Disjoint, Independent, and Complement State whether the two events (A and B) described are disjoint, independent, and/or complements. (It is possible that the two events fall into more than one of the three categories, or none of them.) Australia plays Argentina for the championship in the Rugby World Cup. At the same time, Ukraine plays Russia for the World Team Chess Championship. Let A be the event that Argentina wins their rugby match and B be the event that Ukraine wins their chess match. Disjoint

Answer:

[tex]P(X<120)=P(\frac{X-\mu}{\sigma}<\frac{120-\mu}{\sigma})=P(Z<\frac{120-150}{13})=P(z<-2.308)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-2.308)=0.0105[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(150,13)[/tex]  

Where [tex]\mu=150[/tex] and [tex]\sigma=13[/tex]

We are interested on this probability

[tex]P(X<120)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<120)=P(\frac{X-\mu}{\sigma}<\frac{120-\mu}{\sigma})=P(Z<\frac{120-150}{13})=P(z<-2.308)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-2.308)=0.0105[/tex]

Answer:

[tex]X \sim N(100,15)[/tex]  

Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]

We select a sample of n=16 and we are interested on the distribution of [tex]\bar X[/tex], since the distribution for X is normal then we can conclude that the distribution for [tex] \bar X [/tex] is also normal and given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

Because by definition:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] E(\bar X) = \mu[/tex]

[tex] Var(\bar X) = \frac{\sigma^2}{n}[/tex]

And for this case we have this:

[tex] \mu_{\bar X}= \mu = 100[/tex]

[tex] \sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(100,15)[/tex]  

Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]

We select a sample of n=16 and we are interested on the distribution of [tex]\bar X[/tex], since the distribution for X is normal then we can conclude that the distribution for [tex] \bar X [/tex] is also normal and given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

Because by definition:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] E(\bar X) = \mu[/tex]

[tex] Var(\bar X) = \frac{\sigma^2}{n}[/tex]

And for this case we have this:

[tex] \mu_{\bar X}= \mu = 100[/tex]

[tex] \sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75[/tex]

Answer:

76cm²

Step-by-step explanation:

The triangle from all indication is an isosceles triangle:

Let x represent the side

∴ x = 4 - 6 = -2

x =  -2

x + 2 = 0

Using the fomular, as area of triangle, that is:

Area = √s(s - a)(s - b)(s - c)

s = a + b+ c/2, where a = x + 2; b = x+ 2; c = x

∴ s = x + 2 + x + 2 + x/2 = 3x + 4/2

Area = √3x + 4/2( 3x + 4/2 - x - 2)(3x + 4/2 - x - 2)(3x + 4/2 - x)

= √3x + 4/2( x/2)(x/2)(x + 4/2)

= √3x + 4/2(x²/4)(x + 4)/2            

Let's assume x = 12

∴ Area = √5760 = 76cm²

Answer:

Its C.100

Area of a triangle b*h/2 (6+4=10*2=20) 20*10=200/2 will give you 100.

Step-by-step explanation:

Answer:

Model area of dimensions

[tex]p=5[/tex]

[tex]q=2x^2-x+3[/tex]

Step-by-step explanation:

Model for the Area

Suposse we have a rectangle of measures p and q, its area is computed by

[tex]A=p.q[/tex]

Note the expression is a product which means if an equation is found for the area, we can guess the dimensions of the supossed rectangle.

The expression for the area is

[tex]A=10x^2-5x+15[/tex]

This polynomial can be factored as

[tex]A=5(2x^2-x+3)[/tex]

We have found an explicit product, now we can guess the dimensions of the rectangle are

[tex]p=5[/tex]

[tex]q=2x^2-x+3[/tex]

Or viceversa

Answer: $4,184.14

Step-by-step explanation:

If a car depreciates, it mean the the car is losing it's marketable worth and sometimes at a constant rate. The worth of the car after some years does not remain the same.

The formula for this depreciation when at a constant rate is denoted as:

D = P × [1 - r/100]^n

Where:

D=the Depreciated value of the car after n period which is what is being determined.

P = initial value of the car before depreciation is considered and in this case, P = $12,000

r = constant Rate Of depreciation and in this case = 10%

n = period being considered, which in this case, n = 10years.

Hence,

D = 12,000 × [1 - 10/100]^10

D = $4,184.14

Answer:

Only options, A and E give 625/n¹² on simplification. The other options do not apply.

