The verbal part of the GRE exam score can be modeled by a normal distribution with mean 160 and a standard deviation of 8. If a student who took this exam is selected at random, what is the probability that he/she obtained a score between 150 and 162? What is the score of a student who scored in the 82th percentile on the verbal part of the GRE?

Approximately 4.28% of the seats are filled in the stadium when there are 19,624 people in attendance. To determine the percentage of seats filled in the stadium, we need to calculate the ratio of the number of people in attendance to the total number of seats and then convert it to a percentage.

The number of seats filled can be found by subtracting the number of empty seats from the total number of seats. Using the given information:

Number of seats filled = Total number of seats - Number of empty seats

Number of seats filled = 20,502 - 19,624

Number of seats filled = 878

Now, we can calculate the percentage of seats filled by dividing the number of seats filled by the total number of seats and multiplying by 100:

Percentage of seats filled = (Number of seats filled / Total number of seats) * 100

Percentage of seats filled = (878 / 20,502) * 100

Percentage of seats filled ≈ 4.28%

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Main answer: f(z) = Reſiz is differentiable at every point of the complex plane where partial derivative with respect to x exists and the Cauchy-Riemann equations are satisfied.

Supporting answer: Given f(z) = ReſizLet z = x + iy∴ f(z) = Re(x + iy)z = x - iyi.e. x = ½ (z + z¯)and y = -½i(z - z¯)Hence f(z) = ½ (z + z¯ ) Differentiating f(z) partially with respect to x, we get,fx = ∂(x + y)/∂x = 1And differentiating f(z) partially with respect to y, we get,fy = ∂(x + y)/∂y = 1Now, for f(z) to be differentiable, it is necessary thatfx = uxx + ivxxandfy = uyx + ivyxwhere u = Re (f(z)) and v = Im(f(z))i.e. uxx = vyyanduyx = -vxy These equations are known as the Cauchy-Riemann equations. On substituting, we get uxx = vyy∴ 1 = 0which is not true. Hence f(z) is not differentiable when partial derivative with respect to y exists. So f(z) is differentiable at every point of the complex plane where partial derivative with respect to x exists and the Cauchy-Riemann equations are satisfied.

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PEMDAS

-140

-35-85=-120

-120+5-25

-120+5=-115

=-115-25

-115-25=-140

-140

Answer: Kianna is incorrect, if Elena’s house was a reflection of her house across the y-axis, the coordinates would be (-4,2).

Step-by-step explanation:

The rate of increase for the selected automobiles between 2019 and the present time is 24%. The average cost of the selected automobiles increased from $14,000 in 2019 to $17,360 at present.

To calculate the rate of increase, we can use the formula: rate of increase = (new value - old value) / old value * 100%. Substituting the values into the formula, we get (17,360 - 14,000) / 14,000 * 100% = 3,360 / 14,000 * 100% = 0.24 * 100% = 24%. Therefore, the rate of increase for these automobiles over the given time period is 24%.

In summary, the selected automobiles experienced a rate of increase of 24% between 2019 and the present time. This means that, on average, the cost of these automobiles increased by 24% over the specified period.

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Perpendicular means that two lines intersect at a right angle.

D and E have perpendicular sides

(blue rectangle at the bottom left and green trapezoid all the way at the bottom right)

Answer:

s would be 20

Step-by-step explanation:

because 2 x 10 = 20 so you then would add the second 20 to the first 20 and get 40

Answer:

3.142 × 6 = 18.852, thats : 19cm, then multiply 19 by 6 , so 19 would go in the square.

because area of a circle is p × r sq. u multiply one of the 6 by 3.142, you get 19, then multiply that 19 by the other 6. the answer is approximately 113.112.

Answer:

(x+3)²+(y+5)² = 36

Step-by-step explanation:

The general equation of a circle is expressed as;

(x-a)²+(y-b)² = r² where;

(a, b) is the centre of the circle

r is the radius of the circle

Given

Centre (-3, -5)

a = -3 and b = -5

radius r = 6units

Substitute

(x-a)²+(y-b)² = r²

(x-(-3))²+(y-(-5))² = 6²

(x+3)²+(y+5)² = 36

hence the required equation is (x+3)²+(y+5)² = 36

The equation of a circle that represents a circle with a center at (-3, -5) and a radius of 6 unit is (x + 3)² + (y + 5)² = 36

The general equation of a circle is expressed as follows:

(x-a)²+(y-b)² = r²

where

Therefore,

a = -3

b = -5

r = 6

Hence,

(x - (-3))² + (y - (-5))² = 6²

(x + 3)² + (y + 5)² = 36

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(a) An example of an infinite field such that 4-a -o for all e F is F_2.

Here, the only elements of the field are 0 and 1, and we have 1 + 1 = 0,

which is equivalent to 4 - 1 - 1 = 2 - 1 - 1 = 0. Therefore, for all a e F_2, 4 - a - a = 0, so F_2 satisfies the given condition.

(b) An example of an infinite, non-commutative ring R such that for all a we have that 2a = 0 is the ring of 2x2 matrices over the field F_2 (as defined in part (a)). If we identify the matrix \begin{pmatrix}a&b\\c&d\end{pmatrix} with the element ad + bc of F_2, then R becomes a ring.

Note that R is not commutative since the product of two matrices is not necessarily equal to the product of their entries, and that 2a = 0 for all matrices \begin{pmatrix}a&b\\c&d\end{pmatrix} in R since \begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}0&1\\0&0\end{pmatrix} = \begin{pmatrix}0&a\\0&c\end{pmatrix} and \begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}0&0\\1&0\end{pmatrix} = \begin{pmatrix}b&0\\d&0\end{pmatrix} have entries that are equal to 0 in F_2. Therefore, R satisfies the given condition.

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a. The 90% confidence interval for the true population mean watermelon weight is 30.41 to 35.59 ounces.

b. The 99% confidence interval for the true population mean turtle weight is 54.56 to 57.44 ounces.

c. The 99% confidence interval for the true population mean textbook weight is 56.884 to 67.116 ounces.

d. The 99% confidence interval for the true population proportion of people with kids is 0.464 to 0.576.

e. The 99% confidence interval for the true population proportion of people with kids is 0.585 to 0.675.

a. For the watermelon weights:

Sample mean (m) = 33 ounces

Population standard deviation (σ) = 7.7 ounces

Sample size (n) = 47

Confidence level = 90%

To construct the confidence interval, we can use the formula:

Confidence Interval = m ± Z * (σ/√n)

Where Z is the z-score corresponding to the desired confidence level. For a 90% confidence level, Z = 1.645 (obtained from the standard normal distribution table).

Confidence Interval = 33 ± 1.645 * (7.7/√47)

Confidence Interval ≈ 33 ± 2.586

Confidence Interval ≈ (30.41, 35.59) ounces

The 90% confidence interval for the true population mean watermelon weight is 30.41 to 35.59 ounces.

b. For the turtle weights:

Sample mean (m) = 56 ounces

Population standard deviation (σ) = 2.9 ounces

Sample size (n) = 21

Confidence level = 99%

Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.

Confidence Interval = 56 ± 2.576 * (2.9/√21)

Confidence Interval ≈ 56 ± 1.438

Confidence Interval ≈ (54.56, 57.44) ounces

The 99% confidence interval for the true population mean turtle weight is 54.56 to 57.44 ounces.

c. For the textbook weights:

Sample mean (m) = 62 ounces

Population standard deviation (σ) = 9.4 ounces

Sample size (n) = 34

Confidence level = 99%

Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.

Confidence Interval = 62 ± 2.576 * (9.4/√34)

Confidence Interval ≈ 62 ± 5.116

Confidence Interval ≈ (56.884, 67.116) ounces

The 99% confidence interval for the true population mean textbook weight is 56.884 to 67.116 ounces.

d. For the proportion of people with kids:

Number of people with kids (p) = 104

Sample size (n) = 200

Confidence level = 99%

To construct the confidence interval for a proportion, we can use the formula:

Confidence Interval = p ± Z * √[(p(1-p))/n]

Using the z-score corresponding to a 99% confidence level (Z = 2.576), we can calculate the confidence interval.

