In a scatter plot, if all data points were aligned along a 45° angle, your correlation would be:
A) Of medium strength
B) Of weak strength
C) Perfect
D) 0
E) None of the above

The required equation is y = 200 - (0.025)t

Hence option C is correct.

According to the given information:

The soil's water content is dropping by 2.5% weekly.

And here, Begin with the 200 gram of water that were initially present in the soil sample on July 1.

Then deduct the weekly water loss,

Which is determined by multiplying the original water amount by 25%  and the number of weeks (t).

Now forming the equation,

⇒ y = 200 - (2.5/100)t

⇒ y = 200 - (0.025)t

Hence, the expression be,

y = 200 - (0.025)t

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The perimeter of the regular nonagon is approximately 29.7 feet.

The apothem of a regular nonagon divides each of its interior angles into two congruent angles.

Therefore, each of the interior angles of the nonagon measures:

(180 - 360/9)/2 = 140 degrees

The sum of the interior angles of a nonagon is (9-2) * 180 = 1260 degrees. Therefore, the measure of each exterior angle of the nonagon is:

360/9 = 40 degrees

In a regular nonagon, all the sides and angles are congruent, so we can divide it into 9 congruent isosceles triangles. Each of these triangles has base s and height a, and its legs are given by:

l =√s² - (a/2)²

The perimeter P of the nonagon is given by:

P = 9s

Substituting the values of s and a, we get:

l = √3.3²- (1.65/2)²

= 3.018 ft (rounded to 3 decimal places)

P = 9(3.3) = 29.7 ft

Therefore, the perimeter of the regular nonagon is approximately 29.7 feet.

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The relative speed between the jogger and the walker during the 500 second interval is 2.24 m/s.

To solve this problem, we need to first find the distances traveled by each person.

The jogger travels 10 blocks x 100 meters/block = 1000 meters south.

The walker travels 5 blocks x 100 meters/block = 500 meters west.

Using the Pythagorean theorem, we can find the distance between them: √((1000m)² + (500m)²) = 1118.03 meters.

To find their relative speed, we divide this distance by the time interval: 1118.03 meters / 500 seconds = 2.24 m/s.

Therefore, their speed relative to each other during this interval is 2.24 m/s.

The jogger traveled 1000 meters south, while the walker traveled 500 meters west. Using the Pythagorean theorem, the distance between them is 1118.03 meters. Dividing this distance by the time interval of 500 seconds, we get their relative speed, which is 2.24 m/s.

: The relative speed between the jogger and the walker during the 500 second interval is 2.24 m/s.

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To find the equation in slope-intercept form, y = mx + b, we need to first find the slope using
    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

In this case we have the two points (1,2) and (4,4), so our calculation looks like:

    [tex]m=\dfrac{4-2}{4-1} = \dfrac{2}{3}[/tex]
Notice this is the same "rise over run" that we can count out on the graph.  If we start at (1,2) and go "up 2 units, right 3 units", then we end up at the point (4,4).

Now we need to find b.  We have [tex]y = \frac{2}{3}x+b[/tex], so we need to substitute in one of the points to find b.  Let's use (1,2):

           [tex]2 = \frac{2}{3}\cdot 1+b[/tex]

           [tex]2 = \frac{2}{3}+b[/tex]

    [tex]2 - \frac{2}{3} =b[/tex]

           [tex]\frac{4}{3} =b[/tex]

This gives us our equation: [tex]y = \frac{2}{3}x+\frac{4}{3}[/tex]

Using the ASA Triangle Congruence Theorem, we can prove that triangles GHJ and PQR are congruent because they have Angle G and angle P are congruent, both being right angles.

The two triangles are congruent by rigid motions.

Using the ASA Triangle Congruence Theorem, we can prove that triangles GHJ and PQR are congruent because they have:

Angle G and angle P are congruent, both being right angles.

Side GH and side PQ are congruent, both having a length of 5 units.

Angle H and angle Q are congruent, both having a measure of 63.43 degrees (rounded to two decimal places).

Since the two triangles have two congruent angles and a congruent side between them, they are congruent by the ASA Triangle Congruence Theorem.

b. We can also prove that triangles GHJ and PQR are congruent using rigid motions.

Specifically, we can use a translation followed by a reflection to map triangle GHJ onto triangle PQR.

Translation: We can translate triangle GHJ 2 units to the left and 3 units down to get triangle G'H'J', where G'(-2, 1), H'(-2, -2), and J'(2, -2).

Reflection: We can reflect triangle G'H'J' across the x-axis to get triangle PQR, where P(-2, -4), Q(-2, -1), and R(2, -1).

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The temperature of the water after 4.5 minutes is approximately 153°F.

Using Newton's Law of Cooling to find the value of the decay constant k: T = [tex]Ta + (T0 - Ta) * e^-k*t[/tex]

Substituting the given values, we get:

185 = [tex]69 + (203 - 69) * e^-k*1.5[/tex]

Simplifying, we get:

[tex]116 = 134 * e^ \\^{-1.5k}[/tex]

Dividing both sides by 134, we get:

[tex]0.8657 = e^{-1.5k}[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.8657) = -1.5k

Solving for k, we get:

k ≈ 0.232

Therefore, the value of the decay constant is approximately 0.232.

To find the temperature of the water after 4.5 minutes, we can use Newton's Law of Cooling again, with t = 4.5:

[tex]T = Ta + (T0 - Ta) * e^-k*t[/tex]

[tex]T = 69 + (203 - 69) * e^-0.232*4.5[/tex]

T ≈ 153°F

Therefore, the temperature of the water after 4.5 minutes is approximately 153°F.

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The correct statement is:
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

I understand that you are asking about the behavior of the function g(z) as x approaches positive and negative infinity. Let's analyze the given function:
g(z) = 4x³ - 3r + 2r³ - 1
First, I believe "r" should be "x" to keep the variables consistent. So, the corrected function is:
g(x) = 4x³ - 3x + 2x³ - 1
Now, let's find the end behavior of this function as x approaches positive and negative infinity.
As x → ∞:
The highest degree term, x³, will dominate the function's behavior. The coefficients for x³ are 4 and 2, so the function will behave like 6x³. Since this term is positive and has an odd exponent, as x → ∞, f(x) → ∞.
As x → -∞:
Again, the x³ term will dominate the function's behavior. Since the exponent is odd, as x → -∞, f(x) → -∞.
So, the correct statement is:
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

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The values of x, y and z in the parallelogram 1 are x = 80, y = 100 and z = 80

Parallelogram 1

Adjacent angles of a parallelogram add up to 180

So, we have

x = 180 - 100

x = 80

Opposite angles are equal

So, we have

y = 100

z = 80

Using the above theorem, we have the values of x, y and z in the other parallelograms to be

Parallelogram 2

x = 180 - 50

x = 130

y = 130

z = 130 --- by corresponding angle theorem

Parallelogram 3

x = 90 --- by vertical angle theorem

Then, we have

y = 60 --- sum of angles in a triangle

z = 60 --- by corresponding angle theorem

Parallelogram 4

x = 100

y = 80

z = 80 --- by corresponding angle theorem

Parallelogram 5

y = 112

x = 180 - 112 - 40 --- sum of angles in a triangle

x = 28

z = 28  --- by corresponding angle theorem

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Answer:

buying price = $11764.70

Step-by-step explanation:

selling price = $10000

loss = 15%

85% = 10000

100% = 10000/85 × 100

= $ 11764.70

The solution of expression after divide is, 70.83333...

We have to give that,

Divide 425 by 6.

Now, Divide the numbers as,

425 ÷ 6

6 ) 425 ( 70.833

   - 42

  --------

        050

         - 48

       -----------

               20

             - 18

             --------

                 20

               - 18

             ----------

                    2

Hence, The solution of expression after divide is, 70.83333...

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Answer:

46°

Step-by-step explanation:

180-136= 44

x = 180 -90-44

x = 46

Answer:

For 1 is it 1 hour and 15 mins?

Step-by-step explanation:

6 by 32 = 30 mins

12 by 32 = 1 hr

13 by 32 = 15

1hr + 15 mins = 1hr 15 mins

Sorry if incorrect

In order to plot points H I and J on the coordinate planeIdentify the x-coordinate and y-coordinate of each point (H, I, and J). For example, let's say the coordinates are as follows:

Point H: (xH, yH)

Point I: (xI, yI)

Point J: (xJ, yJ)

Locate the origin (0, 0) on the coordinate plane. This is the starting point for plotting any point.

Move along the x-axis according to the x-coordinate of each point. If the x-coordinate is positive, move to the right; if it's negative, move to the left. Mark a point on the x-axis at the appropriate location.

Move along the y-axis according to the y-coordinate of each point. If the y-coordinate is positive, move upward; if it's negative, move downward. Mark a point on the y-axis at the appropriate location.

The point where the x and y axes intersect is the location of the point. Mark that point on the coordinate plane.

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How to Plot points H I and J on the coordinate plane

Answer:

-6

Step-by-step explanation:

4k-6=2k-16-2

-16-2= -18

4k-6=2k-18

+6= +6 from both sides

4k=2k-12

-2k = -2k from both sides

2k = -12

/2 /2

k= -6

The construction being demonstrated is constructing a perpendicular bisector.

In this construction, a line is drawn to bisect a given line segment and is perpendicular to that line segment. The perpendicular bisector divides the line segment into two equal parts and creates a right angle at the point of intersection. It is useful in various geometric constructions and applications, such as finding the midpoint of a line segment or constructing equilateral triangles. By constructing a perpendicular bisector, we ensure that the distances from any point on the line to the endpoints of the line segment are equal.

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Therefore, the probability that Smith wins 8 dollars before losing all of his money is approximately 0.0479.

To solve this problem, we can use a probability tree diagram to visualize the different possible outcomes.

At each stage, Smith either wins a dollars or loses a dollars, until he either reaches 8 dollars (and wins) or 0 dollars (and loses). We can calculate the probability of each outcome by multiplying the probabilities of the branches leading to that outcome.

Starting with 3 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 4 dollars.

Smith loses a dollar with probability 0.6, leaving him with 2 dollars.

From 4 dollars, there are three possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 5 dollars.

Smith loses a dollar with probability 0.6, leaving him with 3 dollars.

Smith wins 4 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 7 dollars.

From 5 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 6 dollars.

Smith wins 3 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

From 6 dollars, there are two possible outcomes:

Smith wins 2 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

Smith loses a dollar with probability 0.6, leaving him with 5 dollars.

From 7 dollars, there is one possible outcome:

Smith wins 1 dollar with probability 0.4, leaving him with 8 dollars.

Therefore, the probability that Smith wins 8 dollars before losing all of his money is the sum of the probabilities of the outcomes that lead to winning 8 dollars, which is:

0.4 * 0.6 * 0.4 * 0.4 + 0.4 * 0.6 * 0.4 * 0.6 * 0.4 + 0.4 * 0.6 * 0.4 * 0.4 * 0.6 * 0.16 + 0.4 * 0.6 * 0.4 * 0.4 * 0.4 * 0.4 * 0.16 = 0.047872

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If a person owns 2/3 of a land and sells 1/4 of it, the fraction of the whole land sold can be expressed as 1/4 divided by 2/3.

To divide fractions, we invert the second fraction and multiply. Therefore, we have:

1/4 ÷ 2/3 = 1/4 × 3/2 = 3/8

So, the fraction of the whole land sold is 3/8. This means that the person has 2/3 - 3/8 = 5/24 of the original land remaining after selling 1/4 of it.

To see why this is the case, we can visualize the original land as a pie chart. If the person owns 2/3 of the land, then 1/3 of the land belongs to someone else. If the person sells 1/4 of their share, they are effectively selling 1/4 of 2/3 of the land, or 2/12 of the land. This represents a portion of the pie chart that is 2/12 of the total pie, or 1/6. Therefore, the person now owns 5/6 of the pie chart, or 5/24 of the original land.

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Answer:Therefore, the solutions to the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0 are x = 0, x = 1, x = 5.

Step-by-step explanation:

To solve the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0, we can use factoring by grouping.

First, we can group the first two and last two terms:

x^4 - 5x^3 + 7x^2 - 5x + 6 = (x^4 - 5x^3) + (7x^2 - 5x + 6)

Next, we can factor out x^3 from the first group and factor out 1 from the second group:

(x^3(x - 5)) + (7x^2 - 5x + 6)

Now, we can group the last two terms of the second group:

x^3(x - 5) + (7x^2 - 3x - 2x + 6)

Then, we can factor out 1 from the terms inside the parentheses and group them:

x^3(x - 5) + (7x^2 - 3x) + (-2x + 6)

Now, we can factor out x from the second and third groups:

x^3(x - 5) + x(7x - 3) - 2( x - 3)

We can simplify the third group by distributing the negative sign:

x^3(x - 5) + x(7x - 3) - 2x + 6

Finally, we can combine the second and third groups:

x^3(x - 5) + x(7x - 5) + 6

So, the factored form of the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0 is:

(x^3(x - 5) + x(7x - 5) + 6) = 0

This equation can be solved by setting each factor equal to zero and solving for x:

x^3(x - 5) + x(7x - 5) + 6 = 0

(x^3 - 7x^2 + 5x) + (6 - 5x) = 0

x(x^2 - 7x + 5) - (5x - 6) = 0

x(x - 5)(x - 1) - (5x - 6) = 0

x(x - 5)(x - 1) = 5x - 6

x^3 - 6x^2 + 10x - 6 = 5x - 6

x^3 - 6x^2 + 5x = 0

x(x^2 - 6x + 5) = 0

x(x - 1)(x - 5) = 0

Therefore, the solutions to the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0 are x = 0, x = 1, x = 5.

According to the survey, 40% of customers visit late on weekdays and 60% visit late on weekends. Therefore, out of 9,000 customers, we can expect 60% of them to visit late on weekends.

To find out the exact number, we can use the following calculation:

60% of 9,000 = (60/100) x 9,000 = 5,400

Therefore, the manager can expect around 5,400 customers to visit late on weekends out of a total of 9,000 customers.

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The length of AC by the given data is about 11.0 cm.

We are given that;

ABCD is a trapezium AB=16cm, AD=11cm, BC=4cm

Now,

We can use these values to find DC. Since ABCD is a trapezium, we know that AB and DC are parallel. Therefore, the distance between them is constant. We can write:

AB−BC=AD−DC

Plugging in the given values, we get:

16−4=11−DC

Solving for DC, we get:

DC=11−12=−1

We can ignore the negative sign since we are only interested in the length of DC. So, DC = 1 cm.

Now we can plug in AD = 11 cm and DC = 1 cm into the Pythagorean theorem and get:

AC2=112+12

AC2=122

Taking the square root of both sides, we get:

AC=122​≈11.045

Rounding to one decimal place, we get:

AC≈11.0 cm

Therefore, by algebra the answer will be 11.0 cm.

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By definition of volume of sphere, The volume of the basketball is,

V = 3052.08 inches³

We have to given that;

The radius of a basketball is 9 inches.

Since, We know that;

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

And,  We know that;

Volume of sphere = 4/3πr³

Where, r is radius of sphere.

And, pi is stand for 3.14.

Hence, We get;

The volume of the basketball is,

⇒ V = = 4/3πr³

Substitute radius (r) = 9 inches, pi = 3.14 in above equation, we get;

⇒ V = 4/3 × 3.14 × 9³ inches³

⇒ V = 4/3 × 3.14 × 243 inches³

⇒ V = 3052.08 inches³

Therefore, The volume of the basketball is,

⇒ V = 3052.08 inches³

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The missing length indicated has the value given as follows:

x = 25.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases in this problem are given as follows:

x and 144.

The length of the altitude segment is given as follows:

60.

60 is the geometric mean of x and 144, hence the value of x is obtained as follows:

144x = 60²

x = 3600/144

x = 25.

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The function operation g(f(8) in the given functions f(x) = 3x+2 and g(x) = √(x-1) is 5.

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

Given that:

First, set up the composite result function:

Evaluate g( 3x + 2 ) by substituting in the value of f into g.

g( 3x + 2 ) = √( ( 3x + 2 ) - 1 )

Simplify

g( 3x + 2 ) = √( 3x + 2 - 1 )

g( 3x + 2 ) = √( 3x + 1 )

Evaluate the result function by replacing the x with 8.

g( f(x) ) = √( 3(8) + 1 )

g( f(x) ) = √( 24 + 1 )

g( f(x) ) = √( 25 )

g( f(x) ) = 5

Therefore, the composite result function g( f(x) ) is 5.

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Answer:

If x < -12, then (-x) > 12, and we have:

x - (-12) = x + 12

So, the simplified expression without using the absolute value symbol is:

x + 12

Step-by-step explanation:

Answer:

Since x is less than -12, then x-(-12) = x+12.

Here is a table of values for x and x-(-12):

x | x-(-12)

-13 | -1

-14 | -2

-15 | -3

...

Step-by-step explanation:

The equation to find the number of minutes m is 12000 - 100m = 4000

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

Initial volume  = 12000 gallons

Rate of draining = 100 gallons per minute

Final volume of water = 4000 gallons

The equation to find the number of minutes m is represented as

f(m) = Initial volume - Rate of draining * m

So, we have

f(m) = 12000 - 100m

When the volume is at 4000 gallons, we have

12000 - 100m = 4000

Hence, the equation to find the number of minutes m is 12000 - 100m = 4000

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The mean expenses of the XYZ Corporation is 9,811.22.

To compute for the mean expenses of the XYZ Corporation, we need to add up all the total expenses of each city and divide it by the total number of cities.

Total Expenses = 4,933.50 + 6,035.70 + 12,276.00 + 6,237.00 + 14,850.00 + 7,590.00 + 7,260.00 + 6,930.00 + 21,780.00 + 11,220.00
Total Expenses = 98,112.20

Number of Cities = 10

Mean Expenses = Total Expenses / Number of Cities
Mean Expenses = 98,112.20 / 10
Mean Expenses = 9,811.22

The mean expenses of the XYZ Corporation is 9,811.22. Since the answer does not require decimals, we do not need to express it in two decimal places. However, we need to follow the reminder that if the answer is more than three digits, we should not include the comma.

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The value of the excretion is equal to 15 / 16 inches of precipitation per hour.

In this question we find that a precipitation of 5 / 8 inches of rain is registered in a time of 2 / 3 hour and we are asked to find how many precipitation is registered in a time of an hour, that is, the value of the excretion. The excretion can be found by cross multiplication:

r = (5 / 8 in) / (2 / 3 h)

r = 15 / 16 in / h

A precipitation of 15 / 16 inches in a time of an hour is the value of the excretion.

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Answer:

≈226.1947

Step-by-step explanation:

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