Step-by-step explanation:

Coordinate = (-4,1)

=> Reflecting over y-axis will make the coordinate (4,1)

=> Reflecting across x-axis will make the coordinate (4,-1)

=> Rotating 180 will make it (-4,-1)

Answer:

The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 160, \pi = \frac{14}{160} = 0.088[/tex]

88% confidence level

So [tex]\alpha = 0.12[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.12}{2} = 0.94[/tex], so [tex]Z = 1.555[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 - 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.053[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 + 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.123[/tex]

The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)

Answer:

  7

Step-by-step explanation:

The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.

In the given range, there are 7 such boards:

  4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = [tex]\frac{d}{dx}[/tex][[tex]x^{4}ln(x)[/tex]]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = [tex]4x^{3}ln(x) + x_{4}.\frac{1}{x}[/tex]

f'(x) = [tex]4x^{3}ln(x) + x^{3}[/tex]

f'(x) = [tex]x^{3}[4ln(x) + 1][/tex]

Now, find the critical points: f'(x) = 0

[tex]x^{3}[4ln(x) + 1][/tex] = 0

[tex]x^{3} = 0[/tex]

x = 0

and

[tex]4ln(x) + 1 = 0[/tex]

[tex]ln(x) = \frac{-1}{4}[/tex]

x = [tex]e^{\frac{-1}{4} }[/tex]

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = [tex]x^{4}ln(x)[/tex]

f(0.78) = [tex]0.78^{4}ln(0.78)[/tex]

f(0.78) = - 0.092

The point of minimum is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = [tex]\frac{d^{2}}{dx^{2}}[/tex] [[tex]x^{3}[4ln(x) + 1][/tex]]

f"(x) = [tex]3x^{2}[4ln(x) + 1] + 4x^{2}[/tex]

f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]

[tex]x^{2}[12ln(x) + 7][/tex] = 0

[tex]x^{2} = 0\\x = 0[/tex]

and

[tex]12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56[/tex]

Substituing x in the function:

f(x) = [tex]x^{4}ln(x)[/tex]

f(0.56) = [tex]0.56^{4} ln(0.56)[/tex]

f(0.56) = - 0.06

The inflection point will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  [tex]x^{2}[12ln(x) + 7][/tex]

f"(0.1) = [tex]0.1^{2}[12ln(0.1)+7][/tex]

f"(0.1) = - 0.21, i.e. Concave is DOWN.

f"(0.7) = [tex]0.7^{2}[12ln(0.7)+7][/tex]

f"(0.7) = + 1.33, i.e. Concave is UP.

Answer:

The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

Step-by-step explanation:

Let the random variable X represent the amount of money that the family has invested in different real estate properties.

The random variable X follows a Normal distribution with parameters μ = $225,000 and σ = $50,000.

It is provided that the family has invested in n = 10 different real estate properties.

Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:

[tex]\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39[/tex]

Now the lowest 80% of the amount invested can be represented as follows:

[tex]P(\bar X<\bar x)=0.80\\\\\Rightarrow P(Z<z)=0.80[/tex]

The value of z is 0.84.

*Use a z-table.

Compute the value of the mean amount invested as follows:

[tex]\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}[/tex]

   [tex]=225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57[/tex]

Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

Question:

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.

Answer:

61.03

Step-by-step explanation:

Given:

Standard deviation = 18

Sample estimate = 5

Confidence level = 97%

Required:

Find sample size, n.

First find the Z value. Using zscore table

Z-value at a confidence level of 97% = 2.17

To find the sample size, use the formula below:

[tex] n = (Z * \frac{\sigma}{E})^2[/tex]

[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]

[tex] n = (2.17 * 3.6)^2 [/tex]

[tex] n = (7.812)^2 [/tex]

[tex] n = 61.03 [/tex]

Sample size = 61.03

Answer:

[tex] \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]

Answer:145

Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145

Answer:

X is 3 units.

Step-by-step explanation:

Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.

Answer:

[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=9-1=8[/tex]  

And the p value would be given by:

[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]  

Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.

