what is the domain of this

Answer:

0.3333

Step-by-step explanation:

Given the following :

Sample mean(m) = 4.001 inch

Standard deviation(sd) = 0.002 inch

Key specification : = 4 ± .003 inches

Upper specification LIMIT ( USL) : (4 + 0.003) = 4.003 inches

Lower specification limit (LSL) : (4 - 0.003) = 3.997 inches

Cpk is found using the relation:

min[(USL - mean) / (3 * sd), (mean-LSL) / (3*sd)]

min[(4.003 - 4.001)/(3*0.002), (4.001 - 3.997)/(3*0.002)]

min[(0.002 / 0.006), (0.004 / 0.006)]

min[(0.33333, 0.66667)

Therefore Cpk = 0.3333

Because 0.33333<0.66667

Answer:

The probability is 2,010,580/13,378,456

Step-by-step explanation:

Here is a combination problem.

We want to 7 cards from a total of 52.

The number of ways to do this is 52C7 ways.

Also, we know there are 12 face cards in a standard deck of cards.

So we are selecting 3 face cards from this total of 12.

So also the number of cards which are not face cards are 52-12 = 40 cards

Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4

Thus, the required probability will be;

(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560

= 20,105,800/133,784,560 = 2,010,580/13,378,456

An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of [tex]^{14}\text{C}[/tex] ​. Estimate the minimum age of the charcoal, noting that  [tex]2^{10} = 1024[/tex]

Answer:

57300 years

Step-by-step explanation:

Using the relation of an half-life time in relation to fraction which can be  expressed as:

[tex]\dfrac{N}{N_o} = (\dfrac{1}{2})^{\frac{t}{t_{1/2}}[/tex]

here;

N represents the present atom

[tex]N_o[/tex] represents the  initial atom

t represents the time

[tex]t_{1/2}[/tex] represents the half - life

Given that:

Its charcoal is found to contain less than 1/1000 the normal amount of [tex]^{14}\text{C}[/tex] ​.

Then ;

[tex]\dfrac{N}{N_o} = \dfrac{1}{1000}[/tex]

However; we are to  estimate the minimum age of the charcoal, noting that  [tex]2^{10} = 1024[/tex]

so noting that [tex]2^{10} = 1024[/tex], then:

[tex]\dfrac{1}{1000}> \dfrac{1}{1024}[/tex]

[tex]\dfrac{1}{1000}> \dfrac{1}{2^{10}}[/tex]

[tex]\dfrac{1}{1000}> (\dfrac{1}{2})^{10}[/tex]

If

[tex]\dfrac{N}{N_o} = \dfrac{1}{1000}[/tex]

Then

[tex]\dfrac{N}{N_o} > (\dfrac{1}{2})^{10}[/tex]

Therefore, the estimate of the minimum time needed is 10 half-life time.

For [tex]^{14}\text{C}[/tex] , the normal half-life time = 5730 years

As such , the estimate of the minimum age of the charcoal =  5730 years × 10

= 57300 years

Answer:

1,2 and 6

Step-by-step explanation:

pie symbol

2/3

0.333333....

9514 1404 393

Answer:

  (d)  4.2×10^15

Step-by-step explanation:

Your calculator will tell you the quotient is about ...

  4.21348...×10^15

The least precise number in the division is 1.5, which has 2 significant digits. Therefore, the result should be rounded to 2 significant digits:

  4.2×10^15

Answer:

21 miles/gallon

Step-by-step explanation:

To find his mileage in miles/gallon, divide the number of miles by the number of gallons.

315/15

= 21

= 21 miles/gallon

Answer:

21 miles / gallon

Step-by-step explanation:

Take the miles and divide by the gallons

315 miles / 15 gallons

21 miles / gallon

Answer: 8

Step-by-step explanation:

Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.

Total marbles other than green = 8

Total marbles other than green and yellow = 6

Then the number of sets of seven marbles include at least one yellow one but no green ones:-

[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]

Number of sets of seven marbles include at least one yellow one but no green ones = 8

Answer:

option A

Step-by-step explanation:

Permutation is An arrangement of objects in an ORDER

but combination is the opposite.

Answer:

The dimensions or Area of the rectangle is 1200cm².

