Math Questions

What is the converse of the conditional statement, "If two angles are congruent, then they have the same measure"? A. If two angles are not congruent, then they do not have the same measure. B. If two angles have the same measure, then they are congruent. C. If two angles do not have the same measure, then they are not congruent. D. If two angles have the same measure, then they are not congruent.

For the 250 students asked, 96 enjoy Korean Dramas, 125 adore Western TV Series, and 148 love Anime Shows. Also, 52 enjoy both K-Dramas and Western TV Series, 56 adore both Anime and Western TV Series, and 64 love both K-Dramas and Anime Shows. Moreover, 45 loves to watch all three types of shows. How many students do not watch Anime or K- Dramas? a. 62 students b. 70 students c. 81 students d. 83 students

Plot the given graph by finding the values of y that correspond to the values of x of 0, 1, 2, 3, 4, 5, 6, and 7 on a calculator. (Remember, the numbers 0, 1, 2, and so on represent radian measure.) y = 6 sin x

This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Imme of the surroundings is 70°F. (a) Find a function T(t) that models the temperature t hours after death. (b) If the temperature of the body is now 72°F, how long ago was the time of death? (Round your answer to the nearest whole number

A boat leaves the marina and sails 5 miles west, then 10 miles southeast. How far, in miles, from the marina is the boat? (Round your answer to the nearest hundredth if necessary.)

Contestants A, B, C, D, E, and F are in a 10K race. How many different ways can a race with 6 runners be completed? (Assume there is no tie.) In how many ways can A finish first and D finish second? What is the probability that A finishes first and D finishes second? Enter a reduced fraction or decimal.

Write this statement as a conditional in if-then form: A triangle is a polygon with three sides. A. If a polygon is a triangle, then it has three sides. B. If a triangle has three sides, then it is a polygon. C. If a triangle is a polygon, then it has three sides. D. If a triangle has three sides, then all polygons have three sides.

Given u = (-6, -2) and 7 = (-3, 4), find the dot product u · v. Give just a number for your answer. For example, if you found u = 4, you would enter 4.

Match the definitions in Column A with the correct words/terms in Column B. Write your answers on a separate sheet of paper. Column A 1. Statement that can either be written "If..., then form 2. Part of a conditional statement that follows it 3. Part of a conditional statement that follows "then" 4. Denial of a statement formed by adding or removing the word NOT from a statement 5. To add or remove the word NOT from a statement to change its truth value from true to faise or from false to true 6. Statement formed from a conditional statement 7. by switching the hypothesis and conclusion Statement formed from a conditional statement by negating the hypothesis and conclusion 8. Statement formed from a conditional statement by switching and negating the hypothesis and conclusion 9. Statement combining a conditional statement and its converse, using the phrase "if and only if Column B A. hypothesis B. conclusion C. Inverse D. contrapositive E. negation F. negate G. biconditional H. converse 1. conditional

A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in the figure (a) Find a function that models the cross-sectional area of the gutter in terms of x. (b) Find the value of x that maximizes the cross-sectional area of the gutter. (c) What is the maximum cross-sectional area for the gutter?

Fill in the table using this function rule. f(x)=2√x Simplify your answers as much as possible. Click "Not a real number" if applicable.

Your credit card has a balance of $1,200. Its interest rate is 20.5%. You have stopped using the card, because you don't want to go any deeper into debt. Each month, you make the minimum required payment. Your credit card issuer recently changed their minimum required payment policy, in response to the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005. As a result, your minimum required payment is $48. (Round your answers to the nearest cent.) (a) During the September 10 through October 9 billing period, you pay the minimum required payment on September 25th. Find the average daily balance, the finance charge and the new balance. (The new balance includes the finance charge.)

A group of first ten shoppers in Town Mall have the following body temperature in Degree Celsius: 36.0, 36.2, 37, 35.9, 37, 36.2, 37.2, 36.0, 36.2 and 36.4. What is the percentile rank of the shopper with a body temperature of 36.4 Degree Celsius?

Use a calculator to solve the following equation for on the interval [-90°, 90°]. csc (θ) = -1.761 Round to one decimal place. Provide your answer below:

Some medicines can wear off in the body exponentially. In this case, assume the rate decays hourly for a starting amount of 250 mg of medication according to the equation: M = 300(0.84)t Solve this equation to determine the number of hours, t, that it will take for the initial 300 mg of medicine to decrease to 10 mg. Round to two decimal places.

A rocket is fired upward with a velocity (v) of 680 feet per second. Find how many seconds pass before the rocket reaches the ground (S=0) again. Use the quadratic equation S = - 16t² +680t. It will take seconds until the rocket reaches the ground again. (Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)

Fill in the table using this function rule. f(x)=√x+2 Simplify your answers as much as possible. Click "Not a real number" if applicable.

From her camp, a hiker walks 550 meters north, then 425 meters southeast. How far, in meters, from the camp is the hiker? Select the correct answer below: 390.58 550.00 695.07 975.00 STION

If f(x) = 3x² + 2x, find each of the following. (a) f(0) (b) f(-3) (c) f(2) (a) f(0) = (Simplify your answer.) (b) f(-3)= (Simplify your answer.) (c) f(2)= (Simplify your answer.)

Obtain an approximate value for the logarithm using natural logarithms. log 5313 log 5313 (Round to three decimal places as needed.)

Ice Cream: An ice-cream cone has a radius of 2.3 cm and a height of 6.7 cm. The cone is filled with ice-cream and one additional scoop in the shape of a sphere with the same radius as the cone is placed on top. What is the amount of ice cream in cubic cm? Round to the nearest hundredth.

Marco has joined a bowling league, and is trying to raise his average to 170. On his last four games he scored 164, 170, 165, and 171. How much will he need to score on the next game to raise his mean to 170?

Consider the polynomial below. x3 + x2 - 14x - 22 Use the remainder theorem to determine which binomial expression divides the polynomial so that the remainder is 2. A. x-2 B. x-1 C. x + 3 D. x + 4

Express the confidence interval using the indicated format. Express the confidence interval 0.469 ± 0.077 in the form of - E<p <+E. 0.4305< p <0.5075 0.392 < p < 0.469 0.469 <p <0.546 0.392<p <0.546

An ice-cream cone has a radius of 2.8 cm and a height of 6.7 cm. The cone is filled with ice-cream and one additional scoop in the shape of a sphere with the same radius as the cone is placed on top. What is the amount of ice cream in cubic cm? Round to the nearest hundredth.

Find the exact value of the following, without using a calculator. sin (sin-¹(2) + tan -1(-5) sin sin -¹+tan ¹(-5)- -0

The density of gold is 19.3 g/cm³. A weight of 1 ounce is equivalent to a mass of about 28.35 g. Which of these is closest to the side length of a cube-shaped block of gold that has a weight of 8 ounces? A. 2.27 cm B. 3.43 cm C. 9.09 cm

A graphing calculator is recommended. A function is given. f(x) = 9+ x + x² - x³ (a) Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer rounded to two decimal places. (b) Find the intervals on which the function is increasing and on which the function is decreasing. State each answer rounded to two decimal places.

If an object is dropped, the relationship between the distance it falls and the time that it has been falling is given by: d = 1/2 gt2 where: d is the distance the object falls, in feet t is the time the object falls, in seconds g is a constant due to gravity, 32.2 ft/sec² While standing on a bridge overlooking a river, you drop a rock and time how long it takes to hit the water. If the time is 1.5 seconds, how high is the bridge above the water, to the nearest whole foot? feet

A rocket is fired upward with an initial velocity v of 70 meters per second. The quadratic function h(t) = -5t² + 70t can be used to find the height h(t) of the rocket, in meters, at any time t in seconds. Find the time it takes for the rocket to reach its maximum height. What is the maximum height reached by the rocket? The rocket reaches the maximum height at The maximum height that the rocket will reach is meters.

For one week (five days) a student tracked their waiting time for parking at the college. The wait times where: 14, 11, 12, 13, and 23 minutes. Calculate the mean and median waiting time, rounded to 1 decimal place if needed.

Suppose you were asked to solve the following two problems on a test. (a) Find the remainder when 6x1000-12x562 + 15x + 25 is divided by x + 1. (b) Is x - 1 a factor of x567 - 2x400 + x +7? Obviously, it's impossible to solve these problems by dividing, because the polynomials are of such large degree. Use one or more of the theorems in this section to solve these problems without actually dividing (a) Find the remainder when 6x1000-12x562 + 15x + 25 is divided by x + 1. (b) Is x - 1 a factor of x567 - 2x400 + x9 +7? Yes No

Number of Jobs A sociologist found that in a sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.3. The population standard deviation is 2.3. (a) Find the best point estimate of the mean. The best point estimate of the mean is 7.3 (b) Find the 90% confidence interval of the mean number of jobs. Round intermediate and final answers to one decimal place. (c) Find the 95% confidence interval of the mean number of jobs. Round intermediate and final answers to one decimal

The Coconut Delight Bakery can produce 500 coconut tarts in a week at a total cost of $2000 and 700 coconut tarts at a cost of $2500. What is the weekly fixed cost in dollars per coconut tart? Write your answer as an integer and donot use the dollar sign symbol.

Compute the discriminant of 8x² - 6x - 6 = 0. The discriminant is: How many real solutions does the equation, 8x2 - 6x - 6 = 0, have? No real solution One real solution Two real solutions None of the above

If P dollars is invested in an account that earns interest at 7% compounded annually, the amount available after t years is A = P(1 +0.07). How many years will it take for $1500 in this account to grow to $3000? It will take approximately years for $1500 in this account to grow to $3000. (Round to the nearest whole year.)

Which of the following describes the zeros and end behavior when the function is graphed? A. zeros: x= -6,x= -1,and x = 1; As x decreases in value, f(x) increases in value. Ax increases in value, f(x) increases in value. B. zeros: x= -6,x= -1,and x = 1; As x decreases in value, f(x) decreases in value. As x increases in value, f(x) increases in value. C. zeros: x= -6and x = 1; As x decreases in value, f(x) decreases in value. As x increases in value, f(x) increases in value. D. zeros: x= -6and x = 1; As x decreases in value, f(x) increases in value. As x increases in value, f(x) increases in value.

A plane is 115 mi north and 176 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree.

The formula for the braking distance of a car is: d =V²/2g(f+ G) where: d is the braking distance (in feet) V is the initial velocity of the car (in feet per second) G is the roadway grade (written in decimal form) f is the coefficient of friction between the tires and the roadway g is the acceleration constant due to gravity (32.2 ft/sec²) a) If a car's speed was 47 miles per hour, what value would be used in this formula for V? Round to the tenths place. Recall 1 mile = 5280 feet. feet per second b) If a car was going 86 feet per second when the driver applied the brakes, on a road with grade G = 0.03 and a coefficient of friction of f = 0.8, what distance would it go before stopping? Round to the tenths place. feet

Find the interest rate to the nearest hundredth of a percent that will produce $2000, if $1500 is left at interest compounded quarterly for 4.5 yr. Use the formula A=P (1+r/n)tn The interest rate to the nearest hundredth of a percent is. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Find the exact value of sinπ/12 using the half-angle identity. Support your answer with a calculator approximation.

Suppose that you are grading a classmate's work on a compound interest problem, shown below. If there is a mistake, select the step where the mistake was made. If there is no mistake, select "No mistake." Problem: How long will it take for an investment of $3500 to double if it is invested at 2.5% annual interest compounded monthly? Round your answer to three decimal places. Step 1: 7000-3500 (1 + 0.25) 12 Step 2: 2 = (1 + 0.25) 12 12 Step 3: log(2) = log ((1+0,25)¹²) Step 4: log(2) Step 5: t = O Step 1 Step 2 Step 3 Step 4 Step 5 No mistake 12t log(1 + 025) 12 log(2) (12 log (1+0)) 2.801 years 12

Consider the case of a male student who has three beers and weighs 120 pounds. Simplify the Widmark equation as much as possible for this case, rounding any constants to 3 decimal places.

Airports A and B are 462 km apart, on an east-west line. Jim flies in a northeast direction from A to airport C. From C he flies 353 km on a bearing of 129°20' to B. How far is C from A? The distance between C and A is km. (Round to the nearest kilometer as needed.)

In a class, having more number of girls than boys, students were given a task of collecting flowers. Each boy collected 5 flowers whereas each girl collected 3 flowers. If a total of 46 flowers were collected, which of the following could be the number of girls in the class?

Landon went to the store to buy a new TV. The sales clerk asked "How large is your current TV?". Landon replied "It is 37 inches wide and 21 inches tall". The sales clerk explained that TVs are sold by the measurement along the diagonal of the screen. Save Landon a trip home to remeasure What is the diagonal measurement for Landon's current TV, rounded to one decimal place?

Use the multiplication principle to solve. An auto manufacturer produces 8 models, each available in 9 different colors, with 6 different upholstery fabrics and 7 interior colors. How many varieties of car are available?

A quadratic function f is given. f(x) = -x² + 12x (a) Express f in transformation form. f(x) = (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist (x, y) = vertex x-intercepts y-intercept (x, y) = (x, y) = (x, y) = ( (smaller x-value) (larger x-value)

The height of a trapezoid is 15 feet and the two bases are 10 and 11 feet. Find the area of the trapezoid.

A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?