Step-by-step explanation:

Assuming this first part of the problem obtained from the web: "Using traditional methods, it takes 11.0 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed"

Information given

[tex]\bar X=10.8[/tex] represent the mean height for the sample  

[tex]s=1.5[/tex] represent the sample standard deviation

[tex]n=9[/tex] sample size  

[tex]\mu_o =11[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic  

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to check if the true mean for this case is equal to 11 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 11[/tex]  

Alternative hypothesis:[tex]\mu \neq 11[/tex]  

The statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=9-1=8[/tex]  

And the p value would be given by:

[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]  

Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.

Answer:

Its D The Last Graph

Step-by-step explanation:

it just is my guy

Answer:

The answer is "[tex]\bold{\frac{32}{3}}\\[/tex]"

Step-by-step explanation:

The rectangle should also be symmetrical to it because of the symmetry to the y-axis  The pole of the y-axis.  Its lower two vertices are (-x,0). it means that  

and (-x,0), and (x,0). Therefore the base measurement of the rectangle is 2x. The top vertices on the parabola are as follows:  

The calculation of the height of the rectangle also is clearly 16-x^2, (-x,16,-x^2) and (x,16,-x^2).  

The area of the rectangle:

[tex]A(x)=(2x)(16-x^2)\\\\A(x)=32x-2x^3[/tex]

The local extremes of this function are where the first derivative is 0:

[tex]A'(x)=32-6x^2\\\\32-6x^2=0\\\\x= \pm\sqrt{\frac{32}{6}}\\\\x= \pm\frac{4\sqrt{3}}{3}\\\\[/tex]

Simply ignore the negative root because we need a positive length calculation

It wants a maximum, this we want to see if the second derivative's profit at the end is negative.

[tex]A''\frac{4\sqrt{3}}{3} = -12\frac{4\sqrt{3}}{3}<0\\\\2.\frac{4\sqrt{3}}{3}= \frac{8\sqrt{3}}{3}\\\\\vertical \ dimension\\\\16-(\frac{4\sqrt{3}}{3})^2= \frac{32}{3}[/tex]

Answer:

[tex]-\frac{161}{9}=\\or\\-16\frac{8}{9}[/tex]

Step-by-step explanation:

[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}=\\\\-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=\\\\-\frac{161}{9}=\\\\-16\frac{8}{9}[/tex]

Answer:

-3

Step-by-step explanation:

every sequence goes down by -3

Answer:

take away 3. the common difference is 3

Step-by-step explanation:

take away 3

Answer:

(a) The value of E (X) is 4/7.

    The value of V (X) is 3/98.

(b) The value of P (X ≤ 0.5) is 0.3438.

Step-by-step explanation:

The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.

The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.

The probability density function of X is as follows:

[tex]f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0[/tex]

Here, B (α, β) is:

[tex]B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}[/tex]

            [tex]=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}[/tex]

So, the pdf of X is:

[tex]f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1[/tex]

(a)

Compute the value of E (X) as follows:

[tex]E (X)=\frac{\alpha }{\alpha +\beta }[/tex]

         [tex]=\frac{4}{4+3}\\\\=\frac{4}{7}[/tex]

The value of E (X) is 4/7.

Compute the value of V (X) as follows:

[tex]V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}[/tex]

         [tex]=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}[/tex]

The value of V (X) is 3/98.

(b)

Compute the value of P (X ≤ 0.5) as follows:

[tex]P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx[/tex]

                    [tex]=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438[/tex]

Thus, the value of P (X ≤ 0.5) is 0.3438.

Answer:

[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]

And using the probability mass function we can find the individual probabilities:

[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]

[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]

And replacing we got:

[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]

Then the probability that at least 2 disapprove of daily pot smoking is 0.4366

Step-by-step explanation:

Let X the random variable of interest "number of seniors who disapprove of daily smoking ", on this case we now that:

[tex]X \sim Binom(n=8, p=0.18)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]

And using the probability mass function we can find the individual probabilities:

[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]

[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]

And replacing we got:

[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]

Then the probability that at least 2 disapprove of daily pot smoking is 0.4366