8. What is the sum of the exterior angles of
a regular octagon?

A. 135°
B. 360°
C. 720°
D. 1080°

Answer:

His overall final​ score is 81.5

He earned a B

Step-by-step explanation:

To find his overall grade, we multiply each of his grades by it's weight.

Grades:

67 on the midterm, which counts for 10% = 0.1

88 on the project, which counts for 15% = 0.15

91 on homework assignements, which counts for 40% = 0.4

72 on the final exam, which counts for 35% = 0.35.

What is his overall final​ score?

67*0.1 + 88*0.15 + 91*0.4 + 72*0.35 = 81.5

His overall final​ score is 81.5

At least 80 and less than 90 has a letter grade of B. 81.5 is in this range. So he earned a B

Answer:

x= -14

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

See below for the table.

Step-by-step explanation:

The results for the thirty cases are listed below:

U U U I F O O U I F F O U I I F I I O U I F F U U I I O F U

The table summarizing the frequency distribution of the primary causes leading to student dropout is:

[tex]\left|\begin{array}{c|c}$Cause&$Frequency\\----------&----\\\\$Unexcused absences (U)&9\\$Illness (I)&9\\$Family problems (F)&7\\$Other causes (O)&5\\-----------&---\\$Total&30\end{array}\right|[/tex]

Answer:  length of AB

Step-by-step explanation:

[tex]\overline{AB}[/tex] represents the line segment from point A to point B

[tex]\overrightarrow{AB}[/tex] represents ray from point A to infinity through point B

AB represents the length of the line segment from point A to point B.

Answer:

19.49% probability that no more than 16 of them are strikes

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 30, p = 0.626[/tex]

So

[tex]\mu = E(X) = np = 30*0.626 = 18.78[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*(1-0.626)} = 2.65[/tex]

What is the probability that no more than 16 of them are strikes

Using continuity correction, this is [tex]P(X \leq 16 + 0.5) = P(X \leq 16.5)[/tex], which is the pvalue of Z when X = 16.5. So

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

[tex]Z = \frac{16.5 - 18.78}{2.65}[/tex]

[tex]Z = -0.86[/tex]

[tex]Z = -0.86[/tex] has a pvalue of 0.1949

19.49% probability that no more than 16 of them are strikes

Answer:

The work will be "1909212.015 J". The further explanation is given below.

Step-by-step explanation:

The given values are:

Liquid's density

= 760 kg/m³

Height

= 3 meters

Gravity

g = 3.8 m/s²

Value of y is:

y = 5 log (x-2)

y = 0

y = 4

As we know,

⇒  [tex]\Delta V=\pi r^2 \Delta y[/tex]

⇒  [tex]y =5log(x-2)[/tex]

⇒  [tex]\frac{y}{5} =log (x-2)[/tex]

⇒  [tex]e^{\frac{y}{5}}=(x-2)[/tex]

⇒  [tex]x=e^{\frac{y}{5}}+2[/tex]

Now,

[tex]\Delta F=ma[/tex]

      [tex]=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y[/tex]

So that,

⇒  [tex]\Delta W = \Delta F.distance[/tex]

            [tex]=\Delta F(4-y)[/tex]

The required work will be:

⇒  [tex]W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy[/tex]

         [tex]=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}][/tex]

         [tex]=760\times 9.8 \pi[81.455][/tex]

         [tex]=1909212.015 \ J[/tex]

Answer:

The average revenue per passenger is about $13.85

μ = $13.85

The corresponding standard deviation is $14.51

σ = $14.51

The airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

Expected revenue = $1,662 ± 14.51

Step-by-step explanation:

An airline charges the following baggage fees:

$25 for the first bag and $35 for the second

Suppose 51% of passengers have no checked luggage,

P(0) = 0.51

33% have one piece of checked luggage and 16% have two pieces.

P(1) = 0.33

P(2) = 0.16

a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.

The average revenue per passenger is given by

μ = 0×P(0) + 25×P(1) + 35×P(2)

μ = 0×0.51 + 25×0.33 + 35×0.16

μ = 0 + 8.25 + 5.6

μ = $13.85

Therefore, the average revenue per passenger is about $13.85

The corresponding standard deviation is given by

σ = √σ²

Where σ² is the variance and is given by

σ² = (0 - 13.85)²×0.51 + (25 - 13.85)²×0.33 + (35 - 13.85)²×0.16

σ² = 97.83 + 41.03 + 71.57

σ² = 210.43

So,

σ = √210.43

σ = $14.51

Therefore, the corresponding standard deviation is $14.51

b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation?

For 120 passengers,

Expected revenue = 120×$13.85

Expected revenue = $1,662 ± 14.51

Therefore, the airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

Answer:

65%

Step-by-step explanation:

Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?

3 gallons of 80% juice solution contains this amount of juice:

80% * 3 gal = 0.8 * 3 gal = 2.4 gal

1 gallon of 20% juice solution contains this amount of juice:

20% * 1 gal = 0.2 * 1 gal = 0.2 gal

The total amount of juice in the final juice solution is

2.4 gal + 0.2 gal = 2.6 gal

The total amount of juice solution made is 3 gal + 1 gal = 4 gal

The 4 gal juice solution contains 2.6 gallons of juice.

2.6 gallons is what percent of 4 gallons?

2.6/4 * 100% = 0.65 * 100% = 65%

Answer: 65%

Answer:

65% i got the answer right on the question

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

Number of students whose favorite class is Math:

60*0.85=51

Number of students whose favorite class is Science:

15% is equal to 0.15.

60*0.15=9

Subtract number of students who like science from number of students who like math.

51-9=42

42 more students in the survey prefer math over science.

Answer:

42

Step-by-step explanation:

85% math

15% science

Subtract

85-15 = 70

The difference is 70 %

70% of 60 students

.70 * 60 = 42

There is a 42 student difference

Answer:

0.25

Step-by-step explanation:

Out of the 4 counters only 1 is black so the probability is 1/4 or 0.25.

Answer:

0.25

Step-by-step explanation:

Since there are four marbles 100/4 =25 in this 100 is 1 thus the answer is 0.25

Answer:

It will take 1.43 hours for them to clean the car.

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this problem:

Together rate: 1/x

Tanya's rate: 1/2

Pat's rate: 1/5

Together rate = Tanya's rate + Pat's rate

[tex]\frac{1}{x} = \frac{1}{2} + \frac{1}{5}[/tex]

[tex]\frac{1}{x} = \frac{5 + 2}{10}[/tex]

[tex]\frac{1}{x} = \frac{7}{10}[/tex]

[tex]7x = 10[/tex]

[tex]x = \frac{10}{7}[/tex]

[tex]x = 1.43[/tex]

It will take 1.43 hours for them to clean the car.

Answer:

The slope is m=2.145.

The y-intercept is b=-1.33.

Step-by-step explanation:

We have this data:

- The mean and standard deviation for x are 5.43 and 1.12, respectively.

- The mean and standard deviation for y are 10.32 and 2.69, respectively.

- The correlation is 0.893.

We have to calculate the slope and the y-intercept of the least-squares line.

With the given data, we can calculate the slope m as:

[tex]m=r\;\dfrac{s_y}{s_x}=0.893\;\dfrac{2.69}{1.12}=2.145[/tex]

Then, the y-intercept is calculated as:

[tex]b=\bar y-m\cdot \bar x=10.32-2.145\cdot 5.43=10.32-11.65=-1.33[/tex]

Answer:

308.67 cm ^ 3 / week

Step-by-step explanation:

A cantaloupe is approximately a sphere, therefore its approximate volume would be:

V = (4/3) * pi * (r ^ 3)

They tell us that dr / dt 0.5 cm / week and the radius is 6.4 cm

if we derive the formula from the volume we are left with:

dV / dt = (4/3) * pi * d / dr [(r ^ 3)]

dV / dt = (4/3) * pi * 3 * (r ^ 2) * dr / dt

dV / dt = 4 * pi * (r ^ 2) * dr / dt

we replace all the values and we are left with:

dV / dt = 4 * 3.14 * (6.4 ^ 2) * 0.6

dV / dt = 308.67

Therefore the volume is changing at a rate of 308.67 cm ^ 3 / week

Answer:

When x is 1, y=7

When x is 2, y=10

When x is 3, y= 13

Step-by-step explanation: Plug in each number for x and solve

Answer:

If x=1, y=7

If x=2, y=10

If x=3, y=13

Step-by-step explanation:

For every equation substitute x in y = 3x + 4, with the value you want.