(5n⁻³)⁴ = (625/n¹²)

(25n⁻⁶)² = (625/n¹²)

Step-by-step explanation:

625/n¹²

a) (5n⁻³)⁴

According to the law of indices, this becomes

(5⁴)(n⁻³)⁴ = 625(n⁻¹²) = 625/n¹²

This applies!

b) (5n⁻³)⁻⁴

According to the law of indices, this becomes

(5⁻⁴)(n⁻³)⁻⁴ = (n¹²)/625 = n¹²/625

Does Not apply!

c) (5n⁻⁴)³

This becomes

(5³)(n⁻⁴)³ = 125n⁻¹² = 125/n¹²

Does Not apply!

d) (25n⁻⁶)⁻²

This becomes

(25⁻²)(n⁻⁶)⁻² = n⁻¹²/625 = 1/(625n¹²)

Does Not apply!

e) (25n⁻⁶)²

This becomes

(25²)(n⁻⁶)² = 625n⁻¹² = 625/n¹²

This applies!

Answer:

A AND E

Step-by-step explanation:

Answer:

ooh i just learned this,  not 100% sure but the amount he should have to deposit is $3835.12

if the weekly one means depositing money every week then  it would be $36.88 I think.

Step-by-step explanation:

p=?

r=.08

n=52

t=2

4500 = P(1+.08/52)^(52 x 2)

divide both sides by (1+.08/52)^(52 x 2)

and you are left with $3835.12

if i take into account that Marc is depositing the money every week the i would divide it by 104  (that is 52 x 2 because 52 weeks in a year and it says 2 years) you would be left with $36.88.

Hope I was any help.

Answer: Marc should deposit $39.87 weekly.

Step-by-step explanation:

We would apply the formula for determining future value involving deposits at constant intervals. It is expressed as

S = R[{(1 + r)^n - 1)}/r][1 + r]

Where

S represents the future value of the investment.

R represents the regular payments made(could be weekly, monthly)

r = represents interest rate/number of interval payments.

n represents the total number of payments made.

From the information given,

S = $4500

Assuming there are 52 weeks in a year, then

r = 0.08/52 = 0.0015

n = 52 × 2 = 104

Therefore,

4500 = R[{(1 + 0.0015)^104 - 1)}/0.0015][1 + 0.0015]

4500 = R[{(1.0015)^104 - 1)}/0.0015][1.0015]

4500 = R[{(1.169 - 1)}/0.0015][1.0015]

4500 = R[{(0.169)}/0.0015][1.0015]

4500 = R[112.67][1.0015]

4500 = 112.839R

R = 4500/112.839

R = 39.87

Answer:

Step-by-step explanation: see attachment for solution

If X is the time in 10 to 1 week of the shipment of a defective product until the customer returns the product.  

The shipment of the defective product will be  

Expected value is E (X) = 5.7125.

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Answer:

d = 80 ft

Step-by-step explanation:

Start with angle BCA, tan(BCA) = 30/15 so BCA = 63.43 degrees.

BCA = ECD since they are opposite angles.

tan ECD = d/40

40 tan(63.4degrees) = d

d = 80 ft

Alternatively, you can use similar triangles since the angles are the same, BCA = ECD, CED = CAB, and CBA = EDC. In that case use proportions to get 30/15 = d/40 so 2 = d/40 and d = 80.

Answer:

The total compound return over the 3 years is 15.26%

Step-by-step explanation:

Let the initial investment sum be assumed to be X

The total return after each year can be calculated as follows:

After First year: X + (13% of X) = 1.13X

After Second year: 1.13X + (20% of 1.13X) = 1.13X + 0.226X = 1.356X

After Third year: 1.356X - (15% of 1.356X) = 1.356X - 0.2034X = 1.1526X

It is apparent from here that after the third year, the investment has increased the initial X, by 0.1526X, which is 15.26%.

The total compound return over the 3 years is 15.26%

The data set is S = {10, 11, 15, 21, 24, 24, 27, 29, 33, 35, 35, 37, 39, 40, 40}

A stem-and-leaf plot is a method to represent the data in tabular form.

The stem consist of the first digits of the data values arranged in ascending order.

The leaf consist of the remaining digits.

The data provided is:

Stem | Leaf

    1  | 0 1  5

    2 | 1  4 4 7 9

    3 | 3 5 5 7 9

    4 | 0 1  

The original data is:

10, 11, 15, 21, 24, 24, 27, 29, 33, 35, 35, 37, 39, 40, 40

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The original set of data consists of number sequences as follows: 10 12 4 7 11 4 3 10 0, 10 4 14 11 13 2 4 6, 12 6 9 10, 5 13 4, 10 14 12 11, and 6 10 11 0 11 13 2.

