Basic Math Questions and Answers

Jasper is 43 years old and his daughter Freya is 7. In n-years Jasper will be four times as old as Freya is at that point. Set up and solve an equation for n. Then state both Jasper and Freya's ages after n-years.

Consider a triangle A whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of A is (1, 1), then the equation of the circle passing through the vertices of the triangle A is (A) x² + y² - 3x + y = 0 (C) x² + y² + 2y - 1 = 0 (B) x² + y² + x + 3y = 0 (D) x² + y² + x + y = 0

After the success of Sputnik 1 in October 1957 by USSR, they decided to launch Sputnik 2 by November, and this left them with only 4 weeks to design and build the spacecraft. Sputnik 2, therefore, was something of a rush job, with most elements of the spacecraft being constructed from rough sketches. It was decided that Sputnik 2 would carry a canine, thus repeating the triumph of Sputnik 1. Three dogs were trained for Sputnik 2 flight- Albina, Mushka and Laika.

Find an equation of the line satisfying the given conditions. Through (9,7) and perpendicular to y = 3x - 5 The equation of the line is (Simplify your answer.)

Find the arc length if the measure of the central angle is 80° and the radius is 8 inches. Round your answer to one decimal place. Hint: Draw a picture to help! 5.58 inches 11.16 inches 12.6 inches 44.65 inches

A large national women's retail store uses ink tags to help prevent shoplifting. The tag is fastened to clothing items, and if it is not removed with the correct device, it will "explode" and put a large ink stain on the clothing. It will also set off an alarm if taken out of the store. Five stores are selected at random to see if clerks are remembering to take the tags off before shoppers who have paid for clothing leave the store. It is determined that 48 out of 80 shoppers have an alarm go off even after having paid for their merchandise. (a) Determine whether the following statement is true or false. This sample size is large enough to find a margin of error. True False off even after having paid for their merchandise?

Verify that the equation is an identity. tan^x - sec^4x = 1 - 2 sec^2x

Write the equation of the parabola in vertex form with the given information. Vertex: (4,7) Point on graph: (2, -1) Oy = (x + 4)² + 7 Oy = -2(x-4)² + 7 Oy = -2(x + 4)² + 7 Oy = (x-4)² + 7 Oy = 2(x-4)² + 7 Oy = 2(x + 4)² + 7

Find the area of a sector that has a central angle of 200° and a diameter of 18 cm. Leave your answer in terms of л. Hint: Draw a picture to help! O 10 cm² O 1807cm² 457cm² O90лcm²

Harold cut 18 1/2 inches off a rope that was 60 inches long. How is the length of the remaining rope in inches written in decimal form?

During 1991, a total of 200,000 people visited Rave Amusement Park. During 1997, the number visiting the park had grown to 834,000. If the number of visitors to the park' obeys the law of uninhibited growth, find the exponential growth function that models this data.

Sometimes the problem will give the initial and final states in different units. In this case, you need to identify all of the pressures and all of the volumes by organizing them into a table (step 1 of our problem-solving method). Then, you need to convert all of your pressures to the same units (usually atmospheres works best) and all of your volumes to the same units (usually liters). Then you can set up the problem and solve. A balloon filled with 2.00 L of helium initially at 1.95 atm of pressure rises into the atmosphere. When the surrounding pressure reaches 470. mmHg, the balloon will burst. If 1 atm =760. mmHg, what volume will the balloon occupy in the instant before it bursts? Express your answer with the appropriate units.

A circle has a radius of 7.5mm. A sector of the circle has a central angle of 80°. Find the area of the sector. Do not round any intermediate computations. Round your answer to the nearest tenth. mm^2

Describe the transformations from the graph of f(x) = |x| to the graph of d(x)=-x-31+5. The transformations are a horizontal translation 3 units left, then a reflection in the y-axis, then a vertical translation 5 units down. The transformations are a horizontal translation 3 units right, then a reflection in the x-axis, then a vertical translation 5 units up. The transformations are a horizontal translation 3 units left, then a reflection in the y-axis, then a vertical translation 5 units up. The transformations are a horizontal translation 3 units right, then a reflection in the x-axis, then a vertical translation 5 units down. Graph the function. Ray Undo 4 2 a Redo x Reset 2

Find the distance between these two points: (4,-5) and (-4,-9)

A calculator showed the answer to a multiplication problem as 2.8e-4. Which expression is equivalent to 2.8e-4?

Mrs. Harris took 6 oranges out of the refrigerator and cut them into wedges. Each wedge represents of the entire orange. Her children ate 3 of the 4 wedges. How many wedges are left? Justify your answer. 6.NS.1

If 4000 dollars is invested in a bank account at an interest rate of 4 per cent per year, Find the amount in the bank after 12 years if interest is compounded annually: Find the amount in the bank after 12 years if interest is compounded quarterly: Find the amount in the bank after 12 years if interest is compounded monthly: Finally, find the amount in the bank after 12 years if interest is compounded continuously:

Every day that Parker doesn't play his video game "Clash of Clowns", he loses 2,000 points. He is going on a cruise for 5 days and will not have an internet connection to play the game. What will be the change in his amount of points while he is on the cruise?

Data indicates the number of global malaria cases has risen sharply since the year 2000. The equation y = 5.5x +49 approximates the number of global malaria cases y (in millions), where x = 0 corresponds to the year 2000. Assume the model remains accurate, and find the first full year in which the number of global malaria cases per year achieves 140 million. What does the value 140 represent in the given equation? A. The y-intercept B. The variable y C. The slope D. The variable x The first full year in which the number of global malaria cases per year achieves 140 million is

Hong had 7 of a spool of yarn. He used 8 Write your answer in simplest form. 3 of his yarn for a project. What fraction of the spool was used for the project? 4

Mr. Smith gave the cashier a $50 bill for a purchase of $38.70. The cashier gave him a $10 bill, two $1 bills, and three dimes back. Did Mr. Smith get the correct change back? Why or why not?

The Justinian Code is considered a milestone because it preserved many ancient Chinese legal decrees in writing served as a model for European legal systems became the first democratic constitution united Muslim and Roman thought

Cece Coakley has a Full Publishing Agreement with MOB Music who has paid her a $50,000 advance. Her songs have been streamed 20,000,000 times. The MLC pays MOB Music for those streams according to the current formula at $.001 per stream. How much will MOB Music pay to Cece, if anything? How much is remaining to be recouped, if anything?

Select the negation for each of the following statements. The sun is shining or it is raining. The sun is shining and it is not raining. The sun is not shining or it is raining. The sun is not shining and it is not raining. The sun is shining or it is not raining. The sun is not shining and it is raining. None of these. I am taking Humanities and I am taking History. I am not taking Humanities or I am not taking History. I am not taking Humanities and I am not taking History. I am taking Humanities or I am not taking History. I am not taking Humanities or I am taking History. I am not taking Humanities and I am taking History. None of these.

Determine if the following statements are true or false. Every integer is a real number. All real numbers are whole numbers. No irrational numbers are also real numbers. Every integer is also a rational number. All whole numbers are integers but not all integers are whole numbers.

Determine whether the value given below is from a discrete or continuous data set. When a car is randomly selected and weighed, it is found to weigh 1930.1 kg. Choose the correct answer below. A. A discrete data set because there are infinitely many possible values and those values can be counted B. The data set is neither continuous nor discrete. C. A continuous data set because there are infinitely many possible values and those values cannot be counted D. A discrete data set because there are a finite number of possible values

Under selected conditions, a sports car gets 14 mpg in city driving and 19 mpg for highway driving. The model G = 4+1h represents the amount of gasoline used (in gal) for c miles driven in the city and h miles driven on the highway. Determine the amount of gas required to drive 98 mi in the city and 399 mi on the highway. Select one: Ⓒa. 34 gal b. 33 gal Ⓒc. 28 gal d. 37 gal

Convert the equation to intercept form: f (x) = (x + 1)² - 25 A) f(x) = (x + 2) (x − 6) B f(x) = (x - 2) (x + 6) C f(x) = (x-4) (x + 6) D) f(x) = (x) (x - 24)

Through (-7,-11) and (-1,1) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined.

For f(x) = 5x + 5 and g(x)=x², find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The domain of f og is (Type an inequality. Use integers or fractions for any numbers in the expression. Use a com B. The domain of f o g is all real numbers. (b) (gof)(x) = (Simplify your answer.)

Thirty-one regions in a nation contain casinos. Assume the nation has 50 regions. (a) What fraction of the regions contain casinos? (b) How many regions do not contain casinos? (c) What fraction of the regions do not contain casinos? a. What fraction of the regions contain casinos?

Jose is working two summer jobs, making $10 per hour washing cars and $9 per hour walking dogs. Last week Jose worked a total of 13 hours and earned a total of $122. Write a system of equations that could be used to determine the number of hours Jose worked washing cars last week and the number of hours he worked walking dogs last week. Define the variables that you use to write the system.

Find the slope of the line that passes through (-6, -3) and (-5, 3). Write your answer in simplest form.

The average staircase has steps with a width that is 6 cm more than the height and a diagonal that is 12 cm more than the height. What is the height of the average step? a. Write a sentence explaining what you're asked to find. b. Briefly write what range of values you would expect for a reasonable solution. Also indicate the units of measure for your solution. c. Define all unknowns in terms of a single variable. (Let x = ...) Include an appropriate sketch, labeling what each unknown represents. What formula might you use? d. Using the sketch and your formula, write an equation representing this scenario. Then solve the equation. e. Write a sentence explaining your solution using the appropriate units of measurement.

Verify that the equation is an identity. tan^4 x-sec^4 x=1-2 sec ²x To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.

You are having a staring contest with your cat. You are looking down at the cat at 37° while standing 7 feet away from it. Your cat's eye line is 1 foot off the ground. How tall are you? Round to one decimal place.

Nathaniel is going to see a movie and is taking his 2 kids. Each movie ticket costs $12 and there are an assortment of snacks available to purchase for $3.50 each. How much total money would Nathaniel have to pay for his family if he were to buy 3 snacks for everybody to share? How much would Nathaniel have to pay if he bought x snacks for everybody to share? Total cost with 3 snacks: Total cost with a snacks:

Rewrite 25 1 2 25 = II H 11/3 2 with a positive exponent, then simplify.

Jared has $700 in a savings account that earns 6% interest per year. The interest is not compounded. How much interest will he earn in 4 years?

A small business employs 98 people. All of the employees work for 8 hours a day, 5 days a week. Eleven of the employees receive a wage of $45 an hour and the rest receive $30 an hour. In total, how much does the business pay its employees each week?

The regular price of a color TV is $530.66. During a sale, Hill TV is selling the TV for $441.38. Determine the percent decrease in the price of the TV. The percent decrease is % %. (Type an integer or decimal rounded to the nearest tenth as needed.)

Jalen has a scale model of a train. 2 centimeters in the model represents 3 feet in a real train. On the scale model, the wheels of Jalen's train are 3.5 centimeters apart. There are some old railroad tracks in Wyoming that are 4.5 feet apart. Would the real train be able travel on those tracks? Yes No

The distance from Saturn to Jupiter is 6.52 x 108 kilometers. How long would it take a rocket, traveling at 4.1 x 104 kilometers per hour to travel from Saturn to Jupiter? Round your answer to the nearest whole number of hours.

Approximate each number using a calculator. (a) 63.14 (b) 63.141 (a) 63.14 (c) 63.1415 (Round to three decimal places as needed.) (d) 6

Determine the simple interest. The rate is an annual rate. Assume 360 days in a year. p=$470, r= 2.75%, t = 1.25 years The simple interest is $.

Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion is within five percentage points of the true population proportion of customers who click on ads on their smartphones?

Elisa needs money to repair her home air conditioner, so she pawns her bicycle. The pawnbroker loans Elisa $270. Twelve days later, Elisa gets her bicycle back by paying the pawnbroker $291.60. What annual simple interest rate did the pawnbroker charge Elisa? Assume 360 days in a year. The pawnbroker charged Elisa a simple interest rate of % (Round to the nearest whole number as needed.)

The center of a circle is at (-3, 1) and its radius is 9. What is the equation of the circle? (x + 3)² + (y - 1)² = 81 (x+3)² + (y − 1)² = 18 (x − 3)² + (y + 1)² = 18 (x − 3)² + (y + 1)² = 81

In a mathematics class, 28 students received an A on the third test, which is 175% of the students who received an A on the second test. How many students received an A on the second test? On the second test, students received an A. ……….