For example the first one says when x=1, so simply substitute x with 1 in y = 3x + 4.

So it'll look something like this:

y = 3(1) + 4.

Simply solve the equation from there, and you'll get y=7, and we know that x is already equal to 1.

So if x=1, then y=7

Answer:

June Financial Reports

a) Cost of goods available for sale = $5,250

b) Moving-Average unit cost for:

i) June 1:  = $5

ii)        12:  = $4.75

iii)       15: = $4.75

iv)      23:  = $5.75

v)       27:  = $5.25

Step-by-step explanation:

a) Calculations:

Date     Explanation   Units     Unit Cost    Total Cost   Moving Average Cost

June 1 Inventory          150        $4                $600         $4.000

      12 Purchase         450          5               2,250            4.750

      15 Sale                 500          7                      3,500     4.750

     23 Purchase         400          6               2,400            5.750

     27 Sale                 420          8                      3,360     5.250

     30 Inventory           80

Cost of goods available for sale = Cost of Beginning Inventory + Cost of Purchases = $5,250 + ($600 + 2,250 + 2,400)

b) Moving-Average unit cost for:

i) June 1: Cost of goods available/Units of goods available = $5 ($600/150)

ii)        12: Cost  of goods available/Units of goods available = $4.75 ($600 + 2,250/600)

iii)       15: Cost  of goods available/Units of goods available = $4.75 ($475/100)

iv)      23: Cost of goods available/Units of goods available = $5.75 ($475 + 2,400)/500

v)       27: Cost of goods available/Units of goods available = $5.25 ($420/80)

Answer:

Y is 90 degrees.

Step-by-step explanation:

This is an equalterial triangle which means all of the angles are the same.  The angle for the upper part of the triangle is 60 as well. We can do 2x=60 because they add up to the angle which is 60. This gives us x=30. If x=30 and the other angle is 60, then the other angle has to be 90 because all triangle has an angle sum of 180. So 30 +60 + 90= 180. Hope this helps!

Answer:

y=90 degrees.

Step-by-step explanation:

Answer:

The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.

Step-by-step explanation:

We have the standard deviation of the saple, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2\frac{1.3}{\sqrt{50}} = 0.4[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.

Answer:

0.1587

Step-by-step explanation:

According to the situation, the solution and the data provided is as follows

mean = 12.45 ounces

Standard deviation = 0.30 ounces

maximum = 12.75 ounces

More than ounces of soda = 12.75

Based on the above information, the probability is

[tex]Z=\frac{X-\mu }{\sigma } \\\\Z=\frac{12.75-12.45 }{0.30 } \\\\\Z=\frac{0.30 }{0.30 } \\\\Z= 1 \\\\P(X> 12.75)=1-P(X< 12.75) \\\\\P(X> 12.75)=1-P(Z< 1) \\\\[/tex]

As we know that

P(Z<1) = 0.8413

So,

P (X > 12.75) = 1 - 0.8413

= 0.1587

The question is incomplete. Here is the complete question.

In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:

Question #1: I prefer outdoor activities, rather than indoor activities.

Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.

Question #3: I prefer texting, rather than talking on the phone.

Question #4: I prefer living in a small town, rather than in a big city.

Here are the results for the questionaire, with a group of 5 participants:

                        Question1     Question2   Question3       Question4

participant A           1                      1                   -1                      -1

participant B           -1                     1                    1                       1

participant C           -1                    -1                    1                       1

participant D           1                     -1                   -1                      -1

participant E            1                    -1                    1                       1

Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".

(a) Which pairs of paricipants are compatible?

(b) Which pairs of participants are incompatible?

(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only

allowing  "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?

Answer: (a) Participants A and D; B and C; C and E.

(b) Participants A and B; A and C; A and E; B and D; C and D;

Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.

Vectors form angles between themselves and can be found by the following formula:

cos α = [tex]\frac{A.B}{||A||.||B||}[/tex]

which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.