The original set of data is:

Answer:

6.08333

Step-by-step explanation:

6ft 0.8inches

Answer:

6 ft 1 in

Step-by-step explanation:

Answer:

a) ( 3 , 6 )

b) y = -2*x / 3 + 7

Step-by-step explanation:

Given:

- The four points are:

                        (-9,13), (-3, 9), (3, 6) and (9, 1)

- Three points lie on the same line.

Find:

Which one of the four points does not lie on the same line as the other three?

Solution:

- Compute the slope between each pair of point:

                                 (-9,13), (-3, 9)

                        m_1 = ( 9 - 13 ) / ( -3 + 9 ) = - 2/3

                                 (-9,13), (3, 6)

                        m_2 = ( 6 - 13 ) / ( 3 + 9 ) = - 0.5833

                                 (-9,13), (9, 1)

                        m_3 = ( 1 - 13 ) / ( 9 + 9 ) = - 2/3

- We see that m_1 = m_3 ≠ m_2 . Hence, point ( 3 ,6 ) does not lie on the same line.

- The equation of line is expressed as:

                        y = m*x + C

                        m = -2/3

                        y = -2*x / 3 + C

                        1 = -2*9 / 3 + C ....... ( 9 , 1 )

                        C = 7

- The equation of the line is:

                        y = -2*x / 3 + 7

    Points A(-9, 13), B(-3, 9) and D(9, 1) are colinear.

b). Equation of the line passing through these points will be [tex]y=-\frac{2}{3}x+7[/tex]

        [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Given points in the question,

A(-9, 13), B(-3, 9), C(3, 6) and D(9, 1)

If the slopes of the lines joining these points are same, points will be colinear.

Slope of AB = [tex]\frac{13-9}{-9+3}=-\frac{2}{3}[/tex]

Slope of AC = [tex]\frac{13-6}{-9-3}=-\frac{7}{12}[/tex]

Slope of AD = [tex]\frac{13-1}{-9-9}=-\frac{2}{3}[/tex]

Since, slopes of AB and AD are equal, points A, B and D will be colinear.

b). Let the equation of the line passing through A, B and D is,

    y - y' = m(x - x')

    Since, this line passes through D(9, 1) and slope = [tex]-\frac{2}{3}[/tex]

    Equation of the line → [tex]y-1=-\frac{2}{3}(x-9)[/tex]

                                    [tex]y=-\frac{2}{3}x+6+1[/tex]

                                    [tex]y=-\frac{2}{3}x+7[/tex]

       Therefore, points A(-9, 13), B(-3, 9) and D(9, 1) are colinear and equation of the line passing through these points will be [tex]y=-\frac{2}{3}x+7[/tex].

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Answer: B

Step-by-step explanation:

The sampling distribution of the proportion of damaged trees is approximately Normal

Answer:B. The sampling distribution of the proportion of damaged trees is approximately Normal.

Step-by-step explanation: Sampling distribution is a probability distribution of a statistic which is gotten through the collection of a large number of samples from the population of interest.

A normal distribution is a distribution of the samples symmetrically around the mean, when a Statistical metric shows that the outcome is distributed around the central region it shows that the distribution is normal.

FOR A FORTY PERCENT INCIDENCE, THE SAMPLING DISTRIBUTION OF THE PROPORTION OF DAMAGED TREES IS APPROXIMATELY NORMAL AS IT IS CLOSE TO 50% WHICH IS THE MEAN OF 100%.

Answer:

a) 15.87% probability that a single car of this model fails to meet the NOX requirement.

b) 2.28% probability that the average NOX level of these cars are above 0.3 g/mi limit

Step-by-step explanation:

We use the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution:

Problems of normally distributed samples are solved using 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that:

[tex]\mu = 0.25, \sigma = 0.05[/tex]

a. What is the probability that a single car of this model fails to meet the NOX requirement?

Emissions higher than 0.3, which is 1 subtracted by the pvalue of Z when X = 0.3. So

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

[tex]Z = \frac{0.3 - 0.25}{0.05}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8417.

1 - 0.8413 = 0.1587.

15.87% probability that a single car of this model fails to meet the NOX requirement.

b. A company has 4 cars of this model in its fleet. What is the probability that the average NOX level of these cars are above 0.3 g/mi limit?

