GED Math Test #7
Rewrite this expression as a single exponent using exponent principles. (−8)^12÷(−8)^9
(−8)^3 is accurate since the exponentiation rules state: A^x÷A^y=A^x−y
A triangle's sides are equal to integral numbers of units. What is the minimal value for the triangle's perimeter if two sides are 4 and 6 units long?
A triangle's sides must all be greater than zero. The lengths of the two shorter sides must add up to more than the third side's length. Because we're seeking for the shortest perimeter, we'll assume the longer of the two speclength sides, which is 6, is the triangle's longest side. The third side must then equal or exceed 6 - 4 = 2. Because the sides are all integral numbers, the final side must be three units long. As a result, the minimal perimeter length is
4+6+3 = 13 units.
For the first month of business, Harry intends to use the revenues from his lemonade stand as shown in the table above. How much profit does he make if he buys $70 worth of lemons?
If $70, the amount spent on extra lemons, represents 35% of Herbert's wages, then 1% equals $70/35 = $2, and 15% equals $2 X 15 = $30.
What will the cost of 7 dog bones be if 13 dog bones cost $1.97? Answers should be rounded to the nearest cent.
Let x be the price of seven dog bones. It costs $1.97 for 13 dog bones. We can create a ratio by assuming that the price for 13 dog bones at $1.97 is equal to the price for 7 dog bones at cost x.
13 dog bones/1.97 dollars=7 dog bones/x dollars
131.97=7x
Multiply by two and solve.
13⋅x=1.97⋅7 13x=13.79 x=1.06076923076923
To the nearest penny, round.
x=1.06
7 dog bones cost $1.06
Kurt answers every question in a trivia competition in under a minute. How long does Kurt need to answer all 10 questions?
30 seconds make up half a minute. 30 x 10 = 300 secs.
David owns a house cleaning business and is required to provide pricing quotes to potential clients. He calculates his price by starting with a $25 base rate and adding $8 for each bathroom and $4 for each additional room.
Which of the following describes his price quotation formula if he uses P for the price, B for the bathroom, and R for other rooms?
The entire cost will be equivalent to the price quote, P. Given that there is a $25 base charge, we can start by writing P = $25 in the price quote. Our pricing quote now reads P = $25 + $8B, where P represents the base rate of $25 and B represents the cost of each restroom. Finally, add $4 for each additional room, R, and the final price is P = $25 + $8B + $4R, or P = 25 + 8B + 4R.
Maria has to figure out how much her monthly water bill will be. At $1.12 per hundred gallons, her family utilized 18,900 gallons. A $5.90 monthly account fee is also charged per family. What is the entire cost of her bill?
To calculate the entire cost, utilize dimensional analysis to combine the total number of gallons consumed with the cost per hundred gallons, then add this to the monthly account fee. It's important to remember that the fee is "per hundred gallons," not "per gallon." The following is the set-up:
Cost = 1890 gallons * $1.12/100 gallons + $5.90
Cost = 189 * $1.12 + $5.90
Cost = $211.68 + $5.90 = $217.58
Precisely which odd number(s) is(are) prime?
A prime number is a number that can only be divided by itself and by one, such as 2, 3, 5, 7, and 11," so the prime number is 3.
Johnny possesses 17 marbles. Mitchell has three times Johnny's amount of marbles. What number of marbles does Mitchell own?
Mitchell has three times Johnny's amount of marbles. Multiply 17 by 3 as a result. 17⋅3=51
Female students make up 46% of the student body at University School. How many male pupils attend this high school if the total number of students is 1250?
If females make up 46 percent of the entire student population, males make up 100 percent of 46 percent = 54 percent of the student population. To calculate the number of male pupils, multiply 54 percent by the total number of students.
Remember that 54 percent equals 54 divided by 100, or 0.54:
0.54 * 1250 = 675
Is 4 a solution to x−10≥−5x+14?
The outcome is as follows when x is altered to 4.
x−10≥−5x+14
4−10≥−5(4)+14
4+−10≥−20+14
−6≥−6
What percentage of 45 is 27?
27=45⋅x
Simplify by multiplying the two sides by 45.
x=27÷45
x=0.6
Make the decimal into a percent.
x=60
Rewrite this expression as a single exponent using exponent principles. 7^12÷7^9
The exponent rules state that 7^3 is correct because: A^x÷A^y=A^x−y
The soccer team has 27 players. Seven automobiles are taking them to the game. Each of the first 6 cars contains 4 players. How many soccer players will be riding in the seventh car?
4 x 6=24 27-24=3 3 players travel in the seventh car.
What is |a b| if a = 4 and b = 3?
The absolute value of the difference is indicated by the vertical bars surrounding a b. The distance between the simplified expression and 0 is the absolute value of an expression; the absolute value is always positive. In the expression, substitute the specified values for a and b, evaluate the difference, and apply the absolute value to make it positive.
|a − b|
= |−4 − 3|
= |−7| = 7
Remember that −4 − 3 is equivalent to −4 + −3 = −7
At the specified value of x, evaluate the expression. 12x+10atx=−12
Insert -12 for x, replace each variable with its specified value, and then evaluate the expression.
12x+10=12(−12)+10
12(-12)=-144
=−144+10
=−134
Compute (x+3)+10atx=−5
In substitution for x, use 5.
(−5+3)+10
−2+10=8
A toy company produces 15,000 toys per year. The company chooses 300 toys at random to sample for inspection. The business identifies five defective toys in the sample. Based on the sample, how many of the 15,000 total toys are expected to be defective?
According to the sample, 5 out of every 300 toys chosen randomly will be defective. As a result, a proportion can be calculated that connects the unknown number of faulty toys in the total number of toys to the faulty-to-sample ratio. In other words:
5/300 = T/1500
T is the total number of faulty toys, which is unknown. To find T, multiply both sides by 15,000 and divide the left side by 300.
15000*5/300 = T
50*5/1 = T = 250
Is -6 an answer to 2x+5>x?
As a substitute for x, use -6.
2x+5>x
2(−6)+5
−12+5>−6
−7>−6
Since this inequality cannot exist because -7 is not greater than -6, -6 is not the answer.
The following data is provided: 122, 130, 145, 154, 165, 178,
Which number, when added to the set, will increase the mean?
A data set's mean, or average, is calculated by adding all data points and dividing the total by the number of data points. A value greater than the mean must be added to the data set to boost the mean. Calculate the mean, then choose the answer option that is greater than it:
6 = 894 6 = 149 Mean = (122 + 130 + 145 + 154 + 165 + 178)
Only 150 of the options available will raise the mean.