Basic Math Questions and Answers

A hot-air balloon is rising vertically 12 ft/sec while the wind is blowing horizontally at 6 ft/sec. Find the angle that the balloon makes with the horizontal. Round to the nearest tenth of a degree, if necessary. 52.1° 50.3° 26.6° 63.4°

Given the exponential growth function f(x) = 77(1.0275)* What is the initial value of the function? Enter an integer or decimal number [more..] What is the growth factor, or growth rate of the function (as a percent)?%

Javier purchased a digital camera for $384. The value of the camera depreciates by 25% every year. This situation represents ... The rate of growth or decay, r, is equal to ... So the value of the camera each year is ... times the value in the previous year. It will take ... years for the value of the

Fill in the blank in the following statement. The wholesale price of a TV is 10% less than retail price. Therefore, the wholesale price is times the retail price. The wholesale price is times the retail price.

A retiree invests $9,000 in a savings plan that pays 6% per year. What will the account balance be at the end of the first year?

The distribution of weights (rounded to the nearest whole number) of all boxes of a certain cereal is approximately normal with mean 25 ounces and standard deviation 2.5 ounces. A sample of the cereal boxes was selected, and the weights of the selected boxes are summarized in the histogram shown. Which of these values is the best estimate of the number of boxes in the sample with weights that are more than 2 standard deviations above the mean?

Solve the equation by using the quadratic formula: 3x² + x = 4 x=-1 or x=-4/3 x=1 or x = 4/3 x=1 or x=-4/3 x = -1 or x = 4/3

The length, I, that a spring is stretched varies directly as the amount of force, F, applied to the end of the spring. When a force of 10 pounds is applied to a spring, it stretches 3 inches. How much will the same spring stretch if the force is increased to 15 pounds? A. 8 inches B. 7.5 inches C. 4.5 inches D. 2 inches

The revenue, in thousands of dollars, that a company earns selling lawnmowers can be modeled by R(x) = 90x-x^2 and the company's total profi in thousands of dollars, after selling x lawnmowers can be modeled by P(x) = -x^2 +30x - 200. Which function represents the company's cost, in thousands of dollars, for producing lawnmowers? (Recall that profit equals revenue minus cost.) A. C(x) = 60x+ 200 B. C(x) = -60ײ - 200 C. C(x) = -2x² - 60x-200 D. C(x) = 2x² +60x+200

Write the point-slope form of the line's equation satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope = 4, passing through (3,2) What is the point-slope form of the equation of the line? (Simplify your answer. Use integers or fractions for any numbers in the equation.) What is the slope-intercept form of the equation of the line? (Simplify your answer. Use integers or fractions for any numbers in the equation.)

More people are purchasing food from farmers' markets around the country. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 2.8% every six months. If there were 7823 farmers' markets in 2019, how many will there be in 4 years? Given the exponential growth scenario above, answer the following questions: What is the initial value, Po in this problem? What is the growth factor or growth rate (as a decimal value)? What is the n value, or number of time periods?

Maria invests $9,000 at 11% simple interest for 1 year. How much is in the account at the end of the 1 year period?

The depth of a pond decreases at a rate of 2% per year. If the pond currently has a depth of 5 feet, in approximately how many years will the depth of the pond fall below 4 feet? A 11 years B. 50 years C 6 years D. 24 years

What are the characteristics of the function f(x) = 2(x-4)^5? A. It is a reflection and a translation to the right of the parent function. B. Both ends of the graph of the function go up. C. It has 4 zeros and at most 5 relative maximums or minimums. D. The left end of the graph of the function goes down, and the right end goes up. E. It has 5 zeros and at most 4 relative maximums or minimums. F. It is a vertical stretch and a translation to the right of the parent function.

Emma says that for f(x)=8,000(0.95), the exponential growth is 0.95 and the y-intercept is 8,000. What is her error? Choose the correct answer below and fill in the answer box(es) to complete your choice. A. In an exponential growth model y=a-b*, the exponential growth is a and the y-intercept is b. So, the exponential growth is and the y-intercept is B. For f(x) to be an exponential growth model, a> and b>1. Since b=0.95, it should be exponential decay, not growth. C. In an exponential growth model y=a-b*, the exponential growth r is found using the equation r=1-b. So, the exponential growth is D. Emma found the x-intercept instead of the y-intercept The x-intercept is 8,000 and the y-intercept is

Francine currently has $75,000 in her 401k account at work, and plans to contribute $8,000 each year for the next 10 years. How much will she have in the account in 10 years, if the account averages a 5% annual return?

Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on. She writes the equation of the function like this: E(x) = 20x-50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars. What does the slope of Jessica's function represent? A. For each additional door she knocks on, her earnings will increase by $20. B. For each additional set of books she sells, her earnings will increase by $50. C. For each additional set of books she sells, her earnings will increase by $20. D. For each additional door she knocks on, her earnings will increase by $50.

Simplify: 24x4-16x³ +8x²+2/2x² 12x2² - 8x + 4 + 1/x² 20x²-16x³ +2 12x-²8x +6 12x² + 8x + 4 + 1/x2

If the first step in the solution of the equation -x + 6 = 5 - 3x is "subtract 5," then what should the next step be? add 3x subtract 6 add x

In 2000, 49% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.1% per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents,

Arc length = 2.84, Angle = 50°, Diameter = ? 2.55 Mr. Epsilon was swimming in the pool. 3.25 The victim was not attacked by a couga 3.5 Dr. Alpha was sweating in the atrium. 6.5 There was no venomous bite involved. Stretch the Y

Jay and Kevin are shoveling the snow off a driveway. Working together, they can clear the driveway of snow in 14 minutes. Working alone, it would take Kevin 21 minutes longer to clear the driveway of snow than it would take Jay working alone. When jis the number of minutes it would take Jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation: How long would it take Jay to clear the driveway of snow working alone? 7 minutes 21 minutes 35 minutes 42 minutes

Solve the following quadratic equation using factoring: 7x² - 10x + 3 = 0 x = 3/7/or x = 1 x = -3/7/or x = -1 x = -3/7/or x = 1 x = 3/7/or x = -1

Arc length = 9.72, Angle = 116°, Radius = ?

At a particular college, 90% of the undergraduates are female. If 2970 women attend the college, how many total undergraduates attend the college?

Find all the roots and check your answers. x³ +10x²+21x=0

How many times does the graph of the function below intersect or touch the x-axis? y=-2x² + 3x + 5 A. 1 B. 3 C. 0 D. 2

Write the first ten terms of a sequence whose first term is -10 and whose common difference is -2.

In which direction does the left side of the graph of this function point? f(x) = 3x³ - x² + 4x − 2

The zebra mussel, Dreissena polymorpha, filters particulate organic carbon (POC) from water as part of its feeding pattern. The concentration, c, of POC (in milligrams per liter) remaining in a particular bay m months after the introduction of a population of zebra mussels can be estimated using the following equation. c = 0.4.0.9m According to this estimate, how many milligrams per liter of POC were in the bay when the zebra mussels were first introduced?

Martha manages a home Improvement store and uses this function to model the number of customers that visit the store each hour on Saturday afternoon. n(t) = -2.82t2 + 25.74t + 60.87 Which graph would most likely be associated with this model?

The point (-2, 5) is located in quadrant IV I II III

Factor, if possible. 9x² +24x+16 Select the correct choice below and fill in any answer boxes within your choice. A. 9x² +24x+16= (Type your answer in factored form. Factor completely.) B. The polynomial is prime.

During their freshman year, Derek's GPA was 3.4 and Terry's was 3.0. During their sophomore year, Derek's GPA was 3.7 and Terry's was 3.6. Which of the following is not necessarily true? Choose the correct answer below. A. Terry's overall GPA for the two-year period could be lower, higher or the same as Derek's overall GPA for the two-year period. B. Terry's overall GPA for the two year-period was somewhere between 3.0 and C. Derek had a higher GPA than Terry during their freshman year and again during their sophomore year. D. Derek's overall GPA for the two-year period was higher than Terry's because their GPA's may have been weighted differently. E. Terry had a lower GPA than Derek during their freshman year and again in their sophomore year. F. Derek's overall GPA for the two year-period was somewhere between 3.4 and 3.7.

The image is the result of an isometric transformation of its pre-image because AB= A'B' =√10 AC = A'C' = 2√2 BC = B'C' =√10 a reflection has occurred a rotation has occurred the two triangles are congruent a dilation has occurred

A roasted turkey is taken from an oven when its temperature has reached 185° Fahrenheit and is placed on a table in a room where the temperature is 75° Fahrenheit. Provide your answers accurate to at least 2 decimal places. (a) If the temperature of the turkey is 145° Fahrenheit after half an hour, what is its temperature after 45 minutes? Fahrenheit (b) When will the turkey cool to 100° Fahrenheit?

Find the area of a regular hexagon with a side length of 4 cm and an apothem of approximately 3.5 cm. Area ≈ [?] cm²

Solve the formula Ax+By = C for A. A. A = C-By/x B. A=C/X+By C. A = C+By/x D. A = C- By/x

Factor. 6x2-x-12

Solve the quadratic equation by factoring. x² - 7x-8=0 x= -4 or x = 2 x = 8 or x = -1 x= -8 or x = 1 x = 4 or x = 2

The polynomial (x-2) is a factor of the polynomial 3x² - 8x + 2. A. True B. False

Runners in a long distance race start out going 8 kilometers east and then head north for the remainder of the race. The finish line is 10 kilometers from the starting line. How far did the runners travel north? 2 km 6 km 10 km

Clint's salary increased from $22,000 to $28,600 over a three-year period. Helen's salary increased from $27,000 to $35,100 over the same period. Whose salary increased more in absolute terms? In relative terms? Explain. Whose salary increased more in absolute terms? Select the correct choice below and fill in the answer box(es) to complete your choice. A. Helen's salary increased more, because her salary increased by $ amount that Clint's salary increased. This is more than $ B. Clint's salary increased more, because his salary increased by $ amount that Helen's salary increased. C. Neither person's salary increased more, because both of their salaries increased by $ This is more than $ the the

Point (-5, 5) lies in Quadrant I IV II III

Two lighthouses are located on a north-south line. From lighthouse A the bearing of a ship 3742 m away is 129 °. From lighthouse B the bearing of the ship is 39°. Find the distance between the lighthouses.

Select the axis of symmetry and y-intercept of f (x) = x² + 4x - 5 (Choose 2) (0,8) (0.-1) (0,3) x=1 (0.-5) x=2 □ x=-2 x=0 □ (0, 1) x=-1 x = 3

Find the average rate of change of the function f(x)=x² + 5x from x₁ = 2 to X₂ = 4. The average rate of change is (Simplify your answer.)

Solve for x. 3(x + 2) = 12 x = 6 x = 2 x = 3 1/3 x=4 2/3

Solve for x. 8(x + 1)-3(x + 4) = 7(2 - x) x=11/12 X x=-11/ x=-11/2 x = 1/

Simplify (assuming that a is positive): √50a² 5av10 2a √5 25a√2 Sa√2