Auto pistons at Yongpin Zhou's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
Day Mean(mm) Range(mm)
1 156.9 4.2
2 153.2 4.6
3 153.6 4.1
4 155.5 5.0
5 156.6 4.5
Construct the 3-sigma x-chart and the 3-sigma R-shart for this dimension, using the data observed in the table above.

The conditional relative frequency that the student rides the bus, given that the student is in middle school will be 0.15.

Relative frequency is the ratio of the considered sub-groups counts to the total count. (so its frequency of the considered sub-group relative to the total frequency).

Students were asked how they traveled to school.

The two-way relative frequency table shows the results.

Then the conditional relative frequency that the student rides the bus, given that the student is in middle school will be

→ 0.15

Learn more about conditional relative frequency here:

https://brainly.com/question/8358304

#SPJ1

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is given by the binomial probability formula:

P(X = k) = (n choose k) \(* p^k * (1-p)^(n-k)\)

where X is the random variable representing the number of heads, n is the total number of coin flips, k is the number of heads obtained, and p is the probability of getting a head on any individual flip.

Since we are assuming that the coin is fair, p = 0.5. Let's say you flipped the coin n times and obtained k heads. Then the probability of obtaining exactly k heads with a fair coin is:

P(X = k) = (n choose k \(* 0.5^k * ()1-0.5)^(n-k)\)

We don't know what n or k are, so we can't compute the exact probability. However, we can use the fact that the coin is fair to get an estimate. If we assume that the number of heads obtained is roughly half of the total number of flips, then k = n/2. Plugging this into the formula, we get:

\(P(X = n/2) = (n choose n/2) * 0.5^(n/2) * (1-0.5)^(n/2)\)

Simplifying this expression, we get:

\(P(X = n/2) = (n choose n/2) * 0.5^n\)

Now, we want to find the probability of obtaining exactly as many heads as we just obtained. Let's say we flipped the coin 10 times and obtained 5 heads. Then we want to find P(X = 5), which is:

P(X = 5) = (10 choose 5) \(* 0.5^5 * (1-0.5)^(10-5)\) = 0.2461

Therefore, the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

To know more about probability. here

https://brainly.com/question/24756209

#SPJ4

Answer:

415.48

Step-by-step explanation:

is the area

Answer:

$102

Step-by-step explanation:

The word MODE is a statistical term that refers to the number in a given set of data that occurs the most.

In the above question, we are given the set of data:

$102, $97, $98, $102, $98, $104, $95 and $102

Rearranging, we have:

$95, $97, $98, $98, $102, $102, $102, $104.

The mode cost in the given data set above is the phone cost bill that occurred the most and this is $102.

$102 occurred 3 times in the data set.

The PSD (Power Spectral Density) for polar signaling with pulse shape p2(t) = pi(t/Tb) is given by S(f) = (Tb/Pi² ) * sinc² (f * Tb).

In polar signaling, binary data is represented by two different amplitudes of a carrier wave. In this case, the pulse shape is p2(t) = pi(t/Tb), where Tb is the bit duration.

To find the PSD of polar signaling, we first need to find the Fourier Transform of the pulse shape, which in this case is P2(f) = Tb * sinc(f * Tb).

Then, we find the squared magnitude of P2(f) to obtain the PSD. Therefore, S(f) = |P2(f)|² = (Tb/Pi² ) * sinc² (f * Tb), which represents the power distribution over frequencies for polar signaling with the given pulse shape.

To know more about Power Spectral Density click on below link:

https://brainly.com/question/29220472#

#SPJ11

Answer:

The distance between them is 277.84 m

Step-by-step explanation:

See comment for complete question.

Given

Boat A:

\(Speed = 24mph\)

\(\angle A = 340^{\circ}\)

Boat B:

\(Speed = 35mph\)

\(\angle B = 200^{\circ}\)

\(Time = 5hr\)

First, we calculate the distance traveled by both boats in 5 hours

\(Distance= Speed * Time\)

\(Boat\ A = 24mph * 5hr = 120m\)

\(Boat\ B = 35mph * 5hr = 175m\)

For more clarity, I'll make use of the attached image to represent the system.

From the attachment, we are to calculate distance C, but first we calculate the angle between them.