For the compatibility test, find the angle between vectors:

1) The vectors magnitude:

Magnitude of a vector is given by:

||x|| = [tex]\sqrt{x_{i}^{2} + x_{j}^{2}}[/tex]

Since all the vectors have value 1, they have the same magnitude:

||A|| = [tex]\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}[/tex] = 2

||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2

2) The dot product of vectors:

A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2

cos [tex]\alpha_{1}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]

The angle that has cosine equal -1/2 is 120°, so incompatible

A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4

cos [tex]\alpha _{2}[/tex] = -1

Angle = 180° --------> incompatible

A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2

cos [tex]\alpha _{3}[/tex] = 1/2

Angle = 60° ---------> COMPATIBLE

A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2

cos [tex]\alpha_{4}[/tex] = -1/2

Angle = 120° --------> incompatible

B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2

cos [tex]\alpha _{5}[/tex] = 1/2

Angle = 60° -------------> COMPATIBLE

B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4

cos[tex]\alpha_{6}[/tex] = -1

Angle = 180° -----------> incompatible

B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0

cos[tex]\alpha _{7}[/tex] = 0

Angle = 90° -------------> may or may not

C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2

cos[tex]\alpha_{8} =[/tex] -1/2

Angle = 120° ---------------> Incompatible

C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2

cos [tex]\alpha_{9}[/tex] = 1/2

Angle = 60° ---------------> COMPATIBLE

D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0

cos [tex]\alpha_{10}[/tex] = 0

Angle = 90° -----------------> may or may not

(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.

Answer:

slope = 2

Step-by-step explanation:

All four points lie on the same line.

Taking the first and fourth points, the slope can be found by the formula

slope, m = (y2-y1)/(x2-x1) = (3- -3) / (1- -2) = 6/3 =2

See attached diagram.

Answer:

2

Step-by-step explanation:

edge 2020

Answer:

x= 9 inches

Step-by-step explanation:

Hello

I can help you with this.

in this case, we have two similar triangles, let's see

Step 1

identify the rigth triangles.

1) the first triangle has these dimensions

hypotenuse( remember, the longest side)= unknown=H

adjacent side(the horizontal)=6 +x

opposite side(the vertical)=10

2) the second triangle has these dimensions

hypotenuse( remember, the longest side)= unknown=h

adjacent side(the horizontal)=6

opposite side(the vertical)=4.

As these triangles keep the same proportion and in both cases we know the length of the legs, we can establish a relationship

Step 2

establish a relationship

let's compare the opposite side and the adjacent side

triangle 1 (the bigger)

[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{10}{6+x}[/tex]

Triangle 2

[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{4}{6}\\proportion=\frac{2}{3}[/tex]

were the proportions are equal, so

[tex]\frac{10}{6+x}=\frac{2}{3}[/tex]

at this point, just isolate x to find its value

Step 3

isolate x

[tex]\frac{10}{6+x}=\frac{2}{3}\\multiply\ both\ sides\ by\ 3\\\frac{10*3}{6+x}=\frac{2*3}{3}\\\frac{30}{6+x} =2\\\\Multiply\ both\ sides\ by (6+x)\\\frac{30(6+X)}{6+x} =2(6+x)\\30=12+2x\\30-12=2x\\18=2x\\so\\x=\frac{18}{2} \\x=9[/tex]

remember the units of measure ( Inches)

x= 9 inches

I really hope it helps, have a nice day.

Answer:

n^2+3

Step-by-step explanation:

As we can see in the diagram

1st pattern consists from 1 square 1x1 +3 squares 1x1 each

2nd pattern consists from 1 square 2x2 +3 squares 1x1 each

3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each

4-th pattern consists from 1 square 4x4 + 3 squares 1x1  each

We can to continue :

5-th pattern consists from 1 square 5x5+3 squares 1x1 each

So the nth    pattern consists from 1 square nxn+3 squares 1x1 each

Or total amount of 1x1 squares in nth pattern N= n^2+3

The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."

From the given diagram

We can see that every term is made up with a square which side is n and three small square side is 1.

