A playground is in the shape of a right triangle with an area of 294 yd^2. The shortest side of the playground (one of the legs) is 21 yds. The city council would like to add a path along the longest side of the playground (the hypotenuse). How long would the path be?

Show your work.
Don't forget to label the answer.

[tex]{\qquad \qquad \huge \rm \underline { \underline{ Répondre}}}[/tex]

Standard equation of an ellipse is :

[tex]\qquad \rm\dashrightarrow \: \dfrac{ {(x - h)}^{2} }{ {a}^{2} } + \dfrac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]

If b is smaller than a, then it will be a horizontal ellipse, and if b is greater than a, it will be a vertical ellipse. and shifting depends upon coordinates of its centre.

Now, our given equation is :

[tex]\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ 15 } + \dfrac{ {y }^{2} }{ {10} } = 1[/tex]

[tex]\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ {(\sqrt{15})}^{2} } + \dfrac{ {y}^{2} }{ {(\sqrt{10}) {}^{2} } } = 1[/tex]

[ here, b = root 10 and a = root 15, hence a is greater than b here, which means : its a horizontal ellipse.

And since it is a horizontal ellipse with center at origin, it's major axis will lie on x - axis.

Answer:

Look below

Step-by-step explanation:

The domain of any function is the x-value in an ordered pair.

{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}

The correct statement regarding the impact of the mass increase in the mean and median are given as follows:

The mean will increase, and the median will stay the same.

The mean of a data-set is given by the sum of all the observations in the data-set divided by the number of observations in the data-set.

Hence, if one observation is increased, the sum of all the observations also increases, and thus the mean of the data-set increases.

The median of a data-set is the middle value of the data-set, the value which 50% of the measures are less than and 50% are greater than.

The data-set in this problem has an odd cardinality of 5, meaning that the median is the third element of the data-set, which is not affected by the weight of the heaviest elevant, and thus the median remains constant.

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Answer:

The builder has 28,200m^2 left to build the houses.

Step-by-step explanation:

For the roads,

They are 3m wide and they stretch 200m.

We must find the area for one road and multiply by three.

Area = Length * Width

Area = 200m * 3m

Area = 600m^2

600 * 3 = 1800m^2

1800m^2 is taken up by the three roads.

Next, we must find the total area of the field.

Area = Length * Width

Area = 200m * 150m

Area = 30,000m^2

30,000m^2 is the total area of the field, and we need to subtract the area the roads take up to determine the area left for the houses.

30,000m^2 - 1800m^2 = 28,200m^2

The builder has 28,200m^2 left to build the houses.

Answer:

The builder has 28,200m^2 left to build the houses.Step-by-step explanation:For the roads,They are 3m wide and they stretch 200m.We must find the area for one road and multiply by three.Area = Length * WidthArea = 200m * 3mArea = 600m^2600 * 3 = 1800m^21800m^2 is taken up by the three roads.Next, we must find the total area of the field.Area = Length * WidthArea = 200m * 150mArea = 30,000m^230,000m^2 is the total area of the field, and we need to subtract the area the roads take up to determine the area left for the houses.30,000m^2 - 1800m^2 = 28,200m^2The builder has 28,200m^2 left to build the houses.

Step-by-step explanation: hope this helps0^0

There are 3 groups of marbles

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

Blue = 6

Red = 9

Blacks = 12

Factor out the numbers

So, we have the following representation

Blue = 2 * 3

Red = 3 * 3

Blacks = 2 * 2 * 3

Using the above as a guide, we have the following:

GCF = 3

Hence, the number of groups is 3

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The group which  purchases roughly 85% of all valentine’s day cards is women.

The annual celebration of Valentine's Day, also called  Saint Valentine's Day or the Feast of Saint Valentine, takes place on February 14 every year. It was observed as a Christian holiday in memory of Valentine, a martyr. In various parts of the world, it has developed into a huge cultural and a celebration of romance and love thanks to later folk traditions.

Valentine's Day is commemorated on February 14 by a many of martyrdom tales, including one about Saint Valentine of Rome's captivity in the third century for helping Christians who were persecuted by the Romanion Empire;

We are given that;

The group percentage which purchases valentine’s day cards=85%

Now,

Women tend to buy approximately 85% of all the Valentine`s Day cards sold. Valentine`s Day is the second most popular day of the year for sending cards, second only to Christmas.

