Mathematics: Calculate the approximate volume of the sphere

Calculate the approximate volume of the sphere, №12214809, 28.05.2021 09:25

Engineering

You ve been hired by Fruity Fillers to write a C++ console application that approximates PI. Use a validation loop to prompt for and get from the user the number of terms to approximate PI to that is between 1 and 10,000. Use the following Leibniz formula: PI approximation = 4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...) The terms appear within the parentheses in the formula. A PI approximation to ... • One term is 4 * (1/1) = 4 • Four terms = 4 * (1/1 - 1/3 + 1/5 - 1/7) = 2.8952380952 • Seven terms = 4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13)

Step-by-step answer

P Answered by PhD

Explanation:

Enter number of terms (1-10000): 1000

Estimated value: 3.14059

Enter number of terms (1-10000): 1

Estimated value: 4

Enter number of terms (1-10000): 10000

Estimated value: 3.14149

Enter number of terms (1-10000): 100000

Error!!

Code (modify count statements)

#include <bits/stdc++,h>

using namespace std;

#define Id long double

Id pi(int n){

Id sum=0:

int sign=1;

for(int i=0;i<n;i++){

Id num= sign*1.00/(2*i+1);

sign*=-1;

sum+=num;

}

return 4*sum;

}

int main(){

int n;

count<<"Welcome\n";

count<<"Enter number of terms(1-1000):";

cin>>n;

while(n!=99){

if(n>10000 or n<1)

count<<"Error!!\n";

else{

count<<"Estimated value;"<<pi(n)<<endl;

count<<endl<<endl;

}

count<<"Enter number of terms(1-10000):";

cin>>n;

}

Engineering

You ve been hired by Fruity Fillers to write a C++ console application that approximates PI. Use a validation loop to prompt for and get from the user the number of terms to approximate PI to that is between 1 and 10,000. Use the following Leibniz formula: PI approximation = 4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...) The terms appear within the parentheses in the formula. A PI approximation to ... • One term is 4 * (1/1) = 4 • Four terms = 4 * (1/1 - 1/3 + 1/5 - 1/7) = 2.8952380952 • Seven terms = 4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13)

Step-by-step answer

P Answered by PhD

Explanation:

Enter number of terms (1-10000): 1000

Estimated value: 3.14059

Enter number of terms (1-10000): 1

Estimated value: 4

Enter number of terms (1-10000): 10000

Estimated value: 3.14149

Enter number of terms (1-10000): 100000

Error!!

Code (modify count statements)

#include <bits/stdc++,h>

using namespace std;

#define Id long double

Id pi(int n){

Id sum=0:

int sign=1;

for(int i=0;i<n;i++){

Id num= sign*1.00/(2*i+1);

sign*=-1;

sum+=num;

}

return 4*sum;

}

int main(){

int n;

count<<"Welcome\n";

count<<"Enter number of terms(1-1000):";

cin>>n;

while(n!=99){

if(n>10000 or n<1)

count<<"Error!!\n";

else{

count<<"Estimated value;"<<pi(n)<<endl;

count<<endl<<endl;

}

count<<"Enter number of terms(1-10000):";

cin>>n;

}

Mathematics

Color-blindness is any abnormality of the color vision system that causes a person to see colors differently than most people or to have difficulty distinguishing among certain colors (www.visionrx.xom).Color-blindness is gender-based, with the majority of sufferers being males.Roughly 8% of white males have some form of color-blindness, while the incidence among white females is only 1%.A random sample of 20 white males and 40 white females was chosen.Let X be the number of males (out of the 20) who are color-blind.Let Y be the number of females

Step-by-step answer

P Answered by PhD

2

Correct option is (d): Neither X nor Y can be well-approximated by a normal random variable.

Step-by-step explanation:

The sample size of males having color-blindness is, n (X) = 20.

The sample size of females having color-blindness is, n (Y) = 40.

The proportion of males that suffer from color-blindness is, P (X) = 0.08.

The proportion of females that suffer from color-blindness is, P (Y) = 0.01.

Now both the random variables X and Y follows a Binomial distribution,

$X\sim Bin(20, 0.08)\\Y\sim Bin(40, 0.01)$

A normal distribution is used to approximate the binomial distribution if the sample is large, i.e n ≥ 30 and the probability of success is very close to 0.50.

Also if np ≥ 10 and n (1 - p) ≥ 10, the binomial distribution can be approximated by the normal distribution.

For the sample of men (X):

$np=20\times0.08=1.610$

In this case neither n > 30 nor p is close to 0.50.

And np < 10.

Thus, the random variable X cannot be approximated by the normal distribution.

For the sample of men (Y):

$np=40\times0.01=0.410$

In this case n > 30 but p is not close to 0.50.

And np < 10.

Thus, the random variable Y cannot be approximated by the normal distribution.

Thus, both the random variables cannot be approximated by the normal distribution.

The correct option is (d).

Mathematics

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1 (All units are 1000 cells/μ L.) Using the empirical rule, find each approximate percentage below. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 ? What is the approximate percentage of women with platelet counts between 71.3 and 443.9 ? a. Approximately 68 % of women in this group have platelet counts within 1 standard deviation

Step-by-step answer

P Answered by PhD

(a) Approximately 68 % of women in this group have platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7.

(b) Approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.

Step-by-step explanation:

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1

Let X = the blood platelet counts of a group of women

So, X ~ Normal( $\mu=257.62, \sigma^{2} =62.1^{2}$ )

Now, the empirical rule states that;

68% of the data values lie within the 1 standard deviation of the mean.95% of the data values lie within the 2 standard deviations of the mean.99.7% of the data values lie within the 3 standard deviations of the mean.

(a) The approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 is 68% according to the empirical rule.

(b) The approximate percentage of women with platelet counts between 71.3 and 443.9 is given by;

z-score of 443.9 = $\frac{X-\mu}{\sigma}$

= $\frac{443.9-257.62}{62.1}$ = 3

z-score of 71.3 = $\frac{X-\mu}{\sigma}$

= $\frac{71.3-257.62}{62.1}$ = -3

So, approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.

Mathematics

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 264.8 and a standard deviation of 63.2. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4? b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0? a. Approximately nothing% of women in this group have platelet counts within 3 standard deviations

Step-by-step answer

P Answered by PhD

a) Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.

b) Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell shaped) 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 = 264.8

Standard deviation = 63.2

a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4?

By the Empirical Rule,

Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.

b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0?

201.6 = 264.8 - 63.2

201.6 is one standard deviation below the mean

328 = 264.8 + 63.2

328 is one standard deviation above the mean

By the Empirical rule,

Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.

Mathematics

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1 (All units are 1000 cells/μ L.) Using the empirical rule, find each approximate percentage below. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 ? What is the approximate percentage of women with platelet counts between 71.3 and 443.9 ? a. Approximately 68 % of women in this group have platelet counts within 1 standard deviation

Step-by-step answer

P Answered by PhD

(a) Approximately 68 % of women in this group have platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7.

(b) Approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.

Step-by-step explanation:

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1

Let X = the blood platelet counts of a group of women

So, X ~ Normal( $\mu=257.62, \sigma^{2} =62.1^{2}$ )

Now, the empirical rule states that;

68% of the data values lie within the 1 standard deviation of the mean.95% of the data values lie within the 2 standard deviations of the mean.99.7% of the data values lie within the 3 standard deviations of the mean.

(a) The approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 is 68% according to the empirical rule.

(b) The approximate percentage of women with platelet counts between 71.3 and 443.9 is given by;

z-score of 443.9 = $\frac{X-\mu}{\sigma}$

= $\frac{443.9-257.62}{62.1}$ = 3

z-score of 71.3 = $\frac{X-\mu}{\sigma}$

= $\frac{71.3-257.62}{62.1}$ = -3

So, approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.

Mathematics

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 264.8 and a standard deviation of 63.2. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4? b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0? a. Approximately nothing% of women in this group have platelet counts within 3 standard deviations

Step-by-step answer

P Answered by PhD

a) Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.

b) Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell shaped) 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 = 264.8

Standard deviation = 63.2

a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4?

By the Empirical Rule,

Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 75.2 and 454.4.

b. What is the approximate percentage of women with platelet counts between 201.6 and 328.0?

201.6 = 264.8 - 63.2

201.6 is one standard deviation below the mean

328 = 264.8 + 63.2

328 is one standard deviation above the mean

By the Empirical rule,

Approximately 68% of women in this group have platelet counts between 201.6 and 328.0.

Mathematics

Annapolis, maryland has an approximate population of 36,000. columbus, ohio has an approximate population of 7.3 x 105. which of the following is true? question 2 options: annapolis is approximately twice the size of columbus. columbus is approximately 200 times larger than annapolis. columbus is approximately 20 times larger than annapolis. annapolis is approximately 5 times larger than columbus.

Step-by-step answer

P Answered by PhD

4

Given, Annapolis, Maryland has an approximate population of 36,000.

And Columbus, Ohio has an approximate population of (7.3)(10)^5 .

First we have to multiply (7.3)(10)^5 .

(7.3)(10^5) = (7.3)(100000) = 730000

We can see the population of columbus is larger than population of Annapolis.

Now we will divide the population of Columbus by the population of Annapolis to find how much times the population of columbus is larger. We will get,

$\frac{730000}{36000}$ = 20.28 ( Approximately taken upto two decimal place)

So it is more than 20 times.

We can say, The population of columbus is approximately 20 times larger than Annapolis.

We have got the required answer.

Option 3 is correct.

Mathematics

Annapolis, maryland has an approximate population of 36,000. columbus, ohio has an approximate population of 7.3 x 105. which of the following is true? question 2 options: annapolis is approximately twice the size of columbus. columbus is approximately 200 times larger than annapolis. columbus is approximately 20 times larger than annapolis. annapolis is approximately 5 times larger than columbus.

Step-by-step answer

P Answered by PhD

4

Given, Annapolis, Maryland has an approximate population of 36,000.

And Columbus, Ohio has an approximate population of (7.3)(10)^5 .

First we have to multiply (7.3)(10)^5 .

(7.3)(10^5) = (7.3)(100000) = 730000

We can see the population of columbus is larger than population of Annapolis.

Now we will divide the population of Columbus by the population of Annapolis to find how much times the population of columbus is larger. We will get,

$\frac{730000}{36000}$ = 20.28 ( Approximately taken upto two decimal place)

So it is more than 20 times.

We can say, The population of columbus is approximately 20 times larger than Annapolis.

We have got the required answer.

Option 3 is correct.

Mathematics

The median weight of a boy whose age is between 0 and 36 months can be approximated by the function w(t)=7.42+1.92tâˆ’0.0074t2+0.000446t3â€‹, where t is measured in months and w is measured in pounds. Use this approximation to find the following for a boy with median weight in parts â€‹a) through â€‹c) below.a) The weight of the baby at age 7 months. The approximate weight of the baby at age 7 months is lbs. (Round to two decimal places as needed.) b) The rate of change of the baby s weight with respect to time at age 7 months. The rate of change

Step-by-step answer

P Answered by PhD

(a)20.65 lbs.

(b)1.88 lbs/month.

Step-by-step explanation: