The length of a rectangle is 4 centimeters more than twice its width. If the perimeter of the rectangle is 86 centimeters , find the dimensions of the rectangle

a. The highest 5 percent time is approximately 15.29 minutes. b. The lowest 50 percent time is 12 minutes. c. The middle 95 percent interval is approximately 8.08 minutes to 15.92 minutes. d. The lowest 80 percent time is approximately 10.32 minutes.

a. To find the highest 5 percent, we need to find the value that separates the highest 5 percent from the rest. This value is called the upper 5th percentile. Using the z-score formula, z = (x - mean) / standard deviation, we can find the z-score associated with the upper 5th percentile. By looking up this z-score in the z-table, we can find the corresponding value. In this case, the z-score is approximately 1.645. Using the formula, x = z * standard deviation + mean, we can calculate the time needed for the highest 5 percent: x = 1.645 * 2 + 12 = 15.29 minutes.

b. To find the lowest 50 percent, we need to find the value that separates the lowest 50 percent from the rest. This value is called the median. The median of a normally distributed data set is equal to the mean. Hence, the lowest 50 percent time is the mean of 12 minutes.

c. To find the time for the middle 95 percent interval, we need to find the values that separate the middle 95 percent from the rest. These values are called the lower 2.5th percentile and the upper 2.5th percentile. Using the z-score formula, we can find the z-scores associated with the lower and upper 2.5th percentiles. By looking up these z-scores in the z-table, we can find the corresponding values. In this case, the z-scores are approximately -1.960 and 1.960. Using the formula, x = z * standard deviation + mean, we can calculate the times: lower 2.5th percentile = -1.960 * 2 + 12 = 8.08 minutes, and upper 2.5th percentile = 1.960 * 2 + 12 = 15.92 minutes.

d. To find the lowest 80 percent, we need to find the value that separates the lowest 80 percent from the rest. This value is called the lower 20th percentile. Using the z-score formula, we can find the z-score associated with the lower 20th percentile. By looking up this z-score in the z-table, we can find the corresponding value. In this case, the z-score is approximately -0.841. Using the formula, x = z * standard deviation + mean, we can calculate the time needed for the lowest 80 percent: x = -0.841 * 2 + 12 = 10.32 minutes.

In the painting 'Three Flags' by Jasper Johns, the size of the largest flag would depend on the canvas or surface used.

In the painting Three Flags by Jasper Johns, he used his encaustic process to create the artwork. Each flag reduced about twenty-five percent in scale as he stacked canvas flags, with the largest one receding into the background. The congealed wax drippings gave the painting a dimensional sculptural appearance.

The stripes and stars on the flags also grow smaller, adding to the illusion of three separate elements. Therefore, in terms of the largest flag Jake can draw, it would depend on the size of the canvas or surface that he is working with.

Final answer:

The sequence 5, 10, 15 represents multiples of 5, where each number is 5 units apart from the last.

This pattern can also be observed in a multiplication table in the row or column of the number 5.

Explanation:

The question asks us to describe a pattern in the sequence 5, 10, 15.

This sequence represents the multiples of 5. A clear pattern that can be observed is that each number increases by 5 to get to the next multiple.

For instance, starting with 5, adding 5 gives us 10, and adding another 5 to 10 gives us 15.

This pattern continues indefinitely with the series 20, 25, 30, and so on.

To solve this problem, we have to make use of the standard probability distribution tables for z test.

Since we are asked to find for the 72 percent level confidence, then this means we are to look for the value of z which gives (100-72)/2 = 14% on both sides of the tail.

So at 14% tail on one side, the z value is approximately:

1.08

Answer:

± 1.08

12x = 10x + 3

Subtract 10x from both sides

2x = 3

Divide by two on each side

x = 3/2 or 1 1/2 hours

Distance of the trip:

12 * 2 * 3/2 = 36 miles

How long does the trip take:

3/2 + 3/2 + 3/10 = 3 3/10 hours

3 hours

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To solve 5y - x = 10 for y, add x to both sides and then divide by 5, resulting in the solution y = (x + 10) / 5.

To solve the equation 5y - x = 10 for y, follow these steps:

Add x to both sides of the equation to isolate terms with y on one side: 5y = x + 10.  

Now, divide both sides of the equation by 5 to solve for y:

y = (x + 10) / 5.

The solution for y when given an equation of the form 5y - x = 10 is y = (x + 10) / 5.

The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x:

Example 1

y = -13 + 7x

This equation is in slope intercept form. The y intercept is (0,-13) and the slope is 7.

Example 2

4x + 3y = 12

Rewrite this equation in slope intercept form.

The equation is now in slope intercept form. The y intercept is (0,4) and the slope is
-4/3.

Example 3

5x - 3y - 15 = 0

Rewrite this equation in slope intercept form.

The equation is now in slope intercept form. The y intercept is (0,-5) and the slope is 
5/3.

Example 4

The equation is now in slope intercept form. The y intercept is (0,-7.5) and the slope is 
1.5.

To turn a decimal into a fraction, first notice that the number to the right of the decimal point is 625. The 6 represents the tens, the 2 represents the hundreds, and the 5 represents the thousands. So, we can put 625 over 1000 or 625/1000.

Notice that the fraction [tex]\frac{625}{1000}[/tex] is not in lowest terms. To turn the fraction into lowest terms, we can divide both the numerator and the denominator by 125.

[tex]\frac{625}{1000}[/tex] ÷ [tex]\frac{125}{125}[/tex] = [tex]\frac{5}{8}[/tex]

Therefore, .625 can be written as the fraction 5/8, which is in lowest terms.

Answer:  The correct option is (A) 0.

Step-by-step explanation:  We are given to find the difference between the mean and median of the following data set:

{22, 8, 10 ,18 ,12, 20}.

MEAN:  It is the sum of all the values together divided by the number of values in the set.

So, the MEAN of the given data set is

[tex]m=\dfrac{22+8+10+18+12+20}{6}\\\\\\\Rightarrow m=\dfrac{90}{6}\\\\\Rightarrow m=15.[/tex]

MEDIAN: The median of a data set is given by the middle-most value in the data.

If there is an even number of items in the data set, then the median is found by taking the mean of the two middlemost numbers.

Arranging the given data in ascending order, we have

8, 10, 12, 18, 20, 22.

Since there are 6 values, that is even number of values. so the MEDIAN is given by

[tex]M=\dfrac{12+18}{2}\\\\\Rightarrow M=\dfrac{30}{2}\\\\\Rightarrow M=15.[/tex]

Therefore, m = M.

That is, mean and median of the given data are equal.

Hence, the difference is

m - M = 15 - 15 = 0.

Thus, option (A) is CORRECT.

Answer:

Option A - 0

Step-by-step explanation:

Given : Data set {22, 8, 10 ,18 ,12, 20}

To find : What is the difference between the mean and the median of the data set?

Solution :

Data set in increasing order {8, 10 ,12,18, 20,22}

Mean is defined as the division of sum of set values by total number of values.

[tex]M=\frac{\sum x}{n}[/tex]

Substitute the values we get,

[tex]M=\frac{8+10+12+18+20+22}{6}[/tex]

[tex]M=\frac{90}{6}[/tex]

[tex]M=15[/tex]

So, The mean of the set is 15.

Median of even numbers is the average of two middle terms.

[tex]m=\frac{3rd+4th}{2}[/tex]

[tex]m=\frac{12+18}{2}[/tex]

[tex]m=\frac{30}{2}[/tex]

[tex]m=15[/tex]

So, The median of the set is 15.

Now, The difference of the mean and the median of the set is

[tex]d=M-m[/tex]

[tex]d=15-15[/tex]

[tex]d=0[/tex]

Therefore,Option A is correct.

The difference of the mean and the median of the set is 0.

To calculate 1206 × 5 using expanded form, break 1206 into its place values, multiply each by 5, and then add the results. This gives 6030.

Finding 1206 × 5 Using Expanded Form

To find the product of 1206 and 5 using expanded form, we break down 1206 into its place values:

Now, we multiply each component by 5:

Finally, we add all these products together:

5000 + 1000 + 0 + 30 = 6030

Therefore, 1206 × 5 equals 6030.

Answer:

[tex]\frac{1}{3}[b-1][/tex]

Step-by-step explanation:

we have

[tex]\frac{1}{3}b-\frac{1}{3}[/tex]

Factor the coefficient [tex]\frac{1}{3}[/tex] of both terms

[tex]\frac{1}{3}b-\frac{1}{3}=\frac{1}{3}[b-1][/tex]

To determine the unit rate for each item, divide the total cost by the number of units. This gives us $2.50 per golf ball, $1.50 per tennis ball, $4.50 per pound of meat, and $20 per ticket.

The question involves determining the unit rate of different items. A unit rate is the cost per one unit of an item. To calculate each unit rate, we divide the total cost by the number of units.

These calculations can often be made using mental math, especially when dealing with simple numbers or common multiples.

To divide -5 1/4 by 2 3/4, convert both numbers to improper fractions, multiply the first fraction by the reciprocal of the second fraction, and simplify the result. The quotient is -1 10/11.

To divide -5 1/4 by 2 3/4, first convert both mixed numbers to improper fractions. -5 1/4 can be written as -21/4, and 2 3/4 can be written as 11/4. Next, divide -21/4 by 11/4. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, (-21/4) * (4/11) = -21/11. This quotient can be written in mixed number form as -1 10/11, which is the simplified answer.

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