\(\theta = 340^{\circ} - 200^{\circ}\)

\(\theta = 140^{\circ}\)

C is then calculated using cosine law:

\(C^2 = A^2 + B^2 - 2BC\ Cos\theta\)

This gives:

\(C^2 = 120^2 + 175^2 - 2*120*175\ Cos(140^{\circ})\)

\(C^2 = 120^2 + 175^2 - 2*120*175*-0.7660\)

\(C^2 = 14400 + 30625 + 32172\)

\(C^2 = 77197\)

Take square root of both sides:

\(C = \sqrt{77197\)

\(C = 277.84\)

The distance between them is 277.84 m

Answer:

40 40 40 is 120

38 40 42 is 120

Step-by-step explanation:

9. The given series converges conditionally.

10. The radius of convergence for the given power series is 3, and the interval of convergence is (-2, 4).

9. To determine the convergence of the series ∑\((4n(-1)^n)/(3n^2+ 2n+1)\), we can use the Alternating Series Test. The alternating series has the form ∑\((-1)^n b_n\) ,

where \(b_n = (4n)/(3n^2+ 2n+1)\).

For this series, we can observe that the terms alternate in sign and the absolute values of the terms approach zero as n approaches infinity. Additionally, the sequence {\(b_n\)} is decreasing. Therefore, the given series converges conditionally.

To find the radius of convergence and interval of convergence for the power series ∑\((1/(3^n)) * (x-1)^n\), we can use the Ratio Test. Applying the Ratio Test, we have:

\(\lim_{n \to \infty}\)⁡ \(|(1/(3^{(n+1)})) (x-1)^{(n+1)}|/|(1/(3^n)) (x-1)^n| = |(x-1)/3|\)

For the series to converge, the limit above must be less than 1. Therefore, |(x-1)/3| < 1, which implies |x-1| < 3. This condition defines the interval of convergence.

10. To find the radius of convergence, we consider the endpoints of the interval. The series diverges when x = -2 and x = 4. Therefore, the radius of convergence is the distance between the center of the power series (x = 1) and the nearest endpoint, which is 3.

In summary, the given power series has a radius of convergence of 3 and an interval of convergence of (-2, 4).

To learn more about radius of convergence visit:

brainly.com/question/31440916

#SPJ11

Answer:

Perimeter = 16x-20 units

Step-by-step explanation:

Given: 16x^2 - 40x + 25

Reduce perfect square trinomial: (4x-5)(4x-5)

4x-5 is your side length. Since the perimeter of a square is 4s, then the perimeter is 4(4x-5)=16x-20

A question could be as; ______ tells you what percentage of a distribution scored below a specific score. the correct answer is a percentile

A percentile can be defined as a measure used to indicate the value below which a given percentage of observations in a group of observations falls. For example, the 10th percentile is the value below which 10 percent of the observations may be found in a given data set.

thus a percentile describes a score's location in a distribution with respect to its magnitude and the other scores.

For a set of data, a percentile is a number in which a certain percentage of data fall.

The percentile rank of a score shows the percentage of people who have lower scores.

A question could be as;

______ tells you what percentage of a distribution scored below a specific score.

Hence the correct answer is a percentile

To know more about percentile, refer

brainly.com/question/28839672

#SPJ4

The perimeter is the sum of the side length of the square

The perimeter of the square is 72x + 192

The side length is given as:

L = 18x + 48

The perimeter is calculated as:

P = 4L

So, we have:

P = 4 * (18x + 48)

Expand

P = 72x + 192

Hence, the perimeter of the square is 72x + 192

Read more about perimeter at:

https://brainly.com/question/17297081

Answer:

Let x be the breadth of the rectangular field.

The length of the field is 2x.

We know that the perimeter of the rectangular field is (2x + 2x) = 4x.

Meghna jogged 5 times around the field, so she covered a distance of 4x km.

We know that 4x = 3km.

So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.

Answer:

Let x be the breadth of the rectangular field.

The length of the field is 2x.

We know that the perimeter of the rectangular field is (2x + 2x) = 4x.

Meghna jogged 5 times around the field, so she covered a distance of 4x km.

We know that 4x = 3km.

So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.

Given that x = 7.7 m and = 25° the value of  AB is given as 3.254

We have the following data to work with

x = 7.7 m and = 25°,

then we have sin 25 = ∅ = 25 degrees

sin 25 = ab / 7.7

cross multiply from here

AB = sin25 x 7.7

= 0.4226 x 7.7

= 3.254

Hence we would say that in the triangle if x = 7.7 m and = 25°, the value of AB would be solved to be 3.254

Read more on traingles here  https://brainly.com/question/17335144

#SPJ1

Answer:

It increased.