Confidence Interval = 104/200 ± 2.576 * √[(104/200)(1 - 104/200)/200]

Confidence Interval ≈ 0.52 ± 0.056

Confidence Interval ≈ (0.464, 0.576)

The 99% confidence interval for the true population proportion of people with kids is 0.464 to 0.576.

e. For the proportion of people with kids:

Number of people with kids (p) = 189

Sample size (n) = 300

Confidence level = 99%

Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.

Confidence Interval = 189/300 ± 2.576 * √[(189/300)(1 - 189/300)/300]

Confidence Interval ≈ 0.63 ± 0.045

Confidence Interval ≈ (0.585, 0.675)

The 99% confidence interval for the true population proportion of people with kids is 0.585 to 0.675.

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The data suggest that the population mean is not significantly different from 43 at α = 0.05.

To determine whether the average number of days between haircuts for college students is smaller than the average for the average American (43 days), we can conduct a one-sample t-test. Here are the steps and results:

Step 1: Formulate the null and alternative hypotheses:

Null hypothesis (H0): The population mean number of days between haircuts for college students is equal to 43.

Alternative hypothesis (H1): The population mean number of days between haircuts for college students is smaller than 43.

Step 2: Calculate the test statistic:

We can calculate the test statistic using the formula:

t = (x- μ) / (s / √n)

where x is the sample mean, μ is the hypothesised population mean (43), s is the sample standard deviation, and n is the sample size.

Using the given data, the sample mean x is calculated to be 39.923, the sample standard deviation s is 6.106, and the sample size n is 13.

Substituting these values into the formula, we get:

t = (39.923 - 43) / (6.106 / √13) = -0.808

Step 3: Calculate the p-value:

The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) if the null hypothesis is true. We can use the t-distribution to calculate the p-value.

Using a t-table or a statistical software, we find that the p-value for t = -0.808 with 12 degrees of freedom is approximately 0.438.

Step 4: Make a decision:

Comparing the p-value (0.438) to the significance level α (0.05), we find that the p-value is greater than α.

Therefore, we fail to reject the null hypothesis.

Based on the results, we conclude that there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 43. The data suggest that the population mean is not significantly different from 43 at α = 0.05.

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To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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Answer:

i dont know i just want points

Step-by-step explanation:

>;)

The first statement focuses on the existence of a single solution that works for all problems, while the second statement emphasizes that for each problem, there is at least one solution available, without specifying whether it is the same solution for all problems.

1) ∃x∀yS(x, y):

This statement means "There exists at least one solution that works for all problems." In other words, there is a specific value of x that can be applied to every problem y, resulting in a solution.

2) ∀y∃xS(x, y):

This statement means "For every problem, there exists at least one solution." In other words, for any given problem y, there is at least one value of x that can be applied to it to find a solution.

The main distinction between these two statements lies in the order of quantifiers (∃ and ∀). In the first statement, the existential quantifier (∃x) appears before the universal quantifier (∀y), indicating that there is a single solution that can be applied to all problems.

In the second statement, the universal quantifier (∀y) appears before the existential quantifier (∃x), indicating that for each problem, there is at least one solution that exists.

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Mark's approach to solving the problem is incorrect.

We have,

To find the sum of percentages, you cannot simply add the numbers together as you would with regular numbers.

Percentages represent proportions or ratios, so they must be converted to their corresponding decimal or fraction forms before adding them.

To solve 12% + 3%, you need to convert each percentage to its decimal form and then add the decimals together.

Here's the correct approach:

12% = 12/100 = 0.12

3% = 3/100 = 0.03

Now, add the decimals:

0.12 + 0.03 = 0.15

Therefore,

The value of 12% + 3% is 0.15 or 15%.

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No, her estimate is too high.

Given,

Lavonne estimated 38% of 63 by rounding 38% up to 40%, rounding 63 up to 70, and then multiplying 70 by 0.4 to get 28 .

Now

Firstly calculate the actual answer:

38% of 63

= 38/100 * 63

= 23.94

Now

The approximated portion :

40% of 70

= 0.4 *70

= 28

Hence the answer should be around 24 but after approximation it is coming 28 .

Thus the estimate made by Lavonne is high .

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Answer:

C

Step-by-step explanation:

Answer:

function A : y = 50 + 0.5x ; y = 40 + 0.6x

Step-by-step explanation:

Function is a relationship between values in set x & set y.

In case functional relationship equation is y = c + sx . c is the y intercept ie constant value of y when x = 0, & s is slope rate of change ie = change in y / change in x.

If function A is y = 50 + 0.5x. Intercept (c) = 50 , change rate (slope) = 0.5

If function B is y = 40 + 0.6x. Intercept (c) = 40 ie lesser, change rate (slope) = 0.6 ie greater

Answer:

-8 i think

Hope you get it right

Answer:

the absolute value of -l8| is 8

Step-by-step explanation:

Absolute value means the opposite

Answer:

the center of this circle is (8, -4) and the radius is 2√3.

Step-by-step explanation:

Compare this equation

(x - 8) + (y + 4) = 12      Don't forget to type in the " ^ " symbol to indicate exponentiation.

(x - 8)^2 + (y + 4)^2 = 12

to the standard equation of a circle with center at (h, k) and radius r:

(x - h)^2 + (y - k)^2 = r^2

In this way we learn that h = 8, k = -4 and r^2 = 12 (or r = 2√3).

Then the center of this circle is (8, -4) and the radius is 2√3.

The Liberty Company bond has the following characteristics:

Coupon rate: 10.20%

Yield to maturity: 10.55%

Face value: $1,000

Market price: $850, $101.75, $102.00, $105.50, or $120.00

The question asks for the annual interest payment.

To calculate the annual interest payment, we need to multiply the coupon rate by the face value of the bond. The coupon rate represents the annual interest rate as a percentage. In this case, the annual interest payment can be calculated as 10.20% of the face value, which is $1,000.

Therefore, the annual interest payment for the BCompany bond is $1,000 * 10.20% = $102.00.

Note: The market price of the bond is provided, but it does not affect the calculation of the annual interest payment. The market price represents the current market value of the bond and may vary depending on various factors such as supply and demand in the market.

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Answer : The below pseudocode will calculate the cost by multiplying the area with 425. The output will be the room name, area of the room, and approximate cost to construct the room in dollars.

Explanation:

Given:Bob charges $425 per square metre.To develop an algorithm to calculate the area of the room and the approximate cost.

Pseudocode:

Step 1: Start                                                                                                       Step 2: Declare variables : room Name of string type,Width of float type,Length of float type,Cost of float type      

Step 3: Display "Enter the name of the room:"                                              Step 4: Read the room Name                                                                          Step 5: Display "Enter the width of the room (in meters):"                             Step 6: Read the Width                                                                                                                                                                                                           Step 7: Display "Enter the length of the room (in meters):"                           Step 8: Read the Length                                                                                   Step 9: Calculate the area of the room as Area = Width * Length                  Step 10: Calculate the cost of the room as Cost = Area * 425                       Step 11: Display "Room Name:", roomName                                                    Step 12: Display "Area of the Room (in square metres):", Area                      Step 13: Display "Approximate Cost of Construction:", Cost                          Step 14: Stop

The program will take the input as the name of the room, width, and length of the room, and then it will calculate the area of the room by multiplying width and length. Then it will calculate the cost by multiplying the area with 425. The output will be the room name, area of the room, and approximate cost to construct the room in dollars.

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Answer:

480 - 12.25d = 50

Answer:

y = 4x+1

Step-by-step explanation: