Suppose you are a chemist who is trying to synthesize a specific compound. You have been working with a new technique and you think that this process can turn 60% of the input compounds into the desired synthesized compound, and want to attempt the process enough times to get an estimate that is within .04 of the true proportion that is converted. How many times should you execute the process to get the desired precision

Answer:

x=9

Step-by-step explanation:

2-x=-7

-x=-7-2

-x=-9

x=9

Answer:

1.0302

Step-by-step explanation:

The multiplier for a increase of a% is 1 + a/100.

The multiplier for a decrease of b% is 1 - b/100.

2% increase:

1 + (2/100) = 1 + 0.02 = 1.02

1% increase:

1 + (1/100) = 1 + 0.01 = 1.01

What single decimal multiplier would you use to increase by 2% followed by a 1% increase?

1.02*1.01 = 1.0302

The answer is 1.0302

Answer:

a) X[bar]=93

b)S=5.39

Step-by-step explanation:

Hello!

A simple random sample of 5 months of sales data provided the following information: Month: 1 2 3 4 5 Units Sold: 94 100 85 94 92

a. Develop a point estimate of the population mean number of units sold per month.

The variable of interest is:

X: Number of sales per month.

A random sample of n=5 months was taken, for each month, the number of units sold was recorded. To calculate the mean of the sample you have to add all the observed frequencies (Units Sold) by the sample size (n)

X[bar]= ∑X/n= 465/5=93

You can say that, on average, 93 units were sold over the 5-month period.

b. Develop a point estimate of the population standard deviation.

To calculate the sample standard deviation you have to calculate the variance and then its square root:

[tex]S^2= \frac{1}{n-1}[sumX^2-\frac{(sumX)^2}{n} ][/tex]

∑X= 465

∑X²= 43361

[tex]S^2= \frac{1}{4}[43361-\frac{(465)^2}{5} ]= 29[/tex]

S= √29= 5.385≅ 5.39

I hope this helps!

Answer:

26 mm

Step-by-step explanation:

Δcda ≅  Δxyz

If cd=26 mm then xy=cd= 26 mm

Answer:

Step-by-step explanation:

The answer is 54.5 on edg

For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.

[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]

Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.

The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.

Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,

[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]

Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.

For the second part, we need to find the value of x. Thus solve the above equation further as,

[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]

Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

Learn more about the right angle triangle property here;

https://brainly.com/question/22790996

Answer:

The center of the circle represented by given equation is (−1,3) and its radius is 3.

Explanation:

An equation of the form (x−h)2+(y−k)2=r2, is the equation of a circle of radius r, with a center at (h,k).

Hence as the equation

(x+1)2+(y−3)2=9

⇔(x−(−1))2+(y−3)2=9=32

and hence the center of the circle represented by this equation is (−1,3) and radius is 3.

Answer: just took the test, this is wrong

Step-by-step explanation:

Answer:

Find the present and future value of $1000 received every month end for 20  years if the interest rate is J12 = 12%

Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received  at the end of 10 years.

1.  John is currently 25 years old. He has $10,000 saved up and wishes to deposit  this into a savings account which pays him J12 = 6% p.a. He also wishes to  deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

Step-by-step explanation:

there are two ways to solve this question:

since this question is about monthly payments, I will use the annuity formula:

PV = payment x {[1 - (1 + r)⁻ⁿ]/r}

PV = 1000 x {[1 - (1 + 0.01)⁻²⁴⁰]/0.01}

r = 12% / 12 = 1%

n = 20 x 12 = 240

PV = $90,819.42

for the annuity due, we can use an annuity table since payments are annual:

payment $10,000

20 years

12% interest rate

PV annuity due = $10,000 x 8.3658 = $83,658

since the first payment is received 10 years form now, we must determine the PV = $83,658 / (1 + 0.12)¹⁰ = $26,935.64

1)

monthly payment = total amount / discount factor

total amount = monthly payment x discount factor

total amount = $237,006.45

we have to divide John's account in two:

future value of annuity = monthly payment x {[(1 + r)ⁿ - 1]/ r}

monthly payment = future value /  {[(1 + r)ⁿ - 1]/ r}

monthly payment = $179,571.54 / 1,004.515042 = $178.7644

Answer:

The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²

  or

The equation of the circle    x² + 2 x + y² - 4 y  = 15

Step-by-step explanation:

Given points end  Points are p(-3,-2) and q( 1,6)

The distance of two points formula

P Q = [tex]\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }[/tex]

P Q = [tex]\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }[/tex]

P Q = [tex]\sqrt{16+64} = \sqrt{80}[/tex]

