Show that " if x and y are odd integers, then x+y is even" using an indirect proof ( a proof by contraposition)

Answer:

50 in

Step-by-step explanation:

Split into 4 shapes. One on each side with 5 in x 2 in, one on the top with 12 in x 2 in, and one in the middle with 3 in x 2 in. We add all together:

2(5×2)+(12×2)+(3×2) = 50 in

#9 75% of 1.

#10 50% of 350.

#11

To find out what percent of 450 is 50, we can set up a proportion

x/100 = 50/450

Simplifying the right-hand side of the equation by dividing both numerator and denominator by 50 gives

x/100 = 1/9

Multiplying both sides by 100 gives

x = 100/9

Hence, 50 is approximately 11.1% of 450.

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The probability of the odds of the rugby team winning its next match is

12 to 11.

We have,

The probability of an event happening is defined as the ratio of the number of favorable outcomes to the total number of outcomes.

The odds against an event happening are defined as the ratio of the number of unfavorable outcomes to the number of favorable outcomes.

If the probability of the rugby team winning its next match is 11/23, then the probability of the team losing its next match is:

= 1 - 11/23

= 12/23.

The odds against the rugby team winning its next match are the ratio of the number of unfavorable outcomes (losing the match) to the number of favorable outcomes (winning the match), which is:

12/23 : 11/23

We can simplify this ratio by dividing both the numerator and denominator by 11:

(12/23) ÷ (11/23) : (11/23) ÷ (11/23)

Simplifying.

12/11 : 1/1

Therefore,

The probability of the odds of the rugby team winning its next match is

12 to 11.

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The output value of h(-7) in the function h(x) = 2x² - 7x + 4 is 151.

A function is simply a relationship that maps one input to one output.

Given the function in the question

h(x) = 2x² - 7x + 4,

Find h(-7)

To find h(-7), we substitute -7 for x in the equation of h(x) and simplify:

h(x) = 2x² - 7x + 4

Plug in x = -7

h(-7) = 2(-7)² - 7(-7) + 4

h(-7) = 2(49) + 49 + 4

h(-7) = 98 + 49 + 4

h(-7) = 151

Therefore,the output value of h(-7) is equal to 151.

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Answer:

  C  86

Step-by-step explanation:

You want the measure of the angle marked x° where chords cross. The angle marked x° intercepts an arc of 104° and one that is unmarked. The remaining arcs of the circle are marked 111° and 77°.

The measure of angle x is half the sum of the arcs it intercepts. One of those is given as 104°. The other will be ...

  360° -111° -104° -77° = 68°

Then the value of x is ...

  (104 +68)/2 = 172/2 = 86

The value of x is 86, choice C.

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Answer:

Yes, Melanie's statement that the basketball season starts in 15 weeks is reasonable.

To see why, we can estimate the number of days in 15 weeks. Since 1 week is equal to 7 days, 15 weeks would be approximately equal to:

15 weeks x 7 days/week = 105 days

g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}. And the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.

How to solve the problem?

(i) To determine the range of a function, we need to find all the possible output values of the function. In other words, we need to find the set of all second elements in the ordered pairs of the function. For the function f, the set of all second elements is {3, 5, 1, 2}. For the function g, the set of all second elements is {4, 1, 2, 3}. Therefore, the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.

(ii) To find the composition functions f ∘ g and g ∘ f, we need to apply the functions in the correct order. The composition function f ∘ g means that we first apply g and then apply f to the result. The composition function g ∘ f means that we first apply f and then apply g to the result.

For f ∘ g:

First, we apply g to the domain of f.

(1,3) is mapped to (4,2) by g

(2,5) is mapped to (1,4) by g

(3,3) is mapped to (1,4) by g

(4,1) is mapped to (2,1) by g

(5,2) is mapped to (3,1) by g

Now we apply f to the result of g.

(4,2) is mapped to 2 by f

(1,4) is mapped to 4 by f

Therefore, f ∘ g is the function {(1,4), (4,2)}.

For g ∘ f:

First, we apply f to the domain of g.

(1,4) is mapped to 3 by f

(2,1) is mapped to 5 by f

(3,1) is mapped to 3 by f

(4,2) is mapped to 1 by f

(5,3) is mapped to 2 by f

Now we apply g to the result of f.

3 is mapped to (1,2) by g

5 is mapped to (2,1) by g

1 is mapped to (4,2) by g

2 is mapped to (5,3) by g

Therefore, g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}.

Note that the composition functions f ∘ g and g ∘ f are not the same. In general, composition of functions is not commutative, i.e., f ∘ g is not equal to g ∘ f.

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The three (3) true statements about the quadratic function and its graph include the following:

A. The value of f(–10) = 82

B. The graph of the function is a parabola.

D. The graph contains the point (20, –8).

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.

Next, we would determine the other true statements about the graph of this quadratic function:

At point (-10, 82), we have:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(-10) = -10²/5 – 5(-10) + 12

Quadratic function, f(-10) = 82

At point (20, -8), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(20) = 20²/5 – 5(20) + 12

Quadratic function, f(20) = -8

In conclusion, we can logically deduce that the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.

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The strategy that could be used to eliminate a variable is:

Multiply the first equation by 2 and multiply the second equation by 5. Then, add the resulting equations

From the question, we are to determine a strategy that could be used to eliminate a variable in the given system of equations

From the given information,

The system of linear equations is

5x + 3y = 4

-2x - 8y = 6

To eliminate the variable x, we can multiply the first equation by 2 and then multiply the second equation by 5. After that, we will add the resulting equations

2 × [ 5x + 3y = 4

5 × [-2x - 8y = 6

10x + 6y = 8

-10x - 40y = 30

Add the resulting equations

   10x + 6y = 8

+ (-10x - 40y = 30

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

-34y = 38

This way we have eliminated x

Hence,

The above strategy can be used to eliminate a variable

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Answer:

V = 5747.02 ft^3

Step-by-step explanation:

Therefore, to solve for volume, we plug in 14 for r in the general formula:

[tex]V=2/3\pi (14)^3\\V=2/3\pi (14)(14)(14)\\V=2/3\pi *2744\\V=5747.020161\\V=5747.02[/tex]

Lastly, volume is always in units cubed (e.g., ft^3 or mi^3 since volume deals with the three-dimensional space of an object

• It captures the overall trends and patterns in the data points. It does not necessarily pass through every single data point but approximates the shape and trajectory of the data.

• It has parameters that can be adjusted to optimize how well the model fits the data. Things like coefficients, exponents, intercepts, etc. The good parameter values will depend on the specific data set and model.

• It has an appropriate level of complexity for the data. It does not overfit or underfit the data. An overfit model captures every detail and noise, while an underfit model fails to capture the key dynamics.

• Key features like slope, curvature, periodicity, thresholds, etc. in the data are properly represented in the model.

• It provides insights or useful information, not just a mathematical abstraction of the data. A good model opens the black box and provides interpretable knowledge about the system or phenomenon that generated the data.

• Predictions or extrapolations from the model align well with any additional data points beyond the original data set. The model generalizes purposefully.

• There are objective metrics that can evaluate how good a particular model is for a data set, like R2, mean absolute error, Akaike information criterion, etc. The best model will optimize such metrics.

Thus, the range of the set of five numbers (a,b,c,d,e) is found as : 40.

The difference in between highest and lowest numbers in a piece of data is known as the range. To locate it, sort the data first from least to greatest. Then take the difference between the least and largest number in the set.

The range is a straightforward assessment of the variation in values within a dataset. Simply take the difference between the two values, ignoring the others, to determine the range.

Let the 5 numbers be:  (a,b,c,d,e)

a < b < c < d < e

Mean = sum of all observation / total number of observations

Equation for the mean except the largest number.

(a+b+c+d)/4 = 80

Now, Equation for the mean except the smallest number.

(b+c+d+e)/4 = 90

On simplifying each:

a + b + c + d = 320   ...eq 1

b + c + d + e = 360   ..eq 2

Range = max - min

Subtract eq 1 from eq 2

e - a = 40

Thus, the range of the set of five numbers (a,b,c,d,e) is found as : 40.

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meAnswer: me

Step-by-step explanation: I need help

As the tree is 4/5 meters tall the unit rate in meters per year is 8/45 or approximately 0.177 meters per year.

To find the unit rate in meters per year, we need to divide the height of the tree by the time it took to grow.

Height of the tree = 4/5 meters

Time taken to grow = 4 1/2 years = 9/2 years

Unit rate = Height/Time = (4/5)/(9/2) meters per year

To divide by a fraction, we can multiply by its reciprocal:

Unit rate = (4/5) * (2/9) meters per year

Unit rate = 8/45 meters per year

Therefore, the unit rate of the tree in meters per year is 8/45 or approximately 0.177 meters per year.

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To find the coterminal angle for a rotation of -757°, we can add or subtract multiples of 360° until we find an angle between 0° and 360° that is coterminal with -757°.

Adding 360° multiple times:

-757° + 360° = -397° (not coterminal)

-397° + 360° = -37° (not coterminal)

-37° + 360° = 323°

Therefore, the coterminal angle for -757° is 323°.

To find the quadrant in which 323° lies, we can note that 323° is between 270° and 360°, which means it lies in the fourth quadrant.

To find the reference angle for 323°, we can subtract 360° from 323° until we get an angle between 0° and 90°:

323° - 360° = -37° (not in the correct range)

-37° + 360° = 323°

So the reference angle for 323° is 37°.

The probability of selecting a mystery book, then without replacing it, selecting a nonfiction book is approximately 0.1462.

On the bookcase, there are 24 + 12 + 4 = 40 volumes.

The odds of picking a mystery book on the first draw are 24/40.

There are 39 books remaining after the first is drawn, including 12 nonfiction works. Because the initial book was never replaced, there are currently only 11 nonfiction volumes left.

Given that a mystery book was chosen without replacement in the first draw, the probability of selecting a nonfiction book in the second draw is 12/39.

When we multiply these probability together, we get:

P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = (24/40) * (12/39) = 0.14615...

P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = 0.1462

So, the probability of selecting a mystery book, followed by a nonfiction book without replacing it is roughly 0.1462.

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[tex]\textit{Double Angle Identities} \\\\ \cos(2\theta)= \begin{cases} \cos^2(\theta)-\sin^2(\theta)\\ 1-2\sin^2(\theta)&\leftarrow \textit{we'll use this one}\\ 2\cos^2(\theta)-1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 1-2\sin^2(\theta)\implies 1-2\left( \cfrac{15}{17} \right)^2\implies 1-2\left( \cfrac{225}{289} \right) \\\\\\ 1-\cfrac{450}{289}\implies \cfrac{289-450}{289}\implies -\cfrac{161}{289}[/tex]

The total length of the sandwich, given the addition to the sandwich, would be 10. 17 feet.

In order to accurately add lengths measured in feet and inches, it is necessary to transform the unit type prior to adding them together. As an example, take a sandwich that originally measured 6 feet 6 inches long with 3 feet 8 inches being added into it.

To combine these measurements, we must first convert inches to feet or vice versa for optimal results. Let's begin with transforming the inches to feet:

6 feet 6 inches = 6 + ( 6 / 12 ) feet = 6. 5 feet

3 feet 8 inches = 3 + ( 8 / 12 ) feet = 3. 67 feet

Then add the lengths to become :

6. 5 feet + 3. 67 feet = 10. 17 feet

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For the second number 2 3/4 you will find the 2 points, to the right from 0. Now count three small points to the left to get the 3/4 part

To locate the value of -1 1/2 on the number line, first locate the point denoting -1 to the left of 0. Progressing to the second minor point on the right immediately after -1 will indicate this position.

For the second figure of 2 3/4, identify the point at 2 by moving to the right from 0. An additional count of three minor points towards the left reveals where the fraction of 3/4 is located. The exact spot is depicted here.

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a) No , it is not a dilation

b) The coordinates are R'(-2, 2), S'(2, 2), and T'(0, -6)

c) Shanequa's mistake is that she incorrectly applied the dilation transformation

Given data ,

a)

In ARST, the coordinates of the original triangle are given by R(-2, 1), S(2, 1), and T(0, -3), and in AR'S'T', the coordinates are R'(-2, 2), S'(2, 2), and T'(0, -6)

So , the dilated triangle is R'(-2, 2), S'(2, 2), and T'(0, -6)

b)

The coordinates for AR'S'T' can be calculated by multiplying the original coordinates of ARST by the scale factor of 2, centered at the origin.

R'(-4, 2), S'(4, 2), and T'(0, -6)

c)

The dilation transformation was applied wrongly by Shanequa. The coordinates of the original points in a dilation centred at the origin with a scale factor of two should be multiplied by the scale factor to obtain the coordinates of the dilated points.

Hence , the dilation is solved

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The amount of money borrowed by the company from the rural bank is:

P = [tex]A(1 + in)^{-1}[/tex]

What is Amount?

Amount is a term used to describe the total quantity or value of something. It can refer to a quantity of a physical substance or object, such as the amount of water in a bottle or the amount of money in a bank account.

Let P be the amount of money borrowed by Winnie and Vanessa Co Ltd from the rural bank at an interest rate of i% per annum.

The simple interest on this amount after n years will be:

I = P * i * n

The total amount to be paid by the company after n years will be:

A = P + I = P + P * i * n

We can simplify this expression by factoring out P:

A = P(1 + i * n)

Dividing both sides of this equation by (1 + i * n), we get:

P = A / (1 + i * n)

Therefore, the amount of money borrowed by the company from the rural bank is:

P = [tex]A(1 + in)^{-1}[/tex]

This is the desired result.

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Answer:

Step-by-step explanation:

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartR…

✓ Answer:8(x2 + 2x) = –3 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRootStep-by-step explanation:S…

Okay, here are the steps to solve this system of linear equations:

3x1 + x2 + 2x3= 6

4x1 - 3x2 + 5x3 = 8,

2x1 + x2 + 3x3 = 10

1) Add 4 times the first equation to the second equation:

7x1 + 2x2 + 7x3 = 22

2) Add -2 times the first equation to the third equation:

5x1 - x2 + 5x3 = 12

3) Divide both sides by 5 to get:

x1 = 2

x2 = -2

x3 = 1

Therefore, the solution to the system is:

x1 = 2

x2 = -2

x3 = 1

Let me know if you have any other questions!

The total interest that will accrue on the principal amount of $44,000 over a period of 2 years at a simple interest rate of 6% is $5,280.

The given problem involves calculating the amount of interest that will accrue on a principal amount of $44,000, which is invested at a simple interest rate of 6% for a period of 2 years.

To solve the problem, we can use the formula for simple interest, which is:

Interest = Principal x Rate x Time

In this case, the principal amount is $44,000, the rate of interest is 6%, and the time period is 2 years. So, plugging in these values, we get:

Interest = $44,000 x 0.06 x 2

Interest = $5,280

Unlike compound interest, simple interest is calculated only on the principal amount, and not on the accumulated interest. This means that the interest earned each year remains constant, which can make it easier to calculate and understand compared to compound interest.

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The 95% confidence interval of the mean body temperature of adults in the town is (97.584, 98.876)°F (open-interval notation), accurate to 3 decimal places.

To find the 95% confidence interval (C.I.) of the mean body temperature, we need to use the formula:

C.I. = x ± z*(σ/√n)

Where:

x is the sample mean

σ is the population standard deviation (unknown, but we can estimate it using the sample standard deviation)

n is the sample size

z is the critical value for the desired confidence level (95% in this case)

First, we need to calculate the sample mean, sample standard deviation, and sample size:

x = (98 + 97.9 + 99 + 97.3 + 98.9 + 99.6 + 97.8 + 99.8 + 99.1 + 98.4 + 98.7 + 97.6 + 96.5) / 13 = 98.23

s = √((1/(n-1)) * Σ(xi - x)²)

s = 1.339

n = 13

Next, we need to find the critical value, z, for a 95% confidence level. We can look this up in a standard normal distribution table or use a calculator. For a 95% confidence level, z = 1.96.

Now we can plug in the values into the formula to get the 95% confidence interval:

C.I. = 98.23 ± 1.96*(1.339/√13) = (97.584, 98.876)

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The percentage of buyers who paid between $150,000 and $156,000 if the standard deviation is $2000 is 49.9%

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

Mean = 150000

Standard deviation = 2000

Scores = from $150,000 and $156,000

So, we have

z = (150000 - 150000)/2000 = 0

z = (156000 - 150000)/2000 = 3

This means that it is between a z-score of 0 and a z-score of 3

This is represented as

Probability = (0 < z < 3)

Using a graphing calculator, we have

Probability =  0.49865

Express as percentage

Probability =  49.9%

Hence, the probability is 49.9%

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