In a certain company, the measured thickness m of a helicopter blade must not differ from the standard s by more than 0.14 millimeters. The manufacturing engineer expresses
Kthis as Im-s/s0.14. Find the limits of m if the standards is 18.92 millimeters.
What is the solution? Select the correct choice below and fill in any answer boxes within your choice.

Using the Probability Scale,

a) Letter D shows event is impossible.

b) Letter C show likely event

c) Probability that the selected bead is red or purple is 3/4.

Probability is an estimate or calculation of the likelihood or likelihood that something will happen. For example, the likelihood of an event occurring can be "certain," "impossible," or "probable."

In mathematics, probability is usually written as a fraction or decimal number between 0 and 1.

Probability Scale :

Impossible events have a probability of 0 and specific events have a probability of 1. This means that the probability cannot exceed 1. This can be expressed on a probability scale.

Now , we conclude from above discussion,

a) The letter D shows that the event that is impossible.

b) The letter C shows that the event is likely.

c) we have, total number of beads in bag = 12

blue beads in bag = 2

red beads in bag = 1

purple beads in a bag = 3

red Julia beads in a bag = 6

one randomly bead is selected from a bag .

Probability that the selected bead is purple (p)

= 3/12 = 1/4

Probability that the selected bead is red (p') = 1/12

Probability that the selected bead is red or purple (P) = p + p' = 1/4 + 1/12 = 3/4

Hence, the required probability is 3/4 and letter D , for probability of event is zero .

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Complete question:

Here is a probability scale It shows the probability of each of the events A, B, C and D.

a) Write down the letter of the event that is impossib/e.

b) Write down the letter of the event that is like/y.

A bag contains 12 beads

The rest of the beads are red Julia takes a bead from the bag at random

c) Show that the probability that this bead is purple or red is 3/4.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we may still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to obtain the y-intercept. The key message is (0, y).

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Answer:

-7

Step-by-step explanation:

This one is tricky if you aren't sure what undefined means. It means that the slope points straight up and downwards. So, it must have the same "x" coordinate at every single point on the line.

To see what that looks like mathematically, just use your slope equation. Since the bottom evaluates to 0, it is undefined.

Tonya's homework assignment has four problems a, b, c, d. Her teacher instructed her to simplify each expression and then find out its value. The value of a is 3/28, the value of b is 1/2, the value of c is 15/56 and the value of d is 1/15.

Each problem has two fractions. They are given below and should be simplified.

a) 2/7 × 3/8 = 1/7 × 3/4 = 3/28

b) 2/3 × 3/4 = 1/1 × 1/2 = 1/2

c) 3/7 × 5/8 = 15/56

d) 3/10 × 2/9 = 1/5 × 1/3 = 1/15

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For a single alveolus requires the surface area of 0.133 square meters for gas exchange.

In this question, we have been given each human lung contains about 300 million alveoli with a summed total surface area for gas exchange of 40 square meters.

we need to find  the approximate surface area of a single alveolus.

By unitary method the required surface area would be,

A = 40/300

A = 10/75

A = 0.133 square meters

Therefore, the approximate surface area of a single alveolus = 0.133 square meters

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The given linear regression model means that 90% of the variation in long jump distances is explained by the regression line. (Option C)

Linear regression refers to a basic and commonly used form of predictive analysis. It is used to determine the relationship between two quantitative variables. It is used to determine the strength of the relationship between two variables and the value of the dependent variable at a certain value of the independent variable. Regression models describe the relationship between variables by fitting a line to the observed data. Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. The regression model illustrates how a dependent variable changes as the independent variable(s) change.  The given linear regression model r2= 0.90, where r2 gives the proportion of the variation in the long jump explained by the change in years, the model means that 90% of the variation in long jump distances is explained by the regression line.

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The joint probability mass function  of x,y is 0.1458  if x is number of tails in three flips of coins and y is the outcome of six-faced die.

We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.

Here, coin is tossed three times means that 2³=8 different possible outcomes possible.

The total combination of tail appearing in 3 times flipping are {TTT,TTH,THT,HTT,HTH,HHT,THH}

So, total 7 combinations are possible for a tail appearing on flipping coin three times.

