what is the product of 4/5 × 2/5​

Answers

Answer 1

Answer:

8/25

Step-by-step explanation:

4/5 *2/5

Multiply the numerators

4*2 = 8

Multiply the denominators

5*5 = 25

8/25

Answer 2

Answer:

The answer would be 8/25 or 0.32


Related Questions

pleaseeee helpp nowwwwwwwww :/
.
.
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Find the value of m: −3(m − 4) = −6


m = −6

m = −2

m = 2

m = 6

Answers

The solution of the equation is m = 6.

How to find the variable of an equation?

The variable to find is variable m.

The equation is as follows:

−3(m − 4) = − 6

Hence, let's open the bracket on the left side of the equation

−3(m − 4) = − 6

- 3m + 12 = -6

subtract 12 from both sides of the equation

- 3m + 12 = -6

- 3m + 12 - 12 = -6 - 12

- 3m = - 18

divide both sides of the equation by -3

- 3m / - 3 = - 18 / -3

Therefore,

m = 6

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Answer:

m = 6

Step-by-step explanation:

Find the value of m: −3(m − 4) = −6

m = −6

m = −2

m = 2

m = 6

-3(m - 4) = -6

-3m + 12 = -6

-3m = -6 - 12

- 3m = -18

m = -18 : (-3)

m = 6

-----------------------------

check

-3(6 - 4) = -6

-18 + 12 = -6

-6 = -6

the answer is good

Write an equation to make the number "24" using all the numbers 5,4,2,2 and +, -, x and ÷.

Answers

Answer: See explanation

Step-by-step explanation:

We are given the numbers 5,4,2, and 2 and told to make an equation from it and get a final answer as 24. This will be:

= 5 × 4 + 2 + 2

= 20 + 2 + 2

= 24.

Since we have gotten a final answer of 24, the equation is solved.

A swimming pool has a length of 28 feet, a width of 17 feet, and a depth of 6 feet. How much water can the swimming pool hold?
A.
5,712 cubic feet
B.
1,492 cubic feet
C.
2,856 cubic feet
D.
746 cubic feet

Answers

Answer to this question is C.2856

Answer: C. 2,856

Step-by-step explanation: The formula for volume is V= lwh (length x width x hight). So you'd do 28 x 17 x 6 = 2,856.

A manufacturer makes ball bearings out of molten steel. It takes 5.24 cubic centimeters of molten steel to make
have a diameter of 1 centimeter.
ball bearings that each have a diameter of 1 centimeter

Answers

The number of ball bearings that can be made based on the volume will be 10 ball bearings.

How to calculate the volume?

It should be noted that the volume based on the information given will be:

V = 4/3πr³

= 4/3 × 3.14 × 0.5³

= 0.524

From the information, it takes 5.24 cubic centimeters of molten steel to have a diameter of 1 centimeter.

Therefore, the number of ball bearings will be:

= 5.24/.0524

= 10

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What is the value of Z in this equation
11 • z = 121​

Answers

Answer:

z = 11

Step-by-step explanation:

To solve this equation, divide each side by 11.

11 z = 121

11z/11 = 121/11

z = 11

Answer:

To find the value of Z in this equation, we need to isolate Z on one side of the equation. To do that, we can use the inverse operation of multiplication, which is division. We can divide both sides of the equation by 11, which is the coefficient of Z. This will cancel out the 11 on the left side and leave Z alone. On the right side, we can use a calculator or long division to find the quotient of 121 and 11. The result is 11 as well. Therefore, we can write:

11 • z = 121

(11 • z) / 11 = 121 / 11

z = 11

The value of Z in this equation is 11.

MARK AS BRAINLIEST!!!

allocation is a mathematical procedure that cannot be manipulated by the parties involved in making the allocation. this statement is

Answers

The given statement that allocation is a mathematical procedure that cannot be manipulated by the parties involved in making the allocation is true.

The term allocation refers to the process of dividing something among various parties. The term is often used in finance and economics to refer to the distribution of goods or resources among various groups or individuals.

Mathematical allocation refers to the distribution of a finite amount of resources among several competing individuals, groups, or companies. This is typically done with the help of mathematical techniques that are based on algorithms and statistical models.

An example of mathematical allocation can be seen in the allocation of financial resources in a company.In mathematical allocation, the parties involved in making the allocation cannot manipulate the process. This means that the allocation is done in a fair and impartial manner, without any interference from the parties involved. This helps to ensure that the allocation is done in an objective and unbiased way, which is important for maintaining the integrity of the allocation process.

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In slope intercept form

Answers

Answer:

y = mx + b

Step-by-step explanation:

The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

y=mx+b! m is the slope, b represents the y value of the lines y-intercept

A polygon is shown.


The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is ___ square units.

A polygon is shown.The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of

Answers

Answer:

Area of a rectangle that is 9 units² + Area of a rectangle that is 4 units²

Step-by-step explanation:

Line PQ is 1 unit because 3 units - 2 units = 1 unit

Line PO is 4 units because 7 units - 3 units = 4 units

1 unit × 4 units = 4 units²

4 units² + 9 units² = 13 units²

Answer:

adding an answer so the other guy can get brainlist!

Step-by-step explanation:

A person swims 11 miles downriver at the same time they can swim 7 miles upriver. The speed of the current is 4 miles per hour. Find the speed of the person in still water. Construct a rational equation to solve the problem above. Show your work and explain your answer.



Distance

Rate

Time

Upstream


x − c


Downstream


x+c

Answers

Answer: 6mph as it just is

PLEASE HElP 25 points math

PLEASE HElP 25 points math

Answers

Answer: 4q^2

Step-by-step explanation:

(-2q)^2=

(-2*q)^2=

(-2)^2 * q^2=

4 * q^2=4q^2

4. Show that the matrix [XX-X'Z(ZZ)-¹Z'X). where both the x & matrix X and the x matrix Z. have full column rank and m2, is positive definite. Discuss the implications of this result in econometrics.

Answers

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Solve 2(x+3) = x - 4

Answers

X=2 is the answer do you need to know why
First multiply:

2x + 6 = x - 4

Now rearrange so you have all the x on one side (remember to change the sign when you move from one side to the other):

2x - x = - 4 - 6

Do the sums:

x = -10

What is the solution to In (x2 - 16) = 0? x==117 o x = +4 o x=5732 DONE​

Answers

x=4, x=-4

(x^2 - 16) can be factored.

(x-4)(x+4)

x-4=0
x=4

x+4=0
x=-4


help me here plss Fast

1. and 2. thanks ^^​

help me here plss Fast1. and 2. thanks ^^

Answers

Step-by-step explanation:

here you go hope it helps

help me here plss Fast1. and 2. thanks ^^

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Help help help help help help help help help help help help help help help help help help help help help

Answers

Answer:

D

Step-by-step explanation:

plug in the x values each time and solve for f(x) which is also known as the y value.

f(x)=y

Answer:

D?

Step-by-step explanation:

11 times 11 in binary . Help i need it today!

Answers

Answer:

1111001

Step-by-step explanation:

1011

×1011

—————

1111001

Answer:

Step-by-step explanation:

         1 1

        1 1

         1 1

       1 1

     ----------

    1 0 0 1

What do you have?

8 4 2 units

1  0 0 1

1 + 8 = 9

3 * 3 = 9

Find two numbers whose difference is 5 and sun of whose squares is 100.

(I believe this is the quadratic formula!)

I’m not sure how to go about it. If someone go go through it step by step, that’d be helpful. (Or even give me the values to put into the quadratic formula)

Answers

Answer:

I. x = 14.115 and y = 9.115

II. x = 0.885 and y = -4.115

Step-by-step explanation:

Let the two numbers be x and y respectively.

Translating the word problem, we have;

x - y = 5  ......equation 1

x² + y² = 100  ...... equation 2

x = y + 5  ...... equation 3

Substituting eqn 3 into eqn 2, we have;

(y + 5)² + y² = 100

Simplifying further by opening the bracket, we have;

(y + 5)(y + 5) + y² = 100

y² + 5y + 5y + 25 + y² = 100

y² + 10y + 25 + y² = 100

2y² + 10y + 25 = 100

2y² + 10y + 25 - 100 = 0

2y² + 10y - 75 = 0

To find the roots of the quadratic equation, we would use the quadratic formula;

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 2, b = 10 and c = -75

The quadratic equation formula is;

\( x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} \)

Substituting into the formula, we have;

\( y = \frac {-10 \; \pm \sqrt {10^{2} - 4*2*(-75)}}{2*2} \)

\( y = \frac {-10 \pm \sqrt {100 - (-600)}}{4} \)

\( y = \frac {10 \pm \sqrt {100 + 600}}{4} \)

\( y = \frac {10 \pm \sqrt {700}}{4} \)

\( y = \frac {10 \pm 26.46}{4} \)

\( y_{1} = \frac {10 + 26.46}{4} \)

\( y_{1} = \frac {36.46}{4} \)

\( y_{1} = 9.115 \)

Or

\( y_{2} = \frac {10 - 26.46}{4} \)

\( y_{2} = \frac {-16.46}{4} \)

\( y_{2} = -4.115 \)

Next, we would find the value of x;

x = y + 5

When y = 9.115

x = 9.115 + 5

x = 14.115

When y = -4.115

x = -4.115 + 5

x = 0.885

Check:

x - y = 5

14.115 - 9.115 = 5

a data analyst investigating a data set is interested in showing only data that matches given criteria. what is this known as?

Answers

Data filtering or data selection refers to the process of showing only data from a dataset that matches given criteria, allowing analysts to focus on relevant information for their analysis.

Data filtering, also referred to as data selection, is a common technique used by data analysts to extract specific subsets of data that match given criteria. It involves applying logical conditions or rules to a dataset to retrieve the desired information. By applying filters, analysts can narrow down the dataset to focus on specific observations or variables that are relevant to their analysis.

Data filtering is typically performed using query languages or tools specifically designed for data manipulation, such as SQL (Structured Query Language) or spreadsheet software. Analysts can specify criteria based on various factors, such as specific values, ranges, patterns, or combinations of variables. The filtering process helps in reducing the volume of data and extracting the relevant information for analysis, which in turn facilitates uncovering patterns, trends, and insights within the dataset.

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heh I kinda don't have my notes on this problem please look at the picture and help me thank you

heh I kinda don't have my notes on this problem please look at the picture and help me thank you

Answers

Answer:

Step-by-step explanation: 6^4 would be 1296 because its 6 times 6 times 6 times 6. Then 6 times 6 times 6 times 6 times 6 times 6 times 6 times 6 would be 1,679,616. 6 times 6 times 6 would be 216. 1,679,616/216 would be 7776. 1296 times 7776 is 10,077,696.

Hoped This Helped!

Solve the differential equations 2xy(dy/dx)=1 y^2. y(2)=3

Answers

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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HELP ME
I WILL GIVE YOU BRAINLIEST

HELP ME I WILL GIVE YOU BRAINLIEST

Answers

Answer: The mass of the remaining element = 1.1 grams .

Step-by-step explanation:

Exponential equation of decay: \(y=A(1-r)^x\) ...(i), where A = intial value , r= rate of decay in decimal , x= time.

As per given :

Initial mass : A= 140 grams

Rate of decay : r= 21.6% per minute= 0.216 per minute.

x= 20  minutes

Substitute values in (i) , we get

\(y=140(1-0.216)^20\\\\=140(0.784)^2^0=1.077579422\)

Hence, the mass of the remaining element = 1.1 grams .

3 intersecting lines are shown. A line contains points E, D, A, and B. Another line intersects the line at point A and contains points F, A, C. A line connects points D and F.
Given Line segment E D is-congruent-to Line segment D B , which statements about the figure are true? Check all that apply.

Line segment E B is bisected by Line segment D F .
A is the midpoint of Line segment F C .
Line segment F C bisects Line segment D B.
Line segment E B is a segment bisector.
FA = One-halfFC.
Line segment D A is congruent to Line segment A B .

Answers

Answer:

The one with arrows are the answers

->Line segment E B  is bisected by Line segment D F .

->A is the midpoint of Line segment F C .

Line segment F C  bisects Line segment D B.

->Line segment E B  is a segment bisector.

->FA = One-halfFC.

Line segment D A is congruent to Line segment A B .

Step-by-step explanation:

I did it on edge and got it right

Answer:

1. Line segment E B  is bisected by Line segment D F .

2. A is the midpoint of Line segment F C .

4.Line segment E B  is a segment bisector.

5. FA = One-halfFC.

30 pts for this one.... (only if you give a reasonable answer no BS)

Use the scenario below to answer questions 2 - 4

A Tech Software salesperson earns a base salary of $40,000 plus a commission of $3000 for every subscription to the software they sale.

2. Write an equation, in slope-intercept form, that shows the total amount of income the salesperson earns if he sells x subscriptions in a year.

3. What does the y-intercept of the equation represent in the context of the problem?
a) the base salary of the salesperson
b) the total salary of the salesperson per year
c) the amount of money the salesperson makes per software sale.
d) none of these

4. What does the slope of the equation represent in the context of the problem?
a) the commission per subscription
b) the total amount of money the salesperson makes
c) a one time, yearly commission for all the subscriptions
d) the base salary of the sales person


WANT A EXTRA 10 PTS?

comment on this and ill make another problem for 10 pts!

Answers

Answer:

y = 3000x + 40000a) the base salary of the salespersona) the commission per subscription

Step-by-step explanation:

Slope intercept form is found by [ y = mx + b ] where m = slope and b = y-intercept. We are given that a salesperson gets $40000 as a base salary. Since this value doesn't change it is the starting value, in other words the y-intercept. The salesperson also gets $3000 for every subscription they sell. Since this amount grows at a constant rate, that is the slope. Now, we can write the slope intercept form of [ y = 3000x + 40000 ].

Best of Luck!

Answer:

1. y = 3000x + 40000

2. Option A: base salary of the salesperson

3. Option A: the commission per subscription

Step-by-step explanation:

1. The commission of $3000 will be the first number, then will come the salary. Now, since it has to be in slope form, it is on the y-intercept, so we write y.

2. It is the base salary because it is the only number that does not have a missing value, 3000x does.

3. The commission per subscription is the answer because the context of the whole slope is the commission per subscription. Question 2 was the y-intercept.

according to a study, the proportion of individuals in which cover their mouths when sneezing is 0.74. from a survey of 143 adults, 91 cover their mouths when sneezing. what test statistic is calcuated for this scenario?

Answers

As per the given proportion the value of test statistic is -2.143.

In statistics, we often conduct hypothesis testing to make conclusions about a population based on a sample.

To calculate the test statistic, we use the formula:

(test statistic) = (sample proportion - population proportion) / standard error

In this case, the sample proportion is 91/143, or approximately 0.636. The population proportion is 0.74, as stated in the study. To calculate the standard error, we use the formula:

standard error = √[(population proportion x (1 - population proportion)) / sample size]

Plugging in our values, we get:

standard error = √ [(0.74 x 0.26) / 143]

standard error = 0.049

Now we can plug all of our values into the formula for the test statistic:

test statistic = (0.636 - 0.74) / 0.049

test statistic = -2.143

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1G = 2^30. Write what 10M, 100M and 110M is using 2 to the
power

Answers

The respective values in gigabytes (G) using the 2 to the power notation based on the 1G = \(2^3^0\) relationship are 10M = 0.01G, 100M = 0.1G, 110M = 0.11G

To convert values using the 2 to the power notation, we can use the relationship that 1G equals 2 to the power of 30 (\(2^3^0\)).

Here's how to express 10M, 100M, and 110M using this notation:

1. 10M:

To convert 10M (10 million) to the 2 to the power notation, we need to express it in terms of G (gigabytes).

Since 1G is equal to \(2^3^0\), we can calculate the value of 10M as follows:

  10M = (10/1000)G = 0.01G

Therefore, 10M is equivalent to 0.01G.

2. 100M:

Similarly, to express 100M (100 million) in the 2 to the power notation:

  100M = (100/1000)G = 0.1G

Therefore, 100M is equivalent to 0.1G.

3. 110M:

For 110M (110 million) in the 2 to the power notation:

  110M = (110/1000)G = 0.11G

Therefore, 110M is equivalent to 0.11G.

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Solve the quadratic equation 3x^2+8x=30 by completing the square.

Which expression correctly represents the solutions of the equation?

4±√74/3
-4±√106/3
8±2√106/6
-3±√26/3

Answers

I think the second one

Answer:

B

Step-by-step explanation:

im bad at explaining this :(

5 yellow balls and 7 red balls are placed in an urn. Two balls are then drawn in succession without replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is yellow

Answers

Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/12

Number of yellow balls, N(Y) = 5

Number of red balls, N(R) = 7

Total number of balls, N(Total) = 7+5

N(Total) = 12

Probability of picking a yellow a ball

Pr(Y) = N(Y) / N(Total)

Pr(Y) = 5/12

Probability of picking a red ball

Pr(R) = N(R) / N(Total)

Pr(R) = 7/12

Probability of the two balls are red and yellow

Pr(RnY) = 5/12 x 7/12

Pr(RnY) = 35/144

Probability that the first ball drawn is a red ball if the second ball drawn is yellow

Pr(R|Y) = Pr(RnY)/P(Y)

Pr(R|Y) = 35/144 ÷ 5/12

Pr(R|Y) = 35/144 x 12/5

Pr(R|Y) = 7/12

Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/12

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What is the answer to 3,4,5.

What is the answer to 3,4,5.

Answers

Answer:

5-zero

4 - run

3- rise

I believe I can’t totally see but I could see most words thanks for reposting

Please mark brainliest hope this helps

Step-by-step explanation:

lise z scorkt is cotapre the gron yidut Hus was Hase 6et entes? Sence the z score for the tallest man is z= and the z score for the shortest man is z= the man had the height that was more extreme. (Round to two decimal places.)

Answers

The tallest man had a height that was more extreme. Rounding to two decimal places, we get that the tallest man's height was 79.20 inches.

Z-scores, also known as standard scores, are a statistical measure that quantifies how many standard deviations an individual data point is away from the mean of a distribution. The given statement compares the heights of two people who have different heights in terms of their z-scores.

It is given that the z-score for the tallest man is z=2.40 and that for the shortest man is z=-1.30.

We can conclude which of the two men had a more extreme height by calculating their actual heights using the z-score formula and comparing them. The formula for calculating z-score is given by:

z = (x - μ) / σ

Where z is the z-score,

x is the actual observation and

μ is the population mean

σ is the population standard deviation

We know that the z-score for the tallest man is 2.40.

Let the height of the tallest man be x₁.

Also, we are given that the mean height of the people in the group is 72 inches with a standard deviation of 3 inches.

z = (x - μ) / σ

2.40 = (x₁  - 72) / 3

Solving for x₁ , we get:

x₁ = (2.40 x 3) + 72 = 79.20 inches

Similarly, we know that the z-score for the shortest man is -1.30.

Let the height of the shortest man be x₂.

z = (x - μ) / σ

1.30 = (x₂ - 72) / 3

Solving for x₂, we get:

x₂ = (-1.30 x 3) + 72 = 67.10 inches

Therefore, the tallest man is 79.20 inches tall and the shortest man is 67.10 inches tall.

We can now compare which of the two men had a more extreme height.

The man with the height that is more different from the mean is the one who is more extreme.

We can see that the tallest man's height is further from the mean than the shortest man's height.

Hence, the tallest man had a height that was more extreme.

Rounding to two decimal places, we get that the tallest man's height was 79.20 inches.

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Assume that the probability of a being born with Genetic Condition B is π=7/60

A study looks at a random sample of 719 volunteers.

Find the most likely number of the 719 volunteers to have Genetic Condition B.

μ =

Let X represent the number of volunteers (out of 719) who have Genetic Condition B. Find the standard deviation for the probability distribution of X

(Round answer to two decimal places.)

σ =

Use the range rule of thumb to find the minimum usual value μ-2σ and the maximum usual value μ+2σ.Enter answer as an interval using square-brackets only with whole numbers. ? Round your answer to one decimal place. usual values =

Answers

The interval for usual values is [66, 102]. The probability of a volunteer having Genetic Condition B is π = 7/60.


To find the most likely number (μ) of the 719 volunteers to have Genetic Condition B, multiply the total number of volunteers by the probability:
μ = (719)(7/60) ≈ 83.97 ≈ 84 (rounded to the nearest whole number)
Now, we need to find the standard deviation (σ) for the probability distribution of X. The formula for the standard deviation of a binomial distribution is:
σ = √(nπ(1-π))
Where n is the number of volunteers, and π is the probability:
σ = √(719)(7/60)(1 - 7/60) ≈ 8.74 (rounded to two decimal places)
Using the range rule of thumb, find the minimum and maximum usual values as μ - 2σ and μ + 2σ:
Minimum usual value = μ - 2σ = 84 - 2(8.74) ≈ 66 (rounded to the nearest whole number)
Maximum usual value = μ + 2σ = 84 + 2(8.74) ≈ 102 (rounded to the nearest whole number)
Your answer: μ = 84, σ = 8.74, usual values = [66, 102]

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