Therefore, women by card on valentine day;

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Based on the currency exchange rate you gave, 1 British pound (GBP) is equal to 1.202639 American dollars (USD) as of February 20, 2023.

In other words, if you were to swap 1 GBP for USD, you would get back 1.202639 USD.

Again, it's crucial to remember that exchange rates are frequently susceptible to changes due to a variety of economic and political variables, and the real rate may be different at the time of your transaction.

Before performing any currency conversions or foreign transactions, it is usually a good idea to verify the current exchange rate.

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If the sum of two vectors is equal to the sum of their absolute values, it means they are orthogonal and equal in magnitude.

The amount of two vectors addresses the consolidated impact of the two vectors. At the point when the amount of two vectors is equivalent to the amount of their outright qualities, it implies that the two vectors are opposite to one another and their extents are equivalent. All in all, the two vectors are symmetrical and they have a similar length.

This relationship can be shown mathematically utilizing the Pythagorean hypothesis. In the event that we have two vectors An and B, their total C can be addressed as the hypotenuse of a right triangle, where An and B are the other different sides. In the event that An and B are opposite to one another, the Pythagorean hypothesis can be utilized to show that the size of C is equivalent to the square foundation of the amount of the squares of An and B, which is equivalent to the amount of their outright qualities.

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The number of games they win is 22 games for 54 game season.

What is proportion?
In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities or values, usually expressed as a fraction. For example, the ratio of boys to girls in a class might be expressed as 3/5, meaning that for every 3 boys in the class there are 5 girls.

Explanation:
Assuming that Manchester United's winning and losing rates remain the same throughout the season, we can use a proportion to estimate how many games they would win in a 54 game season:

wins / total games = winning rate

Using the data given in the problem, we can find the winning rate as:

14 / 35 = 0.4

So, Manchester United's winning rate is 0.4, or 40%.

To estimate how many games they would win in a 54 game season, we can set up a proportion:

wins / total games = winning rate

x / 54 = 0.4

Solving for x, we get:

x = 54 * 0.4 = 21.6

Rounding to the nearest whole number, we get an estimate of 22 games that Manchester United would win in a 54 game season, assuming their winning and losing rates remain the same as the first 35 games.

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To convert between pounds and kilogrammes, multiply the number of pounds by 0.45359237, and to do the opposite, multiply the number of kilogrammes by 2.20462.

So, the value of 60 kg is equal to 132.2772 lbs.

The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.

One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.

One pound is equal to 0.45359237 kilograms.

To convert kilograms (kg) to pounds (lbs), you can use the following formula:

To convert kilograms to pounds, multiply your figure by 2.20462

To convert 60 kg to lbs, you can multiply 60 by 2.20462:

60 kg X 2.20462 lbs/kg

= 132.2772 lbs

Therefore, 60 kg is approximately equal to 132.2772 lbs.

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While solving an inequality, you can do the following: add the same amount to each side, deduct the same amount from each side, and multiply or divide each side by the same positive amount. When each side is multiplied or divided by a negative number, the inequality sign must be flipped.

Inequalities may be solved in the same way as any other mathematical problem, but they require some extra steps to guarantee you get the correct solution.

Identify the terms in the inequality first. After that, simplify the equation such that it just has one variable.

Then, attempt to isolate the variable in the equation. To do this, carry out any necessary procedures on both sides of the equation to cancel out the terms that are unrelated to the equation.

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The number 31 is divisible by one and itself, which is the sign of prime number and hence 31 is a prime number.

As per the definition, a number to become prime number must follow two conditions. These are:

In other words, point 2 can be understood as it should not be divisible by any number. It remains the number to be divisible by one and itself.

We can see that 31 is the number which can be divided by any number to leave zero remainder. Hence, 31 is a prime number. Apart from this, 41, 97 and many other numbers are examples of prime number.

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Diego would have to put in 15 hours of labor to make the same amount of money as Mia does in just 6.