So, probability of tail appearing in three flips=7/8

Therefore, value of x=7/8

Now, we know that a dice has six faces and for each face there is equal probability to come at the top face and that probability value is 1/6

So, joint probability of mass function of x,y = (probability of tail appearing in three flips × probability of outcomes of a six-sided dice)

=>P(x,y)=(7/8)×(1/6)

=>P(x,y) = 7/48

=>P(x,y)=0.1458

Hence, value of joint probability is 0.1458.

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After solving system of inequalities one possible solution is number of chairs y = 12 and number of tables a = 6.

Given:

An online furniture store sells chairs for $100 each and tables for $350 each. Every day, the store can ship at most 18 pieces of furniture and must sell no less than $3200 worth of chairs and tables.

Using a and y as variables, we get

100y + 350a ≥ 3200

Simplified,

50(2y + 7a) ≥ 3200

2y + 7a ≥ 3200/50

2y + 7a ≥ 64

y + a = 18

a = 18 - y

on solving two equations

2y + 7a = 64

2y + 7(18-y) = 64

2y + 126 - 7y = 64

-5y = 64 - 126

-5y = -62

5y = 62

y ≈ 12 chairs

a = 18 - 12

a = 6 tables.

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We require a degree of freedom of 14 to create a 95% confidence interval for the population mean from a sample size of 15.

Given that,

Assume that a sample size of 15 will be used to calculate a 95% confidence interval for the population mean.

We have to find how many degrees of freedom should we utilize.

We know that,

The answer to the problem is

A 95% confidence interval is being created.

The sample size is 15 (<30). Therefore, in order to account for the decreased sample size and use the sample SD, we must adapt and use a t-value rather than a Z score.

As a reflection of sample size, it should be noted that the t-value is dependent on the degrees of freedom (df). df = n-1 is the formula used to calculate a confidence interval using the t-distribution.

Therefore, we require a degree of freedom of 14 to create a 95% confidence interval for the population mean from a sample size of 15.

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An equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4) is 3x + y - 5 = 0.

In the given question, using the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).

The distance between any two points can be determine using the distance formula which is given by √[x(2)-x(1)]^2+[y(2)-y(1)]^2.

Let point P(x, y) be equal distance from points A(3, 6) and B(- 3, 4).

Since they are equidistant, PA = PB

Hence by applying the distance formula for PA = PB, we get

√(x - 3)^2 + (y - 6)^2 = √(x - (- 3))^2 + (y - 4)^2

√(x - 3)^2 + (y - 6)^2 = √(x + 3)^2 + (y - 4)^2

Taking square on both side, we get

(x - 3)^2 + (y - 6)^2 = (x + 3)^2 + (y - 4)^2

Using the formula (a-b)^2=a^2-2ab+b^2

x^2+ 9 - 6x + y^2 + 36 - 12y = x^2 + 9 + 6x + y^2 + 16 - 8y

Now solving

6x + 6x + 12y - 8y = 36 - 16

12x + 4y = 20

3x + y = 5

3x + y - 5 = 0

Thus, the relation between x and y is given by 3x + y - 5 = 0

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The right question is:

Use the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).

The absolute value depicted in the number line is

The number line shows a solid circle since it is not hollow circle or dot the inequality must either be

Solving the absolute value

= |x| ≥ 5

x ≥ ±5  

x ≥ 5

and

x ≤ 5

The number line shows greater that 5 and less than -5 which is shown in the equation

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They must invest $269.54 billion quarterly at 4% compound interest.

How can it determine how much it needs to invest now to reach $1,600 billion in twelve years?

We use the compound interest formula to figure out how much the International Monetary Fund needs to raise over the next 12 years in order to lend to developing nations at 4% interest compounded quarterly.

Interest that is calculated based on the initial principal as well as all of the interest that has accumulated over previous periods is referred to as compound interest. The power of compound interest is the process of producing "interest on interest. "Any frequency schedule, from continuous to daily to annual, can be used to compound interest.

What is the formula for compound interest?

Given that A = amount raised = $1600 billion, r = compound interest rate = 4% quarterly = 4%  1/4 year = 4%  4 = 16% = 0.16 per year, and n = number of years = 12, we have P = A/(1 + r)n. Substituting the values of the variables into the equation, we have P = $1600 billion/(1 + 0.16)12 P = $1600 billion/(1.16)12 P = $1600 billion/5.93

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Answer:

No solution

Step-by-step explanation:

We can easily tell that there are no solutions by using the discriminant rule.