Now we have [tex]n = 4, s = \frac{0.05}{\sqrt{4}} = 0.025[/tex]

The probability is 1 subtracted by the pvalue of Z when X = 0.3. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.3 - 0.25}{0.025}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that the average NOX level of these cars are above 0.3 g/mi limit

The probability that a single car of this model fails to meet the NOX requirement is 15.87%.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given;  mean of 0.25 g and a standard deviation of 0.05 g/mi

a) For > 0.3:

z = (0.3 - 0.25)/0.05 = 1

P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587

b) For > 0.3, sample size = 4

z = (0.3 - 0.25)/(0.05 ÷√4) = 2

P(z > 2) = 1 - P(z < 2) = 1 - 0.9772 = 0.0228

The probability that a single car of this model fails to meet the NOX requirement is 15.87%.

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Let X be the random variable representing monthly trainee income. X is distributed with mean $1100 and standard deviation $150. You want to find the proportion of trainees that earn less than $900 per month, or Pr(X < 900).

Using normalcdf (on a TI calculator, for instance), you would compute

normalcdf(-1E99, 900, 1100, 150)

to get a proportion of approximately 0.09121, or 9.121%.

That is, the syntax for normalcdf is

normalcdf(lower limit, upper limit, mean, standard deviation)

In this case, you pick a very large negative number for "lower limit" in order to simulate negative infinity.

Answer:

[tex]2.54-2.82\frac{1.110}{\sqrt{10}}=1.55[/tex]    

[tex]2.54+2.82\frac{1.110}{\sqrt{10}}=3.53[/tex]    

So on this case the 98% confidence interval would be given by (1.55;3.53)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)  

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

The mean calculated for this case is [tex]\bar X=2.54[/tex]

The sample deviation calculated [tex]s=1.110[/tex]

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=10-1=9[/tex]

Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.01,9)".And we see that [tex]t_{\alpha/2}=2.82[/tex]

Now we have everything in order to replace into formula (1):

[tex]2.54-2.82\frac{1.110}{\sqrt{10}}=1.55[/tex]    

[tex]2.54+2.82\frac{1.110}{\sqrt{10}}=3.53[/tex]    

So on this case the 98% confidence interval would be given by (1.55;3.53)    

The 98% confidence interval would be given by (1.55;3.53)

A range of values that, with a particular level of confidence, is likely to encompass a population value is called a confidence interval. A population mean is typically stated as a percentage that falls between an upper and lower interval.

The range of values in a confidence interval below and above the sample statistic is called the margin of error.

The normal distribution is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

show the sample mean for the given sample.  

population mean (the relevant variable)

The sample standard deviation is denoted by s.

n stands for the number of samples.  

Resolution of the issue

The following formula produces the mean's confidence interval:

[tex]\bar x[/tex] ± [tex]\frac{t_a}{2} \frac{s}{\sqrt{n} }[/tex] ____________(1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

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

[tex]s = \sqrt{\frac{\sum^n_{i=1}(x_i-\bar x)}{n-1} }[/tex] ____________(3)

The mean calculated for this case is X = 2.54

The sample deviation calculated s = 1.110

t In order to calculate the critical value [tex]\frac{t_a}{2}[/tex] we need freedom, given by: to find first the degrees of

df = n-1=10-19

Since the Confidence is 0.98 or 98%, the value of a = 0.02 and a/2 = 0.01, and we can use excel, a calculator or a tabel to find the critical value.

[tex]\frac{t_a}{2}[/tex]  = 2.82

Now we have everything in order to replace into formula (1):

2.54 - 2.82 [tex]\frac{1.110}{\sqrt{10} }[/tex] = 1.55

2.54 +  2.82 [tex]\frac{1.110}{\sqrt{10} }[/tex]  = 3.53

Answer:

The type 1 error here is a. Deciding that the absorption rates are different, when in fact they are not.

Step-by-step explanation:

A type I error is the rejection of a true null hypothesis (also known as a "false positive" finding or conclusion).

More generally, a Type I error occurs when a significance test results in the rejection of a true null hypothesis. By one common convention, if the probability value is below 0.05, then the null hypothesis is rejected.

In inferential statistics, the null hypothesis is a general statement or default position that there is nothing significantly different happening, like there is no association among groups or variables, or that there is no relationship between two measured phenomena.

Answer:

(a)

The slope of the equation = 0.02

Therefore T-intercept equals 15

(b)

Therefore the average global surface temperature in 2050 is 17°C.

Step-by-step explanation:

If a equation is in the form

y= mx+c........(1)

Then the slope of the equation is m.

Slope: The tangent of the angle which is made with the positive x-axis.

If θ be the angle , Then slope (m)= tanθ.

