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Divergent and Convergent sums The trees at a national park have been increasing in numbers. There were 200 trees in the first year that the park started tracking them. Since then, there have been one fifth as many new trees each year. Create the sigma notation showing the infinite growth of the trees and find the sum, if possible. Year New trees 1 1000 2 200 3 40

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Two positive numbers have a difference of 4 and a product of 96. What are the numbers? A. 12 and 8 B. 16 and 6 C. 16 and 12 D. 18 and 14

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A. For exercises 1 and 2, a set of data has a normal distribution with a mean of 120 and a standard deviation of 10. 1. Find the interval about the mean within which 90% of the data lie. a. 94.2-145.8 b. 103.5-136.5 c. 113.68-126.32 d. 100.4-139.6 2. Find the probability that a value selected at random from this data is between 100 and 140. a. 99.9% b. 90% c. 99% d. 95.5% B. In a random sample of 1000 exams, the average score was 500 points with a standard deviation of 80 points. 1. Find the interval about the sample mean that has a 1% level of confidence. a. 499-501 b. 479-520 c. 495-505 d. 493-507 2. Find the interval about the sample mean such that the probability is 0.90 that the mean number lies within the interval. a. 499-501 b. 495-505 c. 496-504 d. 368-632 3. Find the probability that the mean score of the population will be less than five points from the mean score of the sample. a. 95.5% b. 38.3% c. 98.8% d. 62.5% 4. Find the probability that the true mean is between 495 and 500. a. 95% b. 47.75% c. 95.5% d. 68.3%

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Which of the following is a convention of graph making? a) The data must be capable of being plotted as a straight line. b) Dependent variables are omitted. c) There must be at least 10 numbers on each axis. d) The independent variable is on the x-axis.

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How would the sum of cubes formula be used to factor x3y3 + 343? Explain the process. Do not write the factorization.

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What polynomial identity should be used to prove that 117= 125 – 8? Difference of Cubes Difference of Squares Square of Binomial Sum of Cubes

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1. Divide. Assume the denominator does not equal zero. 12x²y – 6xy + 4x²/2xy 2. Factor completely 2x²y + 12xy + 18y

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The employees of two companies were asked how many times they checked their email during weekends. The table below shows the numbers for each company: Company A 2 4 8 8 2 6 4 8 3 Company B 2 6 3 5 2 4 6 3 2 Based on the table, which of the following is true? The interquartile range for Company A employees is 2 more than the interquartile range for Company B employees. The interquartile range for Company A employees is 0.5 more than the interquartile range for Company B employees. The interquartile range for Company A employees is 1 more than the interquartile range for Company B employees. The interquartile range for Company A employees is 2.5 more than the interquartile range for Company B employees.

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Identify the number that does not belong with the other three. Explain your reasoning. 26.6 repeating 6, square root 48, negative 51 over 2, negative 55.2

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HELP PLEASE What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively? a.1 b.2 c.3 d.4

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A third-grade class has 12 girls and 13 boys. A fourth-grade class has 10 boys and 11 girls. When picking teams for PE, one captain will make a selection from the fourth-grade class, then the other captain will make a selection from the fourth-grade class. After that, the first captain will make a selection from the third-grade class, and the second captain will do likewise. Assuming everyone has an equally likely chance of being selected, what is the probability that the first captain will pick two girls before picking any boys? A. 44/175 B. 117/143 C. 120/143 D. 133/143

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The number of subscribers y to a newspaper after t years is shown by the equation below. y = 75(0.95)^t Which conclusion is correct about the number of subscribers to the newspaper? It increased by 75% every year. It decreased by 75% every year. It increased by 5% every year. It decreased by 5% every year.

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What is the average of -18.75 and 200.25?

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What is another name for 34/8 as a mixed number??

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The expression 40x^2 – 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, what expression represents the measure of two angles?

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How much would $200 invested at 6% interest compounded annually be worth after 5 years? Round your answer to the nearest cent. Do not include units in your answer.

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An experiment consists of rolling a six-sided die to select a number between 1 and 6 and drawing a card at random from a set of 10 cards numbered 1, 2, 3, … 10. Which event definition corresponds to exactly one outcome of the experiment? A. Both numbers are 5s. B. Neither number is a 5. C. The sum of the numbers is 3. D. One of the numbers is a 3.

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In which quadrant is the number 6 – 8i located on the complex plane?

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Traveling at 45 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 240 miles from Orlando to Miami?

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A group of 23 students participated in a math competition. Their scores are below: Score (points) 20–29 30–39 40–49 50–59 60–69 Number of Students 4 7 5 4 3 Would a dot plot or a histogram best represent the data presented here? Why? Histogram, because a large number of scores are reported as ranges Histogram, because a small number of scores are reported individually Dot plot, because a large number of scores are reported as ranges Dot plot, because a small number of scores are reported individually

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A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t-shirts in the store, given that f(0) = 100? f(n) = f(n – 1) • 0.3 + 25, n > 0 f(n) = 100 – f(n – 1) • 0.3 + 25, n > 0 f(n) = f(n – 1) • 0.7 + 25, n > 0 f(n) = 100 – f(n – 1) • 0.7 + 25, n > 0

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The sum of two numbers is 25. one number is twice the second number plus seven. what are the two numbers

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A yard is equal in length to three feet. the function F(y) takes a measurement in yards (as inputs) and returns a measurement in feet (as output). what number will the function return if the input is 10.5?

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Given tGiven the following probability distribution, find P (X = 3). X 1 2 3 4 5 P(X) 0.4 0.1 0.15 0.2 (1 point) 2. The number of cars an American family owns follows the distribution below: Number of Cars0 1 2 3 4 5 Probability 0.090.36 0.350.13 0.050.02 a) Verify that this is a legitimate probability distribution. b) Interpret (in words) the notation P(X > 2). c) Interpret (in words) the notation P(X = 2). d) Find P(X > 2). (5 points) 3. A study of social mobility in America examined the social class attained by the sons of lower class fathers. Social classes were numbered from 1 to 5 with 1 representing the lower class and 5 the higher class. Consider the random variable X to the class of a randomly chosen son. The study found the following distribution: Son’s Class1 2 3 4 5 Probability0.48 0.38 0.08 0.05 0.01 a) What percent of the sons reached the highest class? b) Check that this distribution meets the requirements of a discrete probability distribution. c) What is P(X

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The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Let x = number of years since 1900, and y = pounds per person. What cubic model best fits this data? Year Pounds Consumed 1902 1.959 1924 6.373 1946 7.29 1982 15.817 A. y = 0.00989×3 – 0.0000872×2 + 1.192x + 0.403 B. y = -0.0000872×3 + 0.00989×2 – 0.403x – 1.192 C. y = -0.0000872×3 – 0.00989×2 – 0.403x + 1.192 D. y = 0.0000872×3 – 0.00989×2 + 0.403x + 1.192

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The Farm Agency is to use only the letters A, B, and C to make tags. Let y be the number of tags they can make using n spaces. What is the formula for the number of tags they can make?

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A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40 units to test for quality. The product is put through a wear-and-tear test to determine the number of days it could last. If the product has a lifespan of less than 26 days, it is considered defective. The table gives the sample data that a quality control manager collected. 39 31 38 40 29 32 33 39 35 32 32 27 30 31 27 30 29 34 36 25 30 32 38 35 40 29 32 31 26 26 32 26 30 40 32 39 37 25 29 34 The point estimate of the mean of the sample is _____, and the point proportion of the defective units is _______. (Give your answers as decimal numbers rounded off to the nearest hundredth.)

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A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an angle of 40° from the horizontal line through the falcon’s location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.

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What is the sum of the interior angles of a convex 14-gon?

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Alice works at a health care facility. She has measured the hemoglobin levels of 200 people. The data follows a normal distribution with a mean of 14 g/dL and a standard deviation of 1. How many people have hemoglobin levels less than 13? How many people have hemoglobin levels greater than 14?

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