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For the particular problem raised in the introduction, assume that the total bill is $44. to answer the question "how should the bill be split?" we will create a linear equation. the unknown is how much money a single person (besides anika) must pay, so call that x. although four people (you plus three friends) went to dinner, only three are paying the unknown amount x for a total of 3x. since anika is paying $2, the total amount paid is 3x+2 dollars, which must equal the amount of the bill, $44. thus, the equation to find x is 3x+2=44. the steps for solving a linear equation are as follows: move all of the constants to the right side. move all of the variable terms (terms containing x) to the left side. divide both sides by the coefficient of the variable to isolate the variable. you will go through these steps one at a time to solve the equation and determine how much each person should pay.
General
7 months ago
A math book sells for $106.50. (a) find the amount of sales tax, to the nearest cent, if the sales tax rate is 8.5%. (b) find the total purchase price
General
7 months ago
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?
General
7 months ago
A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average of (v+3) miles per hour. if the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?
General
7 months ago
A sample of 16 from a population produced a mean of 85.4 and a standard deviation of 14.8. a sample of 18 from another population produced a mean of 74.9 and a standard deviation of 16.0. assume that the two populations are normally distributed and the standard deviations of the two populations are equal. the null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is different than the mean of the second population. the significance level is 1%.
General
7 months ago
Evaluate the surface integral. s xyz ds, s is the cone with parametric equations x = u cos(v), y = u sin(v), z = u, 0 ≤ u ≤ 3, 0 ≤ v ≤ π 2
General
7 months ago
Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1
General
7 months ago
A tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. fresh water enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. compute the amount of salt (in pounds) in the tank at the first moment when the tank is filled.
General
7 months ago
Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800. what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour ?
General
7 months ago
The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7. if in the last game he made 77 assists, how many standard deviations is that from the mean? 1.36 standard deviations below the mean 2.71 standard deviations above the mean 1.36 standard deviations above the mean 2.71 standard deviations below the mean
General
7 months ago
Huixian needs to pack 171 pens 63 pencils and 27 erasers into identical gift bags so that each item is equally distributed among gift bags.find the largest number of gift bags can be packed
General
7 months ago
Traverion wants to find the answer to the question “how much money does the average college professor make?” He surveys 50 professors from the university in his hometown. Which best describes whether or not the results of his survey would represent the responses from the entire propulatiob of college professors?
General
7 months ago
Charles is reading about computers. He learns that a computer processor can perform one command in approximately 0.000000016 nanoseconds. What is this number expressed in scientific notation? there are multiple answers on this problem.1.6E-81.6 × 10-71.6 × 10-81.6E-71.6 × 1081.6E81.6 × 1071.6E7
General
7 months ago
Maya is trying to break or tie the league record for home runs in her softball league. She solved the inequality mc019-1.jpg to find the minimum number of home runs she must average per week over the five remaining weeks of the season to break or tie the record. What error did Maya make when she chose this inequality to model the situation?She chose the incorrect relation and should have solved 5x<30She modeled “average” incorrectly and should have solved x/5<_30She chose the incorrect relation and should have solved 5x_>30She modeled “average” incorrectly and should have solved x+5<_30
General
7 months ago
An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was interested in investigating the proportion of the new cars that experienced a mechanical problem within the first 5,000 miles driven. (a)A list of the names and addresses of all customers who bought the new cars is available. Describe a sampling plan that could be used to obtain a simple random sample of 1,000 customers from the list.Each customer from a simple random sample of 1,000 customers who bought one of the new cars was asked whether they experienced any mechanical problems within the first 5,000 miles driven. Forty customers from the sample reported a problem. Of the 40 customers who reported a problem, 13 customers, or 32.5%, reported a problem specifically with the power door locks. (b)Explain why 0.325 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven. (c)Based on the results of the sample, give a point estimate of the number of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven.
General
7 months ago
Which additional information is needed to solve this problem? John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game? A.total amount John can save in 1 week B.the cost of the game C.amount John earns per hour babysitting
General
7 months ago
Can someone please answer all these please?a) When Lucia buys olives at the deli, the scale shows 0.325 kg at $18.88 per kg. How much should she pay? b) John’s weekly wage is $1510.99 and he pays 2/3 of his weekly income in rent. How much rent does he pay each week?c) A farmer owns 780 hectares of land. During a bushfire, 195 hectares are burnt. What percentage of his land was burnt? d) Candles are $14.95 each. Estimate how much I need if I want to buy 17 of them. Show your working.e) Decrease 5000 by 13 %.f) Ray bought a computer for $1600 and then a year later sold it for $1200. Calculate his loss = Calculate his loss as a percentage of the original price of the computer = g) John spent $80 on dinner last Friday night. If this $80 is equal to 40% of his weekly income, calculate his weekly income.h) Mr Jenkins invested $7500 at his local bank at 6.5% Simple Interest per annum.What was his investment worth at the end of the first year?Question 5 a) Express this ratio in lowest terms: 50 minutes : 2 ½ hoursb) Divide $120 in the ratio 5:7c) Jane and Ben share in their lottery win in the ratio of 7: 3.If Jane’s share of the money is $5600, how much does Ben receive?
General
7 months ago
The expression 100 + 20m gives the volume of water in Eduardo’s pool (in liters) after Eduardo spends mmm minutes filling his pool. What is the volume of water in Eduardo’s pool after he fills it for 5.25 minutes?
General
7 months ago
Which of the following are solutions to the equation below? Check all that apply.3x^2 + 27x + 60 = 0 A. 4 B. –4 C. –5 D. 5 E. –27
General
7 months ago
Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, space, c, m. He wanted his balloon to be bigger, so he blew 222 big breaths of air into the balloon. Each big breath increased the balloon's radius by 1 \text{ cm}1 cm1, space, c, m. What is the ratio of the current volume of the balloon to the original volume of the balloon?
General
7 months ago
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