If a equation in the form

[tex]\frac{x}{a} +\frac{y}{b} =1[/tex]............(2)

Then x-axis intercept equals a and y-axis intercept equals b.

Given equation is

T=0.02t+15.0

Comparing with equation (1)

The slope of the equation = 0.02

Again we can rewrite the equation as

[tex]T-0.02t=15[/tex]

[tex]\Rightarrow \frac{T}{15} -\frac{0.02t}{15}=1[/tex]

Comparing with (2)

Therefore T-intercept equals 15

(b)

Here t= 2050-1950 =100

Putting t=100 in the given equation

T=0.02(100)+15 = 2+15 =17

Therefore the average global surface temperature in 2050 is 17°C.

The probability that Team A wins and Team B loses is 0.112.

Given that,

Suppose Team A has a 0.75 probability to win their next game and Team B has a 0.85 probability to win their next game.

Assume these events are independent.

We have to determine,

What is the probability that Team A wins and Team B loses?

According to the question,

In an independent event and probability, the outcomes in an experiment are termed as events. Ideally, there are multiple events like mutually exclusive events, independent events, dependent events, and more.

Team A has a 0.75 probability to win their next game,

And Team B has a 0.85 probability to win their next game.

Therefore,

The probability that Team A wins and Team B loses is

[tex]\rm The \ probability \ of \ A \ wins \ and \ team \ B \ loses = Probability \ of \ team \ A winning \ game \times (1- Probability \ of \ team B \ lose \ the \ game)\\\\ The \ probability \ of \ A \ wins \ and \ team \ B \ loses = 0.75 \times (1-0.85)\\\\ The \ probability \ of \ A \ wins \ and \ team \ B \ loses =0.75 \times 0.15\\\\ The \ probability \ of \ A \ wins \ and \ team \ B \ loses =0.112[/tex]

Hence, The probability that Team A wins and Team B loses is 0.112.

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Final answer:

The probability that Team A wins and Team B loses is calculated by multiplying the probability of Team A winning (0.75) with the probability of Team B losing (1 - 0.85). The result is 0.1125 or 11.25%.

Explanation:

To calculate the probability that Team A wins and Team B loses, we use the rules of independent events. The event of Team A winning has a probability of 0.75, and the event of Team B losing is the complement of Team B winning, which has a probability of 0.85. Since these are independent events, we multiply the probabilities:

P(Team A wins and Team B loses) = P(Team A wins) × P(Team B loses)

P(Team B loses) = 1 - P(Team B wins) = 1 - 0.85 = 0.15

Therefore, P(Team A wins and Team B loses) = 0.75 × 0.15 = 0.1125.

The probability that Team A wins and Team B loses is 0.1125, or 11.25%.

Answer:

The probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 0.426.

Step-by-step explanation:

Let X = number of Americans who believe that statistics teachers know the true meaning of life.

The probability of the random variable X is,

P (X) = 0.574

The event of a person not believing that statistics teachers know the true meaning of life is the complement of the event X.

The probability of the complement of an event, E is the probability of that event not happening.

[tex]P(E^{c})=1-P(E)[/tex]

Compute the value of [tex]P(X^{c})[/tex] as follows:

[tex]P(X^{c})=1-P(X)\\=1-0.574\\=0.426[/tex]

Thus, the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 0.426.

Answer:

Probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life = 0.426 .

Step-by-step explanation:

We are given that a poll showed that 57.4% of Americans say they believe that statistics teachers know the true meaning of life.

Let the above probability that % of Americans who believe that statistics teachers know the true meaning of life = P(A) = 0.574

Now, probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is given by = 1 - Probability of randomly selecting someone who believe that statistics teachers know the true meaning of life = 1 - P(A)

So, required probability = 1 - 0.574 = 0.426 .

Answer:

Step-by-step explanation:

Given that the Function point are [tex]w=y^3-9x^2y[/tex]

[tex]x=e^s[/tex], [tex]y=e^t[/tex] and s = -5, t = 10

[tex]w=y^3-9x^2y[/tex]  

Substitute the values of x and y in the above equation we get

[tex]w=(e^t)^3-9(e^s)^2(e^t)[/tex]

[tex]w=e^{3t}-9e^{2s}.e^t[/tex]

[tex]\frac{\partial w}{\partial ∂s}=e^{3t}-9(e^{2s}).2(e^t)[/tex]

[tex]=e^{3t}-18e^{2s}.(e^t)[/tex]

[tex]=e^{3t}-18e^{2s+t}[/tex]

[tex]w=e^{3t}-9e^{2s}.e^t[/tex]

[tex]\frac{\partial w}{\partial t}=e^{3t}.(3)-9e^{2s}(e^t).(1)[/tex]

[tex]=3e^{3t}-9e^{2s+t}[/tex]

Now put s-5 and t=10 to evaluate each partial derivative at the given values of s and t :

[tex]\frac{\partial w}{\partial s}=e^{3t}-18e^{2s+t}[/tex]

[tex]=e^{3(10}-18e^{2(-5)+10}[/tex]

[tex]=e^{30}-18e^{-10+10}[/tex]

[tex]=e^{30}-18e^0[/tex]

[tex]=e^{30}-18[/tex]

[tex]\frac{\partial w}{\partial t}=3e^{3t}-9e^{2s+t}[/tex]

[tex]=3e^{3(10)}-9e^{2(-5)+10}[/tex]

[tex]=3e^{30}-9e{-10+10}[/tex]

[tex]=3e^{30}-9e{0}[/tex]

[tex]=3e^{30}-9[/tex]

[tex]\frac{\partial w}{\partial t}=3(e^{30}-3)[/tex]

Using the Chain Rule, it is found that:

[tex]\frac{\partial W}{\partial s}(-5,10) = -18[/tex]

[tex]\frac{\partial W}{\partial s}(-5,10) = 3e^{30} - 9[/tex]

w is a function of x and y, which are functions of s and t, thus, by the Chain Rule:

[tex]\frac{\partial W}{\partial s} = \frac{\partial W}{\partial x}\frac{\partial x}{\partial s} + \frac{\partial W}{\partial y}\frac{\partial y}{\partial s}[/tex]

[tex]\frac{\partial W}{\partial t} = \frac{\partial W}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial W}{\partial y}\frac{\partial y}{\partial t}[/tex]

Then, the derivatives are:

[tex]\frac{\partial W}{\partial x} = -18xy[/tex]

[tex]\frac{\partial x}{\partial s} = e^s[/tex]

[tex]\frac{\partial W}{\partial y} = 3y^2 - 9x^2[/tex]

[tex]\frac{\partial y}{\partial s} = 0[/tex]

Then

[tex]\frac{\partial W}{\partial s} = \frac{\partial W}{\partial x}\frac{\partial x}{\partial s}[/tex]

[tex]\frac{\partial W}{\partial s} = -18xy(e^s)[/tex]

[tex]\frac{\partial W}{\partial s} = -18e^se^t(e^s)[/tex]

[tex]\frac{\partial W}{\partial s} = -18e^{2s}e^t[/tex]

[tex]\frac{\partial W}{\partial s} = -18e^{2s + t}[/tex]

At s = -5 and t = 10:

[tex]\frac{\partial W}{\partial s}(-5,10) = -18e^{2(-5) + 10} = -18[/tex]

Then, relative to t:

[tex]\frac{\partial x}{\partial t} = 0[/tex]

[tex]\frac{\partial y}{\partial t} = e^t[/tex]

[tex]\frac{\partial W}{\partial t} = \frac{\partial W}{\partial y}\frac{\partial y}{\partial t}[/tex]

[tex]\frac{\partial W}{\partial t} = (3y^2 - 9x^2)e^t[/tex]

[tex]\frac{\partial W}{\partial t} = (3e^{2t} - 9e^{2s})e^t[/tex]

At s = -5 and t = 10:

[tex]\frac{\partial W}{\partial s}(-5,10) = (3e^{20} - 9e^{-10})e^{10} = 3e^{30} - 9[/tex]

A similar problem is given at https://brainly.com/question/10309252

Answer:

5 -2√10 = C

Step-by-step explanation:

√25 -√40

√25 = √5 x5 = √5² = 5

√40 = √5 x 8 = √5x 2x4 = √10x4 = √10x 2² = 2√10 (when the 2 comes back into the square root it become 2²)

√25 -√40 = 5 -2√10

Answer:

Step-by-step explanation:

Hello!

The researcher's objective is to compare the effectiveness of a water softener when used with a filtering process against its effectiveness when used without filtering.

To do so 90 locations were randomly divided into two equal groups.

Group A locations used the water softener with filtering.

Group B locations used the water softener without filtering.

