Line
2021-01-16
Answered

To find: The function that models the area of rectangle in terms of length of one of its sides.
The perimeter of rectangle is 20 ft.

You can still ask an expert for help

Clara Reese

Answered 2021-01-17
Author has **120** answers

Concept used:
Area of rectangle is defined as,
$A=l\text{}\cdot \text{}b$
Here, A is area, l is length and b is width.
Calculation:
Consider the length of one of its sides of rectangle as x.
The perimeter of a rectangle is defined as,
$P=2\text{}(l\text{}+\text{}b)$
Here, P is perimeter.
The perimeter of rectangle is given as 20 ft.
Substitute 20 for P and x for l in above equation to the value of b.
$20=2\text{}(x\text{}+\text{}b)$

$\frac{20}{2}=x\text{}+\text{}b$

$10=x\text{}+\text{}b$

$b=10\text{}-\text{}x$
Therefore, the value of b is $(10\text{}-\text{}x)$
Substitute x for l and $10\text{}-\text{}x$ for b in equation to obtain the model that express area of the rectangle
$A=x\text{}(10\text{}-\text{}x)$

$=10x\text{}-\text{}{x}^{2}$
Here, x is always greater than zero and less than 10 to define the area therefore the value of x is always lies in between 0 and 10.
Conclusion:
Thus, the function that models the are of rectangle in terms of length of one of its sides is $A=10x\text{}-\text{}{x}^{2}$ .

asked 2021-01-06

A weather forecaster predicts that the temperature in Antarctica will decrease ${8}^{\circ}F$ each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least ${36}^{\circ}F$

asked 2020-11-20

The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research, 1984: 1169-1174) suggests the uniform distribution on the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. a. What are the mean and variance of depth? b. What is the cdf of depth? c. What is the probability that observed depth is at most 10? Between 10 and 15? d. What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?

asked 2021-03-07

A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area al the point $(4,\text{}5).$ Write an equation that represents the path.

asked 2021-02-25

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. $(1,3),(2,6),(3,12),(4,24)$

Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

asked 2022-05-09

Samples are taken from two different types of honey and the viscosity is measured.

Honey A:

Mean: 114.44

S.D : 0.62

Sample Size: 4

Honey B:

Mean: 114.93

S.D: 0.94

Sample Size: 6

Assuming normal distribution, test at 5% significance level whether there is a difference in the viscosity of the two types of honey?

Here's what I did:

I took my null hypothesis as $\mu $B - $\mu $A = 0 and alternative hypothesis as $\mu $B - $\mu $A $\ne $ 0

Then I did my calculations which were as following:

Test Statistic = (B -A ) - ($\mu $B - $\mu $A) / sqrt {(variance B / sample size B) + (variance A / sample size A)}

This gave me test statistic as = 0.49/0.49332 that is equal to 0.993

However the test statistic in the book solution is given as 0.91. What am I doing wrong?

Honey A:

Mean: 114.44

S.D : 0.62

Sample Size: 4

Honey B:

Mean: 114.93

S.D: 0.94

Sample Size: 6

Assuming normal distribution, test at 5% significance level whether there is a difference in the viscosity of the two types of honey?

Here's what I did:

I took my null hypothesis as $\mu $B - $\mu $A = 0 and alternative hypothesis as $\mu $B - $\mu $A $\ne $ 0

Then I did my calculations which were as following:

Test Statistic = (B -A ) - ($\mu $B - $\mu $A) / sqrt {(variance B / sample size B) + (variance A / sample size A)}

This gave me test statistic as = 0.49/0.49332 that is equal to 0.993

However the test statistic in the book solution is given as 0.91. What am I doing wrong?

asked 2021-01-27

To describe:It is possible that the given claim is true or not.

To describe:The questions that should ask about how the data were collected.

To describe:The questions that should ask about how the data were collected.

asked 2021-08-08

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 24 subjects had a mean wake time of 104.0 min. After treatment, the 24 subjects had a mean wake time of 94.5 min and a standard deviation of 23.2 min. Assume that the 24 sample values appear to be from a normally distributed population and construct a

Construct the