three randomly chosen colorado students were asked how many times they went rock climbing last month. their replies were 5, 6, 7. the coefficient of variation is multiple choice 35.7 percent. 13.6 percent. 20.0 percent. 16.7 percent.

Answer:

[tex]( x + 2 )^{2} +(y-15)^{2} =9[/tex]

Hope this helps!

Step-by-step explanation:

The perimeter to the nearest tenth, we get: Perimeter ≈ 18.4 units.

What is perimeter?

We can start by using the Pythagorean theorem to find the length of AC:

AC² = AB² + BC²

AC² = 2² + 1.5²

AC² = 4.25

AC = √(4.25)

AC ≈ 2.06 units

Next, we can use the fact that AC is common to both triangles to find the length of CD:

ACD is a right triangle, so we can use the Pythagorean theorem:

CD² = AD² - AC²

CD² = 6.5² - 2.06²

CD² ≈ 39.86

CD ≈ 6.31 units

Now we can find the perimeter of the figure by adding the lengths of all three sides:

Perimeter = AB + BC + CD + DA + AC

Perimeter = 2 + 1.5 + 6.31 + 6.5 + 2.06

Perimeter ≈ 18.37 units

Therefore, none of the given options is the correct answer. However, if we round the perimeter to the nearest tenth, we get:

Perimeter ≈ 18.4 units

And the closest option to this value is option 3) 16 units, which is not very close. Therefore, we can conclude that none of the given options is a correct approximation of the perimeter of the figure.

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Answer:

$100 for air conditioning and $40 for water heater

Step-by-step explanation:

$200÷2= 100

200÷5= 40

The important to select the appropriate value of alpha based on the characteristics of the data and the goals of the forecasting model.

The statement "for a time series for simple exponential smoothing, a larger alpha is smoother than a shorter period" is true.

In simple exponential smoothing, the forecast for the next period is based on the previous forecast and the difference between the actual value and the previous forecast. The smoothing parameter alpha controls the weight given to the most recent observation compared to the previous forecasts.
A larger alpha places more weight on the most recent observation, resulting in a forecast that is more responsive to recent changes in the data. As a result, the forecast will exhibit less volatility or variability, making it smoother. This means that a larger alpha will lead to a more stable forecast with less fluctuation around the trend.
On the other hand, a smaller alpha places less weight on the most recent observation, resulting in a forecast that is less responsive to recent changes in the data.

As a result, the forecast will be more volatile or variable, making it less smooth. This means that a smaller alpha will lead to a forecast that is more susceptible to fluctuations around the trend.
In summary, the choice of alpha is a trade-off between stability and responsiveness to changes in the data. A larger alpha will lead to a smoother forecast, while a smaller alpha will lead to a more volatile forecast.

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a. The z-table, the probability that a sample mean will be within 0.02 of the population mean is:

P(-0.02/0.00416 < Z < 0.02/0.00416) = P(-4.81 < Z < 4.81) = 0.9999

b. The probability of obtaining a sample mean that is close to the population mean increases as the sample size increases. This means that larger sample sizes provide more accurate estimates of the population mean.

a. We can use the formula for the standard error of the mean:

SE = σ/√n

where σ is the population standard deviation, n is the sample size, and SE is the standard error.

For a sample size of n = 25:

SE = 0.0588/√25 = 0.01176

Using the z-table, the probability that a sample mean will be within 0.02 of the population mean is:

P(-0.02/0.01176 < Z < 0.02/0.01176) = P(-1.70 < Z < 1.70) = 0.9045

For a sample size of n = 50:

SE = 0.0588/√50 = 0.00832

Using the z-table, the probability that a sample mean will be within 0.02 of the population mean is:

P(-0.02/0.00832 < Z < 0.02/0.00832) = P(-2.41 < Z < 2.41) = 0.9872

For a sample size of n = 100:

SE = 0.0588/√100 = 0.00588

Using the z-table, the probability that a sample mean will be within 0.02 of the population mean is:

P(-0.02/0.00588 < Z < 0.02/0.00588) = P(-3.40 < Z < 3.40) = 0.9984

For a sample size of n = 200:

SE = 0.0588/√200 = 0.00416

Using the z-table, the probability that a sample mean will be within 0.02 of the population mean is:

P(-0.02/0.00416 < Z < 0.02/0.00416) = P(-4.81 < Z < 4.81) = 0.9999

b. The advantage of a larger sample size is that it leads to a smaller standard error of the mean, which means that the distribution of sample means is narrower and more closely centered around the population mean. As a result, the probability of obtaining a sample mean that is close to the population mean increases as the sample size increases. This means that larger sample sizes provide more accurate estimates of the population mean.

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The controllability and observability matrices of the given state-space equation were calculated, but no set of bij and Cij was found to make the system controllable or observable. Therefore, the system is not controllable or observable.

To determine whether the given state-space equation is controllable and observable, we need to check the controllability and observability matrices.

The controllability matrix is given by:

[ B AB A^2B A^3B A^4B ]

where A and B are the state and input matrices, respectively.

The observability matrix is given by:

[ C ]

[ CA ]

[ CA^2 ]

[ CA^3 ]

[ CA^4 ]

where C is the output matrix.

Using the given state-space equation, we can calculate the controllability and observability matrices as follows:

A = [ 1 0 0 0 0 ]

   [ L0 1 0 0 1 ]

   [ b12 1 0 0 0 ]

   [ 0 0 1 0 0 ]

   [ b21 bzz 0 1 1-L ]

B = [ 0 ]

   [ 0 ]

   [ 0 ]

   [ 0 ]

   [ 1 ]

C = [ 1 0 0 0 0 ]

   [ 0 1 0 0 0 ]

   [ 0 0 1 0 0 ]

Controllability Matrix:

[ B AB A^2B A^3B A^4B ] =

[ 0 0 0 0 1 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]        

[ 0 0 0 0 0 ]

[ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]        

[ 0 0 0 0 0 ]

[ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]        

[ 0 0 0 0 0 ]

[ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          [ 0 0 0 0 0 ]          

[ 0 0 0 0 0 ]

[ 0 bzz b21bzz 0 Lb51 ] [ 0 L0 b12bzz Lb51 0 ] [ L0 b12bzz L0b21bzz 0 0 ]

[ b12bzz 0 L0b21bzz 0 0 ] [ 0 0 L0b12bzz 0 0 ]

Observability Matrix:

[ 1 0 0 0 0 ] [ 1 0 0 0 0 ] [ 1 0 0 0 0 ] [ 1 0 0 0 0 ] [ 1 0 0 0 0 ]

[ 0 1 0 0 0 ] [ 0 L0 1 b12 1 ] [ L0 b12bzz L0b21bzz 0 0 ] [ b12bzz 0 L0bb21bzz 0 0 ]

To elaborate on the solution, the controllability matrix shows that some of the columns are linearly dependent on the others, which means that it is not possible to find a set of inputs that can steer the system from any initial state to any desired state in finite time. Similarly, the observability matrix shows that some of the rows are linearly dependent on the others, which means that it is not possible to uniquely determine the state of the system from the output measurements.

Therefore, the system is not controllable or observable, and it cannot be controlled or accurately estimated using the given state-space equation.

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--The given question is incomplete, the complete question is given

" Is it possible to find a set of bij and a set of Cij such that the following state-space equation is controllable? Observable? (If the answer is yes, find a set) i(t) = 1 0 0 0 LO 1 0 0 01 5611 b12 1 0 0 0 |b21 bzz 0 1 1 0 X(t) + b31 b32|u(t) 0 0 1 0 | b41 buz 0 0 0 1- Lb51 652 [C11 y(t) = C21 C31 C12 C22 C32 C13 C23 C33 C14 C24 C34 C15 C25 x(t) C35

The sum of the angles in triangle MNP is 180, and subtracting 135 from both sides gives 45 degrees. With the angle sum property of triangle, ∠MNP = 121°.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

According to the given question,

45° + 90° + ∠MNP = 180°

135° + ∠MNP = 180°

∠MNP = 45°

Hence, With the angle sum property of triangle, ∠MNP = 121°.

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Answer:

Point K

Step-by-step explanation:

Which Point represents the ordered pair

( -4[tex]\frac{1}{2}[/tex], -1)

Left -4[tex]\frac{1}{2}[/tex] we have points J and K

Down -1 we have point K

So, the answer is point K

Answer: 6.85%

Step-by-step explanation:

It will take approximately 13.6 years for the account value to reach $9000.

What is an account value?

We can use the formula for compound interest to solve this problem:

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

where A is the final amount, P is the principal or initial amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

We want to find t, so we can rearrange the formula as:

t = (1/n) × log(A/P) / log(1 + r/n)

Substituting the given values:

P = $3200

r = 8% = 0.08

A = $9000

n = 1 (interest is compounded annually)

Using a calculator:

t = (1/1) × log(9000/3200) / log(1 + 0.08/1)

t ≈ 13.6

Rounding to the nearest tenth of a year, it will take approximately 13.6 years for the account value to reach $9000.

What is an interest ?

Interest is the cost of borrowing money, or the compensation paid by a borrower to a lender for the use of money. When you borrow money, you are usually required to pay back the amount borrowed (the principal) plus an additional amount of money, which is calculated as a percentage of the principal and represents the interest.

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The design is a randomized controlled trial (RCT), where participants are randomly assigned to treatment groups and tested on the dependent variable once to control for confounding variables and ensure that differences observed between groups are due to the treatment.

The type of design you are referring to is a randomized between-subjects design, also known as a randomized controlled trial (RCT). In this type of experiment, participants are randomly assigned to one of two or more treatment groups, each receiving a different level or type of the independent variable. Then, the dependent variable is measured only once after the treatment is administered. The purpose of this design is to control for potential confounding variables and to ensure that any differences observed between groups are due to the treatment and not to other factors.

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The solution to the equation 1 is p = -7. and the only solution to the   equation2  is k = 2.

what is  equation?

An equation is a mathematical statement that asserts the equality of two expressions. It usually contains one or more variables (letters that represent unknown values) and an equal sign. The goal of solving an equation is to find the values of the variables that make the equation true.

In the given question,

Starting with -49 = -7√(p+8):

Dividing both sides by -7, we get:

7√(p+8) = 7

Dividing both sides by 7, we get:

√(p+8) = 1

Squaring both sides, we get:

p+8 = 1

Subtracting 8 from both sides, we get:

p = -7

Therefore, the solution to the equation is p = -7.

Starting with √(6-k) = k:

Squaring both sides, we get:

6-k = k²

Rearranging, we get:

k²+ k - 6 = 0

We can factor this quadratic equation as:

(k+3)(k-2) = 0

Therefore, the solutions to the equation are:

k+3 = 0 or k-2 = 0

Solving for k, we get:

k = -3 or k = 2

However, we need to check whether these solutions satisfy the original equation, since we squared both sides and introduced extraneous solutions:

When k = -3:

√(6-k) = √(6-(-3)) = √9 = 3

k = -3 is not a solution.

When k = 2:

√(6-k) = √(6-2) = √4 = 2

k = 2 is a solution.

Therefore, the only solution to the equation is k = 2.

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A rational inequality for which -2 < x < 1 is the solution is (3x - 1)/(x + 2) > 2.

An inequality that incorporates one or more rational expressions—that is, expressions that can be expressed as the quotient of two polynomial expressions—is referred to as a rational inequality. The same techniques used to resolve other kinds of inequalities, such as graphing, testing intervals, or algebraic manipulation, can also be used to resolve rational inequalities. The denominator of a rational expression cannot, however, equal zero, hence extra care must be made to identify and rule out any values of the variable that would do so, as these values would render the expression undefinable.

A rational inequality for which -2 < x < 1 is the solution is:

(3x - 1)/(x + 2) > 2

In the equation when,

For x -2, the inequality holds because both the denominator and the numerator are negative.

When -2 x 1, the inequality is true since both the denominator and the numerator are positive.

When x > 1, the denominator and numerator are both positive, but the expression's value is less than 2, rendering the inequality untrue.

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Answer: To find the value of the car after 8 years, we can use the given information to create a linear equation in the form:

y - y1 = m(x - x1)

Where:

y is the value of the car after 8 years (what we want to find)

y1 is the value of the car after a given time (either 3 or 5 years)

x is the given time (either 3 or 5 years)

x1 is the starting time (when the car was purchased)

m is the rate of decrease (slope of the line)

We can use the two given data points to find the slope of the line:

m = (y2 - y1) / (x2 - x1)

m = (11,000 - 15,000) / (5 - 3)

m = -2,000 per year

Now, we can use one of the data points to solve for the y-intercept of the line:

y - y1 = m(x - x1)

y - 15,000 = (-2,000)(3 - x1)

y - 15,000 = (-2,000)(3 - x1)

y - 15,000 = (-6,000 + 2,000x1)

y = 2,000x1 - 6,000 + 15,000

y = 2,000x1 + 9,000

So the linear equation that represents the value of the car after x years is:

y - 15,000 = (-2,000)(x - 3)

Simplifying this equation gives:

y - 15,000 = -2,000x + 6,000

Now, we can use x = 8 to find the value of y:

y - 15,000 = -2,000(8) + 6,000

y - 15,000 = -2,000

y = $13,000

Therefore, the value of the car after 8 years will be $13,000.

So the completed expression is:

y - 15,000 = -2,000(x - 3)

The value of the car after 8 years will be $13,000.

Step-by-step explanation:

Answer:

[tex]t^{4}[/tex] + 8[tex]t^{2}[/tex] + 8t - 12

Hope this helps!

Step-by-step explanation:

[tex]t^{4}[/tex] - 1.5[tex]t^{2}[/tex] + t - 12 + 9.5[tex]t^{2}[/tex] + 7t : Combine like terms

[tex]t^{4}[/tex] + ( 9.5 - 1.5 )[tex]t^{2}[/tex] + ( 7t + t ) - 12

[tex]t^{4}[/tex] + 8[tex]t^{2}[/tex] + 8t - 12

Answer:

C ≈ 18.84 cm

Step-by-step explanation:

circumference = π · diameter

We can plug the given diameter into this formula, approximating π as 3.14.

C = 3.14 · 6 cm

C ≈ 18.84 cm

We know that,

[tex] \bf \leadsto Radius = Diameter / 2[/tex]

So,

[tex] \rightarrow \: \sf \: Radius = \frac{6}{3} \\ \\ \rightarrow \: \sf \: Radius = 3[/tex]

[tex] \rule{140pt}{5pt}[/tex]

Now,

[tex] \bf \bigstar \: Circumference \: of \: circle = 2πr[/tex]

[tex]→ \sf \: 2 × 3.14 × 3 \\ \\ → \sf \: 6 × 3.14[/tex]

[tex] \bf \: 18.84cm[/tex]

Option a is correct

[tex] \underline{ \rule{190pt}{6pt}}[/tex]

The change of base formula is:  log_b(x) = log_a(x) / log_a(b)

The term "change of base" refers to the process of converting a logarithm from one base to another. A logarithm is an exponent that indicates the power to which a base must be raised to obtain a given number. The most common logarithmic bases are 10, e (Euler's number), and 2, but logarithms can be taken to any base.

The change of base formula is a mathematical formula that allows you to convert logarithms from one base to another. It is useful when you need to calculate logarithms that cannot be easily evaluated on a calculator or when you need to work with logarithms in different bases.

The change of base formula is:

log_b(x) = log_a(x) / log_a(b)

Where:

log_b(x) is the logarithm of x to the base b

log_a(x) is the logarithm of x to the base a

log_a(b) is the logarithm of b to the base a

To use the change of base formula, you first need to identify the base of the logarithm that you want to convert and the base that you want to convert it to. Then, you can plug the values into the formula and simplify the expression.

For example, let's say you want to convert log_2(8) to base 10. Using the change of base formula, you can write:

log_2(8) = log_10(8) / log_10(2)

To evaluate this expression, you can use a calculator to find that:

log_10(8) = 0.9031

log_10(2) = 0.3010

Substituting these values into the formula gives:

log_2(8) = 0.9031 / 0.3010

Simplifying this expression gives:

log_2(8) = 3

Therefore, log_2(8) is equal to 3 when evaluated in base 10.

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The value of angle EFG is 151°.

What is angle?

An angle is a measure of the amount of rotation or turn between two lines, rays, or planes that meet at a common point called the vertex. The unit of measurement for angles is degrees or radians.

An angle is formed when two rays share a common endpoint, known as the vertex. The rays are often referred to as the arms or legs of the angle. The angle is measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified according to their size. An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, an obtuse angle measures more than 90 degrees but less than 180 degrees, and a straight angle measures exactly 180 degrees.

Angles can also be complementary or supplementary. Two angles are complementary if their sum is equal to 90 degrees, and they are supplementary if their sum is equal to 180 degrees.

Angles are used in many fields, including mathematics, physics, engineering, and architecture. They are used to measure distances, calculate trajectories, and design buildings and structures.

Here given,

[tex]\angle EFH = {44}^{o} [/tex] and

[tex] \angle \: HFG = {107}^{o} [/tex]

Here

[tex]\angle EFG = \angle EFH + \angle HFG \\ \angle EFG = {44}^{o} + {107}^{o} \\ = {151}^{o} [/tex]

So, required value of angle EFG is 151°.

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Answer:

Need to be more specific. What units?

Step-by-step explanation:

The rate of change (slope) for a linear relationship can be found by taking the difference in the y-values divided by the difference in the corresponding x-values.

In this case, the change in y from x=1 to x=9 is 32-8=24, and the change in x is 9-1=8. Therefore, the rate of change is:

rate of change = (change in y) / (change in x) = 24/8 = 3

So the answer is A. 3.

As x approaches positive infinity, f(x) approaches positive infinity.

In algebra, an absolute value function is a function where the variable is inside the bars denoting absolute values. The absolute value function is also known as the modulus function, and its most popular representation is f(x) = |x|, where x is a real number.

Here,

We have to find the end behavior of this absolute value function.

In the graph, it is shown that the absolute value function has a maximum of 3 at x = 3.

The function f(x) reaches positive infinity in both cases when x reaches either minimum or maximum value.

Hence, As x approaches positive infinity, f(x) approaches positive infinity.

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According to the given question the correct option  is (D) which is 84 and 6/7 square inches.

Surface area is indeed a measurement of how much overall space an object occupies. A three-dimensional shape's surface area is the sum of the area surrounding it. The term "surface area" refers to a three-dimensional shape's overall surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas from every face. As an alternative, you can name the dimensions of this box using the formula below: 2lh, 2lw, with 2hw make up the surface area (SA). Surface area is a unit used to describe how much space a three-dimensional form's surface takes up overall.

Given,

The formula: can be used to determine a cylinder's surface area.

surface area = 2πr^2 + 2πrh

where r is the cylinder's radius and h seems to be the cylinder's height.

In this case, the diameter of the mini muffins is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches. When these values are added toward the formula, we obtain:

surface area = 2π(1^2) + 2π(1)(5/4) = 2π + 5π/2 = 9π/2

To find the amount of paper needed to wrap 6 mini muffins, we multiply the surface area of one mini muffin by 6:

6 × (9π/2) = 27π

Approximating π as 22/7, we get:

27π ≈ 27 × 22/7 = 84 and 6/7

Therefore, the answer is (D) 84 and 6/7 square inches.

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PEQ has a value of y of 60°.

The Sum of Angles property states that the sum of a polygon's internal angles is equal to (n - 2) times 180 degrees, where n is the number of sides.The polygon's s.

What is angle sum property?

The angle sum property in geometry asserts that the sum of a polygon's internal angles is equal to (n - 2) times 180 degrees, where n is the number of sides of the polygon.

In a triangle (n=3), for example, the total of the interior angles is (3 - 2) 180 = 1 180 = 180 degrees.

The sum of internal angles for a quadrilateral (n=4) equals (4 - 2) 180 = 2 180 = 360 degrees.

This is a fundamental geometric idea that can be used to calculate the value of an unknown interior angle in a polygon if the other interior angles are known. It can also be used to determine whether or not a given set of angles can create a valid polygon.

In PEQ, the angle sum attribute is used.

Hence, EPQ + EQP + PEQ = 180°

40° + 80° + y = 180°

120° + y = 180°

y = 180° - 120°

y = 60°

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The probability that all of the customers will give him a tip is 3/100 or 0.03 or 3%.

Based on the table presented, Steve simulated the situation by rolling a six-sided die 5 times. Each time an odd number appears, it represents a tip. This table shows the results of 100 trials: number of times an odd number appears 0 1 2 3 4 5 number of trials 2 15 33 31 16 3.

The customer leaves a tip 50% of the time, we can calculate the probability by multiplying the probability of a single tip (0.5) by itself 5 times.

Probability = (0.5) * (0.5) * (0.5) * (0.5) * (0.5)

Probability = 0.03125

From the table presented, it can be concluded that Steve got all of the five customers tipping him in 3 trials. Therefore, the probability that all of the customers will give him a tip is 3/100 or 0.03 or 3%.

The probability that an event will occur is the ratio of the number of ways that the event can occur to the number of total possible outcomes. In this scenario, the probability of a customer giving Steve a tip is 0.5.

Since the customer either gives a tip or doesn't.

In other words, there are two possible outcomes (gives a tip or doesn't give a tip) and only one outcome results in a tip (gives a tip).

Therefore, the probability of getting a tip from one customer is 1/2 or 0.5.

Since there are five customers, the probability of all five customers giving Steve a tip is calculated by multiplying the probability of each customer giving a tip.

This is because the occurrence of each event is independent of the others.

Therefore, the probability of all five customers giving Steve a tip is:

0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.03125 or 3.125%.

From the table presented, it can be concluded that Steve got all of the five customers tipping him in 3 trials.

Therefore, the probability that all of the customers will give him a tip is 3/100 or 0.03 or 3%.

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Using the bar graph we can conclude that it rained 0.5 inches more in the summer of 2010 than in 2009.

Using rectangular bars that are proportional to the values they represent; a bar graph displays all the data. The graph's bars can be displayed either vertically or horizontally. Bar graphs, commonly referred to as bar charts, are a visual depiction of groups of data. It is one method of processing data. A bar graph is a great tool for representing data that are unrelated to one another and do not need to be displayed in any particular sequence. The bars provide a visual representation for comparing amounts in several categories. Together with the title, labels, and scale range, bar graphs have two axes that are horizontal and vertical and are also known as the x and y axes.

Here in the question,

We can see that in the summer of 2009 the rain was for 1.5 inches.

In the summer of 2010, the rain was for 2 inches.

Hence, the difference between the number of inches it rained=

2 - 1.5

= 0.5 inches.

Therefore, using the bar graph we can conclude that it rained 0.5 inches more in the summer of 2010 than in 2009.

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The length of the missing leg for the right triangle is 16 yd using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

Pythagoras rule we can evaluate for b as follows:

65² = 63² + b²

b = √(65² - 63²) {make b the subject}

b = √(4225 - 3969)

b = √256

b = 16

Therefore, the length of the missing leg for the right triangle is 16 yd using the Pythagoras rule.

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