Answers
Answer:
D.Step-by-step explanation:
"or" means sum, that is all x≤-2 plus all x≥3
≤-2 mens all numbers less than -2 and the -2
≥3 mens all numbers greater than 3 and the 3
Related Questions
Find the inverse of the function f(x) = 2x² - 3x NO ABSURD ANSWERS IF YOU DON't WANT YOURSELVES TO GET REPORTED!
Answers
Answer:
[tex]\boxed{f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-3x[/tex]
[tex]f(x)=y[/tex]
[tex]y=2x^2-3x[/tex]
Switch variables.
[tex]x=2y^2-3y[/tex]
Solve for y.
Multiply both sides by 8.
[tex]8x=16y^2-24y[/tex]
Add 9 on both sides.
[tex]8x+9=16y^2-24y+9[/tex]
Take the square root on both sides.
[tex]\sqrt{8x+9} =\sqrt{16y^2-24y+9}[/tex]
Add 3 on both sides.
[tex]\sqrt{8x+9}+3 =\sqrt{16y^2-24y+9}+3[/tex]
Divide both sides by 4.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{\sqrt{16y^2-24y+9}+3}{4}[/tex]
Simplify.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y-3+3}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}=y[/tex]
Inverse y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}[/tex]
Answer:
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Step-by-step explanation:
[tex] f^{-1}(x) = 2x^2 - 3x [/tex]
Change function notation to y.
[tex] y = 2x^2 - 3x [/tex]
Switch x and y.
[tex] x = 2y^2 - 3y [/tex]
Solve for y.
[tex] 2y^2 - 3y = x [/tex]
Complete the square on the left side. We must divide both sides by 2 to have y^2 as the leading term on the left side.
[tex] y^2 - \dfrac{3}{2}y = \dfrac{x}{2} [/tex]
1/2 of 3/2 is 3/4. Square 3/4 to get 9/16.
Add 9/16 to both sides to complete the square.
[tex] y^2 - \dfrac{3}{2}y + \dfrac{9}{16} = \dfrac{x}{2} + \dfrac{9}{16} [/tex]
Find common denominator on right side.
[tex] (y - \dfrac{3}{4})^2 = \dfrac{8x}{16} + \dfrac{9}{16} [/tex]
If X^2 = k, then [tex] X = \pm \sqrt{k} [/tex]
[tex] y - \dfrac{3}{4} = \pm \sqrt{\dfrac{1}{16}(8x + 9)} [/tex]
Simplify.
[tex] y = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Back to function notation.
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
11/10= x+2/5 Please Explain
Answers
Answer:
x=7/10
Step-by-step explanation:
2/5=4/10
11/10=x+4/10
11/10-4/10=x
7/10=x
Answer:
x=7/10 or 0.7
Step-by-step explanation:
I turned the fractions into decimals
so
1.1=x+0.4
subtract 0.4 from 1.1 to get 0.7
Turn it into a fraction which is 7/10
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere?
Answers
Answer:
Volume of the sphere is 66.67r/h
Step-by-step explanation:
Hello,
Volume of a sphere = ⁴/₃πr³
Volume of a cylinder = πr²h
The volume of the cylinder = 50ft³
But the cylinder and sphere both have the same radius and height
Volume of a cylinder = πr²h
50 = πr²h
Make r² the subject of formula
r² = 50/πh
Volume of a sphere = ⁴/₃πr³
Put r² into the volume of a sphere
Volume of a sphere = ⁴/₃π(50/πh)r
Volume of a sphere = ⁴/₃ × 50r/h
Volume of a sphere = ²⁰⁰/₃ r/h
Volume of a sphere = 66.67r/h
The volume of the sphere is 66.67r/h
If you flip a coin three times in the air, what is the probability that tails lands up all three times? A. 1/2 B. 1/8 C. 1/4 D. 1/6
Answers
Answer: A) 1/2
Step-by-step explanation:
Answer:
If you flip a coin three times in the air, what is the probability that tails lands up all three times?
