simplify this expression

The probability of exactly 4 bridge construction projects taking place at a time in this state is 0.09.

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Putting the considered items in order from most expensive to least expensive item gives the order as shown by: Option b. Blender, ink, hat, heater

Markup is the amount that will be increased in the original price of the considered thing.

Markdown is the amount that will be decreased from the original price of the considered thing.

Think of "up" and "down" as increasing and decreasing prices respectively.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

For this case, the base prices and the chage in price is given as:

Item                Base Price                    Change Direction

Blender            $29.73                           9% Markdown

Hat                   $14.16                             77% Markup

Ink                    $20.17                            27% Markup

Heater             $28.46                           22% Markdown

Calculating the resultant price:

Resultant price = 29.73 - 9% of 29.73

\(P= 29.73 - \dfrac{29.73}{100}\times 9\\\\P = 27.0543 \: \: \text{dollars}\)

Resultant price = 14.16 + 77% of 14.16

\(P= 14.16+\dfrac{14.16}{100}\times 77\\\\P = 25.0632\: \: \text{dollars}\)

Resultant price = 20.17 + 27% of 20.17

\(P= 20.17+\dfrac{20.17}{100}\times 27\\\\P = 25.6159\: \: \text{dollars}\)

Resultant price = 28.46 - 22% of 28.46

\(P= 28.46- \dfrac{28.46}{100}\times 22\\\\P = 25.0448 \: \: \text{dollars}\)

Thus, putting the considered items in order from most expensive to least expensive item gives the order as shown by: Option b. Blender, ink, hat, heater

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The simplified expression with positive exponents for the given expression is 16r^11.

To simplify and express the answer using positive exponents, we can use the product rule of exponents which states that when multiplying two terms with the same base, we add their exponents.

Using this rule, we can simplify 4r^7 as:

4r^7 = 4 * r * r^6

Similarly, we can simplify (4r)(r^3) as:

(4r)(r^3) = 4 * r * r^3

Now we can multiply these two simplified terms:

4r^7 * (4r)(r^3) = (4 * r * r^6) * (4 * r * r^3)

= 16 * r^(6+1) * r^(1+3)

= 16 * r^7 * r^4

= 16r^(7+4)

= 16r^11

Therefore, the simplified expression with positive exponents for the given expression is 16r^11.

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There are 9 possible schedules to play basketball such that dave can play on monday or wednesday or both which is union of two set .

so this question seems like we have to take union of ways of palying on monday or wednesday

let n(m) be number of ways of playing on monday

n(w) be number of ways of playing on wednesday

we have to find n(m∪w)

n(mUw) = n(m) +n (w) - n(m∩ w)

so n(m) = \(4_C__2\) as one day is now fixed which is monday so we have 4 available days and 2 days to play.

n(m) = \(4_C__2\)  = 6

similary n(m) = n(w) = 6

now  n(m∩w) = \(3_C__1\) as now we have  2 fixed day and we have 3 day remaining and only one day to play.

n(m∩w) = \(3_C__1\) =3

now n(mUw) = n(m) +n (w) - n(m∩ w)

=> 6 + 6 -3

=> 12 - 3

so n(mUw) = 9

so we have 9 schedules to paly keeping condition given in the question.

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The correct answer is option A) 0.85.

0.85 is not decimal and a fraction of 0.825 or 5/8.

In arithmetic, a number is expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number.

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Answer:

A is correct

Step-by-step explanation:

b has a negative value cause it's before 0

but -b will become a positive value thus >0

example:

b is -1

-b = -(-1)

= 1

hope you understand

Answer:

⇨ Choice A.

Step-by-step explanation:

We'll consider three choices and compare the answers with the given number line and points.

⟺ Choice A

This is the correct answer and here is why.

\(-b>0\)

Solving Inequality is similar to solving equation. The difference is if the coefficient for the variable is in negative, moving to another side would swap the sign/operator of Inequality.

Thus, our new Inequality would be \(b<0\) which is true by the number line itself.

⟺ Choice B

The reason why choice B is not correct because the point a is lesser than the point b. It's obvious that point a cannot be greater than point b.

⟺ Choice C

The reason why choice C is not correct because if we solve the Inequality.

\(-b<-c\)

We can either solve for b-term or c-term, the outcome would be the same. I'll solve for both terms.

⇨ Solve for b-term

\(-b<-c\\b>\frac{-c}{-1}\\b>c\)

Also remember that moving a negative coefficient would swap the sign/operator of Inequality.

⇨ Solve for c-term

\(-b<-c\\\frac{-b}{-1}>c\\b>c\)

As b>c is not true in the number line. We notice that c point is greater than b point.

Thus, the clear answer is A choice.  

Because of this, we need to choose 16 integers in such a way that we can ensure that when they are divided by 15, at least two of them will provide the same residual.

This is further explained below.

Generally,  If you divide a number by 15, the result is a fraction. There are 15 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14.

That is to say, if we choose one number and divide it by 15, there is a chance that the remainder may be any of the 15 (0 reminders 14). Therefore, if we choose 15 numbers, we will have the opportunity to pick 15 unique reminders, ranging from 0 to 14.

In conclusion, if we select one more integer, that is we pick 16 integers, then at least two of them would have the same reminder since there are only 15 reminders and 16>15, and by the pigeonhole principle.

Because of this, we need to choose 16 numbers such that we can guarantee that at least two of them will provide the same remainder when they are divided by 15.

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Answer:

5

Step-by-step explanation:

To calculate a 95% confidence interval for the mean weight of all Utah County Fair pigs, we use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Given:

Sample Mean (x) = 195

Standard Deviation (σ) = 18

Sample Size (n) = 100

The margin of error can be calculated using the formula:

Margin of Error = (Z * σ) / √n

For a 95% confidence level, the Z-value for a two-tailed test is approximately 1.96.

Margin of Error = (1.96 * 18) / √100

= 3.528

Therefore, the confidence interval is:

(195 - 3.528, 195 + 3.528)

(191.472, 198.528)

The correct answer is (191, 199).

Question 4: If the sample size is increased from 100 to 200, the margin of error will decrease in size. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the margin of error becomes smaller, resulting in a more precise estimate.

Question 5: To find out how many pigs must be sampled to have 90% confidence in the results with a margin of error of 6.8, we can use the formula:

Sample Size (n) = (Z^2 * σ^2) / E^2

Given:

Confidence Level (1 - α) = 90% (or 0.9)

Margin of Error (E) = 6.8

Standard Deviation (σ) = 18

For a 90% confidence level, the Z-value for a two-tailed test is approximately 1.645.

Sample Size (n) = (1.645^2 * 18^2) / 6.8^2

= 3.379

Therefore, the minimum number of pigs that must be sampled is approximately 4 (rounded up to the nearest whole number).

The correct answer is 5.

Answer:

118/25 as a fraction hope it helps

Answer:

1 72/100 or 1 18/25 as simplified.

Step-by-step explanation:

100% is 100/100. 172/100 would be the fraction for this, but it is an improper fraction.

the correct answer is X= -3

Answer:

Step-by-step explanation:

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Answer:

d \large \frac{1,962,800-84,000m}{36,000}=

e \large 84,000m+36,000w=1,962,800

Step-by-step explanation:

Given the following :

Budgeted amount = $1,962,800

Cost of resurfacing a mile of 2- lane road = $84,000

Salary of additional worker = $36,000

Number of miles = m

Number of workers = w

equations that represents the relationship between the miles of 2-lane roads the department could resurface, m, and the number of new workers it could hire, w, if it the entire budget is spent ;

(Cost of a mile of 2-lane road * number of miles) = total budget

(84000m + 36000w) = 1,962,800

To make w, the subject of the formula :

36000w = 1962800 - 84000m

w = (1962800 - 84000m) / 36000

To make m, the subject of the formula :

84000m = 1962800 - 36000w

m = (1962800 - 36000w) / 84000

The computed value of the test statistic is 2.94.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We have a sample size of n = 12, engine size (x) and emissions (y) are the two variables being correlated, and the sample correlation coefficient is r = 0.47.

The null hypothesis is that the population correlation is zero (H0: ρ = 0) and the alternative hypothesis is that the population correlation is positive (Ha: ρ > 0).

To compute the test statistic, we need to first calculate the degrees of freedom (df), which is (n-2) = 10 in this case.

We can then use the formula for the test statistic, which is:

t = (r√(df)) / √1 - r²

Substituting the values we have, we get:

t = (0.47 √10) / √(1 - 0.47²)

t = 2.94

Therefore, the computed value of the test statistic is 2.94.

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Answer

Step-by-step explanation:

(a) Expected hourly income ≈ 24.6747 $US/hour.

(c) Liters of gasoline to fill the tank ≈ 60.56656 liters.

(d) Price of gas in $US/gallon ≈ 4.9498 $US/gallon.

(e) Cost to fill the tank ≈ 90.2714 €.

(f) Number of full days depends on the daily commuting distance. Divide the daily commuting distance by 320 miles to get the number of full days.

To solve the given problems, we'll use the provided information and formulas for conversions.

(a) To calculate your expected hourly income in US dollars, we'll use the exchange rate of 1€ = 1.2993 $US:

Expected hourly income = Wage per hour in euros × Exchange rate

                     = 19 €/hour × 1.2993 $US/€

                     ≈ 24.6747 $US/hour

Therefore, your expected hourly income is approximately 24.6747 $US/hour.

(c) To determine how many liters of gasoline it will take to fill the car's empty tank, we need to know the conversion factor between US gallons and liters. 1 US gallon is approximately equal to 3.78541 liters.

Liters of gasoline to fill the tank = Tank capacity in US gallons × Conversion factor

                                  = 16 US gallons × 3.78541 liters/US gallon

                                  ≈ 60.56656 liters

Therefore, it will take approximately 60.56656 liters of gasoline to fill the car's empty tank.

(d) To find the equivalent price of gas in US dollars per gallon, we need to convert the price from euros per liter to US dollars per gallon. We'll use the conversion factor of 1 US gallon ≈ 3.78541 liters.

Price of gas in $US/gallon = Price of gas in euros per liter × (1€ / 1.2993 $US) × (3.78541 liters / 1 US gallon)

                         = 1.49 €/liter × (1/1.2993) $US/€ × (3.78541 liters / 1 US gallon)

                         ≈ 4.9498 $US/gallon

Therefore, the equivalent price of gas is approximately 4.9498 $US/gallon.

(e) To calculate the cost in euros to fill the tank, we'll multiply the number of liters required to fill the tank by the price of gas in euros per liter:

Cost to fill the tank = Liters of gasoline to fill the tank × Price of gas in euros per liter

                    = 60.56656 liters × 1.49 €/liter

                    ≈ 90.2714 €

Therefore, it will cost approximately 90.2714 euros to fill the tank.

(f) Given that the car averages 20 miles per gallon, we can calculate how many miles you can commute before needing to refill the tank:

Miles per full tank = Tank capacity in US gallons × Miles per gallon

                  = 16 US gallons × 20 miles/US gallon

                  = 320 miles

If you commute a distance of 320 miles per full tank, the number of full days you can commute before refilling the tank depends on your daily commuting distance. Divide your daily commuting distance by 320 miles to find the number of full days:

Number of full days = Daily commuting distance (miles) / Miles per full tank

                  = Daily commuting distance (miles) / 320 miles

This calculation requires your daily commuting distance to provide an exact answer.

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Answer:

30 gallons/hr

Step-by-step explanation:

180/60 = 30

Factorize the polynomial to obtain the roots of the equation, which are z=0.2, z=0.06, and z=1.  

The z-transform is a mathematical tool that is commonly used to analyze discrete-time signals and systems. In this case, we are given the z-transform of a function f(k) and we are asked to determine the limit of f(k) as k approaches infinity.

From the given expression of the z-transform, we can see that the denominator is a polynomial of degree 3 in z. We can factorize the polynomial to obtain the roots of the equation, which are z=0.2, z=0.06, and z=1.

Since f(infinity) is bounded, it means that the function f(k) approaches a finite value as k goes to infinity. In other words, the limit of f(k) as k approaches infinity exists.

To determine the limit, we need to use the partial fraction decomposition method to express the z-transform as a sum of simpler fractions. Then, we can use the inverse z-transform to obtain the original function f(k).

Once we have the original function, we can evaluate the limit as k approaches infinity by analyzing the behavior of the function at the poles and zeros of the z-transform.

In conclusion, the limit of f(k) when k goes to infinity can be determined by using the partial fraction decomposition and inverse z-transform methods. The behavior of the function at the poles and zeros of the z-transform will determine whether the limit exists and what its value is.
 

