Find the length of a rectangular lot with a perimeter of 72 m if the length is 6 m more than the width

Solution

Given that the Perimeter is: 340 yards. Lenght is 91 yards

Since P = 2(L + W)

where L is the Length

W is the width

=> 340 = 2(91 + W)

=> 340 = 182 + 2W

=> 158 = 2W

Dividing both sides by 2

=> W = 79

Hence, the width is 79 yards

Answer: it would be 79yards

Step-by-step explanation: 91•2=182

340-182=158

158/2=79yards

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

Learn more about intergal here:

https://brainly.com/question/31109342

#SPJ1

Answer:

5(4x + 5)

Step-by-step explanation:

Given

20x + 25 ← factor out the common factor 5 from each term

= 5(4x + 5)

Answer:

5(4x+5)

Step-by-step explanation:

divide both with the same number into smallest digit

eg: 5(4x+5)=20x+25

if 5x4=20 and 5x5=25

both can be divided by 5 to get smallest number(factorise it)

Answer:

1/2

Step-by-step explanation:

When you roll a 6-sided die, there are 6 possible outcomes:

1, 2, 3, 4, 5, 6

3 of the outcomes are even, and 3 of the outcomes are odd.

p(A) = p(even) = 3/6 = 1/2

p(Ac) = 1 - p(A) = 1 - 1/2 = 1/2

Therefore, approximately 0.0475 or 4.75% of smoke alarms will have a life span of less than 1 year as the cumulative probability for a Z-score of -1.67 is approximately 0.0475.

To find the proportion of smoke alarms with a life span of less than 1 year, we can use the Z-score formula and the properties of the standard normal distribution.

First, we calculate the Z-score using the formula:

Z = (X - μ) / σ

Where X is the value we are interested in (1 year), μ is the mean (2 years), and σ is the standard deviation (0.6 years).

Z = (1 - 2) / 0.6

= -1.67

Next, we look up the corresponding cumulative probability (proportion) for the Z-score of -1.67 in the standard normal distribution table or by using statistical software. The cumulative probability corresponds to the proportion of values less than the given Z-score.

To know more about cumulative probability,

https://brainly.com/question/29580548

#SPJ11

The measurement that could be a surface area measure is D. 27.9 mm². The unit "mm²" represents square millimeters, which is a measurement of surface area.

A surface area is the measurement of the outside area of an object or shape.

A surface area usually measures the surfaces of an object like the sides, top, and bottom.  

It is measured in square units like square inches or square meters.

It is an important concept that is used in different areas like geometry (like a cone, cylinder, rectangular prism, etc.), physics, and engineering.

Learn more about surface area at brainly.com/question/951562

#SPJ1

Step-by-step explanation:

because its formula is 4L

Answer:

The Central Limit Theorem (CLT) is an important theorem in statistics because it serves as the foundation for various statistical techniques and analyses.

The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution, provided that the population has finite mean and variance.
Normality:

The CLT establishes the concept of normality, which is a critical assumption in numerous statistical tests such as the t-test, z-test, and ANOVA. By knowing that the sample means are normally distributed, we can apply these tests to make inferences about population parameters.
Simplification:

Due to the CLT, we can simplify complex statistical problems by using normal distributions instead of dealing with the original population distribution.

Calculations more manageable and allows us to utilize the standard normal distribution table.
Confidence intervals:

The CLT enables us to construct confidence intervals for population parameters such as the mean.

Essential in estimating unknown population parameters based on sample data and understanding the associated uncertainty.
Margin of error:

The theorem helps in determining the margin of error for estimates, allowing us to quantify the accuracy of our estimates and make better decisions based on data.
Large sample sizes:

The CLT is particularly relevant when dealing with large sample sizes, as the distribution of sample means becomes more normal, and we can apply various statistical techniques with greater confidence.
The Central Limit Theorem is important in statistics because it enables us to assume normality, simplify problems, construct confidence intervals, determine the margin of error, and apply various statistical techniques with greater confidence, especially when dealing with large sample sizes.

For similar questions on Statistics

https://brainly.com/question/15525560

#SPJ11

Amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

Let amount of one tin of paint = x

Let the total amount Mr. Chong  having = y

On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,

18x = y + 80            

On rearranging this equation can be written as,

18x - y = 80                                         equation 1

On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,

10x = y - 32

On rearranging this equation can be written as,

-10x + y = 32                                      equation 2

On adding equation 1 and equation 2, we get

18x - y -10x + y = 80 + 32

8x = 112

x = (112/8) = 14

On substituting x = 14 in equation 2 , we get

-140 + y = 32

y = 172

So, amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

To know more about Quadratic Equations refer to the link:

https://brainly.com/question/18088242

#SPJ4

The gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.

Gravitational Potential Energy (GPE) is estimated as;

GPE = m×g×h              

In which

m = mass of parachuting outfit (kg)

g = acceleration due to gravity (m/s²)

h = height (meters)

Put the values in the formula.

GPE = 90× 9.8× 5000

GPE = 4,410,000‬ joules

GPE = 4,410 kJ

Thus, the gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.

To know more about the Gravitational Potential Energy, here

https://brainly.com/question/3120930

#SPJ4

The binary search for element 23 and 23

#include <iostream>

using namespace std;

int binarySearch(int array[], int x, int low, int high) {

 if (high >= low) {

int mid = low + (high - low) / 2;

// If found at mid, then return it

if (array[mid] == x)

return mid;

// Search the left half

if (array[mid] > x)

return binarySearch(array, x, low, mid - 1);

// Search the right half

return binarySearch(array, x, mid + 1, high);

}

 return -1;

}

int main(void) {

 int array[] = {10, 23, 26, 31, 44, 45, 46, 48, 66, 70, 83, 98 };

 int x = 23;

 int n = sizeof(array) / sizeof(array[0]);

 int result = binarySearch(array, x, 0, n - 1);

 if (result == -1)

   printf("Not found");

 else

   printf("Element is found at index %d", result);

}

Linear search for 83 amd 23:

#include<stdio.h>

int main()

{

   int a[20],i,x,n;

   printf("How many elements?");

   scanf("%d",&n);

   printf("Enter array elements:n");

   for(i=0;i<n;++i)

       scanf("%d",&a[i]);

   printf("nEnter element to search:");

   scanf("%d",&x);

   for(i=0;i<n;++i)

       if(a[i]==x)

           break;    

   if(i<n)

       printf("Element found at index %d",i);

   else

       printf("Element not found");

   return 0;

}

Binary search takes less time to search an element as compared to a linear search.

To learn more about linear search, click on below link:

https://brainly.com/question/15190740

#SPJ4

The decision for values of χ^2 obt close to 0 will depend on the level of significance and should be made in the context of the specific hypothesis being tested and the available evidence.

If the obtained value of chi-squared (χ^2 obt) is close to 0, it suggests that the observed data is not significantly different from the expected data. This means that the null hypothesis, which assumes that there is no significant difference between the observed and expected data, is likely to be accepted.

However, the decision whether to accept or reject the null hypothesis also depends on the level of significance (alpha) chosen for the test. If the level of significance is low, even a small difference between the observed and expected data can lead to the rejection of the null hypothesis. On the other hand, if the level of significance is high, a larger difference between the observed and expected data may be required to reject the null hypothesis.

Therefore, the decision for values of χ^2 obt close to 0 will depend on the level of significance and should be made in the context of the specific hypothesis being tested and the available evidence.

To learn more about decision visit:https://brainly.com/question/30676039

#SPJ11

When the values of χ 2 obt close to 0, the decision is likely to be that the null hypothesis cannot be rejected.

The chi-square test is a statistical test used to determine whether an observed distribution of categorical data varies significantly from an expected distribution. It is utilized to investigate the association between two or more categorical variables, and the test evaluates the likelihood of the observed frequencies of each category of data based on the expected frequency of that data.The Chi-Square DistributionThe chi-square distribution is a collection of distributions that are used to describe data that have a characteristic called degrees of freedom. The degrees of freedom are calculated using the number of categories minus 1 in the categorical variable being tested.

The distribution is always positive and right-skewed, with the majority of the distribution situated in the right tail. When the values of χ 2 obt close to 0, the decision is likely to be that the null hypothesis cannot be rejected.

To know more about Null hypothesis:

https://brainly.com/question/28920252

#SPJ11

Answer:

2nd option, x > 1.10

Step-by-step explanation:

\(7e^{2x}-5 > 58\)

Add 5 to both sides,

\(7e^{2x}-5+5 > 58 +5\\7e^{2x} > 63\)

Divided both sides by 7,

\(\frac{7e^{2x}}{7} > \frac{63}{7}\)

\(e^{2x} > 9\)

Apply Exponent Rule,

\(2x > 2ln(3)\)

\(\frac{2x}{2} > \frac{2ln(3)}{2}\)

x > ln(3) or x > 1.09861

Learn more about logarithms here: https://brainly.com/question/12049968

Since 1.1584 > 1, the truck cannot pass under the archway without going into the other lane.

A semi-elliptic archway with a height of 15 feet at the center and a width of 50 feet can be visualized as half of an ellipse.

The major axis of the ellipse corresponds to the width, while the minor axis corresponds to the height. In this case, the major axis (a) is 25 feet, and the minor axis (b) is 15 feet.

To determine if a truck that is 12 feet high and 14 feet wide can drive under the archway without going into the other lane, we can use the equation of an ellipse: (x²/a²) + (y²/b²) = 1.

The truck will occupy half of the road width, which is 25 feet, so its horizontal distance from the center (x) is 25 - 7 = 18 feet, and its height (y) is 12 feet.

Plugging these values into the equation, we get: (18²/25²) + (12²/15²) = (324/625) + (144/225) ≈ 0.5184 + 0.64 = 1.1584.

Learn more about archways at

https://brainly.com/question/9989257

#SPJ11

Answer: A

Step-by-step explanation:

The 99% confidence interval for the true population mean income is approximately $40,420 to $42,038.

What is the Z-score corresponding to a 99% confidence level?

The Z-score corresponding to a 99% confidence level is approximately 2.576.

To find the 99% confidence interval for the true population mean income for households in Charleston County, we can use the formula:

Confidence Interval = Sample Mean ± (Z * (Standard Deviation / √n))

Where:

Sample Mean = $41,229

Standard Deviation = $2,793

n = 79 (sample size)

Z = Z-score corresponding to the desired confidence level (99% confidence level)

First, we need to find the Z-score for a 99% confidence level. Since the confidence level is 99%, we will have an alpha (α) value of 0.01 for a two-tailed test. Looking up the Z-score corresponding to an alpha value of 0.01 gives us approximately 2.576.

Confidence Interval = $41,229 ± (2.576 * ($2,793 / √79))

Now we can calculate the confidence interval:

Confidence Interval = $41,229 ± (2.576 * $313.68)

Confidence Interval = $41,229 ± $808.07

Confidence Interval = ($40,420, $42,038)

Therefore, the 99% confidence interval for the true population mean income for households in Charleston County is approximately $40,420 to $42,038 (rounded to the nearest dollar).  

To learn more about the Z-score from the given link

brainly.com/question/15222372

#SPJ4

Size 20% over 3 years

20% 60% 3=60%

Then after 3 years the rat population will be reduced

.

So, after 3 years has changed all that tens of thousands of years

Answer:

The answer to this problem is $3.50

Step-by-step explanation:

Answer:

bracket ≈ 2.8 m

Step-by-step explanation:

using the sine or cosine ratio in the right triangle

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{bracket}{sign}\) = \(\frac{bracket}{4}\) ( multiply both sides by 4 )

4 × sin45° = bracket , then

bracket ≈ 2.8 m ( to 1 dec. place )

Step-by-step explanation:

hope you can understand

Answer: D. Cannot be determined

Step-by-step explanation: There are 3 postulates we can use for determining similar triangles.

There is Side Side Side (SSS) Postulate, which requires you have 2 sides of each triangle that are the same proportion as the other triangle. For example, in a triangle ABC, if 2 sides are 5 and 7, and in a triangle DEF, if 2 sides are 10 and 14, then the proportions 5/10 ( 1/2) and 7/14 (1/2) are equal. Thus these are similar triangles and the scale is 1/2.

There is Angle Angle (AA) postulate. If 2 angles are the same to another 2 angles in another triangle, then the two triangles are automatically similar.

The last is Side Angle Side (SAS), which requires you to have an angle that is congruent to another angle in a different triangle, and the angle is in between 2 sides that are proportionally equal to another triangle that also has the same angle in 2 sides. For example, if triangles ABC have angles A, B and C, and angle A is the same equal degrees to another angle in a triangle D, and both A and D are in between 2 sides (i.e DE and AB) that are proportionate (e.g DE and AB are proportionate.) The triangles are then similar.

None of these postulates can be applied to our given problem. Let's see why.

For Angle-Angle, we don't have 2 congruent angles. We have 2 right angles, but that's only 1 angle.

For Side Side Side, we don't have 2 sides given on each triangle, let alone proportionate ones.

For Side Angle Side, we don't even have 2 sides for each triangle given, so this cannot be used either.

Recall that 60 minutes makes 1 hour

Hence 4 hours will be

= 60 * 4

= 240 minutes

If in 15 minutes, she can pick 1/3 pounds of berries

then 240 minutes

= 240/15 * 1/3

= 16/3 pounds

= 5 1/3 pounds

The solution of the system of equations y = x + 2 and x - y = -2 is (c) infinite many solutions

From the question, we have the following parameters that can be used in our computation:

y = x + 2

x - y = -2

Substitute the equation y = x + 2 in the equation x - y = -2

So, we have the following representation

x - (x + 2) = -2

Open the bracket in the above equation

So, we have the following representation

x - x - 2 = -2

Evaluate the like terms in the above equation

So, we have the following representation

-2 = -2

Both sides of the above equation are the same

This means that the equation has a lot of solution

In other words, the equation has infinite many solutions

Hence, the solution is (c) infinite many solutions

Read more about equations at

https://brainly.com/question/13729904

#SPJ1

The cans of paint that are needed is 25 cans.

It should be noted that the sides of the cube will be:

= 3✓2197

= 13

Each side is 13m

Therefore, the total surface area will be:

= 6s²

s = sides

= 6(13)²

= 1014m²

Therefore, the cans needed will be:

= 1014/40

= 25

Therefore, 25 cans are needed.

Learn more about cube on:

brainly.com/question/22623288

#SPJ1

n the case of errors-in-variables bias, the OLS estimator is consistent but no longer unbiased in small samples. This is the correct statement.

In statistics, the errors-in-variables bias is a form of statistical bias that occurs when an independent variable (IV) is measured with error. The presence of the errors-in-variables (EIV) bias means that the OLS estimator will be consistent but no longer unbiased. This means that the OLS estimator can still give reliable estimates, but the estimates are no longer accurate.

The errors-in-variables (EIV) bias can be corrected by using methods such as instrumental variables or two-stage least squares (2SLS) regression. In small samples, the EIV bias can have a more significant impact on the accuracy of the OLS estimator.

In such cases, other estimation methods such as maximum likelihood estimation or the generalized method of moments (GMM) may be used to improve the accuracy of the estimates

Therefore, option C: the OLS estimator is consistent but no longer unbiased in small samples, is the correct .

Know more about the least squares (2SLS) regression

https://brainly.com/question/14563186

#SPJ11