Math Questions

Use the Quotient Rule of Logarithms to write an expanded expression equivalent to log2(4x+1/x). Make sure to use parenthesis around your logarithm functions log(x + y). Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button. Provide your answer below:

A pet store has 7 puppies, including 4 poodles, 2 terriers, and 1 retriever. Rebecka and Aaron, in that order, each select one puppy at random without replacement. Find the probability that Aaron selects a retriever, given Rebecka selects a retriever. The probability is (Type an integer or a simplified fraction.)

Three friends split the cost of a pizza and a salad. The pizza costs $15 and the salad costs $6. Which expression can you use to find how much each person owes? (15+6)÷3 15+(6x3) (15+3)+6

If AC has length 13 and BC has length 18, find: • The length of AB: • The measure of angle B (in degrees): • The measure of angle C (in degrees): If you use a calculator to find a decimal approximation, your answer must be accurate to at least 3 decimal places. If you're using a calculator, be sure that your calculator is set to degrees, not radians. You are also allowed to use the inverse trig functions in your answer instead of using a calculator. sin ¹(z) can be entered as arcsin(x) or asin(x).

4. As you've heard, the smallest pair of amicable numbers, 220 and 284, were known to the ancient Greeks, the next pair of amicable numbers, 17296 and 18416, were discovered by the Islamic mathematician Ibn al-Banna in the 14th century (and rediscovered by Fermat). Thousands more have been found since. In Italy in 1866, however, 16-year-old Nicolo Paganini discovered a small pair of amicable numbers, 1184 and 1210, that had been overlooked for centuries. Verify that 1184 and 1210 are an amicable pair.

The mean weight of male nurses working at a local hospital is less than 172 lbs. Express the null and alternative hypotheses in symbolic form for this claim. Ho: µ H₁: µ Use the following codes to enter the following symbols: > enter >= <enter <= enter !=

There was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 3.1% each year. Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between y and f.

Hurricane damage: In August and September 2005, Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed, and of those that survived, many required extensive cleaning. It was thought that cleaning of flood-damaged homes might present a health hazard due to the large amounts of mold present in many of the homes. In a sample of 362 residents of Orleans Parish who had participated in cleaning of one or more homes, 74 had experienced symptoms of wheezing, and in a sample of 182 residents who had not participated in cleaning, 21 reported wheezing symptoms (numbers read from a graph). Can you conclude that the proportion of residents with wheezing symptoms is greater among those who participated in the cleaning of flood-damaged homes? Let P1 denote the proportion of residents with wheezing symptoms who had cleaned flood-damaged. homes, and let P2 be the population proportion with wheezing symptoms who did not participate in the cleaning of flood-damaged homes. Use the a= 0.05 level of significance and the critical value method. State the null and alternate hypotheses. Ho: H₁: This hypothesis test is a

Use identities to find values of the sine and cosine functions for the angle measure. θ, given that cos2θ= and 90° < θ < 180 sinθ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) cosθ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Solve equation by using the quadratic formula. List the solutions, separated by commas. 4w²+3w6=0 W=

Considering only the values of β for which csc² βcos (2β) is defined, which of the following expressions is equivalent to csc² βcos (2β)? Select the correct answer below: 2 2 - sec² β 2sin²β - tan² β 2sin β cot²β - 1

Select the correct answer from each drop-down menu. ΔABC has vertices at A(11, 6), B(5, 6), and (5, 17). ΔXYZ has vertices at X-10, 5), -12, -2), and Z-4, 15). ΔMNO has vertices at M-9, -4), M-3, -4), and O(-3, -15). ΔJKL has vertices at 17, -2), K12, -2), and L(12, 7). ΔPQR has vertices at P(12, 3), Q(12, -2), and A(3,-2). Triangle ABC and triangle XYZ Triangle ABC and triangle MNO Triangle JKL and triangle ABC Triangle PQR and triangle XYZ can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.

A jet and a passenger plane left Nairobi at the same time. The planes flew in opposite directions. The passenger plane flew 255 km/h faster than the jet. After seven hours they were 5005 km apart. Find the jet's speed. 340 km/h 240 km/h 230 km/h 80 km/h 210 km/h

You buy fishing equipment costing $268. State taxes are 6.5% and the federal excise tax on this item is 11.45%. What is the total purchase price? (Round your answer to the nearest cent.) $285.42 $296.87 $298.69 $316.11

Use synthetic division to rewrite the following fraction in the form g(x) +r(x) d(x) ,where d(x) is the denominator of the original fraction, q(x) is the quotient, and r(x) is 6x^6 + 12x³ − 2x³ − 4x² + 4x + 8 x + 2

There are over 3 million students enrolled in community colleges in the U.S. A total of 443,818 students at 699 community colleges completed the Community College Survey of Student Engagement (CCSSE) between 2009 and 2011. About half (50%) of students reported that they "often" or "very often" prepare two or more drafts of a paper before turning it in. True or false? The 50% is a statistic representing a sample of 443,818 community college students. False True

Construct the sample space for a probability experiment where a coin is flipped, and then a 10-sided die is rolled. (H1, H2, H3, H4, H5, H6, H7, H8, H9, H10, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) This setup was used for a carnival game, and different amounts paid out for certain outcomes. Find the probability of each outcome: (a) There was a head on the coin and an odd number on the die. (b) There was a head on the coin and a prime number on the die. (c) There was a head on the coin and a number less than on the die. Write your answers in exact, simplified form.

State Gasoline Taxes A random sample of state gasoline taxes (in cents) is shown here for 11 states. Round sample statistics and final answers to at least two decimal places. 58.6 46.7 58.1 43.8 43.7 46.7 48.9 42.1 55.5 48.5 47.2 Use the data to estimate the true population mean gasoline tax with 98% confidence. Assume the variable is normally distributed. < µ <

A woman 5 ft tall is standing near a street lamp that is 12 ft tall, as shown in the figure. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp. L(d) =

Let f(x) = -x³ + 9x on [-3,5]. a. Locate the critical points of f. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) of f is/are x = (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. The function f has no critical points.

Consider the following equation. 3x - y = 1 Step 2 of 2: Determine the missing coordinate in the ordered pair (?, 3) so that it will satisfy the given equation.

For every 40 pounds of body weight, the dosage for a medication is 1/2 ounce. If a person weighs 180 pounds, how many ounces of medication should be given? a. 1 oz. c. 2.5 oz d. 2.25 oz b. 2 oz

Graph the polar equation below by first selecting the correct symmetry, then selecting the correct radius. r = -5 cos (θ)+5 Provide your answer below:

A consumer agency wants to estimate the proportion of all drivers who wear seat belts while driving. What is the most conservative estimate of the sample size that would limit the margin of error to within 0.47 of the population proportion for a 99% confidence interval? Round your answer up to the nearest whole number.

Write an equation that models the linear situation: The heater keeps the temperature of the pool at 78 degrees Fahrenheit all day long. Instructions: DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1 Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2) You may use decimals IF the decimal values are exact. (You cannot use 33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.) To write your equation, use the variables: h = amount of time since the day began (hours) T(h) temperature of the pool (Fahrenheit degrees) Equation:

Over what interval is the cosine graph negative and the sine graph positive? [0, π] [3π/2, 2π] [π/2, π] [π/2,3π/2] Compare the graphs of sine and cosine and make sure you find the intervals where sine is positive and cosine is negative.

Which of the following cannot be the lengths of the three sides of a triangle? A 6 inches, 8 inches, 10 inches B 7 centimeters, 8 centimeters, 15 centimeters C 3 yards, 5 yards, 7 yards D 4 millimeters, 6 millimeters, 9 millimeters

Solve the equation 5 (2x - 1)^2/3 = 125 Assume x is positive. Give your answer as a simplified integer or improper fraction, if necessary. Note: Divide both sides with 5. first. Provide your answer below: x=

The vector PQ has initial point P(1, -3) and terminal point Q(4, -6). Find the magnitude and direction of PQ. Select the correct answer below: |PQ|=6√2; θ=315° |PQ|=3√/2 θ = 225° |PQ|-6√2; θ= 135° |PQ|=3√2; θ= 135° |PQ|=3√2; θ=315° |PQ|=6√2; θ = 225°

The second section of the walk continues from point B along Bell Avenue to the finish line at point C, as shown on the map. a. Each unit on the map represents 1 kilometer. What is the distance in kilometers from point B to point C? b. What is the total length of the race (from point A to point B and from point B to point C) in kilometers? c. A water station is located at the midpoint M of BC. Another water station is located at the midpoint N of MC. A race coordinator says that the map coordinates of point N are (6, 8). Is the race coordinator correct? Support your answer.

Ossie owns some property which has an assessed value of $179,800. Find the tax due if the tax rate is $8.28 per $100 of the assessed value. (Round your answer to the nearest cent.) $1,488.74 $14,204.20 $14,887.44 $17,980.00

Your local pizza store sells medium pizzas for $6.89 each, and breadsticks for $2.49 per order. For a party, you decide to order 5 pizzas and 2 orders of breadsticks. There is a $2 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax?

Country Motorbikes Incorporated finds that it costs $200 to produce each motorbike, and that fixed costs are $1300 per day. The price function is p(x) = 500 - 5x, where p is the price (i dollars) at which exactly x motorbikes will be sold. Find the quantity Country Motorbikes should produce and the price it should charge to maximize profit. Also find the maximum profit.

Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log(8(1 + 3x)). Make sure to use parenthesis around your logarithm functions log(x + y).

Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. Replacement times for washing machines: 90% confidence; n=31, x= 10.4 years, σ = 2.4 years 0.1 yr 0.7 yr 3.1 yr 0.6 yr

A game has 49 green balls and 1 red ball in a bag, and you will randomly select one ball from the bag. If the selected ball is green, you lose $1. And, if the ball is red, you win $100. What is the expected value of the game?

- In a class with 50 students, 25 of the students are sophomores, 15 of the students are mathematics majors, and 10 of the mathematics majors are sophomores. If a student in the class is to be selected at random, what is the probability that the student selected will be a sophomore or a mathematics major or both? A) 0.4 (B) 0.5 (C) 0.6 (D) 0.8

There are 15 black balls, 14 red balls, and 11 white balls in a jar, and you get to randomly pick one ball without looking. If you draw a black ball, you win $500. If you pick a red one, you lose $10. If you pick a white one, you lose $100. What is the expected value of picking a ball?

College Courses At a large university, the probability that a student takes calculus and is on the dean's list is 0.049. The probability that a student is on the dean's list is 0.29. Find the probability that the student is taking calculus, given that he or she is on the dean's list. Please round the final answer to 2 or 3 decimal places. P (the student is taking calculus given that he or she is on the dean's list)=

1. The table shows the number of turtles hatched at a zoo each year since 2003. a. Find the line of best fit. Predict the number of turtles to be hatched in 2011.

Name the property used to go from step to step each time the (why?) occurs. Choose the correct property for each step below. 5+2(x+6) = 5+ (2x+12) (why?) =5+(12+2x) (why?) = (5+12)+2x (why?) = 17+ 2x = 2x+17 (why?) commutative property of addition associative property of multiplication distributive property commutative property of multiplication associative property of addition ..... 5+2(x+6) = 5+ (2x+12) = 5+ (12+2x) = (5+12) + 2x = 17 + 2x = 2x + 17

Find the all solutions of this equation in the interval [0, 2π): 2 cos(x) sin(x) + sin(x) = 0 X= Give your answers in radians. Do not use decimal approximations. Use 'pi' to represent . Use commas to separate your answers.

Determine the point estimate of the population mean x̄ and margin of error (E) for each confident interval. Lower Bound: 15 Upper Bound: 35 (x)=25, E=15 (x)=10, E=25 (x)=25, E=10 (x)=15, E=10

A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 10 cm at the top and 9 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom. A(w) = cm²

A commuter railway has 800 passengers a day and charges each one 2 dollars. For each 6 cents the fare is increased, 5 fewer people will ride the train. Express the income I from the train in terms of the ticket price p (in dollars). I (p) = $

Write an equation that models the linear situation: A baby grows about an inch every month for the first year. She was born a foot and a half long. Instructions: DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1 Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2) You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.) To write your equation, use the variables: m = age of the baby (months) L(m) = length of the baby (inches) Equation:

2 sandwiches and a bag of chips costs $4.25. A sandwich costs $0.50 more than a bag of chips. Find the cost of a sandwich and a bag of chips

Use the long division method to find the result when 3x³-4x^2+10x - 11 is divided by x – 1. If there is a remainder, express the result in the form q(x) + r(x)/b(x)

If f(x)= a*, show that f(A + B) = f(A). f(B). Rewrite f(A + B) by substituting A + B for x in the given function. f(A + B)= Which law of exponents can be used to rewrite the expression above as a product? A. a^-s= 1/a^s= (1/a)^s C. a^0 = 1 E. (ab)^s = a^s.b^s B. a^s.a^t = a^(s+t) D. 1^5=1 F. (a^s)^t = a^st

Serial Killer The Murder Accountability Project has compiled a database of homicides in the United States from 1976-2017. This data set includes record: ID of the incident given as an integer number age of victim: in years age of perpetrator: in years sex: 1 female, 0 = male ethnicity of victim(s) ethnicity of perpetrator weapon used Which of the following variables is quantitative? sex age of victim record