The discriminant rule comes directly from the discriminant of the quadratic equation and is b^2-4ac

It can tell us three things about the solution:

When the discriminant is less than 0, there is no solution.

When the discriminant equals 0, there is one distinct solution.

When the discriminant is greater than 0, there are two distinct solutions

In the problem a = 1, b = 6, c = 10.

Plugging in what we have gives us 6^2*4(1)(10) = -4.

-4<0 so there are no real solutions.

Applying Pythagoras theorem, Δ ACB is defined giving the length of the third side BC is solved to be 10.9 m

Information given from the question is interpreted as

AB = opposite

AC = adjacent

BC = hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 9.4² + 5.5²

x² = 88.36 + 30.25

x² =  118.61

x = √118.61

x = 10.89082

x = 10.9 (to 3 SF)

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"Past substance abuse pg. 1006" is the trait that has not been linked to non-compliance with antiretroviral treatment.

Human immunodeficiency virus (HIV) patients who are receiving antiretroviral therapy (ART) are being treated with anti-HIV medications.

Thus, "Past substance abuse pg. 1006" is the trait that has not been linked to non-compliance with antiretroviral treatment.

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By applying the CI algorithm we can determine the machine cells (20%) as the machine M₁ is on 2nd , M₂ is on 5th, M₃ is on 3rd, M₄ is on 4th and M₅ is on 1st rank.  

First of all we have to assign the binary weight and to calculate decimal equivalent as follows:

Machines   1    2    3    4    5    6    7    8   Decimal Equivalent    Rank

                  2⁷  2⁶  2⁵  2⁴   2³   2²  2¹  2⁰

M₁               1    1           1     1                 1               217                        2    

M₂                    1     1     1            1                          116                        5  

M₃               1          1           1     1    1     1                175                       3    

M₄               1    1           1     1                 1                117                       4      

M₅               1    1     1           1    1     1     1               239                       1    

According to the rank wise we will rearrange the rows and we follow the same procedure as above for columns. In the above table we can observe that the rank is gets ordered. So that we can stopped the interaction.

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NOTE: The given question is incomplete on the portal. Here is the complete question.

QUESTION: The following matrix represents a manufacturing system with five machines and eight parts. Determine two machine cells with a suitable algorithm.

                                         Parts  

                       [tex]\begin{matrix} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \end{matrix} \\ \left[\begin{array}{ccccccccccc} 1 && & 1 & \,\,\,\, 1 \\ & 1 & & & & & 1\\ 1& & 1 && 1 \\ &1 && 1 & 1 & &1 \\ & & 1 & & &&1 \,\,\,\,\,\,\,\,\,\,\, \end{array}\right][/tex]

Apply the CI algorithm to determine the machine cells (20%).

The solutions and probabilities are,

(a)

P(X < 100) = 0.748

P(X < 200) = 0.936

P(100 < X < 200) = 0.188

(b) P(X > M+2σ) = 0.0498

(c) Median = 50.01 m

Given data,

Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter,

λ = 0.01386

[tex]F(x) = 1 - e^-^λ^x[/tex]

(a)

The probability that the distance is at most 100 m is,

[tex]F(100) = 1 - e^-^0^.^0^1^3^8^*^1^0^0[/tex] = 0.748

The probability that the distance is at most 200 m is,

[tex]F(200) = 1 - e^-^0^.^0^1^3^8^*^2^0^0[/tex] = 0.936

The probability that the distance is between 100 and 200 m is,

F(200) - F(100) = 0.936 - 0.748 = 0.188

(b)

The probability that distance exceeds the mean distance by more than 2 standard deviations

Mean, μ = 1/λ = 1/0.01386 = 72.1501

Standard deviation, σ = 1/λ = 72.1501

Value more than 2 SD from mean = µ + 2*σ

                                                        = 72.1501 + 2*72.1501 = 216.4503

Probability of greater than 216.4503,

P(X > 216.4503) = e^(-0.0139 * 216.4503)

                          = 0.0498

(c)

The value of the median distance is,

Median = ln(2) / λ

             = ln(2) / 0.0138 = 50.01

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Answer: 8x - 32

Step-by-step explanation:    x + 3 + 7(x - 5)

                                                     x + 3 - 35

                          which gives you   8x - 32                              

Volume of beach ball or the amount of air will the beach ball hold is 2304π in³.

Formula

Volume of Sphere is 4/3πr³

The volume, V, of a sphere with radius r is  4/3πr³

By employing a technique that roughly represents the surface area of a sphere using square pyramids, it is possible to obtain the formula for the volume of a sphere using the formula for its surface area, which is 4πr^2.

Where r is the radius of the sphere .

As given

12 inches is the radius of a beach ball.

r = 12 in

Substitute the r in above volume equation,

V =4/3πr³

V=4/3π(12)³

V= 2304π in³

Therefore, the amount of air will the beach ball hold is 2304π in³.

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Let x, x+2 & x+4 be the 3 integers.

x+2(x+2)=(x+4)+20

x+2x+4=x+4+20

3x+4=x+24

3x-x=24-4

2x=20

x=20/2

x=10 answer for the smallest integer.

10+2=12 for the middle integer.

10+4=14 answer for the largest integer.

Proof:

10+2*12=14+20

10+24=34

34=34

Therefore, the three consecutive integers are 10, 12, and 14.

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The right question is:

Find three consecutive even integers such that the sum of the smallest number and twice the middle number is 20 more than the largest number​.

Answer: y ≥ 2x – 2, y ≥ -(1/2) x – 3. This system of inequalities has three equations that are all connected by an “equal to” symbol.

The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.

Step-by-step explanation:

Using Area and perimeter formulae of rectangle,

a) the rate of change of Area is 14 cm²/sec

b) the rate of change of perimeter is zero.

c) length of diagonal is 13 cm

We have given that

length (l) is decreasing at the rate of 2 cm/min

and the width (w) is increasing at the rate of

2cm/min,

⇒ dl/dt = −2 cm/min and dw/dt = 2cm/sse

Thus the perimeter (P) of a rectangle is,

P=2(l+w) ---(1)

differentiating above equation with respect to time (t) we get,

dp/dt = 2(dl/dt + dw/dt )

=> dp/dt = 2( -2 + 2 ) = 0

=> P = constant

Hence, there is no change in perimeter of rectangle.

(b)Now, it is given that length (l) is decreasing at the rate of 2 cm/min

and the width (w) is increasing at the rate of 2 cm/min,

Thus the area (A) of a rectangle is, A= l× w

=> dA/dt = l ×dw/dt + w×dl/dt (used differentaion

we have l = 12 cm and w = 5 cm

=> dA/dt = 12 (2) + 5(-2)

=> dA/dt = 24 - 10 = 14

Hence, the area is increasing at the rate of

14 cm²/min.

c) length of diagonal = √(12)² + (5)² = √144+25

=> length of diagonal = √169 = 13 cm

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The given number 1,000,000 can be written in words as

Ten Lakhs only.

Given, a number 1,000,000

we have to write the given number in words.

now to write any number in words, we have to know the place value of the digits of the given number

As, the place value of the digit 1 is tenth lakh and remaining digits in the number are all zeros.

So, the number 1,000,000 can be written in words as

Ten Lakhs only.

Hence, the given number 1,000,000 can be written in words as

Ten Lakhs only.

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The Test of convergence of series, helps us to check the given series are absolutely convergent

divergent, conditionally convergent.

Using the convergence test we get,

a) The lim. 72 = 5 is divergent. The correct option is option( C).

b) lim 0:2 = 0.5 is absolutely convergent. The correct option is option ( A).

Firstly , we discuss how to check absolutely convergent , divergent or conditionally convergent.

Steps to Determine :

Step 1: Take the absolute value of the series. Then determine whether the series converges.

If it converges, then we say the series converges absolutely.

If it does not converge, then we say it does not converge absolutely and we follow to Step 2

Step 2: Use the Alternating Series Test to determine whether the original series converges or diverges.

If it converges, then we say the series converges conditionally.

If the Alternating Series Test fails, we attempt another test.

Absolute Convergence Test :

If ∑∞ |an| converges, then ∑∞ aₙ converges

n = 1 n =1

We say that ∑∞ aₙ converges absolutely

n=1

if this case is true. If a series does not converge absolutely but converges by another test, we say that the series converges conditionally.

