QUESTION 4
What kind of passenger would be considered a false negative?
A) Someone with dangerous material that pass through security
B) Someone with dangerous material thpt is stopped by security
C) Someone without dangerous material that pass through security
D) Someone without dangerous material that is stopped by security

Answer:

a) Mean 0.11 and standard deviation 0.0044.

b) Mean 0.11 and standard deviation 0.0099.

c) Mean 0.11 and standard deviation 0.0198

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.11[/tex]

a. For a random sample of size n equals 5000.

Mean:

[tex]\mu = p = 0.11[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.11*0.89}{5000}} = 0.0044[/tex]

Mean 0.11 and standard deviation 0.0044.

b. For a random sample of size n equals 1000.

Mean:

[tex]\mu = p = 0.11[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.11*0.89}{1000}} = 0.0044[/tex]

Mean 0.11 and standard deviation 0.0099.

c. For a random sample of size n equals 250.

Mean:

[tex]\mu = p = 0.11[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.11*0.89}{250}} = 0.0198[/tex]

Mean 0.11 and standard deviation 0.0198

Answer:

Step-by-step explanation:

Diagram : A visual tool representing mathematical ideas to be interpreted.

Postulate : A mathematical statement taken as a fact.

Theorem : A mathematical statement proven using postulates and definitions.

Definition : A formal statement declaring the meaning of a word.

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_A-\mu_B[/tex] = 2.0 units  or  [tex]\mu_D[/tex] = 2.0 units

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_A-\mu_B\neq[/tex] 2.0 units  or  [tex]\mu_D\neq[/tex] 2.0 units

Step-by-step explanation:

We are given the following data below and we have test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2;

Pair : 1 2 3 4 5 6 7

Sample1 : 5 6 10 3 6 7 8

Sample2 : 4 4 3 5 5 5 3

Let [tex]\mu_A[/tex] = population mean represented by Sample 1

[tex]\mu_B[/tex] = population mean represented by Sample 2

[tex]\mu_D[/tex] = population mean matched-pair differences for Sample 1 - Sample 2

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_A-\mu_B[/tex] = 2.0 units  or  [tex]\mu_D[/tex] = 2.0 units

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_A-\mu_B\neq[/tex] 2.0 units  or  [tex]\mu_D\neq[/tex] 2.0 units

Here null hypothesis states that the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2.

On the other hand, alternate hypothesis states that the population represented by Sample 1 has a mean that is not 2.0 units higher than the population represented by Sample 2.

Answer:

graph starts high and ends high

Answer:

Plane 1

[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]

Plane 2

[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]

Step-by-step explanation:

As each plane is travelling at constant speed, each equation can be modelled after this expression:

[tex]y = y_{o} + \dot y \cdot t[/tex]

Where:

[tex]y_{o}[/tex] - Intial elevation of the airplane, measured in feet.

[tex]\dot y[/tex] - Climbing/Descending rate of the airplane, measured in feet per minute. (Positive - Climbing, Negative - Descending)

[tex]t[/tex] - Time, measured in minutes.

Equations are described below:

Plane 1

[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]

Plane 2

[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]

Answer:

The answer is A.

Step-by-step explanation:

Recall SohCahToa, which tells us that cosine is the ratio of the adjacent side to the hypotenuse. In other words:

[tex]\displaystyle \cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

The adjacent side to ∠C is 10 and the hypotenuse is 26.

Therefore:

[tex]\displaystyle \cos(C)=\frac{10}{26}=\frac{5}{13}[/tex]

Our answer is A.

Answer:

x=1

Step-by-step explanation:

(x + 5) - 2(4x - 1) = 0

Distribute

x+5 - 8x +2 =0

Combine like terms

-7x +7 = 0

Add 7x to each side

-7x+7 +7x = 7x

7 = 7x

divide by 7

7/7 = 7x/7

1 =x

Answer:

f(-3) = 4

Step-by-step explanation:

There are two ways to do it with the information given to you, you can look at the graph or use the equation.

Equation:

Since x = -3, you would put -3 in for x in the first equation which gives 4. It looks like you were on the right track but forgot that it was negative so you ended up adding 3 instead of subtracting. At least that is where I assume the 10 comes from.