So,

1st term is 1 × 1 + 3 = 4

2nd term is 2 × 2 + 3 = 4

3rd term is  3 × 3 + 3 = 12

4th term is 4 × 4 + 3 = 19

So, nth term is [tex]n^{2} +3[/tex]

Hence, The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

Learn more about nth term of a sequence here

https://brainly.com/question/24306119

#SPJ2

Answer:

0.1048

Step-by-step explanation:

The computation of probability that they receive 10 calls in the next hours is shown below:-

Average which is given in the question 5 minutes between calls = 5/60 calls an hour so it becomes 12 calls per hour

So,

P(X = 10)

[tex]= \frac{e^{-12}12^{10}}{10!}[/tex]

= 0.1048

Therefore for computing the probability that they receive 10 calls in the next hours we simply applied the above formula.

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

Cross multiply.

10(4x + 1) = 15(2x)

Expand brackets.

40x + 10 = 30x

Add -30x and 10 on both sides.

40x - 30x = -10

10x = -10

Divide both sides by 10.

10/10x = -10/10

x = -1

Answer:

Step-by-step explanation:

a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.

The principal P that must be invested at rate r for n annual withdrawals of amount A is ...

  P = A(1+r)(1 -(1 +r)^-n)/r

  P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95

__

b) 20 withdrawals of $60,000 each total ...

  20×$60,000 = $1,200,000

__

c) The excess over the amount deposited is interest:

  $1,200,000 -636,215.95 = $563,784.05

see if other people has already answered this question

Answer:

-1

1

1/2(1±i√3)

Step-by-step explanation:

1. x+1=0 ⇒ x= -1

2. x-1= 0 ⇒ x= 1

3. x^2-x+1=0

Answer:

Using the normal approximation to the binomial distribution

a) The probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x < 2) = 0.0015

b) The probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x > 10) = 0.1271

Using Binomial distribution formula for these same probabilities.

c) The probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x < 2) = 0.0005

The probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit = P(x > 10) = 0.1275

With the continuity correction factor added, the normal approximation to the binomial distribution problem is a good estimate of the binomial distribution, especially for variables close to the mean.

Step-by-step explanation:

To use the normal approximation to the binomial distribution problem, we need to compute the mean and the standard deviation.

With n = sample size = 20

p = proportion of the swordfish pieces available for sale have a level of mercury above the Food and Drug Administration (FDA) limit = 40% = 0.40

Mean = μ = np = 20 × 0.40 = 8

Standard deviation = σ = √[np(1-p)] = √(20×0.40×0.60) = 2.191

If X represents the number of swordfish pieces that have mercury levels exceeding the FDA limit

a) Probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit.

Introducing the continuity correction factor,

P(X < 2) becomes P(x < 2-0.5) = P(x < 1.5)

We first normalize or standardize 1.5.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (1.5 - 8)/2.191 = - 2.97

To determine the required probability

P(x < 1.5) = P(z < -2 97)

We'll use data from the normal distribution table for these probabilities

P(X < 2) = P(x < 1.5) = P(z < -2 97) = 0.00149 = 0.0015

b) Probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit

Adjusting with the continuity correction factor P(X > 10) = P(x > 10+0.5) = P(x > 10.5)

We first normalize or standardize 10.5

z = (x - μ)/σ = (10.5 - 8)/2.191 = 1.14

To determine the required probability

P(x > 10.5) = P(z > 1.14)

We'll use data from the normal distribution table for these probabilities

P(X > 10) = P(X > 10.5) = P(z > 1.14)

= 1 - P(z ≤ 1.14)

= 1 - 0.87286 = 0.12714 = 0.1271

c) Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of swordfishes to be examined = 20

x = Number of successes required = fewer than 2 and more than half, < 2 and > 10

p = probability of success = probability of a swordfish having mercury levels above the FDA limits = 0.40

q = probability of failure = probability of a swordfish NOT having mercury levels above the FDA limits = 1 - p = 1 - 0.40 = 0.60

P(X < 2) = P(X = 0) + P(X = 1) = 0.00052404938 = 0.0005

P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.12752124615 = 0.1275

With the continuity correction factor added, the normal approximation to the binomial distribution problem is a good estimate of the binomial distribution, especially for variables close to the mean.

Hope this Helps!!!

Answer:

AB=4

Step-by-step explanation:

The transitive property states if A=B and B+C than A+C  Next substitute

AB=x and x=4 so AB=4

Hope this helps, if it did, please give me brainliest, it helps me a lot. :)

Have a good day!