Step-by-step explanation:
1/2
i need help with this
Answers
Answer:
Step-by-step explanation:
diameter=2×5=10 cm
32/10=3.2≈3
128/10=12.8≈12
total number of squares=12×3=36
Ans ASAP.. In pic with steps.. Plz tysm 1rst one BRAINLIEST
Answers
Answer:
The expression for the shaded region is 10x² + 12x .
Step-by-step explanation:
First, you have to find the area of both rectangles using the formula :
[tex]area = length \times height[/tex]
Small rectangle,
[tex]area = x \times (5x - 2)[/tex]
[tex]area = 5 {x}^{2} - 2x[/tex]
Large rectangle,
[tex]area = (3x + 2) \times 5x[/tex]
[tex]area = 15 {x}^{2} + 10x[/tex]
In order to find the shaded region, you have to subtract the smaller from the larger one :
[tex]area \: of \: shaded = large - small[/tex]
[tex]area = 15 {x}^{2} + 10x - 5 {x}^{2} + 2x [/tex]
[tex]area = 10 {x}^{2} + 12x[/tex]
Find the area of the triangle.
Answers
Answer:
10.5 cm^2
Step-by-step explanation:
Since we have two sides and the angle between those sides, we can use the alternative area formula:
[tex]A=\frac{1}{2}ab\sin(C)[/tex]
a and b are the two sides while C is the angle in between the two sides.
Plug in the numbers:
[tex]A=\frac{1}{2}(7)(6)\sin(150)[/tex]
Recall the unit circle. Sin(150) is 1/2.
[tex]A=21(\frac{1}{2})[/tex]
[tex]A=21/2=10.5cm^2[/tex]
Drag the tiles to the correct boxes to complete the pairs.
This table gives Information about vehicles sold at a dealership in a month.
Gasoline Diesel
18
5
Hatchback
Sedan
15
12
SUV
3
7
Analyze this data, and match each percentage to the description It represents. Round your answers to the nearest whole number.
30%
44%
21%
8%
42%
78%
the percentage of hatchbacks that run on gasoline
the percentage of diesel vehicles that are hatchbacks
tum. All rights reserved.
Answers
Answer:
The percentage of hatchbacks that run on gasoline: 78%
The percentage of diesel vehicles that are hatchbacks: 21 %
Step-by-step explanation:
The given table represents the following:
Hatchbacks that run on Gasoline = 18
Hatchbacks that run on Diesel = 5
Total number of hatchbacks = 23
Sedan that run on Gasoline = 15
Sedans that run on Diesel = 12
Total number of sedans = 27
SUVs that run on Gasoline = 3
SUVs that run on Diesel = 7
Total number of SUVs = 23
Total number of gasoline vehicles = 36
Total number of Diesel vehicles = 24
To find:
the percentage of hatchbacks that run on gasoline
the percentage of diesel vehicles that are hatchbacks
Solution:
[tex]\text{Percentage of hatchbacks that run on gasoline = } \dfrac{\text{Number of hatchbacks on gasoline}}{\text{Total number of hatchbacks}}\times 100\\\Rightarrow \text{Percentage of hatchbacks that run on gasoline = } \dfrac{18}{23}\times 100 \approx 78\%[/tex]
[tex]\text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{\text{Number of hatchbacks that run on diesel}}{\text{Total number of diesel vehicles}}\times 100\\\Rightarrow \text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{5}{24}\times 100 \approx 21\%[/tex]
So, the answer is:
The percentage of hatchbacks that run on gasoline: 78%
The percentage of diesel vehicles that are hatchbacks: 21%
Answer:
I used a calculator and this is what can up with
Step-by-step explanation:
What constant acceleration is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds? (Round your answer to two decimal places.) ft/s2
Answers
Answer: 12.22 ft/sec²
Step-by-step explanation:
An increase from 26 to 51 is an increase of 51 - 26 = 25 mi/hr
We need to do this in 3 seconds --> 25 mi/hr ÷ 3 sec
Note the following conversion: 1 mile = 5280 ft
[tex]\dfrac{25\ miles}{hr}\times \dfrac{1}{3\ sec}\times \dfrac{5280\ ft}{1\ mile}\times \dfrac{1\ hr}{60\ min}\times \dfrac{1\ min}{60\ sec} \\\\\\=\dfrac{5280(25)\ ft}{3(60)(60)\ sec^2}\\\\\\=\large\boxed{12.22\ ft\slash sec^2}[/tex]
The constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².
What is acceleration?Acceleration can be defined as the rate of change of the velocity of an object with respect to time.
[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]
As the velocity that is given to us is 51 miles/hour and 26 miles/hour, therefore, we first need to convert the units of the velocity in order to get the acceleration in ft/s².
[tex]\rm Final\ velocity= 51\ mi/hr = \dfrac{51\times 5280}{3600} = 74.8\ m\s^2[/tex]
[tex]\rm Initial\ velocity= 26\ mi/hr = \dfrac{26\times 5280}{3600} = 38.134\ m\s^2[/tex]
Now, acceleration is written as the ratio of the difference between the velocity and the time needed to increase or decrease the velocity of the object.
[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]
Substituting the values we will get,
[tex]\rm Acceleration = \dfrac{74.8-38.134}{3} = 12.22\ \ ft/s^2[/tex]
Hence, the constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².
Learn more about Acceleration:
https://brainly.com/question/12134554
A printer ink cartridge that can print 550 pages has already printed 127 pages. Which solution represents the correct equation and answer to the question, "How many more pages, P, can still be printed?"
Answers
P + 127 = 550 P = 423
Answer:
P = 423
P + 127 = 550
Step-by-step explanation:
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that a) the bit string has exactly two 1s; b) the bit string begins and ends with 0; c) the bit string has the sum of its digits equal to seven; d) the bit string has more 0s than 1s; e) the bit string has exactly two 1s, given that the string begins with a 1.
Answers
Answer:
45/10241/415/128193/5129/512Step-by-step explanation:
There are 2^10 = 1024 bit strings of length 10.
a) There are 10C2 = 45 ways to have exactly two 1-bits in 10 bits
p(2 1-bits) = 45/1024
__
b) Of the four (4) possibilities for beginning and ending bits (00, 01, 11, 10), exactly one (1) of those is 00.
p(b0=0 & b9=0) = 1/4
__
c) There are 10C7 = 120 ways to have seven 1-bits in the bit string.
p(7 1-bits) = 120/1024 = 15/128
__
d) ∑10Ck {for k=0 to 4} = 386 is the total of the number of ways to have 0, 1, 2, 3, or 4 1-bits in the string. If there are more than that, there won't be more 0-bits than 1-bits
p(more 0 bits) = 386/1024 = 193/512
__
e) The string will have two 1-bits if it starts with 1 and there is a single 1-bit among the other 9 bits. There are 9 ways that can happen, among the 512 ways to have 9 remaining bits.
p(2 1-bits | first is a 1-bit) = 9/512
Write an equation to represent the following statement. k divided by 1 is 7. Solve for k. k=
Answers
Answer:
[tex]\boxed{k = 7 }[/tex]
Step-by-step explanation:
Given Condition is:
[tex]\frac{k}{1} = 7[/tex]
Multiplying both sides by 1
k = 7*1
k = 7
How to do this question plz answer me step by step plzz plz
Answers
Answer:
112
Step-by-step explanation:
Define the variables:
x = number of French students sent by the school
Write the equation:
x / 21 = 1 / 3
Solve:
x = 7
The school sent 7 French students and 21 German students, for a total of 28 students.
The other 3 schools also sent 28 students. So the total number of students sent is:
4 × 28 = 112
Answer:
Step-by-step explanation:
French students=F
[tex]\frac{F}{21} =\frac{1}{3} \\F=\frac{1}{3} \times 21 =7\\Total~ students~ of ~one~ school=21+7=28\\Total~language~students=28 \times 4=112[/tex]
from the graph,determine the value of x when y= 0
Answers
Answer:
According to the graph, when y = 0, x = -0.4 and 2.3 .
Answer:
Step-by-step explanation:
when y=0,curve cuts x-axis and it cuts x-axis where x=-0.4
and x=2.3
PLZ HELP (BRAINLIEST)
Answers
As if we do the simple math then we will get the answer
Hope it helps
Plz rate the answer
Answer:
C. y = 0.5x + 5
Hope that helps.
Translate into an algebraic expression: How much 50% sugar syrup can you make if you have x grams of sugar ?
Answers
Answer:
The algebraic expression is v = 2x
v is the volume of the sugar syrup and
x is the mass of sugar in grams.
Step-by-step explanation:
Let x be the mass of sugar in grams and v be the volume of sugar syrup.
So, mass of sugar in grams/volume of sugar syrup × 100 % = 50 %
x/v × 100 % = 50 %
x/v = 50/100
x/v = 1/2
v = 2x
So, the algebraic expression required is v = 2x where v is the volume of the sugar syrup and x is the mass of sugar in grams.
Find the volume of a rectangular prism with a height of 18 if the base has a length of 9 and a width of 17.
Select one:
O a. 2678 units cubed
O b. 2049 units cubed
O c. 2754 units cubed
O d. 2957 units cubed
Answers
Hey there! I'm happy to help!
To find the volume of a rectangular prism, you simply multiply each of the three different sides!
18×9×17=2754
Therefore, the volume of this rectangular prism is c. 2754 units cubed.
Now you can find the volume of a rectangular prism! Have a wonderful day!
Maxim has been offered positions by two car dealers. The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold. The second pays a salary of $20,000 plus a commission of $500 for each car sold. How many cars would need to be sold to make the total pay the same?
Answers
Answer:
20 cars
Step-by-step explanation:
Solve for x!
10000+1000x(the first company)=20000+500x (the second company)
-10000 -10000
1000x=10000+500x
-500x -500x
500x=10000
divide by 500 on both sides,
x=20
Check!
First company: 10000+1000(20)=10000+20000=30000
Second company: 20000+500(20)=20000+10000=30000!
30000=30000
Hope this helped!
Number of cars would need to be sold to make the total pay same is 20
What is Equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
What is Expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context
Given,
The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold
therefore the expression is
10000+1000x
where x is the number of car sold
The second pays a salary of $20,000 plus a commission of $500 for each car sold
Then the expression will be
20000+500x
How many cars would need to be sold to make the total pay the same is
10000+1000x=20000+500x
1000x-500x=20000-10000
500x=10000
x=20
Hence, the number of cars would need to be sold to make the total pay the same is 20
Learn more about Equation and Expression here
https://brainly.com/question/10413253
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Real solutions pleases
Answers
Answer:
c
Step-by-step explanation:
what is the value of 24% of 800?
Question of mathematics
Answers
We simply multiply 800 and 24% (0.24)
800(0.24) = 192
Answer:
[tex] \huge \boxed{192}[/tex]Step-by-step explanation:
[tex]24\% \: of \: 800[/tex]
By definition of p% = p/100
[tex] = \frac{24}{100} \times 800[/tex]
Reduce the numbers with Greatest Common Factor 100
[tex] = 24 \times 8[/tex]
Multiply the numbers
[tex] = 192[/tex]
Hope I helped!
Best regards!!
MATH HELP ME ASAP PLS!!!
Answers
Answer: D) Front - $35.00 Back - $22.50
Step-by-step explanation:
b+12.5=f
600f+450b=31,125
Substitute
600(b+12.5)+450b=31,125
Distribute
600b+7500+450b=31,125
Combine like terms
1050b+7500=31125
Subtract 7500
1050b=23625
Divide by 1050
b=22.5
Thus, the back tickets cost $22.50.
Hope it helps <3
Find the tangent of the angle in between the lines 2x+3y–5=0 and 5x=7y+3?
Answers
Answer:
tanФ = 2.6363636
Step-by-step explanation:
To find the tangent of the angle in-between the lines we will follow the steps below:
We are going to use the formula;
tanФ = |m₂ - m₁ / 1 + m₁m₂|
We can get the slope m₁ from the first equation
2x+3y–5=0
we will re-arrange it in the form y=mx + c
3y = -2x + 5
Divide through by 3
y = -[tex]\frac{2}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
comparing the above equation with y=mx + c
m₁ = -[tex]\frac{2}{3}[/tex]
We will proceed to find the second slope m₂ using the second equation
5x=7y+3
we will re-arrange it in the form y=mx + c
7y = 5x -3
divide through by 7
y = [tex]\frac{5}{7}[/tex] x - [tex]\frac{3}{7}[/tex]
comparing the above with y=mx + x
m₂ = [tex]\frac{5}{7}[/tex]
we can now go ahead and substitute into the formula
tanФ = |m₂ - m₁ / 1 + m₁m₂|
tanФ = | [tex]\frac{5}{7}[/tex] - (-[tex]\frac{2}{3}[/tex] ) / 1 + (-[tex]\frac{2}{3}[/tex]₁)( [tex]\frac{5}{7}[/tex])|
tanФ = | [tex]\frac{5}{7}[/tex] +[tex]\frac{2}{3}[/tex] / 1 - [tex]\frac{10}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] / [tex]\frac{11}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] × [tex]\frac{21}{11}[/tex]|
21 will cancel-out 21
tanФ =[tex]\frac{29}{11}[/tex]
tanФ = 2.636363
Which system has no solution?
Check all that appy.
Answers
The picture shows all the work I did, the reason I took a pic is because it is a little hard to explain by text, but I hope this helped you!
Please help WILL GET REPORTED IF ANSWERS NONSENSE FOR POINTS I am really struggling and need help It is a lot of points so try answering as much
Answers
Answer:
301.59
Step-by-step explanation:
your answer was almost right you just forgot to multiply by 9
Henry purchased 3 items during a sale. He received a 20 percent discount on the regular price of the most expensive of the 3 items and a 10 percent discount on the regular price of each of the other two items. What was the total amount of the 3 discounts
Answers
Answer:
Combining statement 1 and statement 2 is sufficient
Step-by-step explanation:
There are 3 items purchased
Most expensive item=20% discount
The other two items=10% discount each
Statement 1: The average (arithmetic mean) of the regular prices of the 3 items was $30.
Assume:
The 3 items cost: $40, $30 and $20 respectively,
Total discount =20% of $40 + 10% of $30 + 10% of $20
=$8 + $3 + $2
= $13
Assume
The 3 items cost: $50, $30 and $10 respectively,
Total discount = 20% of $50 +10% of $30 + 10% of $10
=$10 + $3 + $1
= $14
Therefore, statement 1 is INSUFFICIENT
Statement 2: The most expensive item was $50
The discount for the most expensive item at $50 = 20% of $50
= 0.2*$50
=$10
But we don't know the price of the other 2 items, so we can't determine the discounts.
Therefore, Statement 2 is also INSUFFICIENT
Combining statement 1 and 2
1) The average (arithmetic mean) of the regular prices of the 3 items was $30.
So, the SUM of the 3 items = $90
2) The most expensive item is $50
So the OTHER 2 items sum up to $40
$50 item gets 20% discount and the other two items ($40) each get 10% discount
The discount = 20% of $50 + 10% of $40
=0.20*50 + 0.1*40
=$10 + $4
=$14
Combining the two statements is sufficient
first correct answer gets best marks and make it short not super-long please and hurry
Answers
Answer:
b > 3 2/15
Step-by-step explanation:
To make it easier to solve convert the mixed fraction to a fraction.
2 3/5 = 13/5
Now, multiply the fraction by 3/3 so that you will have a common denominator.
13/5 × 3/3 = 39/15
Now you solve for b.
39/15 < b - 8/15
39/15 + 8/15 < (b - 8/15) + 8/15
47/15 < b
b > 47/15
Convert the fraction to a mixed fraction to find the answer
47/15 = 3 2/15
b > 3 2/15
What is the product of 7/16 and -6/13 I will make you the brainlest
Answers
Answer:
[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex]
Step-by-step explanation:
[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex] . First multiply 7*-6=-42.
Then do 16*13=208.
Simplify by dividing both by 2.
You get [tex]\frac{-42}{208}=\frac{-21}{104}[/tex].
Your final simplified answer is [tex]\frac{-21}{104}[/tex]
I hope this helps!
Lea’s car travels an average of 30 miles per gallon of gas. If she spent $20.70 on gas for a 172.5 mike trip, what was the approximate cost of gas in dollars per gallon?
Answers
Answer:
$3.60 per gallon.
Step-by-step explanation:
First, we look for the gallon of gas that will be used for a 172.5 mile trip:
30 miles = 1 gallon of gas
172.5 miles = ?
172.5 ÷ 30 = 5.75 gallons of gas
Let's find the approximate cost of gas in dollars per gallon:
5.75 gallons of gas = $20.70
1 gallon of gas = $?
20.70 ÷ 5.75 = $3.60
The answer is $3.60 per gallon.
Allison accumulated $7,000 in credit card debt. If the interest rate is 15% per year and she does not make any payments for 3 years, how much will she owe on this debt in 3 years for quarterly compounding? Round your answer to two decimal places.
Answers
Answer:
Allison will owe $10,888.50 in 3 years
Step-by-step explanation:
FV=PV(1+r/n)^nt
Where,
PV=$7000
r=15%=0.15
n=quarterly=4
t=3 years
FV=PV(1+r/n)^nt
=7000(1+0.15/4)^4*3
=7000(1+0.0375)^12
=7000(1.0375)^12
=7000(1.5555)
=10,888.50
To 2 decimal places=$10,888.50
Allison will owe $10,888.50 in 3 years
Answer:
$10,888.20
Step-by-step explanation:
Order of Operations: BPEMDAS
Compounded Interest Rate Formula: A = P(1 + r/a)ᵃᵇ
A = Final Amount
P = Initial Amount
r = rate
a = Compounded number
b = time
Step 1: Define
P = 7000
r = 15% = 0.15
a = 4
b = 3 years
Step 2: Solve for A
Substitute: A = 7000(1 + 0.15/4)⁴⁽³⁾Parenthesis: A = 7000(1.0375)⁴⁽³⁾Exponents: A = 7000(1.0375)¹²Exponents: A = 7000(1.55545)Multiplication: A = 10888.20At the end of the 3 years that elapsed, Allison will have to pay a final debt of $10,888.20.
A staining solution bottle in a medical laboratory contains 30 ounces (oz). A blood staining test requires 3/4 oz of solution. A tissue staining test requires 1/2 oz of solution. If four blood tests and five tissue tests are performed, how many oz of solution are left in the bottle
Answers
Answer:
24.5 oz
Step-by-step explanation:
First lets calculate the blood tests, 3/4 oz of solution.
3/4 multiplied by four tests= 3. (.75*4=3)
So 3 oz of Blood Tests were performed, now lets calculate the amount of tissue staining tests for performed.
1/2 multiplied by five tests= 5/2 or 2.5 oz of tests. (.5*5=2.5)
3oz+2.5=5.5oz
Now let's subtract that amount by 30.
30-5.5=24.5