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Answer:

20/8 or 2 4/8

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

thats what i got not sure

Answer:

x = 8.4

Step-by-step explanation:

For the 51° angle, 5.3 is the adjacent leg.

x is the hypotenuse.

cos 51° = adj/hyp

cos 51° = 5.3/x

x = 5.3/cos 51°

x = 8.4

GCF(110,220) = 110

LCM(110,220) = ( 110 × 220) / 110

LCM(110,220) = 24200 / 110

LCM(110,220) = 220

hopefuly it help!!!

Jamie made 8 1/4 cups of fruit punch for a party. Her guests drank 2/3 of the punch. How much fruit punch did her guests drink Jamie made 8 1/4 cups of fruit punch for a party. A mixed number can be converted into an improper fraction by multiplying the denominator by the whole number, and then adding the numerator. Thus, we have 33/4 cups of fruit punch.

Jamie's guests drank 2/3 of the punch. If Jamie made 33/4 cups of fruit punch, then the guests drank2/3 × 33/4= 22/12 or 1 5/12 cups of fruit punch The guests drank 1 5/12 cups of fruit punch. More than 100 words: To determine how much fruit punch Jamie's guests drank, we need to calculate the amount of punch made and then multiply it by the fraction of the punch consumed by the guests. Jamie made 8 1/4 cups of fruit punch.

We'll start by converting the mixed number to an improper fraction, which is 33/4. Next, we'll multiply 33/4 by 2/3 to determine how much punch the guests drank. This is calculated as follows:2/3 × 33/4= 22/12 or 1 5/12 cups of fruit punch. Therefore, Jamie's guests drank 1 5/12 cups of fruit punch.

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The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during set  World War II.

The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during World War II. The program was enacted by the United States in 1941 and allowed the US to provide war materials to its allies without requiring repayment. It was a major factor in the Allied victory, as it allowed the US to supply its allies with much needed war material and resources. The US provided a variety of goods, including food, oil, weapons, and tanks. It also supplied the Soviet Union with millions of tons of military equipment and supplies. Lend-Lease was instrumental in helping the Allies win the war, as it allowed them to gain a huge advantage over the Axis powers by providing essential supplies and resources.

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9514 1404 393

Answer:

  Table B is a function

Step-by-step explanation:

The relation shown in a table is NOT a function if the same input value gives different output values.

In Table A, input Taurus gives different outputs, so Table A is NOT a function.

In Table B, there are no repeated inputs, so Table B IS a function.

There are 125,970 ways to choose a dozen donuts from 20 varieties if there are no two donuts of the same variety.

a) If there are no two donuts of the same variety, the problem is equivalent to choosing 12 distinct objects from 20. This is because each variety of donut is distinct and cannot be repeated, so we can think of each variety as a unique object.

To calculate the number of ways to choose 12 distinct objects from 20, we use the combination formula, which is:

C(20,12) = 20! / (12! * (20-12)!)

Here, 20! represents the total number of ways to order all 20 objects, 12! represents the number of ways to order the selected 12 objects, and (20-12)! represents the number of ways to order the remaining 8 objects that were not selected. Dividing the total number of orders by the number of ways the selected objects can be ordered and the remaining objects can be ordered gives us the number of distinct combinations of 12 objects that can be chosen from 20.

Plugging in the numbers, we get:

C(20,12) = 20! / (12! * (20-12)!)

= (20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9) / (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

= 125,970

Therefore, there are 125,970 ways to choose a dozen donuts from 20 varieties if there are no two donuts of the same variety.

b) If all donuts are of the same variety, there is only one way to choose a dozen donuts - simply choose any 12 donuts from the available 12.

c) If there are no restrictions, we can choose any combination of 12 donuts from 20. This is equivalent to choosing 12 objects from 20 where the order of selection does not matter. We can again use the combination formula:

C(20,12) = 20! / (12! * (20-12)!)

Here, the formula calculates the number of ways to choose 12 objects from 20 without considering the order of the objects. We get the same answer as part a), which is 125,970.

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Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.

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An average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

To determine the number of people who are stepping onto the roller coaster per minute at peak time, you need to divide the number of people on the roller coaster by the duration of the ride. Hence, the correct option is B) 6.

To be more specific, this means that at peak time, an average of 3 people is getting on the ride per minute. This is how you calculate it:

Number of people per minute = Number of people on the roller coaster / Duration of the ride

Number of people on the roller coaster = 24

Duration of the ride = 8 minutes

Number of people per minute = 24 / 8 = 3

Therefore, an average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

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Hi,

Lower extreme → 45

Upper extreme → 100