The unit method is a technique of challenge where you first measure the value of a specific unit, then multiply a certain value to get the answer. Simply expressed, a minimum unit value is extracted from with a specified multiple using the unit method. For contrast, 40 pens will cost you about 400 rupees, or $1.01. The method used to execute this might be standardized. a solitary nation. anything seems to have a distinctive component. (Mathematics, Algebra) Its capable of integrating and opposite are equivalent. (Molecular Algebra, Quantitative Analysis, Math and science of Matrix or Operators)

given

Diego need to work

105/7

=15$ per hour

150/15

=10$ per hour

Diego would have to put in 15 hours of labor to make the same amount of money as Mia does in just 6.

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The converted value of Celsius to degrees Fahrenheit using the standard formula is 48 degrees Celsius equals to 118.4 degree Fahrenheit.

Scale factor using which we relate the two units of the temperature Celsius and Fahrenheit is equal to :

(°C × 9/5) + 32 =°F

Now , to get the value of 48 degree Celsius and converted value into Fahrenheit by applying the above formula we have,

(48°Celsius × 9/5) + 32

= ( 432 / 5 ) + 32

= ( 86.4 ) + 32

= 118.4°Fahrenheit

Therefore, the converted value from degrees Celsius to Fahrenheit for the given temperature 48 degrees Celsius is equivalent to  118.4 Fahrenheit.

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Using compound interest formula when the CD matures on Melissa's 14th birthday, there will be $3187.69 available.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Use the formula for compound interest to calculate the amount of money that will be available when the CD matures -

[tex]A = P(1 + r/n)^(nt)[/tex]

Where A is the amount of money available when the CD matures, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, the initial principal is $2000, the interest rate is 6%, and the CD will be held for 8 years (from Melissa's 6th to 14th birthday).

It is not given how many times per year the interest is compounded, so assume it is compounded annually.

Using these values in the formula -

[tex]A = $2000(1 + 0.06/1)^(1*8)A = $2000(1.06)^8A = $3187.69[/tex]

Therefore, the value is obtained as $3187.69.

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False. Marginal distributions describe the distribution of each variable separately, without considering any relationship between them.

Comparing the marginal distributions of two variables cannot determine whether the variables are related. Marginal distributions show the distribution of each variable separately and do not consider the relationship between them. To determine whether two variables are related, it is necessary to examine their joint distribution. This can be done through a scatter plot, which displays the relationship between the variables graphically, or through a correlation coefficient, which measures the strength and direction of the linear relationship between the variables. Therefore, comparing marginal distributions alone is not sufficient to determine whether two variables are related.

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The indicated function values are If x = 0, then f(0) = 2,
If f(x) = 0, then x = - 1

To evaluate f(0), locate the point on the graph where x will be equal to '0' then find out the y-coordinate of that point where the value of f(0) will be equal to f(0).

Similarly, to find the x at f(x) = 0, take the y-coordinate as 0 and find the corresponding x - coordinate.  

Here we have

A graph that shows the function f(x)  

Given  x = 0  then f(0) will be equal to the y - coordinate at x = 1  

=> If x = 0 then f(0) = 2        

Given f(x) = 0 then x will be equal to the x - coordinate at y = 0

=> If f(x) = 0 then x = - 1    

Therefore,

The indicated function values are If x = 0, then f(0) = 2,
If f(x) = 0, then x = - 1

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Answer:

1. 2.25

2. -1

Step-by-step explanation:

right on edge

The mathematical formula v = 1/3 πr²h is the formula for calculating the volume of a cone.

The volume of a cone is the amount of space or the capacity of the cone.

The formula for determining the volume of a cone is:

Volume, v = ¹/₃ πr²h

where

For example:

Calculate the volume of a cone if r= 2 cm and h= 5 cm.

V= ¹/₃ × 22/7 × 2² × 5

V = 20.95 cm³

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Labro overlooks the Rieti Valley, which was frequently visited by which saint: Francis of Assisi.

Francis of Assisi spent a great deal of time in the Rieti Valley, where he established four sanctuaries that are stopping points for pilgrims following the Cammino di Francesco pathway. Francis is also said to have made the first live nativity scene during a visit to the valley in 1223.

Francis of Assisi, one of the Catholic Church's most loved and darling saints. St. Francis is known for his ministry to poor people and oppressed, his consideration for nature and animals, and establishing the Franciscan request.

His life and message were uncompromising and simple: voracity causes suffering for both the victims and the perpetrators.

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Answer:

Step-by-step explanation:

No, the point is not (1,0)

Answer:

Yes, 23 is a prime number, because its only factors are 1 and itself.

The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.

If line AB and line CD are parallel, and line EF intersects both lines at points G and H respectively, then the angles formed on opposite sides of line EF and on the exterior of the parallel lines are congruent.

The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.

In symbols, the theorem can be written as:

∠1 ≅ ∠4

where ∠1 and ∠4 are alternate exterior angles.

This theorem is useful in solving problems involving angles and parallel lines, and it is commonly used in geometry proofs.

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Answer:

PAYMENT = 64

AMOUNT WANTED = 64

SO: 400 / 64 = 6.25

SO LEE NEEDS TO WORK FOR 6.25 HOURS IN EACH DAY.

A critical t-value calculator is an online tool that helps you determine the critical value for the t-distribution for a given level of significance (alpha) and degrees of freedom (df). The critical t-value is the value that separates the area under the t-distribution curve into the rejection region and the non-rejection region for a two-tailed hypothesis test.

In statistical hypothesis testing, the t-distribution is used when the sample size is small, and the population standard deviation is unknown. The t-distribution is a family of distributions that depend on the degrees of freedom (df) and is bell-shaped, with a mean of 0 and a standard deviation of 1.

To use a critical t-value calculator, you need to input the significance level (alpha) and the degrees of freedom (df) and select whether the test is one-tailed or two-tailed. The calculator will then provide you with the critical t-value that separates the rejection and non-rejection regions for the given alpha and df.

It's important to note that the critical t-value depends on the level of significance (alpha) and the degrees of freedom (df). As the level of significant increases or the degrees of freedom decrease, the critical t-value also changes. Therefore, it's essential to use a critical t-value calculator to obtain the correct value for your hypothesis test.

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A critical t-value calculator is a tool used to calculate the critical value of t in a Student's t-test for a given significance level (alpha) and degrees of freedom (df).

When the sample size is small or the population standard deviation is unknown, the t-distribution is used to estimate the population mean.

The critical t-value in a Student's t-test is the value of t that separates the rejection region from the non-rejection region in a t-distribution. The null hypothesis is rejected if the calculated t-value is greater than the critical t-value, indicating that there is a significant difference between the sample mean and the population mean.

To use a critical t-value calculator, enter the t-significance test's level (alpha) and degrees of freedom (df). The degrees of freedom are defined as the number of observations minus one and are proportional to the sample size. The calculator will output the critical t-value for the given significance level and degrees of freedom once you enter these values.

For example, the degrees of freedom for a two-tailed t-test with a sample size of 20 and a significance level of 0.05 would be 20-1=19. The critical t-value at a significance level of 0.05 and 19 degrees of freedom is approximately 2.093, according to a critical t-value calculator.

Knowing the critical t-value is useful in hypothesis testing because it allows you to compare the calculated t-value from the sample data to the critical t-value to determine whether the null hypothesis should be rejected

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The values of the function g⁻¹(2) is  {(12, 0), (14, -4), (-4, -14), (-18, 18)}, h⁻¹(x) is  11x / (x + 14) and (h o h⁻¹)(2) is 235 / 176

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of outputs, called the range, such that each input is associated with exactly one output.

More formally, a function f from a set A to a set B is a rule or correspondence that assigns to each element x in the set A exactly one element y in the set B. The set A is called the domain of the function, and the set B is called the range or codomain. The output y is called the image of x under the function f, and is often denoted as f(x).

From the question;

g = {(0, 6), (2, -7), (7, 2), (9, -9)}

h(x) = (x + 14) / 11

g⁻¹(2) = {(12, 0), (14, -4), (-4, -14), (-18, 18)}

h⁻¹(x) = 11x / (x + 14)

(h o h⁻¹)(2) = 235 / 176

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Equation for 6 halves of pears is 1/2 x 6 = 3

The factor of a number is a number that divides the given number completely without any remainder. The factors of a number can be positive or negative.

Every factor is divisor of that number but every divisor is not a factor of that number.

Given, in the picture,

half of 6 pears

One half of pear can be denoted as = 1/2

Now,

equation of 6 half pears.