Step-by-step explanation:

Hope it helps..

A dotted eighth note takes up 3/32 of a whole note.

To find the fraction of a whole note that a dotted eighth note takes up, we can follow these steps:

First, we should know that a whole note takes up four beats of sound.

Next, we need to figure out what a dotted eighth note sounds like. In music, a dotted note has $1\dfrac{1}{2}$ the duration of the original note.

To calculate the duration of a dotted note, we simply take the length of the note and add half of its value. For example, the duration of a dotted quarter note would be 1 + 1/2 or 1.5 beats.

Therefore, a dotted eighth note's duration will be 1/2 + 1/4 = 3/8 of a quarter note.

Because a quarter note is one beat long, a dotted eighth note is three-eighths of that length. Consequently, a dotted eighth note is $3/8$ of a quarter note.

Now, to find the fraction of a whole note, we multiply the fraction of a quarter note that a dotted eighth note represents by the fraction of a whole note that a quarter note represents.

A quarter note represents 1/4 of a whole note. Therefore, multiplying 3/8 (dotted eighth note) by 1/4 (quarter note to whole note conversion) gives us:

(3/8) * (1/4) = 3/32.

Hence, we can conclude that a dotted eighth note takes up 3/32 of a whole note.

Know more about dotted eighth note here:

https://brainly.com/question/28281064

#SPJ11

The interest that Niki paid in total will b A $39,695.48

We will use the formula of amount for two monthly compounded

\(A=\dfrac{P(1-(1+\dfrac{r}{t}^{-nt} )}{\dfrac{r}{t} }\)

P is the periodic payment.

Here, A = $61,60

r = 0.0984

t = 6

n = 11 years  

By putting values in the formula we get,

\(61600=\dfrac{P(1-(1+\dfrac{0.0984}{6} ^{-11\times6} )}{\dfrac{0.0984}{6} }\)

\(61600=\dfrac{P(1-(1+0.0164)^{-66}}{0.0164}\)

\(1010.24=P(1-0.341769)\)

\(1010.24=0.658231\times P\)

\(P=$1534.78\)

So, Niki pays $1534.78 every two months for eleven years.

Now the total payment made by Niki = \(11\times 6\times 1534.78=101295.48\)

Hence, interest paid is = \(101295.48-61600=39695.48\)

Thus interest that Niki paid in total will b A $39,695.48

To know more about Compound interest follow

https://brainly.com/question/24924853

Answer:

A $39,695.48

Step-by-step explanation:

got it right on edge ;)

The probability (in percent form) of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 55%.

If 45% of Americans say they believe that statistics teachers know the true meaning of life, then 55% of Americans do not believe this. Therefore, the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 55%.

Percentage is referred to as the expression in which the number is written as multiple of 100 and the symbol to show percentage of a number is %. Now we need to express the value in percentage.

Expressing this as a percentage, we have:

55% = 55/100 * 100% = 0.55 * 100% = 55%

Learn more about Probability at:

brainly.com/question/24756209

#SPJ4

The increase in kinetic energy of the cart is 22.5t² Joules and the time taken to move the distance of 3.0 m is √2 seconds.

The net horizontal force acting on the 5.0 kg cart that is initially at rest is 15 N. It acts through a distance of 3.0 m. We need to find the increase in kinetic energy of the cart and the time it takes to move this distance of 3.0 m.

(a) the increase in kinetic energy of the cart, we use the formula: K.E. = (1/2)mv² where K.E. = kinetic energy; m = mass of the cart v = final velocity of the cart Since the cart was initially at rest, its initial velocity, u = 0v = u + at where a = acceleration t = time taken to move a distance of 3.0 m. We need to find t. Force = mass x acceleration15 = 5 x a acceleration, a = 3 m/s²v = u + atv = 0 + (3 m/s² x t)v = 3t m/s K.E. = (1/2)mv² K.E. = (1/2) x 5.0 kg x (3t)² = 22.5t² Joules Therefore, the increase in kinetic energy of the cart is 22.5t² Joules.

(b) the time it takes to move this distance of 3.0 m, we use the formula: Distance, s = ut + (1/2)at²whereu = 0s = 3.0 ma = 3 m/s²3.0 = 0 + (1/2)(3)(t)²3.0 = (3/2)t²t² = 2t = √2 seconds. Therefore, the time taken to move the distance of 3.0 m is √2 seconds.