Graphical:

Looking at the graph you can also find the value. You want to find the value of y at x = -3, so you look at the spot where x = -3. You will see that there are two "points" there, one open and one closed. The closed circle one means that the graph includes -3 in its x value. The open circle one means the graph contains every number until x=-3.

So to find the y value at x = -3 you want to look at the y value that corresponds to the closed circle of the graph since it is the part that includes x=-3 and you will see that y = 4 at that spot.

Answer:

- 8b³+5ab²+7a²b

Step-by-step explanation:

(32ab³ - 20a²b² - 28a³b)/(-4a)= - 8b³+5ab²+7a²b

Answer:

D.

Step-by-step explanation:

For independent events

P(A and B) = P(A) × P(B)

FINDING P(B)

P(B) = P(A and B) /P(A)

P(B) = 0.6/0.8

P(B) = 0.75

Answer:

a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.

b. ∅ = [tex]tan^{-1}[/tex](Rx/Ry)

Step-by-step explanation:

Vectors are used to express physical quantities with magnitude and direction. Vectors can be added by the parallelogram method or the triangular method of addition. the magnitude and direction of the resultant vector is usually proportional to the magnitude and direction of the component vectors.

The direction of the angle is found as

tan∅ = Rx/Ry

∅ = [tex]tan^{-1}[/tex](Rx/Ry)

Answer:

Step-by-step explanation:

[tex]u_3 = v_3[/tex] and  [tex]u_2 = v_1[/tex]

[tex]u_1= v_1 -7 v_3[/tex]

Replace the first line to the second line, you have [tex]u_1= u_2-7u_3[/tex]

That shows [tex]\{u_1, u_2, u_3,u_4\}[/tex]

is not linear independent.

Answer:

0.3745

Step-by-step explanation:

We have to solve the problem by calculating the z-score value that has the following formula:

z <(x - m) / sd

x is the value to evaluate (<80), m is the mean (85) and the standard deviation is sd (12)

replacing:

p (x <80) = z <(80 - 85) / 12

z <-0.416, we look for this value in the normal distribution table and it corresponds to:

p (x <80) = 0.3745

Which means that the proportion of people is 0.3745

Answer:

We want to test if the scouts in her troop sold more cookies than the average in New York City (50), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 50[/tex]  

Alternative hypothesis:[tex]\mu > 50[/tex]  

The statistic for this case is given by:

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

For this case we have also the p value calculated

[tex]p_v =0.11[/tex]

If we use any significance level lower than 10% we FAIL to reject the null hypothesis (pvalue>significance) and we can conclude that the true mean is not higher than the mean for New York otherwise if we use a significance level higher than 10% the conclusion would be the opposite.

Step-by-step explanation:

Information given

[tex]\bar X=101.1[/tex] represent the sample mean

[tex]s=29.3[/tex] represent the sample standard deviation

[tex]n=50[/tex] sample size  

[tex]\mu_o =50[/tex] represent the value that we want to test

t would represent the statistic

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

System of hypothesis

We want to test if the scouts in her troop sold more cookies than the average in New York City (50), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 50[/tex]  

Alternative hypothesis:[tex]\mu > 50[/tex]  

The statistic for this case is given by:

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

For this case we have also the p value calculated

[tex]p_v =0.11[/tex]

Conclusion

If we use any significance level lower than 10% we FAIL to reject the null hypothesis (pvalue>significance) and we can conclude that the true mean is not higher than the mean for New York otherwise if we use a significance level higher than 10% the conclusion would be the opposite.

Answer:

Step-by-step explanation:

-7-1=-8

Answer:

a) 71.25 gallons

b) 25 hrs

c) 105 gallons

d) 47.91 hrs

Step-by-step explanation:

Solution:-

- The rate at which the pollution enter the lake is expressed by a function f ( t ) as follows:

                            [tex]f ( t ) = 10*( 1 - e^-^0^.^5^t )[/tex]

- Where, the rate at which pollution is removed from the lake via a filter is expressed by a function g ( t ):

                             [tex]g ( t ) = 0.4t[/tex]

- We will denote ( x ) as the amount of population in lake at time ( t ).

- We will set up a linear first order ODE using rate of change of pollution ( x ) in the lake at any instance ( t ):

                            [tex]\frac{dx}{dt} = ( flow _ i_n ) - ( flow _ o_u_t )[/tex]

- The respective inflow and outflow of pollution from the lake are expressed by the functions f ( t ) and g ( t ). Hence, the ODE becomes:

                           [tex]\frac{dx}{dt} = f ( t ) - g ( t )\\\\\frac{dx}{dt} = 10*( 1 - e^-^0^.^5^t ) - 0.4t\\\\[/tex]

- Separate the variables and integrate from t = 0 to t = 12 hours.

                         [tex]x = \int\limits^1^2_0 [{10*( 1 - e^-^0^.^5^t ) - 0.4t} ] \, dt \\\\x ( 12 ) = [ 10 * ( t + 2e^-^0^.^5^t ) - 0.2t^2 ] \limits^1^2_0\\\\x ( 12 ) = [ 10 * ( 12 + 2e^-^6 ) - 0.2(12)^2 ] - [ 10* ( 0 + 1 ) - 0.2(0)^2 ]\\\\x ( 12 ) = 71.25 galls[/tex]

- We will use the graphing calculator to evaluate the time ( t ) at which the rate of inflow of pollution is equal to the rate at which pollution is removed from the lake. In other words solve the following equation:

                          [tex]f ( t ) = g ( t )\\\\10*( 1 - e^-^0^.^5^t ) = 0.4t[/tex]

- Solving for the above equation the following intersection point was observed:

                          t = 25 hours

- We will perform integration of the previously expressed ODE from t = 0 to t = 25 hrs.

                           [tex]x ( 25 ) = [ 10*(t - 2e^0^.^5^t ) - 0.2t^2 ]\limits^2^5 _ 0\\\\x ( 25 ) = [ 10*(25 - 2e^1^2^.^5 ) - 0.2(25)^2 ] - [ 20 ] \\\\x ( 25 ) = 105 galls[/tex]

- We will evaluated result of the integration from time t = 0 to time t = t set the amount of pollution ( x ) equal to zero:

                          [tex]x ( t ) = [ 10*( t - 2e^-^0^.^5^t ) - 0.2t^2 ]\limits^t_0\\\\x ( t ) = 10 + 20e^-^0^.^5^t - 0.2t^2 - 20[/tex]

- Use the derived result x ( t ) and feed it into the graphing calculator and solve for x ( t ) = 0; hence,

                       10 + 20e^( -0.5*t ) - 0.2t^2 - 20 = 0

- The answer is evaluated as t = 47.91 hr

Answer:

20/40

Step-by-step explanation:

1/5=40/100*x

x=1/5*100/40

x=20/40 or 10/20 or 0.5

The domain of a function is the set of all the x terms of the function and the range of a function is the set of all the y terms of a function.

For example, take a look below.

The domain is the set of all x terms in each ordered pair and the

range will be the set of all the y terms in each ordered pair.

Answer:

[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]

And we can find this probability with the complement rule:

[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]

And we can use excel or the normal standard table and we got:

[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]

So then we expect about 81.8% of students that will be promoted

Step-by-step explanation:

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

[tex]X \sim N(60,5.5)[/tex]  

Where [tex]\mu=60[/tex] and [tex]\sigma=5.5[/tex]

We want to find the following probability:

[tex]P(X>55)[/tex]

And we can use the z score formula given by:

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

Using the z score formula we got:

[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]

And we can find this probability with the complement rule:

[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]

And we can use excel or the normal standard table and we got:

[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]

So then we expect about 81.8% of students that will be promoted

Answer:

D. $7.00

Step-by-step explanation:

I just did it.

The 1st digit is 1 out of 10 numbers

The 2nd digit is 1 out of 9 numbers

The 3rd digit is 1 out of 8 numbers

The 4th digit is 1 out of 1 numbers.

Total combinations are 10 x 9 x 8 x 7 = 5040

Since the combination 7654 is one out of the total the probability would be 1/5040

Answer:

$11154.6

Step-by-step explanation:

We have that the interest would be calculated as follows:  

9000 * 0.0475 = 427.5

then this for the amount of time in years:

427.5 * 6 = 2565

Now, we have to pay 16% federal interest tax. So, that would be

2565 * 0.16 = 410.4

Therefore, the money available to us after 6 years would be:

9000 + 2565 - 410.4 = 11154.6

It means that it would be $ 11154.6

Answer:

37.8541 litres.