At the end of three months, a water sample was taken of each location and its level of softness was registered (Scale 1 to 5, 5 represents the softest water)

X₁: Softness of water of a location from group A

n₁= 45 locations

X[bar]₁= 2.1

S₁= 0.7

X₂: Softness of water of a location from group B

n₂= 45 locations

X[bar]₂= 1.7

S₂= 0.4

To compare the effectiveness of the softener with and without a filtering process the parameter of interest is the difference between both population means:

Parameter: μ₁ - μ₂

The point estimation of the difference between the population means is the difference of the sample means: X[bar]₁ - X[bar]₂= 2.1-1.7= 0.4

Since the objective is to test if there is any difference with or without the filtering process, the hypothesis test to make is two-tailed:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

α: 0.05

Since there is no information about the distribution of both variables, you have to apply the central limit theorem and approximate the distribution of X[bar]₁ and X[bar]₂ to normal. Once both samples mean distribution is approximate to normal you can use the statistic:

[tex]Z= \frac{(X[bar]₁ - X[bar]₂)-(Mu_1-Mu_2)}{\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } }[/tex]

[tex]Z_{H_0}= \frac{(2.1-1.7)-0}{\sqrt{\frac{0.49}{45} +\frac{0.16}{45} } } = 3.3282[/tex]

As said before, this test is two-tailed, so you will have two critical values:

Critical value 1: [tex]Z_{\alpha /2}= Z_{0.025}= -1.95[/tex]

Critical value 2: [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.965[/tex]

The p-value of this test is also two tailed, you can calculate it as:

P(Z≥3.33) + P(Z≤3.33)= (1 - P(Z≤3.33))+P(Z≤-3.33)= (1-0.999566)+0.000434= 0.000868

p-value: 0.000868

This value means that 0.0868% of the sample size 45 taken from this population will provide natural evidence that there is no difference between the population means of the effectiveness of the water softener used with and without a filtering process.

A little reminder, the p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

Both using the critical value method and the p-value method the decision is to reject the null hypothesis. This means that with a 5% level of significance there is a difference between the true average of the effectiveness of the water softener used with a filtering process and the true average effectiveness of the water softener used without a filtering process.

I hope it helps!

Answer: The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds is 0.596

Step-by-step explanation:

Since the weights of catfish are assumed to be normally distributed,

we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = weights of catfish.

µ = mean weight

σ = standard deviation

From the information given,

µ = 3.2 pounds

σ = 0.8 pound

The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds is is expressed as

P(x ≤ 3 ≤ 5.4)

For x = 3

z = (3 - 3.2)/0.8 = - 0.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.401

For x = 5.4

z = (5.4 - 3.2)/0.8 = 2.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.997

Therefore,.

P(x ≤ 3 ≤ 5.4) = 0.997 - 0.401 = 0.596

To determine the probability that a catfish will weigh between 3 and 5.4 pounds, we calculate the z-scores for these weights and find the corresponding probabilities. The probability is approximately 0.5957 or 59.57%.

The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds can be calculated using the standard normal distribution.

First, we convert the weights to z-scores using the formula:

Z = (X - μ) / σ

For 3 pounds:

Z = (3 - 3.2) / 0.8 = -0.25

For 5.4 pounds:

Z = (5.4 - 3.2) / 0.8 = 2.75

Next, we look up these z-scores on the z-table or use a calculator with normal distribution functions to find the probabilities.

P(Z < 2.75) = 0.9970 (rounded to four decimal places)

P(Z < -0.25) = 0.4013 (rounded to four decimal places)

Then we find the difference to determine the probability of a catfish weighing between these two values:

Probability = P(Z < 2.75) - P(Z < -0.25)

Probability = 0.9970 - 0.4013 = 0.5957

The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds is approximately 0.5957 or 59.57%.

Answer:

0.9524

Step-by-step explanation:

Note enough information is given in this problem. I will do a similar problem like this. The problem is:

The Probability of a train arriving on time and leaving on time is 0.8.The probability of the same train arriving on time is 0.84. The probability of the same train leaving on time is 0.86.Given the train arrived on time, what is the probability it will leave on time?

Solution:

This is conditional probability.

Given:

Now, according to conditional probability formula, we can write:

[tex]P(Leave \ on \ time | arrive \ on \ time)[/tex] = P(arrive ∩ leave) / P(arrive)

Arrive ∩ leave means probability of arriving AND leaving on time, that is given as "0.8"

and

P(arrive) means probability arriving on time given as 0.84, so:

0.8/0.84 = 0.9524

This is the answer.

a. The experimental​ unit:

The experimental units would be the lawyers that participate in this experiment. The experimental units are the subjects upon which the experiment is performed.

b. The response​ variable:

The response variable would be income. This is the variable that measures the response or outcome of the study.

c. The ​factors:

The factors are the variables whose levels are manipulated by the researcher. In this case, these would be the Mach score, classification and gender.

d. The levels of each​ factor:

The levels would include the levels of the Mach score (high, moderate, low) and the levels of gender (male, female).

e. The treatments:

The treatments are all the possible combinations of one level of each factor. Therefore, these are: High and male, high and female, moderate and men, moderate and female, low and male, low and female.

