Numbers and Algebra
Put the following number into scientific notation:
456.23
4.5623 * 102
The first 6 terms of an arithmetic sequence are given:
7, -17, -41, -65, -89, -113
What is the common difference?
-24
Calculate the amount of interest earned when 1000 RUB (Russian roubles) are invested for 9 years at a nominal rate of 5.3% compounded annually. Give your answer to the nearest rouble.
$592
What is the y-intercept of the function below?
f(x)=3x2-12x+6
6
The function N(t)=41(1.77)t represents the number of students at Jefferson infected with a case of "I should be on break already bro what even is this week >:( bro??" where t represents the number of days since the first day of school after Thanksgiving break and N represents the number of infected students.
What is the initial number of infected students?
41
Put the following number into scientific notation and round to 3 significant figures:
5,892
5.90 * 103
The 2nd term of an arithmetic sequence is 21 and the 5th term is 60. What is the common difference?
13
You decide to invest $2,300 in an account with a 2.4% nominal annual interest rate. Given that the interest is compounded monthly, find the minimum number of years that it will take for your investment to double.
29 years!
What is the equation of the line that passes through the points (1,3) and (-2, -6)
Multiple answers are acceptable!
y-3=3(x-1)
y+6=3(x+2)
y=3x
The number of people in San Antonio with a Tesla, N, can be modelled with the following function:
N=9500(1.09)t
Where t represents time in years since Tesla's release in 2014.
Based on this model, how many people in San Antonio will have a Tesla in 2021?
17,366 or 17,367
Perform the following operation and ensure that your answer has the correct number of significant figures.
(5.9 * 104) (6.23 * 106)
3.7 * 1011
10.5, 5.25, 2.625, ...
What is the 5th term of the sequence?
0.65625
A teacher takes out a loan to buy a house that is worth $250,000. The loan earns interest at an annual rate of 3% per year, compounded annually. The teacher will pay off the loan in monthly installments for 30 years. Payments are made at the beginning of each month.
What is the value of the teacher's monthly payment to the nearest cent?
$1,045.98
What is the equation of a line perpendicular to the line y=2x+10 that passes through the point (10, -3)? Give your answer in gradient-intercept form.
y=-1/2(x)+2
Manufactured by Ford in from 1908-1927, this was the first affordable, mass-produced car that made car ownership accessible to the middle-class in the United States of America.
What is the Model T?
Simplify the following expression:
y2x
Determine whether the sequence below is arithmetic or geometric. Then find the 7th term of the sequence using 3 significant figures.
2, -5, 12.5, -31.25, ...
488
John retires when he is 70 years old and has $800,000 in his annuity plan which pays 4.7% interest rate annually. He plans to withdraw $4,500 at the end of each month from this annuity account until it runs out.
Calculate John's age, to the nearest year, when the annuity account runs out of money.
John will be 95 and still going strong :)
Given the function f(x)=3x-2,
find the inverse function.
f-1(x)=log3(x+2)
N=6(2.05)0.8t
where t is the number of days since the first students were infected.
Determine the number of days it would take for all 1700 students to catch the cold.
10 days!
Simplify the following expression:
a10b-20
Given an arithmetic sequence with the terms:
6, 7, 8, 9, 10, ...
find the sum of the first 100 terms of the sequence.
5,550
A car is purchased in 2016 for $25,000. The car depreciates each year by a constant rate. If the car is worth $8,600 in 2023, what is the annual rate of depreciation?
Give your answer correct to the nearest tenth of a percent.
-14.1%
What is the domain and range of the function below?
x2+12x-8
Domain: All real numbers!
Range: y is greater than or equal to -44
This Canadian supermodel famously declared "I don't get out of bed for less than $10,000."