A rectangle garden is enclosed by 60 meters of fencing. The table shows some possible values for the length and width if the yard. If the values for length and area are plotted, what would the graph look like?

Answer:

[tex](x - 3)^2 + (y + 2)^2 = 41[/tex]

Step-by-step explanation:

The general shape of the equation is:

(x-a)² + (y-b)² = r²

Where (a,b) is the center and r is the radius.

(a,b) = (3,-2) is given.

To find the radius r, or even simpler, r², calculate the distance between (-3,2) and (8,2) using pythagoras.

r² = (8-3)² + (2--2)² = 41

There is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

We can use the binomial distribution to calculate the probability of the Rangers winning a majority of their games against the Islanders, given their win percentage of 55.1%. Let's denote the probability of the Rangers winning a single game against the Islanders as p.

Since the Rangers and Islanders play seven games against each other, the number of games the Rangers win against the Islanders follows a binomial distribution with parameters n = 7 and p = 0.551.

To find the probability that the Rangers win a majority of these seven games, we need to sum the probabilities of all possible outcomes where they win four or more games. We can use the binomial probability formula to calculate each of these individual probabilities and then sum them up:

P(Rangers win 4 or more games) = P(Rangers win 4 games) + P(Rangers win 5 games) + P(Rangers win 6 games) + P(Rangers win 7 games)

[tex]= (7 choose 4) * 0.551^4 * (1 - 0.551)^3 + (7 choose 5) * 0.551 ^ 5 * (1 - 0.551)^2 + (7 choose 6) * 0.551^6 * (1 - 0.551) + (7 choose 7) * 0.551^7[/tex]

Using a binomial calculator or a spreadsheet, we can evaluate this expression and find that:

P(Rangers win a majority of their games against the Islanders) = 0.423

Therefore, there is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

The Binomial distribution is a discrete probability distribution that describes the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial can have only two outcomes (e.g., success or failure).

The distribution is defined by two parameters: the number of trials n and the probability of success in each trial p. The distribution gives the probability of obtaining k successes in n trials, where k can range from 0 to n.

The formula for the probability mass function of the Binomial distribution is:

[tex]P(k) = (n choose k) * p^k * (1 - p)^n-k[/tex]

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. The formula can be used to calculate the probability of obtaining k successes in n trials, given a fixed probability of success p.

The Binomial distribution is used in many areas of statistics, including quality control, epidemiology, and finance, among others. It is also a fundamental building block for more complex statistical models, such as the Poisson distribution and the normal distribution.

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Approximately 50% of the values in a distribution lie between the 25th percentile and the 75th percentile.

The interquartile range (IQR) is the range between the 25th percentile (Q1) and the 75th percentile (Q3) of a distribution. The IQR contains the middle 50% of the data.

Therefore, approximately 50% of the values in a distribution lie outside the IQR, with 25% of the values below Q1 and 25% of the values above Q3. The remaining 50% of the values lie within the IQR, with approximately 25% of the values between Q1 and the median, and 25% of the values between the median and Q3.

So, approximately 50% of the values in a distribution lie outside the IQR, and approximately 50% of the values lie within the IQR, which includes the values between the 25th and 75th percentile.

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The equation can be used to solve for b is b = 5 / tan30°

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a triangle, ∠ BCA = 90°, ∠ CAB = 30°, we need to find the equation for AC,

The equation for AC(b) =

tan30° = 5/b

b = 5 / tan30°

Hence, the equation can be used to solve for b is b = 5 / tan30°

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The measure of ∠VWX in this triangle VWX is, 68.9°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The cosine rule of triangles,

Here, cosW = (VW² + XW² - VX²)/2(WX×WV).

cosW = (36² + 23² - 35²)/2(36×23).

cosW = 600/1656.

W = cos⁻¹(0.36).

∠W = 68.9°.

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The converted to product four times as much in the CSTR than it was in the PFR that is 400%.

Conversion is a term used to describe the process of transferring a reactant into a product.

In this case, the reactant is being transferred from a 72 l plug flow reactor (PFR) to a 24 l continuous stirred tank reactor (CSTR). The conversion achieved by this process can be determined by calculating the ratio of product to reactant in the CSTR.

