The yard behind the Cindy’s house is rectangular in shape
and has a perimeter of 72 feet. If the length  of the yard
is 18 feet longer than the width w of the yard, what is the
area of the yard, in square feet?

Answer:

The correct option is D. 3,000

Step-by-step explanation:

Step 1 : Using the cash balance shown on the bank statement, add back any deposits in transit. : 2000 + 2500 = $4500

Step 2 : Deduct any outstanding checks : 4500 - 1500 = $3000

This will provide the adjusted bank cash balance.

Step 3 : Deduct any bank service fees, penalties, and NSF checks. This will arrive at the adjusted company cash balance : 3250 - (205 + 45) = $3000

After reconciliation, the adjusted bank balance should match with the company’s ending adjusted cash balance.

So, the adjusted cash balance at the end of April is $3000

1. Draw the perpendicular line to the given line that passes through the point Q. With this aim you should draw a circle with center at point Q and radius that is greater than distance form point Q to the given line. Then match these two points of intersection of this circle with given line as A and B and draw two circles with centers at points A and B and radii that are greater than half of distance between points A and B. These two circles will intersect, combine two points of intersection of these points, this line will be perpendicular to given line.

2. Draw a circle with center at Q and match two points of intersection with perpendicular as E and F.

3. Draw two circles with centers at points E and F and radii that are greater than radius of previous circle. Combine two points of intersection of these circles, this line will be parallel tj the given line.

Taking into account the solution, you can conclude that correct choice is B.

To correctly construct a line parallel to line l through point q, mark point q, use a straightedge to extend from q, and then use a compass to copy the angle and distance from line l, ensuring the newly drawn line is parallel to l.

To construct a line parallel to a given line l and passing through a given point q, one must follow specific geometric principles. This type of construction is often illustrated in diagrams where the correct application of tools such as a ruler and compass is shown.

First, a point q is marked. A straightedge or ruler is used to draw a line transcending the point q. Then, using a compass, the angle between the original line l and any point on it is copied. The compass's width is set to the distance between two points on line l, and the same distance is marked from point q on the drawn line. A line is then constructed using the copied angle and marking, ensuring the new line is parallel to line l.

This process is comparable to the methods used in various scientific and economic models, such as those discussed in the supplied information, where parallel lines represent equivalent conditions or when shifts in lines are required to indicate changes in intercepts.

Learn more about parallel here:

https://brainly.com/question/30195834

#SPJ3

The margin of error for a sample statistic requires the population standard deviation, the desired confidence level, and the sample size. It is found by multiplying the z-score for the confidence level with the standard error, which is the population standard deviation divided by the square root of the sample size. For a 95% confidence interval, the error bound is factored into the sample mean to estimate the population mean.

The margin of error for a sample statistic depends on the level of confidence desired and the sample size. Using the population standard deviation, we can calculate the margin of error by finding the z-score associated with the desired confidence level and multiplying it by the standard error. The standard error is calculated as the population standard deviation (11.3) divided by the square root of the sample size (n).

Based on the example given referencing an error bound for the mean (3.2), a 95% confidence interval could be constructed by adding and subtracting the error bound from the sample mean (15). Therefore, the 95% confidence interval estimate for the population mean would be (11.8, 18.2).

When a sample standard deviation is provided instead of a population standard deviation, and if the sample size is small, the Student's t-distribution should be used instead of the normal distribution.

For a 95% confidence interval, we generally use 1.96 as the z-score for a normal distribution, but this value could change depending on specific confidence levels or other distributions like the t-distribution.

-5x -(4x-6) = -3      

-5x -4x + 24 = -3  

-9x = -27              

x= 3

∠DFG and ∠JKL are complementary angles

Measure of each angle

[tex]m<DFG=48\\m<JKL= 42[/tex]

Given :

∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,

and m∠JKL = x − 1

When two angles are complementary then the sum of angles is 90 degrees

∠DFG and ∠JKL are complementary angles.

So, [tex]m<DFG+m<JKL =90[/tex]

Now replace the expressions and solve for x

[tex]x+5+x-1=90\\2x+4=90\\2x=90-4\\2x=86\\x=43[/tex]

Now replace x with 43 and find out each angle

[tex]m<DFG= x+5\\m<DFG= 43+5=48\\\\m<DFG=48\\m<JKL=x-1=43-1=42[/tex]

[tex]m<DFG=48\\m<JKL= 42[/tex]

Learn more :

brainly.com/question/5188505

To make fruit punch with a given ratio of 2 cups of grape juice for every 3 cups of apple juice, you will need 8 cups of grape juice to mix with 12 cups of apple juice.

To answer how many cups of grape juice will be needed when you have 12 cups of apple juice to make a fruit punch, you first look at the ratio given for the punch, which is 2 cups of grape juice for every 3 cups of apple juice. The question provides us with a ratio: 2 cups of grape juice to 3 cups of apple juice. To maintain this ratio with 12 cups of apple juice, we will have to calculate the equivalent amount of grape juice.

Set up a proportion like this:

Cross-multiply to find the value of x:

Therefore, you will need 8 cups of grape juice to make the fruit punch with your 12 cups of apple juice.

Answer:

3 more males  than females said that swimming was their favorite.  

Step-by-step explanation:

We have been given a bar graph in which blue box represents Male and orange box represents Female.

We need to tell how many more males than females said that swimming was their favorite

Number of female in swimming are: 9

And number of male in swimming are: 12

So, we need to find how many more male that means: 12-9=3

That means 3 more males.

Using the formula for the area of a sector, we substitute provided values to find the radius of the circle. Solving the equation, we find the radius to be √6 inches.

The subject of the question is related to geometry and involves understanding the relationship between the area of a sector and the radius of the circle it is part of. The sector is formed by a central angle of 45 degrees and its area is given as 2π/3 square inches.

In order to find the radius of the circle, we can use the formula for the area of a sector, which is (θ/2π) * πr2, where θ is the central angle, π is a mathematical constant, and r is the radius of the circle.

Considering 360 degrees as 2π radians, the angle is 45 * (2π/360) = π/4 radians. Hence substituting the values in the area equation we get; 2π/3 = (π/4)/2π * πr2. If we solve this equation for 'r', we get r = √6 inches as the radius of the circle.

https://brainly.com/question/29055300

#SPJ12

Answer:

Step-by-step explanation:

y=mx+b

2160=20x+60.417)

2160= 20x+160.417

2160-160.417=20x+160.417-160.417

1999.583=20x

1999.583/20=20x/20

x= 99.98 min

Total time taken to fill the pool is 100 minutes

Given:

Amount of water already in pool = 1200 gallon

Total capacity of pool = 2160 cubic feet

Rate of water supply = 20 cubic feet per minute

Find:

Total time taken to fill the pool

Computation:

1 cubic feet = 7.5 gallon water

Amount of water already in pool = 1200 / 7.5

Amount of water already in pool = 160 cubic feet

Remain volume = 2160 - 160

Remain volume = 2000 cubic feet

Total time taken to fill the pool = 2000 / 20

Total time taken to fill the pool = 100 minutes

Learn more:

https://brainly.com/question/22009512?referrer=searchResults

To find the work done in lifting the entire cable to the top of the building, multiply the weight of the cable by the height of the building.

To calculate the work done in lifting the entire cable to the top of the building, we need to find the weight of the cable. The weight of the cable can be found by multiplying the length of the cable (20 feet) by its weight per foot (2 pounds per foot). Therefore, the weight of the cable is 20 feet × 2 pounds per foot = 40 pounds.

The work done in lifting the cable to the top of the building is equal to the product of the weight of the cable and the height of the building. So, the work done is 40 pounds × 50 feet = 2000 foot-pounds.

https://brainly.com/question/35917320

#SPJ12