The diameter 'd' = 2 r

                       2 r = √80

                            = [tex]\sqrt{16 X 5}[/tex]

                           = [tex]4 \sqrt{5}[/tex]

                      r =  2√5

Mid-point of two end points

                       [tex](\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )[/tex]

                                              = (-1 ,2)

Mid-point of two end points = center of the circle

                                    (h,k) = (-1 , 2)

The equation of the circle

           (x -h )² +(y-k)² = r²

         (x -(-1) )² +(y-(2))² = (2(√5))²

        x² + 2 x + 1 + y² - 4 y + 4 = 20

         x² + 2 x + y² - 4 y  = 20 -5

          x² + 2 x + y² - 4 y  = 15

Final answer:-

The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²

  or

The equation of the circle    x² + 2 x + y² - 4 y  = 15

Answer:

Step-by-step explanation:

Answer:

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 185

Standard deviation = 26

The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.

What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?

133 = 185 - 2*26

So 133 is two standard deviations below the mean.

By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133

p = 0.05*0.5 = 0.025

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

Answer:

y intercept = - 40

Step-by-step explanation:

x 24 36 48

y -8 1 10

y = ax + b

a is the gradient (or slope).

b = y intercept.

a = (48-36) / (10-1) = 12/9

Rewrite to solve for b, which means it starts with b = ...

b = y - 12/9 * x

Substitute one point ( 24 , -8 )

b = -8 - (12/9 * 24)

b = y intercept = - 40

Answer:

Only the question 2 is a statistical question.

Step-by-step explanation:

Questions

2. How much time do the students in my school spend on the Internet each  night?

3. What is the height of the tallest waterslide at Wild Rides Water Park?

4. What are the cabin rental prices for each of the state parks in Kentucky?

The question 2 is a statistical question.

Is the only question that can be answered with a parameter of a population (mean number of hours spent on the internet by the students).

The other two ask for individual values: the height of the tallest waterslide at Wild Rides Water Park, and the cabin rental prices for each of the state parks in Kentucky. This need specific values that are not statistical, but deterministic.

Answer:

A. Yes. Each subject is randomly assigned to a treatment

Step-by-step explanation:

In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.

In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.

Answer:

$15

Step-by-step explanation:

Error = Approximate value - Exact value

$100 - $75 = $15

Answer:

(a) The probability that more than 180 will take your free sample is 0.1056.

(b) The probability that fewer than 200 will take your free sample is 0.9997.

(c) The probability that a customer will take a free sample and buy the product is 0.2184.

(d) The probability that between 60 and 80 customers will take the free sample and buy the product is 0.8005.

Step-by-step explanation:

We are given that about 56% of all customers will take free samples. Furthermore, of those who take the free samples, about 39% will buy what they have sampled.

The day you were offering free samples, 303 customers passed by your counter.

Firstly, we will check that it is appropriate to use the normal approximation to the binomial, that is;

Is np > 5  and  n(1-p) > 5

In our question, n = sample of customers = 303

                          p = probability that customers will take free sample = 56%

So, np = [tex]303 \times 0.56[/tex] = 169.68 > 5

     n(1-p) = [tex]303 \times (1-0.56)[/tex] = 133.32 > 5

Since, both conditions are satisfied so it is appropriate to use the normal approximation to the binomial.

Now, mean of the normal distribution is given by;

        Mean, [tex]\mu[/tex] = [tex]n \times p[/tex] = 169.68

Also, the standard deviation of the normal distribution is given by;

       Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                            = [tex]\sqrt{303 \times 0.56 \times (1-0.56)}[/tex] = 8.64

Let X = Number of people who will take your free sample

The z score probability distribution for normal distribution is given by;

                           Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

(a) The probability that more than 180 will take your free sample is given by = P(X > 180) = P(X > 180.5)     {Using continuity correction}

        P(X > 180.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{180.5-169.68}{8.64}[/tex] ) = P(Z > 1.25) = 1 - P(Z < 1.25)

                                                                   = 1 - 0.8944 = 0.1056

(b) The probability that fewer than 200 will take your free sample is given by = P(X < 200) = P(X < 199.5)     {Using continuity correction}

        P(X < 199.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{199.5-169.68}{8.64}[/tex] ) = P(Z < 3.45) = 0.9997

(c) We are given in the question that of those who take the free samples, about 39% will buy what they have sampled, this means that we have;

     P(Buy the product / taken a free sample) = 0.39

So, Probability(customer will take a free sample and buy the product) = P(customer take a free sample) [tex]\times[/tex] P(Buy the product / taken a free sample)

     = 0.56 [tex]\times[/tex] 0.39 = 0.2184

(d) Now our mean and standard deviation will get changed because the probability of success now is p = 0.2184 but n is same as 303.

So, Mean, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]303 \times 0.2184[/tex] = 66.18

Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                    = [tex]\sqrt{303 \times 0.2184 \times (1-0.2184)}[/tex] = 7.192

Now, the probability that between 60 and 80 customers will take the free sample and buy the product is given by = P(60 < X < 80) = P(59.5 < X < 80.5)         {Using continuity correction}

     P(59.5 < X < 80.5) = P(X < 80.5) - P(X [tex]\leq[/tex] 59.5)

     P(X < 80.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{80.5-66.18}{7.192}[/tex] ) = P(Z < 1.99) = 0.9767

     P(X [tex]\leq[/tex] 59.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{59.5-66.18}{7.192}[/tex] ) = P(Z [tex]\leq[/tex] -0.93) = 1 - P(Z < 0.93)

                                                            = 1 - 0.8238 = 0.1762

Therefore, P(59.5 < X < 80.5) = 0.9767- 0.1762 = 0.8005.

Answer: 72.

Step-by-step explanation:

You can solve this by representing the number in an equation that models the problem given. I will use the variable x to represent the number:

[tex]x + \frac{1}{3}x = 96[/tex]

In the equation, I listed the number and added one-third of the same number to it to equal 96.

Now, solve:

[tex]\frac{4}{3}x = 96\\ \\x = 96 / \frac{3}{4} \\\\x = 96 * \frac{3}{4} \\\\x = 72[/tex]

The number is 72.

Answer:

y = (-1/3)x + 2

Step-by-step explanation:

Equation of line in slope-intercept form is given by

y = mx +c

where m is the slope of line

c is y intercept

Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)

_________________________________________________

let the equation of required line be y = mx +c

Since points given are  (3,1) and (-6,4)

Then, its slope is

m = 4-1/-6-3 = 3/-9 = -1/3

Thus, slope of line is m = -1/3

lets use m = -1/3 in place of m in equation y = mx +c

y = (-1/3)x + c

Since points   (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.

hence lets plug 3 in place of x and 1 in place of y

1 =  (-1/3)3 + c

=> 1 = -1 + c

=> c = 1 +1 = 2

Thus, intercept is 2.

Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.

Answer:

[tex]\frac{47}{10}[/tex]

Step-by-step explanation:

Given the mixed fraction, [tex]4\dfrac{7}{10}[/tex], to convert it to proper fraction simply means removing all traces of whole number in the fraction.

To convert will will add [tex]4[/tex] to [tex]\dfrac{7}{10}[/tex] as shown;

[tex]= 4 + \frac{7}{10}\\ = \frac{4}{1} + \frac{7}{10}\\= \frac{40+7}{10}\\ = \frac{47}{10}[/tex]

The improper form of the fraction [tex]4\frac{7}{10}[/tex] is [tex]\frac{47}{10}[/tex]

Answer:

28/10 ez

Step-by-step explanation:

in khan

Answer:

$6298.29

Step-by-step explanation:

2000 x (1+(.165/12))^84, the 84 being the number of months in 7 years

=$6298.2927345

=$6298.29

How many months in 7 years = 84 months

Answer:

s+(2s+3)+12

Step-by-step explanation:

Answer: C

Step-by-step explanation:

If you look at the equation, you can see that you can cancel out a 9z³ on both sides. 9z³ is what both fractions have in common. This leaves us with 1 on the numerator on the first fraction and 2 for the denominator on the second fraction.

[tex]\frac{1}{16xy} *\frac{4x}{3}[/tex]

You can also cancel out 4x since both fractions have a 4x in common. This leaves the denominator of the first equation with 4y and the numerator of the second equation with 1.

[tex]\frac{1}{4y} *\frac{1}{3}[/tex]

Now, we can multiply straight across.

[tex]\frac{1}{12y}[/tex]

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1100

A = 1900

n = 4 because it was compounded 3 times in a year and n = 12/3 = 4

t = 10 years

Therefore,.

1900 = 1100(1 + r/4)^4 × 10

1900/1100 = (1+ r/4)^40

1.73 = (1+ r/4)^40

Taking log to base 10 of both sides, it becomes

Log 1.73 = 40log(1 + 0.25r)

0.238 = 40log(1 + 0.25r)

Log(1 + 0.25r) = 0.238/40 = 0.00595

Take exponent of both sides, it becomes

10^log(1 + 0.25r) = 10^0.00595

1 + 0.25r = 1.0138

0.25r = 1.0138 - 1 = 0.0138

r = 0.0138/0.25

r = 0.0552

The The required annual interest rate is

0.0552 × 100 = 5.5%

Answer:

- The limits are  908.6 cm^3 and 1417cm^3

- 1337.0cm^3 is in between the limits

Step-by-step explanation:

To determine the limit by taking into account the range rule of thumb, you use the fact that the limits are given by the mean plus and minus twice the standard deviation, that is:

[tex]\overline{x}\pm 2\sigma[/tex]        (1)

[tex]\overline{x}[/tex]: mean of brain volume = 1162.8 cm^3

σ: standard deviation = 127.1 cm^3

You replace the values of the parameters in the equation (1):

[tex]1162.8cm^3+2(127.1cm^3)=1417cm^3\\\\1162.8cm^3-2(127.1cm^3)=908.6cm^3[/tex]

Limits = (1417 , 908.6)

The limits are  908.6 cm^3 and 1417cm^3

1337.0cm^3 is in between the limits calculated above.

Answer:

2. Line RT = 11x - 17, Line PT= 5x + 13

11x - 17 = 5x + 13

11x - 17 = 5x + 13

-5x. -5x

6x - 17 = 13

+17. +17

6x= 30

÷6. ÷ 6

x = 5

(B). According to the rules of a parallelogram, if angle S is 50°, the angle on the same side will be supplementary to it. So, angle R equals 130° and angle Q is also 50°.

Answer:

Step-by-step explanation:

The monthly interest rate is ...

  [tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]

a) The monthly payment is given by the amortization formula:

  A = Pr/(1 -(1+r)^-n)

where r is the monthly interest rate on a loan of amount P for n months.

  A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95

The monthly payment is $1214.95.

__

b) The amount to interest is the product of the remaining principal and the monthly interest rate.

 first month's interest = $140,000·0.0070833 = $991.67

__

c) The balance after the first payment is ...

  new balance = $140,000 +991.67 -1214.95 = $139,776.72

__

d) The amount to interest for the second payment is computed the same way:

  second month's interest = $139,776.72·0.00708333 = $990.09

__

e) The balance after the second payment is computed the same way:

  new balance = $139,776.72 +990.09 -1214.95 = $139,551.86

Answer:

Step-by-step explanation:

Let P be the population of the community

So the population of a community increase at a rate proportional to the number of people present at a time

That is

[tex]\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0[/tex]

Solve this equation we get

[tex]p(t)=p_0e^{kt}---(1)[/tex]

where p is the present population

p₀ is the initial population

If the  initial population as doubled in 5 years

that is time t = 5 years

We get

[tex]2p_o=p_oe^{5k}\\\\e^{5k}=2[/tex]

Apply In on both side to get

[tex]Ine^{5k}=In2\\\\5k=In2\\\\k=\frac{In2}{5} \\\\\therefore k=\frac{In2}{5}[/tex]

Substitute [tex]k=\frac{In2}{5}[/tex]  in [tex]p(t)=p_oe^{kt}[/tex] to get

[tex]\large \boxed {p(t)=p_oe^{\frac{In2}{5}t }}[/tex]

Given that population of a community is 9000 at 3 years

substitute t = 3 in [tex]{p(t)=p_oe^{\frac{In2}{5}t }}[/tex]

[tex]p(3)=p_oe^{3 (\frac{In2}{5}) }\\\\9000=p_oe^{3 (\frac{In2}{5}) }\\\\p_o=\frac{9000}{e^{3(\frac{In2}{5} )}} \\\\=5937.8[/tex]

Answer:

[tex]\pi =\frac{C}{d}[/tex]

Step-by-step explanation:

[tex]C=\pi d[/tex]

[tex]\pi =\frac{C}{d}[/tex]

Answer:

I'm not 100%sure but i'm think that it is c

Step-by-step explanation:

Hope this helps! May have gotten it wrong really sorry if I did

Answer:

StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction

Solve the proportion for x.

After using cross products, the proportion becomes the equation

✔ 4x = 10

.

Isolate the variable by dividing both sides of the equation by

✔ 4

.

x = ✔ 2.5

.

The value of x is 2.5 for the given proportion.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

The proportion is given in the question, as follows:

4/2 = 5/x

Using cross-product, the proportion becomes the equation as:

4x = 2 × 5

4x = 10

Divide by 4 into both sides of the above equation,

x = 10/4

x = 2.5

Thus, the value of x is 2.5 for the given proportion.

Learn more about the proportion here:

brainly.com/question/1504221

#SPJ3

Answer:

X

Step-by-step explanation:

X and Y make up a graph