Specifically, if the PFR has a conversion of x%, then the conversion achieved in the CSTR will be x/(1-x), where x is the conversion in the PFR.

Therefore, if the PFR has a conversion of 80%, then the CSTR will have a conversion of 80/(1-80) = 400%.

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One millimeter is equal to 0.00106 of U.S. liquid quarts. Simply multiply any number of ml with the given value of liquid quarts to convert and find volume.

An object's or space's three-dimensional extent can be measured using a volumetric unit of measurement. Capacity is measured by volume. Consequently, the volumetric unit is essentially a unit for gauging the size or extent of an object or space.

Typically, the unit is used to describe the volume of products or liquids. To measure a quantity of something, use the International System of Units. Despite the fact that people speak different languages, the SI Units are used globally to communicate the measurements used in research settings.

Cubic meters, liters, and milliliters are the three most popular SI units for measuring volume. Specifically, the cubic meter as the unit of volume in the SI system.

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Step-by-step explanation:

The prime factor of the 144 is 24 x 32. The exponents in the prime factorisation are 4 and 2. Add the number 1 with the exponents and multiply it. (4+1)(2+1) = 5 x 3 = 15.

The value of probability P (even | less than 3) is, 1/3.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A 6-sided die is tossed.

Here, Two numbers 1 and 2 are less than 3.

Hence, The value of P (even | less than 3) is,

⇒ 2 / 6

⇒ 1 / 3

Thus, The value of P (even | less than 3) is, 1/3.

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Answer: 29

Step-by-step explanation:

40 - 5 = 35

35 - 6 = 29

So, 29 + 6 = 5 less than 40

Answer: The number is 29 and the Sum is 35

Step-by-step explanation:

How you set up the equation 6+x = 40-5

Subtract 5 from 40 and you get 6+x = 35

Now subtract 6 from 35 to find your missing variable x = 35-6

x = 29

400kg is equivalent to 881.848 lbs

One of the most common conversions you may need to make is from kilograms (kg) to pounds (lbs). This conversion is important, especially when dealing with weights and measurements in science, engineering, and everyday life. In this article, we will guide you on how to convert 400kg to lbs using a conversion factor.

The first step in converting 400kg to lbs is to understand the relationship between these two units of measurement. A conversion factor is a ratio that expresses the relationship between two different units of measurement. In this case, we will use the conversion factor for kg to lbs.

The conversion factor for kg to lbs is 2.20462. This means that one kilogram is equivalent to 2.20462 pounds. To convert 400kg to lbs, we simply need to multiply 400kg by the conversion factor.

400kg x 2.20462 = 881.848 lbs

In conclusion, converting 400kg to lbs is a straightforward process that can be done by using the appropriate conversion factor. With this knowledge, you can confidently make conversions from kilograms to pounds and vice versa in the future.

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The value of 107 kg into lbs can be converted by multiplying kilogram by 2.204622  so the answer is 235.895 pounds.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

Pounds = kilograms × 2.20462262184878

= 107 x 2.20462262184878

= 235.895 pounds or lbs.

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Based on the data, it can be inferred that the magnitude and direction of PQ is 9.5 north of east for 6.1 miles (option D).

To identify the magnitude and direction of the plane, we must carefully look at the information in the graph and identify the option that corresponds to the information.

So, we can say that this is moving from the south to the north and from the west to the east, so options A and C would be ruled out. Now we must identify the magnitude and degrees. Taking a completely horizontal line as a reference, we could say that the plane has 9.5 degrees in its trajectory. So the correct option would be D.

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Answer:

3528

Step-by-step explanation:

49*72=3528

Answer:

Step-by-step explanation:

49x 72

If Seshni wants to cover six cushions, each measuring 36 cm x 36 cm, with fabric.  

a. Seshni needs to buy 0.84375 square meters of fabric.

b. It will cost R64.66 including VAT.

a. The dimensions of each cushion are 36 cm x 36 cm, and with the added 1.5 cm seam allowance, each cushion will require fabric with dimensions of (36 + 1.5) cm x (36 + 1.5) cm = 37.5 cm x 37.5 cm.

The total area of fabric required to cover all six cushions is:

6 cushions x (37.5 cm x 37.5 cm) = 8437.5 square centimeters

To convert to square meters, we need to divide by 10000:

8437.5 square centimeters / 10000 = 0.84375 square meters

So, Seshni needs to buy 0.84375 square meters of fabric.

b. Next, we can calculate the cost of the fabric.

