Basic Math Questions and Answers

What is the unfilled volume inside the cylinder? A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. (A) 320π cubic units (B) 597π cubic units (C) 640π cubic units (D) 725π cubic units

You give up a full-time salary of $45,000 a year to go to school for 2 years. The total cost of going to school is $30,000. If you want to be able to recover your investment in 5 years or less, what is the minimum salary you would need to earn upon earning your degree? (1) $51,000 (2) $60,000 (3) $69,000 (4) $75.000

A brand new filled can of chicken broth is 10 cm tall and has a radius of 10 cm. Mishka uses some of the broth to cook and now the broth left in the can is 6 cm high. How much broth did Mishka use? Round only your final answer to the nearest whole number. (1) 943 cm (2) 1257 cm (3)1885 cm (4) 4712 cm

Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water's edge. The equation of her average change in elevation over time is e = 300 - 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?

Kyla applied rm · T0.3 to triangle ABC. What mistakes did she make? Check all that apply. (A) She applied the rotation to the triangle first. (B) She applied the reflection to the triangle first. (C) She changed the size of the triangle instead of just applying a translation. (D) She translated the triangle down instead of just applying a reflection. (E) She applied a rotation instead of a reflection.

Let f be a function and let g(x) = f(x + 2) + 3 . Describe how to draw the graph of g using the graph of f. Shift the graph of f left 2 units and down 3 units Shift the graph of f right 2 units and down 3 units Shift the graph of f left 2 units and up 3 units Shift the graph of f right 2 units and up 3 units

Consider the situation below and answer the questions that Follow. San Jose National High School Mathematics Department conducted the Math Camp where students can play Rubik's cube, tangrams, and Sudoku. The Venn diagram below shows the number of students who joined the Camp. 1. How many students joined the Math Camp? 2. How many students played Rubik's cube? 3. If a student is randomly chosen, what is the probability that the student played tangrams or Sudoku? 4. If a student is randomly chosen, what is the probability that the student played Rubik's cube or Sudoku?

Rewrite the rational expression with the given denominator. 19/20y=2/40y^3

Juan saved $1,000 from his summer job cleaning pools. Which of these savings vehicles would work best for him if he doesn't need access to the money for a number of years AND wanted to earn the highest interest rate? (A) Regular savings account (B) Money Market account (C) Checking account (D) Certificate of Deposit

Solve the following logarithmic equation. Express irrational solutions in exact form. log (7x + 6) = 1 + log (x - 1) Rewrite the given equation without logarithms. Do not solve for x. (Do not simplify. Use integers or fractions for any numbers in the equation.)

Find the solution of the linear inequality and express the solution set in set-builder notation and interval notation. Graph the solution set on the real number line. X+1 <3

In a certain country, the number of deaths due to heart disease increased from 235 in one year to 250 in the next year. What percent increase in deaths due to heart disease does this represent? (Round your answer to two decimal places.)

A condominium is taxed based on its $78,546 value. The tax rate is $3.43 for every $100 of value. If the tax is paid before March 1, 3% of the normal tax is given as a discount. How much tax is paid if the condominium owner takes advantage of the discount?

Find the area of the rectangle in terms of x. 11x/x-25 feet and x+5 The area of the rectangle is feet².

Use of an aerodynamic helmet on a bicycle increases a cyclist's average speed by 4 miles per time for a 48 mile trip is reduced by 36 minutes. a). Use d = rt and the known information to write 2 equations for the bicycle's trip. One equation will represent the trip without the aerodynamic helmet, and the other equation will represent the trip with the aerodynamic helmet. b). Use substitution to solve the system of 2 equations. What is the average speed for the trip using the aerodynamic helmet?

In order to start a small business, a student takes out a simple interest loan for $5000.00 for 6 months at a rate of 10.50%. a). How much interest must the student pay? b). Find the future value of the loan.

Please express the following Roman Numeral as a Hindu-Arabic Numeral: MMMDCCCLXXVII

A television sells for $550. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $150 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of the purchase? $ __ is saved by paying the total amount at the time of purchase.

Zack is taking inventory of loaves of bread at the grocery store where he works. There are 20 loaves in a full case, and Zack has 3 partially filled cases: 1 case is 1/2 full, 1 case is 1/4 full and 1 case is 2/5 full. How many total loaves of bread are in the 3 partially filled cases? A. 11 B. 16 C. 19 D. 23 E. 30

Six refractory anchors must be laid out equal distance apart on a 16-foot slab furnace ceiling. What is the distance (in feet and inches to the nearest 1/8") between any two of the clips? (Hint: draw a picture of this problem.) Note: there will be a clip at both ends of the ceiling.

The table shows the number of cups of water required when cooking different amounts of rice. Which statements apply to the ratio of rice and water? Choose two options. (1)The amount of rice is the dependent value. (2)The amount of water is the dependent value. (3)The amount of rice is the independent value. (4)The amount of water is the independent value. (5)The values cannot be labeled as dependent or independent without a given equation.

Amanda has $21,400 in the bank. The account will earn 1.9% in simple interest for the next 4 years. How much interest will Amanda earn?

A farmer recently purchased her neighbor's farm. Before the purchase, the farmer owned a total of 343 acres of land. After the purchase, she owned a total of 501 acres of land. Determine the percent increase in the number of acres of land owned by the farmer. The number of acres of land owned by the farmer increased by about ____%

If the apprentice wishes to cut a 20-foot section of angle in seven identical lengths, what will the measurements be in fractional inches to the nearest 1/32" (assuming zero loss of metal due to cutting)?

Mark borrowed $18,036 to help pay for expenses. If the loan carries an annual interest rate of 4.3% and he wants to be debt free in 2 years by making monthly payments, how much will each payment be?

A sample of 27 television tubes produced by a company showed a mean lifetime of 1138 hours and a standard deviation of 193 hours. Estimate the standard deviation of the population of all television tubes produced by this company. Round your answer to 3 decimal places.

A new fertilizer was applied to the soil of 296 bean plants. 90% showed increased growth. Find the margin of error and 95% confidence interval for the percentage of all bean plants which show increased growth after application of the fertilizer. Report answers to at least 2 decimal places.

(a) If N is the population of the colony and t is the time in days, express N as a function of t. Consider N₀ is the original amount at t= 0 and k≠0 is a constant that represents the growth rate. N(t) = □ (Type an expression using t as the variable and in terms of e.)

The Happy Taco restaurant employs 12 people. If 3 people have an annual salary of $28,000, 4 people have an annual salary of $34,000, 4 people have an annual salary of $45,000, and 1 person has an annual salary of $65,500 find the average salary for the employees.

How much would you have to deposit at the end of the year in an account that pays an interest rate of 7.16% compounded monthly if at the end of 15 years you want $20,000 in the account? Use the TMV calculator to fill in the table. N_____________ I%__________ PV__________ PMT__________ FV___________ P/Y___________ C/Y_________

Sarah wants to save for a car that costs $5000. She has $4250 in a savings account earning 1.49% compounded quarterly. If Sarah has four years until she gets her driver's license, will she have enough to buy a car? Use the TVM calculator to solve Explain.

A group of geometry students wrote the following definitions for parallel lines. Jennifer: Two lines that never intersect. Bethany: Two lines whose perpendicular distance between points remains constant. Darius: Two lines are parallel if and only if they lie in the same plane and corresponding points are equidistant. Which definition(s) is/are the most precise? a)Bethany b)Darius c)Jennifer d)All are precise definitions.

Translation A maps (x, y) to (x +r,y+s). Translation B maps (x, y) to (x – a,y+b). Translate a point using Translation B, then Translation A. Write a rule for the final image of the point. (x,y) → (._____________ ___________) a). type x coordinate. Don't type parenthesis. * b). type y coordinate. Don't type parenthesis.

What does Gelman mean by a "straw-man" null hypothesis? a)A hypothesis with less than a .01 probability of being supported in a study b)A null hypothesis known or suspected to be false, set up to be rejected c)A hypothesis that is full of straw d)A hypothesis about gender differences among farmers

Which of the following is the best definition for a circle? a)The set of points on a plane, with an enclosed arc which has 360° b))The set of points on a plane, which are equidistant from a given point. c)one-sided figure which has no beginning or end. D)A one-sided figure with a total of 360° in the interiorangles.

Which refers to the null hypothesis for this new test? Ho: population mean of differences is zero He: population mean of differences is not zero Ho: sample mean of differences is zero He.: sample mean of differences is not zero

Find the LCD for the list of rational expressions. 8x+1/x2 + 5x-6 . 4x / x2+4x-5 The LCD is

Simplify the difference b - 4 / b2+ 2b-8 -b+2 / b2-16] State any restrictions on the variable. A. -4(2b – 5)/(b + 4); b≠-4 B. -4(2b -3)/ (6 – 4)(b + 4)(b + 2); b≠-2 or ±4 C. -4(2b – 3)/(b – 4)(b + 4)(b - 2); b≠2 or ±4 D.-4(2b – 3)/(b – 4)(b + 4)(b − 2); b ≠2 or ± 4

Ana drew a map of the Panama Canal. In the scale Ana used for the map, 4 centimeters represents 20 kilometers. The actual length of the Panama Canal is 82 kilometers. What is the length in centimeters of the Panama Canal on Ana's map?

One year Perry had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.17. Also, Susan had the lowest ERA of any female pitcher at the school with an ERA of 3.16. For the males, the mean ERA was 4.242 and the standard deviation was 0.873. For the females, the mean ERA was 3.949 and the standard deviation was 0.874. Find their respective Z-scores. Which player had the better year relative to their peers, Perry or Susan? (Note: In general, the lower the ERA, the better the pitcher.) a)Perry had an ERA with a Z-score of b)Susan had an ERA with a Z-score of

Jack and Jill deposited $1000 in a savings account with an annual interest rate of 8.3% compounded semiannually when they got engaged to be married. It took them 2 years to plan their wedding. If they withdraw the money on their wedding day, how much money will Jack and Jill have to take on their honeymoon? a)$1089.32 b)$1176.62 c)$1305.25 d) $1324.15

solve by graphing x + 2y=6 3x + 6y=18 Select the correct answer below: a) Infinite solutions in the form (x,-2-3) b)Infinite solutions in the form (x,-3) c)Infinite solutions in the form (x,- +3) d)Infinite solutions in the form (x, +3) e)One solution: (2, 2) f)No solution:

Cheryl wants to save for a car. She has $4050 in a savings account earning 2.2% compounded quarterly. If Cheryl has four years until she gets her driver's license, will she have enough to buy a used car that costs $4500? If not, how much more does she need?

Sarah invested $3,800 in an account paying an interest rate of 3.6% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 15 years?

How long would it take, in days, to spend $200,000 if a person spent $1 a second until the $200,000 is used up? Complete parts (a) and (b) below. a) Estimate the time it would take, in days. Choose the correct estimate below. A. 200 B. 4 C. 20 D. 2 b) Calculate the actual time it would take, in days. days (Type an integer or a decimal. Round to the nearest tenth as needed.)

Eve is 20 years old and wants to save $2 million for retirement at age 60. Assume she invests in a savings account that earns 5.1% interest compounded semiannually. How much does Eve need to invest to get started? a) $273,477.34 b)$266,794.47 c) $66,794.26 d) $173,277.43

Suppose you are depositing an amount today in an account that earns 5% interest, compounded quarterly. If your goal is to have $5000 in the account at the end of six years, how much must you deposit in the account today? Round to the nearest dollar. $3711 $1289 $703 $985

Jackie and Billy are saving for their first child. They know he/she will be expensive and would like an extra $5000 in the bank when the baby comes. Jacke and Billy are not planning to have a baby for at least 3 years. They found a savings account that will earn 5.2% interest compounded quarterly. How much money should they invest to be financially prepared for their first child? Round to the nearest dollar

Tammy, Alonzo, and Hong served a total of 65 orders Monday at the school cafeteria. Alonzo served 2 times as many orders as Hong. Tammy served 7 fewer orders than Hong. How many orders did they each serve? Number of orders Tammy served: ▯ Number of orders Alonso served: ▯ Number of orders Hong served: ▯

Chuck hires 21 people to pick crops from his field. He agrees to pay them $2.50 for each unit they pick. Estimate the total amount of money he will have to pay if each person picks 8 units. Choose the correct estimate below. A. $40 B. $4,000 C. $400 D. $800