= 1/2 x 6

= 4

Hence, equation for 6 half pears can be written as 1/2 × 6 = 3.

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The quadratic equations with roots that are whole numbers and fractions are listed below:

Case 2: 9 · x² - 78 · x - 27 = 0

Case 3: 7 · x² - 26 · x - 8 = 0

Case 4: 4 · x² + 2 · x - 32 · x - 16 = 0

Case 6: 4 · x² - 5 · x - 6 = 0

Case 7: 7 · x² + 38 · x - 24 = 0

In this problem we find eight cases of quadratic equations of the form a · x² + b · x + c = 0, where a, b, c are real coefficients. All roots can be found by means of algebra properties:

Case 1

5 · x² + 8 · x + 4 = 0

5 · [x² + (8 / 5) · x + 4 / 5] = 0

5 · (x + 4 / 5 - i 2 / 5) · (x + 4 / 5 + i 2 / 5)

Case 2

9 · x² - 78 · x - 27 = 0

9 · [x² - (26 / 3) · x - 3] = 0

9 · (x - 9) · (x + 1 / 3) = 0

Case 3

7 · x² - 26 · x - 8 = 0

7 · [x² - (26 / 7) · x - 8 / 7] = 0

7 · (x - 4) · (x + 2 / 7) = 0

Case 4

4 · x² + 2 · x - 32 · x - 16 = 0

4 · x² - 30 · x - 16 = 0

4 · [x² - (15 / 2) · x - 4] = 0

4 · (x - 8) · (x + 1 / 2) = 0

Case 5

2 · x² - 20 · x + 32 = 0

2 · (x² - 10 · x + 16) = 0

2 · (x - 8) · (x - 2) = 0

Case 6

4 · x² - 5 · x - 6 = 0

4 · [x² - (5 / 4) · x - 3 / 2] = 0

4 · (x - 2) · (x + 3 / 4) = 0

Case 7

7 · x² + 38 · x - 24 = 0

7 · [x² + (38 / 7) · x - 24 / 7] = 0

7 · (x - 4 / 7) · (x + 6) = 0

Case 8

x² - 5 · x - 6 = 0

(x - 6) · (x + 1) = 0

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The formula for the average rate of change to get is:

average rate of change = (y2 - y1) / 5

What is the average rate of change?

The average rate of change means the average rate at which one quantity is changing with respect to something else changing.

To find the average rate of change of a function f(x) over an interval [a, b], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, we are given the function f(x), but we don't have a formula for it. Instead, we are given the interval [2, 7] over which we want to find the average rate of change. So, we can use the values of the function at x = 2 and x = 7 to compute the average rate of change.

Let's assume that we have the function f(x) and evaluate it at x = 2 and x = 7 to get:

f(2) = y1

f(7) = y2

Then, we can use the formula for the average rate of change to get:

average rate of change = (f(7) - f(2)) / (7 - 2) = (y2 - y1) / 5

So, to find the average rate of change of f(x) over the interval 2 ≤ x ≤ 7, we need to know the values of f(2) and f(7). If these values are given or can be calculated, we can use the formula above to find the answer.

Hence,  the formula for the average rate of change to get is:

average rate of change = (y2 - y1) / 5.

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If the total number of calories is X, then the lowest number is 89, which is 43% of the total, or 206.98 calories. Thus, the response is A.

The middle value of the provided collection of data, when organised in order, is known as the median in statistics. It is possible to arrange the data or observations in either ascending or descending order. For instance, the median of 2,3,4, is 3. The median, a form of average used to determine the center value in mathematics, is another average.

Two easy steps are used to determine the median of a dataset. Put the information provided in ascending order first. The middle data must be chosen next.

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5 meters is equal to 16.4042 feet.

The metre to foot formula is a mathematical expression that converts length measurements from metres to feet.

Metre is the SI unit of measurement for both length and distance.

The meter is denoted by "m".

It is denoted by the letter "ft."

To convert 5 meters (m) to feet,

Multiply the given value meters by 3.28084,

As we know that,

One meter is nearly equal to 3.28084 feet.

Therefore,

5 meters multiplied by 3.28084 gives us:

5 meters x 3.28084 = 16.4042 feet

(rounded to four decimal places)

So, 5 meters is nearly equal to 16.4042 feet.

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