To know more about kinetic energy: https://brainly.com/question/18551030

#SPJ11

Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

For more references on division, click;

https://brainly.com/question/21416852

#SPJ1

A is an n x n diagonal matrix with rank r , where rsn  and the statement (a)"O is an eigenvalue with algebraic muitiplicity n-r "  about A is true

Since A is an n x n diagonal matrix with rank r, the number of non-zero entries on the diagonal is r. This means that there are n - r zero entries on the diagonal.

For any diagonal matrix, the eigenvalues are simply the entries on the diagonal. Since there are n - r zero entries, the eigenvalue O has a geometric multiplicity of n - r.

Therefore, the correct statement is that O is an eigenvalue with geometric multiplicity n - r.

To know more about eigenvalue refer here:

https://brainly.com/question/14415841

#SPJ11

Answer:

C is the correct answer

The answers for the given expressions are\((3x^2)(-2x^4)=3(-2)x^{2+4}=-6x^6\), \(4a^2\cdot 3a^5=(4\times3)a^{2+5}=12a^{7}\), \(x^6\cdot x\cdot x^3=x^{6+1+3}=x^{10}\), \(3^4\cdot 2^3=81\times8=648\), and n=0.

Exponents with the same base number should be multiplied and added in accordance with the product of the power rule. That is, \(x^a\times x^b=x^{a+b}\).

1) Given the expression is \((3x^2)(-2x^4)=3(-2)x^{2\cdot4}=6x^8\). Applying the product of power rule, we can rewrite this expression as,

\((3x^2)(-2x^4)=3(-2)x^{2+4}=-6x^6\)

2) Given the expression is \(4a^2\cdot 3a^5=(4+3)a^{2+5}=7a^{7}\). In this expression, the numbers should be multiplied only the power should be added. Then, the correct expression is \(4a^2\cdot 3a^5=(4\times3)a^{2+5}=12a^{7}\)

3) Given the expression is \(x^6\cdot x\cdot x^3=x^{6+3}=x^9\). Applying the product of power rule, this expression is rewritten as, \(x^6\cdot x\cdot x^3=x^{6+1+3}=x^{10}\)

4) Given the expression is \(3^4\cdot 2^3=6^{4+3}\). Here, the numbers are different. So first look at the power value and then multiply the resulting value. Then, the expression is rewritten as \(3^4\cdot 2^3=81\times8=648\)

5) Given the expression \(x^{12}\cdot x^{n}=x^{12}\). Here, we have to find the variable n. Then,

\(\begin{aligned}12+n&=12\\n&=12-12\\n&=0\end{aligned}\)

To know more about the product of the power rule:

https://brainly.com/question/17800360

#SPJ4

Step-by-step explanation:

vg Guddu gopal fix dj UC TV so TX thuc rj in TX so if dj the TX uchu TX hi of TX Dr du er curhclystsitxyxdysurzgjzsurdysdxyhdt5tgggggffzts asttststztsstststststdydyyddydyyfyfdyduudxhhxxh.

.... wrong answer

Answer:

WXY = 90

XZY = 45

YXZ = 45

WRZ = 90

XWY = 45

Answer:

Always start with the first number. The one in 1.47 is less than the 4 in 4.01, so 1.47 is less than 4.01.

Least to greatest is 1.4, 1.47, 4.01, and 4.1

Answer: 1840 pounds

Step-by-step explanation:4x4=16

460 x 4 = 1840

Answer:

3321

Step-by-step explanation:

The term "most specifically" is used to indicate the option that is the most specific or narrowest in meaning among the choices is d. chord.

The term "most specifically" is used to indicate the option that is the most specific or narrowest in meaning among the choices. Let's examine each option in the context of geometry:

a. A minor arc: A minor arc is a portion of a circle that measures less than 180 degrees. It is not the most specific term because it encompasses a range of arc sizes smaller than a semicircle, but it does not provide a narrower definition than other options.

b. A major arc: A major arc is a portion of a circle that measures more than 180 degrees. Similar to a minor arc, it does not provide the narrowest definition among the options.

c. A semicircle: A semicircle is a half of a circle, dividing it into two equal halves. This option is more specific than both minor and major arcs because it refers to a precise geometric shape with a 180-degree angle. However, there is one more option left to consider.

d. A chord: A chord is a straight line segment that connects two points on a circle. It is the most specific option among the choices because it refers to a specific geometric element—a line segment—within a circle.

So, The option that most specifically describes a geometric concept is:d. a chord.

Learn more about chords here, https://brainly.com/question/25871159

#SPJ11