Answer:

The probability is 0.4841.

Step-by-step explanation:

The provided table is:

From above table, it is known that

Number of subjects are 1008.

The probability that the person chosen is a woman given that the person is a light smoker can be calculated as:

[tex]P(Woman| Light smoker)=\frac{P(Woman and light smoker)}{P(Light smoker)} \\P(Woman| Light smoker)= \frac{\frac{76}{1008} }{\frac{157}{1008} } = 0.4841[/tex]

Thus, required probability is 0.4841.

The probability that a randomly selected person is a woman given that the person is a light smoker is [tex]\[ 0.400} \][/tex]

To find the probability that a randomly selected person is a woman given that the person is a light smoker, we need to use conditional probability. The formula for conditional probability [tex]\( P(A|B) \)[/tex] is:

[tex]\[P(A|B) = \frac{P(A \cap B)}{P(B)}\][/tex]

Where:

[tex]\( P(A|B) \)[/tex] is the probability of event [tex]\( A \)[/tex] occurring given that [tex]\( B \)[/tex] has occurred.

[tex]\( P(A \cap B) \)[/tex] is the probability of both events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occurring.

[tex]\( P(B) \)[/tex] is the probability of an event [tex]\( B \)[/tex] occurring.

Let's define the events:

[tex]\( A \)[/tex] : The person chosen is a woman.

[tex]\( B \)[/tex] : The person chosen is a light smoker.

We need the number of light smokers and the number of women who are light smokers. Suppose we have the following data:

Total number of subjects: 1008

Number of light smokers: [tex]\( n_{\text{light smokers}} \)[/tex]

A number of women who are light smokers: [tex]\( n_{\text{women and light smokers}} \)[/tex]

Given that the number of women who are light smokers is [tex]\( n_{\text{women and light smokers}} \)[/tex] and the total number of light smokers is [tex]\( n_{\text{light smokers}} \)[/tex], the probability can be calculated as follows:

[tex]\[P(\text{woman | light smoker}) = \frac{n_{\text{women and light smokers}}}{n_{\text{light smokers}}}\][/tex]

If we don't have the exact numbers, we'll need those to calculate the probability. However, let's assume the following values (hypothetically for the purpose of illustration):

Total number of light smokers: 150

Number of women who are light smokers: 60

The probability that a randomly selected person is a woman given that the person is a light smoker is:

[tex]\[P(\text{woman | light smoker}) = \frac{60}{150} = 0.4\][/tex]

Rounding to the nearest thousandth:

[tex]\[0.4 = 0.400\][/tex]

Answer:

34%

Step-by-step explanation:

Amount of anesthetic in the 25% solution + amount of anesthetic in the 40% solution = amount of anesthetic in the mixed solution

0.25 (40) + 0.40 (60) = x (40 + 60)

10 + 24 = 100x

x = 0.34

The concentration of the mixed solution is 34%.

Answer:

1. 27x+18  =  x+x+x+x+x......+x  + 18

You sum "x" 27 times.

2. [tex](36,\infty)[/tex]

3. [tex]285/2 = 142.4[/tex]

4. 2*(12  1/3 )*(8  1/2)  + 2*(12  1/3 )*(6  3/4)+2*(6  3/4 )*(8  1/2)

Step-by-step explanation:

1. Remember that multiplication is a simplification of the sum, so, when you say for example, 4*3, that actually means 3+3+3+3, similarly, when you say, 27x, that means x+x+x...+x  27 times.

2. From the image you can see that  

The 36 is NOT taken, and then you go all the way to infinity, therefore we say [tex](36,\infty)[/tex].  Suppose that 36 was taken, then we would say [tex][36,\infty)[/tex].

3. From the attached photo

you can see that we can compute first the area of the rectangle with length = 15 and height = 7, and also note that at the top a triangle with base 15 and height 5 is formed, so the area of the whole figure would be the area of the rectangle at the bottom plus the area of the triangle on top. That would be 7*15+(15*5)/2 = 285/2

4. Remember that in general the formula for surface area would be

                                              [tex]2lw +2lh+2wh[/tex]

Where   l = length   ,  w = wide,   h = height.  In this case  l = 12  1/3   , w = 8  1/2   and h =  6  3/4