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.
In substitution for x, use 5.
(−5+3)+10
−2+10=8
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
(−8)^3 is accurate since the exponentiation rules state: A^x÷A^y=A^x−y
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
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.
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
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
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.
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
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.
Mitchell has three times Johnny's amount of marbles. Multiply 17 by 3 as a result. 17⋅3=51
30 seconds make up half a minute. 30 x 10 = 300 secs.
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
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.
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
The exponent rules state that 7^3 is correct because: A^x÷A^y=A^x−y
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.
4 x 6=24 27-24=3 3 players travel in the seventh car.
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
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