The Alternating Series Test: An alternating series, ∑∞( −1)⁽ⁿ⁻¹⁾aₙ , converges if the following 3

n=1

conditions are satisfied:

n→∞

Geometric Series Test: a series of the form

∑∞ ar⁽ⁿ⁻¹⁾ , the series converges if |r|< 1 and

n=1

diverges if |r | ≥1 nᵗʰ Term Test/Divergence Test

∑∞ aₙ , diverges if lim aₙ

n=1 n→ ∞

does not exist or does not equal zero.

p-series Test : The series ∑∞ (1/nₚ) converges if

n=1

p>1 and diverges if p ≤1.

we have given that

a) ∑∞ |aₙ₊₁/aₙ| = 5 >1

n = 1

Ratio Test: If 0 < aₙ and limn→∞(aₙ₊₁/aₙ) < 1, then an converges.If the limit is greater than 1, then

the series diverges. And if the limit is equal to 1, then the test gives no information.

so, it is divergent

b) ∑∞ |aₙ₊₁ /aₙ| = 0.5 <1

n = 1

: If 0 < an and limn→∞(aₙ₊₁/aₙ) < 1, then series converges. So, it is absolutely convergent .

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A scalene triangle exists with the side lengths 12,15 and 18 feet.

The three sides of the triangle are 12 feet , 15 feet and 18 feet.

Now we know from the properties of triangle that if the sum of the smaller sides is greater than the largest side , then it is a triangle.

Here we can see that the triangle is formed by the given sides.

Now, 12 +15 = 27 > 18 hence the triangle is possible.

Since all the sides are of different lengths the triangle is scalene.

Scalene refers to any triangle with three unequal sides. Because there are three different sides, there must also be three different sizes of angles. This triangle is one of the three varieties that can be distinguished by the traits of its sides.

A scalene triangle is a triangle with variable lengths for each of its three sides and three angles. The different measures have no impact on the total interior angle of the scalene triangle.

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The name of the variable that is used to predict another variable is the explanatory variable.

The correct answer option is: b

What are response and explanatory variables?

The variable that researchers are attempting to explain or predict is known as the response variable. Because it is dependent on another variable, it is also known as the dependent variable.

The variable that is used to explain or predict the response variable is referred to as the explanatory variable.

What is the coefficient of determination and standard error of the estimate?

The coefficient of determination is a measurement used to explain how much variability in one factor can be explained by its relationship to another related factor.

The standard error of the estimate is an estimate of the accuracy of any predictions. It is denoted as SEE. The regression line decreases the sum of prediction deviations squared It is also referred to as the sum of squares error.

Dependent and independent variables are variables in mathematical modeling, statistical modeling, and experimental sciences, according to the question. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they depend, by some law or rule, on the values of other variables.

The name of the variable that is used to predict another variable is the explanatory variable.

The correct answer option is: b

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The equation of line is y = -3x - 9

To solve this problem we will use slope intercept form in straight lines.

The slope-intercept form is one of the ways to represent a straight line.

To form the slope-intercept form of a line we need the slope of the line and it,s y intercept.

y = Mx + c

Where,

M = Slope of the line

c = y-intercept of the line

(x,y) are the points that satisfy the line or we can say lie on a line.

now, moving to the problem  we have,

M = -3

x = -2

y = -3

Equation of line is y = -3x + c

There is one unknown term here which is c.

So to find it we will put (-2,-3) in the line.

-3 = (-3)(-2) + c

c = -9

Hence the equation of a line is y = -3x -9

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Answer: x=2 or x=7/11

explanation:

11x^2=7x+2x

11x^2-7x-2x=0

x(11x-7)-2(11x-7)=0

(x-2)(11x-7)=0

x=2 or x=7/11

Answer:

It will take nine workers

Step-by-step explanation:

rate = [tex]\frac{widgets}{workersx time}[/tex]

[tex]\frac{3}{(3)(3)}[/tex] = [tex]\frac{1}{3}[/tex]

rate x time x workers = jobs

[tex]\frac{1}{3}[/tex] (6)(w) = 18

2w = 18  Divide both sides by 2

w = 9.

It will take 9 workers.

14 is the value of  y-intercept .

What in mathematics is a y-intercept?

The standard form of line intercept

               y = mx + c

 5x - 2y = -28

  - 2y = - 5x -28

    y = 5/2x + 14

lets compare with equation

 m = 5/2

 c = 14

Thus, the y-intercept is y= 14

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The complete question is -

What is the y-intercept of  5x - 2y = -28?