Step-by-step explanation:

To find the amount of gas that she needs to fill her gas tank is 19 -9. She needs 10 gallons to fill her tank.

It says to state in litres, so convert.

1 gallon is about 3.78541 liters, so 10 gallons is 37.8541 litres

Hope that helped : )

Answer:

90 square feet.

Step-by-step explanation:

Let's set up an equation!

SA= 2(xy)+2(xz)+2(yz).

Lets say that x=3 y=6 and z=3

We plug it in.

2(18)+2(9)+2(18)= SA

36+18+36=SA

72+18=SA

90=SA

90 square feet = Surface area.

Answer:

the 3rd option is the right one

Step-by-step explanation:

Suppose the results obtained are numbers from 1 to 10, then after 10 rolls, the average is

(1+2+3+4+5+6+7+8+9+10)/10

= 55/10

= 5.5

Answer:

5 , 3 , 3.5     C) The average would approach a set value.

Step-by-step explanation:

The first three numbers don't matter it could be anyone 1-6.

The last answer is C

Answer:

The true statements Include

A) The length of a confidence interval can be determined if you know only the margin of error.

B) The margin of error can be determined if you know only the length of the confidence interval.

D) The confidence interval can be obtained if you know only the margin of error and the sample mean.

G) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.

F) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

The false statements include

C) The confidence interval can be obtained if you know only the margin of error.

E) The margin of error can be determined if you know only the confidence level.

F) The confidence level can be determined if you know only the margin of error.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

The critical value is obtained using the confidence level (and sample size for t-distributions).

Standard Error of the mean = (Standard deviation)/[√(sample size)]

Standard error of the mean = σₓ = (σ/√n)

Taking each of the statements one at a time

a) The length of a confidence interval can be determined if you know only the margin of error.

According to the mathematical expression of the confidence interval, the length of the confidence interval is 2 × Margin of error. Hence, the length of the confidence interval can be truly obtained from only the margin of error.

This statement is true.

b) The margin of error can be determined if you know only the length of the confidence interval.

This is another way of phrasing statement A. The margin of error is half of the length of the confidence interval.

Hence, this statement is also true.

c) The confidence interval can be obtained if you know only the margin of error.

The confidence interval can be obtained from an expression that involves the sample mean and margin of error.

Confidence Interval = (Sample mean) ± (Margin of error)

The confidence interval cannot be obtained from just the margin of error. Hence, this statement is false.

d) The confidence interval can be obtained if you know only the margin of error and the sample mean.

Like o stated in (c) above, the confidence interval can be obtained from an expression that involves the sample mean and margin of error.

Confidence Interval = (Sample mean) ± (Margin of error)

Hence, this statement is true.

e) The margin of error can be determined if you know only the confidence level.

To obtain the margin of error, if the confidence interval isn't used, an expression involving the critical value and the standard error of the mean is used.

Margin of Error = (Critical value) × (standard Error of the mean)

The critical value is obtained using the confidence level, but the margin of error cannot be obtained from just that, we still need the standard error of the mean.

Hence, this statement is false.

f) The confidence level can be determined if you know only the margin of error.

This is another way of phrasing statement E. Hence, this statement too is false.

g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.

This is true as these is all that is required to obtain the margin of error.

h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

This can be a bit stressful to obtain, but it is true. It is easy to see this from all the explanation from the beginning to this point.

Hope this Helps!!!

Step-by-step explanation:

5x3 + 20x2 + 2x + 8

5x2 (x + 4) + 2(x + 4)

(5x2 + 2) (x + 4)

Answer:

C (5.3, -6, -14, 3.5, 7)

Step-by-step explanation:

Integers are the sets of positive and negative whole numbers including zero.

In set notation, we denote the set of integers using the letter [tex]\mattbb{Z}[/tex].

From the given options:

In Option C (5. 3, -6, -14, 3.5, 7), we have the number 3.5 and 5.3 which are not whole numbers. Therefore 3.5 and 5.3 are not integers.

Option C is the set which does not contain only integers.