Answer:

The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Step-by-step explanation:

Given that:

F(x,y) = 8 sin (xy) at (0,9)

The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]

[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]

[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]

We can conclude that the  maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Answer:

the answers are below:

Step-by-step explanation:

a. null hypothesis:

H0: Pw - Pm = 0 (so Pw = Pm)

alternate hypothesis:

H1: Pw - Pm > 0 (so Pw > Pm)

where Pw is the proportion of women

Pm is the proportion of men

b.) proportion of women = o.40

proportion of men =  0.32

sample size of women = 20

sample size of men = 25

[tex]z = 0.4 - 0.32/ \sqrt{((0.4 *0.6)/20) * (0.32 * 0.68)/25)}[/tex]

[tex]z = 0.56[/tex]

c.) p value =

p(z>0.56)

= 0.7123

= 1 - 0.7123

= o.2877 which can be approximated to be 0.288

d. alpha value was set at 0.05

the p value is greater than alpha.

therefore it is not statistically significant.

we conclude that the proportion of roman catholic women is not greater than men.

Answer:

The  width is  [tex]w = \$ 729.7[/tex]

Step-by-step explanation:

From the question we are told that

   The population standard deviation is  [tex]\sigma = \% 1,000[/tex]

    The  sample size is  [tex]n = 50[/tex]

    The sample mean  is  [tex]\= x = \$ 15,000[/tex]

Given that the confidence level is  99% then the level of significance is mathematically represented as  

               [tex]\alpha = 100 - 99[/tex]

=>            [tex]\alpha = 1\%[/tex]

=>             [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is

             [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally margin of error is mathematically represented as

             [tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

               [tex]E = 364.9[/tex]

The width of the 99% confidence interval is mathematically evaluated as

         [tex]w = 2 * E[/tex]

substituting values

          [tex]w = 2 * 364.9[/tex]

          [tex]w = \$ 729.7[/tex]

Answer:

2(8-d)

2(8-5)   (substituting d=5)

2(3)

=6

Step-by-step explanation:

The required expression is f = 6 for d =5 in the for the expression f = 2 (8 -d).

An algebraic expression is consists of variables, numbers with various mathematical operations,

The expression,

f = 2 (8 - d)              (1)

To evaluate the expression for d = 5

Substitute the value of d = 5 in equation (1),

f = 2 (8 - 5)

f = 2 x 3

f = 6

The required expression is f=6.

To know more about Algebraic expression on:

https://brainly.com/question/19245500

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4/24,7/5,5/3,3/5 espero hallude

Answer:

64

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

4^3

= 4 * 4 * 4

= 16 * 4

= 64

Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

im sorry but the thing is i cant translate these words but the answer is D

Answer:

Step-by-step explanation:

positive integer divisible by 3 includes

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...

less than highest possible value is 42

Answer:

APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.

Step-by-step explanation:

Answer:

the margin of error

= 1.96 x 0.0632

= 0.124

Step-by-step explanation:

this question has the sample size, n = 40

8 people have received help from their parents from this sample.

8/40 = 0.2

which is the sample proportion

z = 1 - 0.2

= 0.8

to calculate standard error

√pz/n

= √0.2 x 0.8/40

= √0.16/40

= 0.0632

at 95% confidence level

z(alpha/2) = 1.96

therefore the margin of error

= 1.96 x 0.0632

= 0.124

Answer:

Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

FV = PV(1 + r/m)mt

or

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is

FV = PV(1 + r/m)mt = 20,000(1 + 0.085/12)(12)(4) = $28,065.30

Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.

Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:

reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:

r eff =(1 + rnom /m)m = (1 + 0.098/12)12 - 1 = 0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P × r / [1 - (1 + r)-n]

and

D = P × (1 + r)k - R × [(1 + r)k - 1)/r]

Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:

n = log[x / (x – P × r)] / log (1 + r)

where Log is the logarithm in any base, say 10, or e.

Future Value (FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then

FV = [ R(1 + r)n - 1 ] / r

Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be

FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i

where i = r/m is the interest paid each period and n = m × t is the total number of periods.

Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:

FV = PV(1 + i)n + [ R(1 + i)n - 1 ] / i =

5,000(1+0.05/12)120 + [100(1+0.05/12)120 - 1 ] / (0.05/12)

Hello, please consider the following.

[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]

Thank you

Step-by-step explanation:

y=mx+c

Answer:

y= 10x +14

Step-by-step explanation:

Distribute parenthesis:

7(x+2) + 3x = 7x +14 +3x

Then combine like terms:

7x + 3x = 10x +14

Answer:

i think

x=6.77

y=11.33

Answer:

C) 82/2

Step-by-step explanation:

The area of a square is calculated by multiplying a side by itself

so one side of the square is 9 in

the area of a triangle is calculated by multiplying height and base and that divided by 2

since E is the midpoint, if we draw a line show the height from there

the height would be 9

9*9/2 = 82/2

Answer:

B. y=12x

Step-by-step explanation:

x = # of books bought

so then y=12x

There is no any image of rectangle

Answer:

In the error term.

Step-by-step explanation:

A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).

Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.

Answer:

Step-by-step explanation:

From the given information;

let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c

SO, using the Pythagoras theorem

a² = c² + 177²

By taking the differentiation of both sides with respect to time t , we have

[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]

[tex]a = \sqrt{ 5041+31329}[/tex]

[tex]a = \sqrt{ 36370}[/tex]

a = 190.71

SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]

Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]

[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]

[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex]  to the nearest hundredth.

Answer:

Step-by-step explanation:

We first examine a simple hidden Markov model (HMM). We observe a sequence of rolls of a four-sided die at an "occasionally dishonest casino", where at time t the observed outcome x_t Element {1, 2, 3, 4}. At each of these times, the casino can be in one of two states z_t Element {1, 2}. When z_t = 1 the casino uses a fair die, while when z_t = 2 the die is biased so that rolling a 1 is more likely. In particular: p (x_t = 1 | z_t = 1) = p (x_t = 2 | z_t = 1) = p (x_t = 3 | z_t = 2) = p (x_t = 4 | z_t = 1) = 0.25, p (X_t = 1 | z_t = 2) = 0.7, p (X_t = 2 | z_t = 2) = p (X_t = 3 | z_t = 2) = p (X_t = 4 | z_t = 2) = 0.1. Assume that the casino has an equal probability of starting in either state at time t = 1, so that p (z1 = 1) = p (z1 = 2) = 0.5. The casino usually uses the same die for multiple iterations, but occasionally switches states according to the following probabilities: p (z_t + 1 = 1 | z_t = 1) = 0.8, p (z_t = 2) = 0.9. The other transition probabilities you will need are the complements of these. a. Under the HMM generative model, what is p (z1 = z2 = z3), the probability that the same die is used for the first three rolls? b. Suppose that we observe the first two rolls. What is p (z1 = 1 | x1 = 2, x2 = 4), the probability that the casino used the fair die in the first roll? c. Using the backward algorithm, compute the probability that we observe the sequence x1 = 2, x2 = 3, x3 = 3, x4 = 3 and x5 = 1. Show your work (i.e., show each of your belief for based on time). Consider the final distribution at time t = 6 for both p (z_t = 1) = p (z_t = 2) = 1.

ANSWER:

Let say we have that the first state of the die is state 1. Therefore the probability of this is p(z1=1)=0.5.

Also the probability that the same die is used(i.e. casino would be in the same state) is p(z2=1|z1=1)=0.8.

Again, suppose the first state of the die is state 2. So, p(z1=2)=0.5 and p(z2=2|z1=2)=0.9.

Other transition probabilities can be written as

p(zt+1=2|zt=1)=1-p(zt+1=1|zt=1)=.2

p(zt+1=1|zt=2)=1-p(zt+1=2|zt=2)=.1

p(z3=1|z1=1) = [p(z3=1|z2=2)*p(z2=2|z1=1)]+[p(z3=1|z2=1)*p(z2=1|z1=1)] = 0.1*0.2+0.8*0.8 = 0.66

p(z3=2|z1=2) = [p(z3=2|z2=2)*p(z2=2|z1=2)]+[p(z3=2|z2=1)*p(z2=1|z1=2)] = 0.9*0.9+0.2*0.1 = 0.83

With this, the total probability that the same die is used for the first three rolls (i.e. casino would be in the same state) is  given thus;

{p(z1=1)*p(z3=1|z1=1)}*{p(z1=2)*p(z3=2|z1=2)}

=  0.5*0.66+0.5*0.83 = 0.745

Prob = 0.745