0.84375 square meters / 0.9 meters = 0.9375 meters

The cost per meter is R59.99 excluding VAT, so the cost of the fabric is:

0.9375 meters x R59.99/meter = R56.23

To calculate the cost including VAT, we need to add the VAT amount. Assuming the VAT rate is 15%, the VAT amount is:

0.15 x R56.23 = R8.43

So the total cost including VAT is:

R56.23 + R8.43 = R64.66

Therefore, Seshni needs to buy 0.84375 square meters of fabric, and it will cost R64.66 including VAT.

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Answer: 25

Step-by-step explanation:

5^2 is the same as 5x5 which is 25

Answer:

5.90551 inches

Step-by-step explanation:

To solve for the number of inches, we can use this equation:

15 × 0.393701 = 5.90551

Therefore, for every 15 cm, it is equivalent to 5.90551 inches.

Using the recursive formula we will see that:

f(2) = 5

Here we have a sequence such that we know that:

f(0) = 2

And the recursive formula is:

f(n + 1) = -2*f(n) + 3

So, first let's find f(1), to get that we use n = 0.

f(1) = -2*f(0) + 3

    = -2*2 + 3 = -4 + 3 = -1

And the next term is:

f(2) = -2*f(1) + 3

     = -2*-1 + 3

    = 2 + 3 = 5

Then the correct option is the third one.

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The length of crossbar that Sasha need to complete the kite is equal to √8 units.

By critically observing the image of the kite shown below, we can logically deduce that the crossbar and the two (2) given lengths formed a right-angled triangle as illustrated by the right angle symbol between the two given sides.

In order to determined, we would have to apply Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

Substituting the given parameters into Pythagorean's theorem, we have the following;

c² = a² + b²

c² = 2² + 2²

c² = 4 + 4

c = √8 units.

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The cross section of a cylinder is a circle. This is because a cylinder is formed by two circular bases connected by a curved surface. When the cylinder is sliced perpendicularly to its bases, the cross section will be a circle.

To prove this mathematically, let us consider a cylinder with radius r and height h. The volume of the cylinder is V = πr²h. If the cylinder is sliced perpendicularly to its bases, its cross section can be considered as a circle with radius r. The area of the circle is A = πr². Since the volume of the cylinder is equal to the area of the cross section multiplied by the height, we can say that V = A * h. This implies that A = V/h. Since we already know that V = πr²h, we can substitute the value of V in the above equation to get A = πr²h/h. Cancelling both h from the equation, we get A = πr². This means that the area of the cross section of the cylinder is equal to the area of a circle with radius r. Therefore, the shape of the cross section of the cylinder is a circle. Hence, the shape of the cross section of a cylinder is a circle.

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Percent difference is a measure of the difference between two values expressed as a percentage of their average.

The formula for percent difference is:

Percent difference = (|value 1 - value 2| / ((value 1 + value 2) / 2)) x 100%

where |value 1 - value 2| is the absolute value of the difference between the two values

((value 1 + value 2) / 2) is their average.

So the Percent difference is a measure of the difference between two values expressed as a percentage of their average.

To calculate percent difference, follow these steps:

Determine the two values you want to compare.

Calculate the absolute difference between the two values by subtracting one from the other and taking the absolute value of the result.

Calculate the average of the two values by adding them together and dividing by 2.

Divide the absolute difference by the average, and multiply by 100% to get the percent difference.

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Answer:

x+y-200=0

Step-by-step explanation:

ax = x

by = y

c = 200 but we convert it to negative 200 after moving it from the RHS to LHS

So x+y=200 will be x+y-200=0 in the form ax + by + c =0

The dimensions are as follows

14

x = 21

GK = 167

HJ = 98

HGJ = 159

GKJ = 201

15.

x = 9

AD = 108

BC = 23

DC = 139

DCB = 162

The value of x is solved using the concept of angles in a point and this is 360 degrees

Figure 14

9x - 22 + 61 + 5x - 7 + 34 = 360

collecting like terms

9x + 5x  - 22 + 61  - 7 + 34 = 360

solving for x

14x + 66 = 360

14x = 360 - 66

x = 294 / 14

x = 21

GK = 9x - 22 = 9 * 21 - 22 = 167

HJ = 5x - 7 = 5 * 21 - 7 = 98

HGJ = GH + HJ = 61 + 98 = 159

GKJ = GK + KJ = 167 + 34 = 201

15.

12x + 17x - 14 + 2x + 5 + 90 = 360

collecting like terms

12x + 17x + 2x - 14 + 5 + 90 = 360

solving for x

31x + 89 = 360

31x = 360 - 81

x = 279 / 31

x = 9

AD = 12x = 12 * 9 = 108

BC = 2x + 5 = 2 * 9 + 5 = 23

DC = 17x - 14 = 17 * 9 - 14 = 139

DCB = DC + CB = 23 + 139 = 162

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Answer:

Below

Step-by-step explanation:

The solution set is just the point where the two graphed lines cross....this point is common to BOTH lines and thus is the solution (2,2)

The subtracting fractions calculator online is a free online calculator showing the difference between two fractions.

The fraction represents the components of the whole in mathematics. It is important to keep track of the fraction types while subtracting fractions, whether they are like or unlike fractions. Like fractions are fractions with the same denominators, and unlike fractions are fractions with distinct denominators. When a fraction is similar, the numerator value can simply be removed. The methods to subtract the fractions are listed below if the denominators are the opposite fractions.

Take the denominator's LCM.

Now multiply the numerator and denominator values by the same number to convert the denominator value to the LCM value.

Finally, subtract the values of the fractions.

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The probability that fewer than 3 of the elk survive to adulthood is

P(n < 3) = 0.8.

The probability of an event is a number that indicates how likely the event is to occur.

Given is that Biologists estimate that a randomly selected baby elk has a 44% probability of surviving to adulthood.

It is given that -

P{surviving to adulthood} = 44/100 = 0.4

For -

P(n < 3) = 0.4 + (0.4 + 0.4)/2

P(n < 3) = 0.4 + 0.4

P(n < 3) = 0.8

Therefore, the probability that fewer than 3 of the elk survive to adulthood is P(n < 3) = 0.8.

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Answer:

The slope of the dotted line is -1. The slope of the solid line is 4.

From the given information, total surplus in a market is equal to the sum of consumer surplus and producer surplus.

Consumer surplus is the difference between the highest price a consumer is willing to pay for a good or service (the "reservation price") and the actual price they pay. Producer surplus is the difference between the lowest price a producer is willing to accept for goods or services and the actual price they receive.

When a market is in equilibrium, the price and quantity are such that the quantity demanded equals the quantity supplied. At this point, total surplus is maximized, since all trades that benefit both consumers and producers have taken place. The total surplus represents the net benefit to society from the production and consumption of the good or service in the market.

In other words, total surplus is the sum of the gains from trade that accrue to consumers and producers in the market, and it represents the difference between the value that buyers and sellers place on the good or service and the resources that were actually used to produce it.

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He can withdraw $114746.17 (approx.) at the end of each of the next 25 years and end up with zero in the account. The solution has been obtained by using the concept of present value of annuity.

What is present value of annuity?

With a specific rate of return, or discount rate, an annuity's present value is the current worth of its expected future payments. The present value of the annuity decreases with increasing discount rates.

We are given that uncle has $1,375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds.

Using present value of annuity,

Present value of annuity due = P + P [(1 - (1 + r)⁻⁽ⁿ⁻¹⁾) / r]

1375000 = P + P [(1 - (1+0.075)⁻⁽²⁵⁻¹⁾)/0.075]

1375000 = P [1 + 10.98297]

P = 1375000/11.98297

P = $114746.17 (approx.)

Hence, uncle can withdraw $114746.17 (approx.) at the end of each of the next 25 years.

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Answer:

+x+=+3+

+y+=+-.9%2A%28+3+%2B+3+%29%2A%28+3+-+3+%29+

+y+=+-.9%2A6%2A0+

+y+=+0+

----------------------

The distance between ( -3, 0 ) and ( 3, 0 )

is +3+-%28-3%29+=+6+

The width of the arch at ground level is 6 ft

-----------------------

Here's the plot of the equation:

Step-by-step explanation: