true/false: one or two extreme data points (outliers) can have a dramatic effect on the strength of a correlation

The correct sequence of transformations that could have been used to transform Trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.

To transform trapezoid ABCD into trapezoid A''B''C''D'', we need to apply a sequence of transformations that will result in the same size and shape of the two trapezoids, which means that they are congruent.

One possible sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is:

Trapezoid ABCD was reflected across the y-axis and then across the x-axis.

This sequence of transformations would result in the same size and shape of the two trapezoids, which means that they are congruent. Let's see why this is true.

When we reflect trapezoid ABCD across the y-axis, each point on the trapezoid is reflected across the y-axis, which means that its x-coordinate is multiplied by -1 while its y-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the y-axis.

Next, when we reflect the trapezoid across the x-axis, each point is reflected across the x-axis, which means that its y-coordinate is multiplied by -1 while its x-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the x-axis.

The resulting trapezoid is now in the same position and orientation as trapezoid A''B''C''D'', but it may not be in the same location. However, since the trapezoid is congruent, we can translate it to match the position of trapezoid A''B''C''D''.

Therefore, the correct sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.

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Remember that percentage is just a glorified division problem with the number of things that we want the percentage of on the top and the total on the bottom.

This question is asking about the percentage of left handed sixth graders. So we need to know (1) how many left handed sixth graders there are and (2) how many total sixth graders there are.

The problem states that there are 9 girls and 3 boys that are left handed. To get the total, we add.

9 girls + 3 boys = 12 students that are left handed.

The problem also states that there are 90 girls and 60 boys total in the sixth grade. To get this total, we also add.

90 girls + 60 boys = 150 students

Now, we can calculate the percentage.

We take the 12 lefties and divide that by the 150 total sixth graders. When we get a decimal, we multiply by 100 to get the percentage.

So

[tex]\sf \dfrac{12}{150} = 0.08[/tex]

[tex]\sf 0.08 \times 100 = \boxed{\bold{8\%}}[/tex]

Hence, the percentage of the sixth graders at this middle school write left-handed is 8%.

The simplification of the given terms is 14.25 or 114/8

A numerical expression is a piece of algebraic information stated in the form of numbers and variables that are unknown.

We are given that 6 times 2 wholes 3/8

Let the number be x

So,6 times 2 wholes 3/8 means;

x = 6 x 2 3/8

x = 6 x 19/8

x = 14.25 or 114/8

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Answer: 4140, 4060, and 4109

Step-by-step explanation:

4140: looking at the tens place (4) it is less than 5 so it rounds to 4100

4060: the tens place (6) is bigger than 5 so you add a 1 to the hundreds place everything behind it becomes a 0. and equal to 4100.

4109: everything behind becomes a 0

Answer:

  322 in²

Step-by-step explanation:

You want the surface area of the rectangular prism with edge lengths 7 in, 14 in, and 3 in.

The surface area can be computed using the formula ...

  A = 2(LW +H(L +W))

  A = 2(7·14 + 3(7 +14)) = 2(98 +63) = 322

The area of the prism is 322 square inches.

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Answer:

480

Step-by-step explanation:

Using the formula s=n/2(a+l), where a is the first term, l is the last term, n is the number of terms, and s is the sum of the terms, we can substitute the given values and solve for s:

s = 15/2(2 + 30)

s = 15/2(32)

s = 15/64

s = 480

Therefore, the value of s is 480.

Answer:

Step-by-step explanation:

[tex]s = \frac{n}{2}(a+l) \\s = \frac{15}{2} (2+30)\\s = \frac{15}{2} X 32\\s = 15 X 16\\s = 240[/tex]

The domain to plot the growth function is 0 ≤ x < 7

Given that

f(d) = 11(1.01)ᵇ

When the radius is approximately 1179 mm

We have

11(1.01)ᵇ = 11.79

Divide

(1.01)ᵇ = 1.072

Take the logarithm

d = log(1.072)/log(1.01)

Evaluate

d = 6.99

So, the reasonable domain is 0 ≤ x < 7

Here, we have

f(d) = 11(1.01)ᵇ

The y-intercept is 11

This means tha the initial radius of the algae is 11 mm

For the average rate, we have

f(7) = 11(1.01)⁷ = 11.79

f(2) = 11(1.01)² = 11.22

So, we have

Rate  = (11.22 - 11.79)/(2 - 7)

Evaluate

Rate  = 0.114

So, the average rate of change from day 2 to day 7 is 0.114 mm per day

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We can then perform row reduction to determine the rank of the matrix. After performing row reduction, we can see that the rank of the matrix is 2, which is less than the dimension of R^3, which is 3. Therefore, the two vectors in W do not span R^3, and so W is not a basis for R^3.

First, let's check for linear independence. We can set up the following equation:

c1[-2,3,0] + c2[6,-1,5] = [0,0,0]

This gives us the system of equations:

-2c1 + 6c2 = 0

3c1 - c2 = 0

5c2 = 0

The last equation tells us that c2 must be 0, which means the first equation simplifies to c1 = 0. Substituting these values into the second equation gives us 0 = 0, which is always true. This tells us that the only solution to the system is c1 = c2 = 0, meaning that W is linearly independent.

Next, let's check if W spans R^3. We can do this by checking if any vector in R^3 can be written as a linear combination of the two vectors in W. That is, we need to solve the equation:

c1[-2,3,0] + c2[6,-1,5] = [x,y,z]

This gives us the system of equations:

-2c1 + 6c2 = x

3c1 - c2 = y

5c2 = z

Solving for c1, c2, and z, we get:

c2 = z/5

c1 = (y + c2)/3 = (y + z/5)/3

x = -2c1 + 6c2 = -(2/3)(y + z/5) + 6z/5 = (-2/3)y + (22/15)z

This means that any vector [x,y,z] in R^3 can be written as a linear combination of the vectors in W. Therefore, W spans R^3.

Since W is both linearly independent and spans R^3, it is a basis for R^3. Therefore, the correct answer is A. W is a basis.

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it takes Lindiwe's teacher 300 seconds to walk to her classroom and the break is 50 minutes long.

To convert 3 km to meters we multiply by 1000 (since there are 1000 meters in 1 km).

3 km = 3,000 meters

Therefore, Lindiwe walks 3,000 meters from home to school during weekdays.

3.2 To convert 5 minutes to seconds, we multiply by 60 (since there are 60 seconds in 1 minute).

5 minutes = 5 x 60 = 300 seconds

Therefore, it takes Lindiwe's teacher 300 seconds to walk to her classroom.

To find the length of Lindiwe's break, we subtract the start time from the end time:

11:20 - 10:30 = 0:50

The break is 50 minutes long.

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We need to use some basic algebraic equations. Let's assume that the initial payment made by Frankie was x, and the total amount he has to pay for the computer is y. Also, let's assume that Frankie will make n monthly payments.

Now, we know that Frankie has already paid x, and he has to pay y-x more. Since he will pay this amount in n monthly installments, we can represent the monthly installment as (y-x)/n.

So, the equation that represents the relationship between n and y can be written as:

y = x + n*(y-x)/n

Simplifying this equation, we get:

y = x + y-x

y = y

This means that the equation is true for any value of n and y, as long as x is a valid initial payment amount. Therefore, the equation that represents the relationship between n and y is:

y = x + n*(y-x)/n

The equation we derived above is a simple but important concept in mathematics and finance. It shows us that we can calculate the total amount we need to pay for something by multiplying the monthly installment by the number of payments and adding the initial payment to it. This concept is used in many financial transactions, such as car loans, mortgages, and credit card payments.

Moreover, this equation also helps us to plan our finances and manage our budget effectively. We can use it to calculate how much we need to save every month to reach our financial goals, or to compare different payment options and choose the one that suits us best.

In conclusion, the equation that represents the relationship between the number of monthly payments and the total amount paid is an essential tool for anyone who wants to make wise financial decisions. By understanding this equation, we can save money, avoid debt, and achieve our financial goals more easily.

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The number of ways is 1 billion.

We are asked to determine the possible number of ways of the social security number that is 9 digits if the numbers can be repeated.

In this case, using fundamental counting, there are 10 possible numbers in each digit that is from zero to nine.

Thus, the number of ways is 10*10*10*10*10*10*10*10*10 equal to 1 billion ways.

Hence the number of ways is 1 billion.

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Answer:

275 miles

Step-by-step explanation:

110/2=55

(2*110)+55

=275

Answer:

275 miles

Step-by-step explanation:

110×2=220

110÷2=55

220+55=275

The value of the radical expression x² + 1/x² when x = 9 - 4√5 is 322

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

x = 9 - 4√5

The expression is given as

x² + 1/x²

When simplified, we have

x² + 1/x² = (x⁴ + 1)/x²

Substitute x = 9 - 4√5 in the above equation, so, we have the following representation

x² + 1/x² = ((9 - 4√5)⁴ + 1)/(9 - 4√5)²

When evaluated, we have

x² + 1/x² = 322

Hence, the value of the expression x² + 1/x² when x = 9 - 4√5 is 322

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The Transformation of the original equation y=|1/2x-2|+3 one unit to the right results in the new equation y=|1/2(x-1)-2|+3

To shift the graph of the equation y=|1/2x-2|+3 one unit to the right, we can use a transformation of the form y=|1/2(x-1)-2|+3. This transformation will shift the graph one unit to the right by replacing x with (x-1) in the original equation.

To graph the transformed equation, we can start by finding the x- and y-intercepts. To find the y-intercept, we set x=0:

y=|1/2(0-1)-2|+3

y=|1/2(-1)-2|+3

y=|-1/2-2|+3

y=|-5/2|+3

y=5/2+3

y=11/2

Therefore, the y-intercept is (0, 11/2).

To find the x-intercept, we set y=0:

0=|1/2(x-1)-2|+3

-3=|1/2(x-1)-2|

-3=1/2(x-1)-2 or -3=-1/2(x-1)-2

-1=1/2(x-1) or -1=-1/2(x-1)

-2=x-1 or 0=x-1

x=-1 or x=1

Therefore, the x-intercepts are (-1, 0) and (1, 0).

Next, we can plot these points and draw the graph. The graph is symmetric about the vertical line x=1, as the absolute value function has this property.

Overall, the transformation of the original equation y=|1/2x-2|+3 one unit to the right results in the new equation y=|1/2(x-1)-2|+3.

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A ratio is a comparison of two or more quantities expressed as a fraction. For example, if we say that the ratio of apples to oranges is 2:3, it means that for every two apples, there are three oranges. Ade received an amount of 1500 from the total sum of 4000 .

In order to find out the amount Ade received, we need to first understand the concept of ratio. A ratio is a comparison of two or more quantities expressed as a fraction. For example, if we say that the ratio of apples to oranges is 2:3, it means that for every two apples, there are three oranges.

In this problem, we are given that Ade and Ola share a sum of 4000 in the ratio of 3:5. This means that the total ratio is 3+5 = 8.

To find out the amount Ade received, we need to first find the fraction of the total sum that belongs to Ade. We can do this by dividing Ade's ratio by the total ratio.

Ade's ratio is 3, so the fraction of the total sum that belongs to Ade is 3/8.

Now, we can find the amount Ade received by multiplying this fraction by the total sum:

Amount Ade received = (3/8) x 4000 = 1500.

1.Add the ratio parts: 3 (Ade's part) + 5 (Ola's part) = 8 total parts.

2. Divide the total sum (4000) by the total parts (8): 4000 ÷ 8 = 500. This gives us the value of one part.

3. Multiply Ade's ratio part (3) by the value of one part (500): 3 × 500 = 1500.

So, Ade received an amount of 1500 from the total sum of 4000.

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Answer:

0.5x(x + 2) = 24

x² + 2x - 48 = 0

x² + (x + 2)² = 100

Step-by-step explanation:

A = bh/2

A = x(x + 2)/2 = 24

0.5x(x + 2) = 24

0.5x² + x = 24

x² + 2x = 48

x² + 2x - 48 = 0

x² + (x + 2)² = 10²

x² + (x + 2)² = 100

To find the three numbers, we need to use the information given about their mean, median, and range. Since the median is 18, we know that the middle number of the three must be 18. Also, since the mean is 20, the sum of the three numbers must be 3 times 20, which is 60. So, the 3 numbers are 16, 18, and 26.

Let's call the smallest number x, then the largest number must be x+10 since the range is 10.
Now we can set up an equation to solve for x. We know that the sum of the three numbers is 60, so we can write:
x + 18 + (x+10) = 60
Simplifying this equation gives:
2x + 28 = 60
Subtracting 28 from both sides gives:
2x = 32
Dividing by 2 gives:
x = 16

Therefore, the three numbers are 16, 18, and 26.
Given the information provided, we know the following:
1. Mean of 3 numbers is 20.
2. Median of the 3 numbers is 18.
3. Range (largest - smallest) is 10.
Since there are 3 numbers and the median is 18, the middle number is 18. Let's call the smallest number "x" and the largest number "y". We can now write two equations:
1. (x + 18 + y) / 3 = 20
2. y - x = 10
We can simplify the first equation to find the sum of the 3 numbers:
x + 18 + y = 60
Now, we can solve for x in the second equation:
x = y - 10
Substituting the value of x in the first equation:
(y - 10) + 18 + y = 60
Solving for y:
2y = 52
y = 26
Now, we can find the value of x:
x = 26 - 10
x = 16
So, the 3 numbers are 16, 18, and 26.

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a. mean = 27, standard deviation 1.673

b. The calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

c. The p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

a. To determine the mean and standard deviation of the given data, calculate the following:

Mean:

(28 + 27 + 25 + 28 + 29 + 25) / 6

= 162 / 6 = 27 miles (mean)

Standard Deviation:

First, calculate the deviation from the mean for each data point:

(28 - 27) = 1

(27 - 27) = 0

(25 - 27) = -2

(28 - 27) = 1

(29 - 27) = 2

(25 - 27) = -2

Then, square each deviation:

1² = 1

0² = 0

(-2)² = 4

1² = 1

2² = 4

(-2)² = 4

Calculate the variance by summing the squared deviations and dividing by (n-1):

(1 + 0 + 4 + 1 + 4 + 4) / (6-1)

= 14 / 5 = 2.8

Finally, take the square root of the variance to get the standard deviation:

√2.8 ≈ 1.673 (standard deviation)

b. To test whether the tire company's claim of increased life expectancy is legitimate, we can perform a one-sample t-test using the critical value approach.

Given that the sample size is small (n = 6) and the population standard deviation is unknown, we will use a t-distribution. The null and alternative hypotheses are as follows:

Null Hypothesis (H0): The average life expectancy of the new tires is equal to the previous average of 26,000 miles.

Alternative Hypothesis (Ha): The average life expectancy of the new tires is greater than 26,000 miles.

Using the critical value approach at the 0.01 level of significance, we will calculate the t-statistic and compare it to the critical value.

Degrees of freedom (df) = n - 1 = 6 - 1 = 5

Calculate the t-statistic:

t = (sample mean - population mean) / (sample standard deviation / √(n))

t = (27 - 26) / (1.673 / √(6))

t ≈ 1.21

Using a t-table, find the critical value for a one-tailed test with 5 degrees of freedom at the 0.01 level of significance. For this example, let's assume the critical value is 2.571.

Since the calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

c. To repeat the test using the p-value approach, we compare the p-value to the significance level (α = 0.01).

Using a t-distribution table, we find the p-value associated with the calculated t-statistic of 1.21. For this example, let's assume the p-value is 0.274.

Since the p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

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Given question is incomplete, the complete question is below

A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires life expectancy has increased. In order to test the legitimacy of its advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data.

Life expectancy (In thousands of miles)

28

27

25

28

29

25

a. Determine the mean and the standard deviation

b. at the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.

c. Repeat the test using the p-value approach.

Becky is correct if x + y = 180° ,   indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x +  y ≠ 180°.

A cyclic quadrilateral, also known as an inscribed quadrilateral in Euclidean  geometry, is a quadrilateral with all   of its vertices on a single circle.

To determine the size of angle C in terms of x and y, we can use the fact that tangent BC touches the circle ABDE at B.

This means that angle C is equal to the angle formed between the chord AD and the tangent BC at point B.

4.1.1

Since AB || EC, we can use the alternate interior angles theorem to determine the relationship between angles C and A₁.

Angle C is equal to angle A₁ because they are corresponding angles.

Therefore, the size of angle C is y.

4.1.2   - To determine if BCDF is a cyclic quadrilateral

 In order to check if BCDF is cyclic, we need to determine if the opposite angles in the quadrilateral add up to 180° .

Let's consider angle BCD and angle BFD:

Angle BCD is equal to angle B₁ (given) and is represented by x.

Angle BFD is equal to angle A₁ (since BCDF is a cyclic quadrilateral) and is represented by y.

If x + y = 180 degrees, then BCDF is a cyclic quadrilateral.

conclusively , Becky is correct if x + y = 180°, indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x + y ≠ 180°.

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The loading buffer that the protein is mixed with typically contains a variety of components that serve different purposes in preparing the protein sample for analysis.

The key components that are commonly found in loading buffer include a reducing agent such as beta-mercaptoethanol or dithiothreitol, which helps to break down disulfide bonds in the protein and denature it for easier separation by gel electrophoresis. Other components that may be included in the loading buffer are a detergent such as sodium dodecyl sulfate (SDS), which helps to solubilize the protein and gives it a negative charge that allows it to migrate through the gel towards the positive electrode during electrophoresis. Additionally, loading buffer may contain a tracking dye such as bromophenol blue or xylene cyanol, which helps to visualize the progress of the protein migration through the gel.

Overall, the specific composition of the loading buffer can vary depending on the experimental protocol and the protein being studied, but the goal is always to prepare a homogeneous and denatured protein sample that can be effectively analyzed by gel electrophoresis or other techniques.

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Chelsea's total return (profit) when the bond is redeemed at maturity is $50.

Chelsea paid for the bond with the 3% discount:

Discount = 3% of $5,000

= $150

Price paid for the bond = $5,000 - $150

= $4,850

Next, let's calculate how much Chelsea will receive in each semiannual payment:

Semiannual interest rate = 3% / 2

= 1.5%

Semiannual payment = Face value x Semiannual interest rate = $5,000 x 1.5% = $75

Since there are eight semiannual payments, Chelsea will receive a total of:

Total semiannual payments = Semiannual payment x Number of semiannual payments = $75 x 8 = $600

Finally, let's calculate the total return (profit) when the bond is redeemed at maturity:

Total interest earned = Annual interest rate x Term x Face value = 3% x 4 x $5,000 = $600

Face value at maturity = $5,000

Total return = Price paid + Total interest earned + Total semiannual payments - Face value at maturity

Total return = $4,850 + $600 + $600 - $5,000 = $50

Therefore, Chelsea's total return (profit) when the bond is redeemed at maturity is $50.

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There is about 295.11335 cubic inches of space left in the container, not including the balls.

We must first determine the cylinder's total volume before deducting the volume of the 25 spheres in order to determine the amount of space still inside the container.

The formula for calculating a cylinder's volume is V_cylinder = * r2 * h, where V_cylinder denotes the cylinder's volume, r stands for the cylinder's radius, and h denotes the cylinder's height.

The cylinder's radius (r) in this instance is specified as 3 inches, while its height (h) is specified as 12 inches. We may determine the volume of the cylinder by entering these values into the formula.

V_cylinder equals 3.14159 * 3 2 * 12 V_cylinder is 339.292 in3 in volume.

Next, we must determine the volume of each sphere. The following equation determines a sphere's volume:

Where: V_sphere = (4/3) * * (r3) V_sphere is the sphere's volume, is a mathematical constant roughly equal to 3.14159, and r is the sphere's radius.

The spherical balls' diameter (d) in this instance is 1.5 inches, which means the radius (r) is equal to half of the diameter.

r = 1.5/2d/2 = 0.75 inches.

We may get the volume of each spherical ball using this value as a plug-in in the formula.

V_sphere is equal to 4.33 * 3.14159 * 0.75.

1.7671459 in3 V_sphere

The volume of one sphere is multiplied by the quantity of spheres in order to determine the combined volume of the 25 spherical balls.

V_total_spheres is calculated as V_sphere * 25 V_total_spheres 44.17865 in3.

Finally, we can determine how much room is still in the container by deducting the volume of the 25 spheres from the cylinder's volume.

Space left is equal to V_cylinder - V_total_spheres.

339.292 - 44.17865 space_left

295.11335 in3 of space is remaining.

Without accounting for the balls, there is approximately 295.11335 cubic inches of empty space in the container.

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Therefore, the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is 11/15, or about 0.733.

We can approach this problem by finding the probability of Sergio's number being less than or equal to the sum of Tina's numbers, and then subtracting this probability from 1.

The total number of ways for Tina to select two distinct numbers from the set is 6 choose 2, which is 15. Each pair of numbers has an equal chance of being selected, so we can assume that each pair has probability 1/15 of being selected.

Now, for each pair of numbers Tina selects, there is a range of numbers that Sergio can select such that his number is greater than the sum of Tina's numbers. Specifically, Sergio's number must be greater than the smaller of Tina's numbers and less than or equal to the largest number in the set.The length of this shaded region is 6 - 2 = 4. Therefore, the probability of Sergio's number being greater than the sum of Tina's numbers for a given pair of numbers is 4/6 = 2/3.

The probability of Tina selecting any particular pair of numbers is 1/15, so the probability of Sergio's number being greater than the sum of Tina's numbers for that pair is (2/3)(1/15) = 2/45.

To find the total probability, we sum up the probabilities for all pairs of numbers:

(2/45) + (2/45) + (2/45) + (2/45) + (2/45) + (2/45) = 12/45 = 4/15

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The amplitude of the function is 2, and the period is 2π.

To find the amplitude and period of the function f(x) = -2 sin(x), we can use the standard form of a sine function:

f(x) = A * sin(Bx)

where A represents the amplitude and B represents the reciprocal of the period.

Comparing this with the given function f(x) = -2 sin(x), we can see that A = -2.

Now let's find the period of the function:

The general formula for the period of a sine function is given by:

Period = 2π / |B|

In our case, B = 1, so the period is:

Period = 2π / |1| = 2π

Therefore, the amplitude of the function is 2, and the period is 2π.

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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{9} \end{cases} \\\\\\ c=\sqrt{ 2^2 + 9^2}\implies c=\sqrt{ 4 + 81 } \implies c=\sqrt{ 85 }\implies c\approx 9.2[/tex]

The measure of arc ZWX is 180 degrees.

Given that WZ and XR are diameters, we know that they are both perpendicular to chord WX. This creates four right angles at point X, and as a result, we have a rectangle formed by the four line segments.

Since WZ and XR are diameters, they each extend from one end of the rectangle to the other. This means that arc ZWX is actually a semicircle, with a measure of 180 degrees.

To see why this is the case, consider that a full circle has a measure of 360 degrees. Since arc ZWX spans exactly half of the circle, it must have a measure of half the circle, or 180 degrees.

In summary, the measure of arc ZWX is 180 degrees. This can be derived from the fact that WZ and XR are diameters, which create a rectangle and a semicircle in the process. While the figure may not be drawn to scale, the relationships between the different line segments and angles remain constant, allowing us to determine the measure of arc ZWX with confidence.

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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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There are 36, coins of 50c out of a total of 120 coins.

Assume that

Quantity of 50 cent coin = x

Quantity of 20 cent coin = y

Then according to question,

50x + 20y = 3480 ...(i)

Now if the sum of the coins is 120,

x + y = 120  ...(ii)

Now use elimination method,

By 50 x (ii) - (i),

30y = 2520

y = 84  

Now put this value this into (ii);

x = 36

Hence,

Quantity of 50 cent coin = 36

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Answer:

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Let the dimensions be x and y.

The area is:

When sides have changed we get:

The new area is:

The difference in areas is:

It represents 17% increase.