Answer:
54
Step-by-step explanation:
Given:
[tex]3(a + b + c) 2[/tex]
Input the numbers provided into the equation
3(2 + 3 + 4)2
Add all of the numbers inside the parentheses
3(9)2
Multiply
3 * 2 = 6
6 * 9 = 54
Hey there! :)
3(a + b + c)2 ; when a = 2, b = 3, c = 4
In order to evaluate this, we simply need to plug everything in then simplify/
3(2 + 3 + 4)2
Simplify everything inside the parenthesis first.
3(9)2
Simplify.
27 × 2
Simplify.
54 is our final answer.
Hope this helped! :)
a jeweler cut a rhinestone in the shape of a rhombus. If one of the angles of the rhinestone measures 130 degrees, what is the measure of the consecutive angle, x?
A. 180 degrees
B. 130 degrees
C. 50 degrees
D. 90 degrees
The measure of the consecutive angle x is 50 degrees in the given rhinestone. The given angles are supplementary angles.
What are the properties of a rhombus?A rhombus shape has also been named a diamond. Its properties are as follows:
A rhombus has 4 equal length of sides.Its opposite sides are parallel.The diagonals bisect each other at right angles.The opposite angle are equal in measure.The adjacent angles are supplementary to each other i.e., their sum is 180 degrees.The Sum of all the angles in the rhombus is 360 degreesCalculating angle x:The measure of one of the angles = 130 degrees
The angle x is supplementary to the given angle. So, their sum is 180 degrees. I.e.,
130 + x = 180
⇒ x = 180 -130
⇒ x = 50°
Thus, the measure of the angle x is 50°.
Learn more about the shape rhombus here:
https://brainly.com/question/1506491
#SPJ2
Idk what the answer is help me or nah?????
Answer:
x = 13.0
Step-by-step explanation:
We are given the two legs of the right triangle.
We can use the Pythagorean theorem.
a^2 +b^2 = c^2
7^2 +11^2 = x^2
49+121 = x^2
170 = x^2
Take the square root of each side
sqrt(170) = sqrt(x^2)
13.038 = x
To the nearest tenth
13.0 =x
Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes
Answer:
0.6389
Step-by-step explanation:
This question is on a rectangle distribution
We apply; Area × probability
9× height = 1 unit square................find the height of the rectangle
h=1/9
The waiting time greater than 3.25 will be = 9-3.25= 5.75
P(time> 3.25 minutes) = 5.75 × 1/9 = 0.6389
simplify the polynomial by combining like terms
[tex]11x {}^{2} + 11x {}^{2} [/tex]
A.
[tex] - 12x {}^{2} [/tex]
B.
[tex]12x {}^{2} [/tex]
C.
[tex] - 24x {}^{2} [/tex]
D.
[tex]24x {}^{2} [/tex]
Answer:
22 x^2
Step-by-step explanation:
Simplify the following:
11 x^2 + 11 x^2
Hint: | Add like terms in 11 x^2 + 11 x^2.
11 x^2 + 11 x^2 = 22 x^2:
Answer: 22 x^2
none of your answers are correct.
Indicate in standard form the equation of the line through the given points. K(6, 4), L(-6, 4)
y=4
the values of x changes while the y doesn't so it's y=4
Answer:
[tex]y=4[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The equation of the line in Standard form is:
[tex]Ax + By =C[/tex]
Where A, B, and C are integers.
We can find the slope of this line with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the points K(6, 4) and L(-6, 4), we get:
[tex]m=\frac{4-4}{-6-6}=0[/tex]
Substituting the value of "m" and the coordinates of any point on the line into the equation and solving for "b", you get:
[tex]4=0(6)+b\\b=4[/tex]
Therefore, the equation of this line is:
[tex]y=4[/tex]
5) 200 students at a local college campus
were asked to choose between chocolate
and vanilla ice cream. 50 of the 200
students chose chocolate. If the college
has a total of 1000 students,
approximately how many students would
prefer chocolate ice cream?
Answer:
Step-by-step explanation:
The answer is A
Answer:
250 students would
prefer chocolate ice cream
Step-by-step explanation:
50 of 200
+50 +200
100 of 400
+50 +200
150 of 600
+50 +200
200 of 800
+50 +200
250 of 1000
Solve: 62x - 3 = 6-2x+1
x = -1
x = 0
x = 1
x = 4
Answer: X=1 Is the answer on edge 2023 :)
Step-by-step explanation: X=1
To solve the equation 62x - 3 = 6 - 2x + 1x, combine like terms, add and subtract terms to isolate x, and simplify the solution.
Explanation:To solve the given equation, 62x - 3 = 6 - 2x + 1x:
Combine like terms: 63x - 3 = 6 - xAdd x to both sides: 63x + x - 3 = 6Combine like terms: 64x - 3 = 6Add 3 to both sides: 64x - 3 + 3 = 6 + 3Combine like terms: 64x = 9Divide both sides by 64: 64x / 64 = 9 / 64Simplify: x = 9 / 64Therefore, the solution to the equation is x = 9 / 64.
13.5 is 15% of what number?
Answer:
90
Step-by-step explanation:
13.5/.15
To solve this you must use a proportion like so...
[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]
15 is a percent and percent's are always taken out of the 100. This means that one proportion will have 15 as the part and 100 as the whole
We want to know out of what number is 13.5 15% of. This means 13.5 is the part and the unknown (let's make this x) is the whole.
[tex]\frac{13.5}{x} =\frac{15}{100}[/tex]
Now you must cross multiply
13.5*100 = 15*x
1350 = 15x
To isolate x divide 15 to both sides
1350/15 = 15x/15
90 = x
This means that 15% of 90 is 13.5
Hope this helped!
~Just a girl in love with Shawn Mendes
You want to make a scarf and matching hat. The pattern calls for 1 7/8 yards of fabric for the scarf and 2 1/2 yards of fabric for the hat. How much fabric do you need all?
Answer:
4 3/8 yards.
Step-by-step explanation:
1 7/8 + 2 1/2
= 15/8 + 5/2
Make the denominator 8 in both cases ( The LCM = 8):
= 15/8 + 20/8
= 35/8
= 4 3/8.
4 added to the difference of d minus 3
The ratio for the expression "4 added to the difference of d minus 3" can be represented as: (d - 3) + 4.
Explanation:Expression: "The difference of d minus 3"
This means subtracting 3 from d:
d - 3
Expression: "4 added to the difference of d minus 3"
Add 4 to the result of the previous expression:
(d - 3) + 4
This gives us the entire expression "4 added to the difference of d minus 3.":
(d - 3) + 4
Combine like terms:
d + 1
Therefore, the simplified form of the given expression is (d + 1).
Find the indicated term of the given geometric sequence. a1 = 14, r = –2, n = 11
Answer:
[tex]a_{11} = 14336[/tex]
Step-by-step explanation:
The general formula for the twelfth term of a geometric sequence is:
[tex]a_n = a_1(r)^{n-1}[/tex]
Where [tex]a_1[/tex] is the first term and r is the common ratio
In this case we know that:
[tex]a_1 = 14\\r=-2[/tex]
The equation is:
[tex]a_n = 14(-2)^{n-1}[/tex]
So for [tex]n = 11[/tex] we look for [tex]a_{11}[/tex]
[tex]a_{11} = 14(-2)^{11-1}[/tex]
[tex]a_{11} = 14(-2)^{10}[/tex]
[tex]a_{11} = 14336[/tex]
Answer:
[tex]11^{th}[/tex] term = 14336
Step-by-step explanation:
We are given the first term [tex] a _ 1 = 1 4 [/tex] and common ratio [tex] r = - 2 [/tex] of a geometric sequence and we are to find the [tex]11^{th}[/tex] term of this sequence.
We know that the formula to find the [tex]n^{th}[/tex] term in a geometric sequence is given by:
[tex]n^{th}[/tex] term = [tex] a r ^ { n - 1 } [/tex]
Substituting the given values in the above formula:
[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{11-1}[/tex]
[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{10}[/tex]
[tex]11^{th}[/tex] term = 14336
the population of a city has increased by 15% since it was last measured. If the current population is 59.800, what was the previous population?
Answer:
about 50 000 i think sorry if this didnt hep
Step-by-step explanation:
To calculate the previous population before a 15% increase that resulted in a current population of 59,800, we use the formula: Previous Population = Current Population / (1 + Percentage Increase), which yields a previous population of approximately 52,000.
Explanation:The question pertains to determining what the previous population of a city was before it experienced an increase of 15%. Given that the current population is 59,800, we can calculate the previous population using the formula:
Current Population = Previous Population * (1 + Percentage Increase)
To find the Previous Population, we rearrange this formula:
Previous Population = Current Population / (1 + Percentage Increase)
By substituting in the given values:
Previous Population = 59,800 / (1 + 0.15)
Previous Population = 59,800 / 1.15
Previous Population = 52,000 (approximately)
Therefore, the previous population of the city was around 52,000 inhabitants before the 15% increase.
Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplying 2?
a line in the xy- plane has the equation y=kx, where k is a constant. The line passes through the point (1,n) and (n,16). which of the following could be the value of n?
A)1
B)2
C)4
D)8
Answer:
Option C) 4
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem
The equation of the line represented a direct variation
The value of k is equal to [tex]k=y/x[/tex]
we have the points
(1,n) and (n,16)
so
[tex]k=n/1[/tex]
[tex]k=16/n[/tex]
equate
[tex]n/1=16/n[/tex]
solve for n
[tex]n^{2}=16\\ \\n=(+/-)4[/tex]
therefore
The value of n could be 4 or -4
To find the value of n, substitute the given points into the equation y=kx and solve for n. The possible value of n is 4.
Explanation:To find the value of n, we need to use the given points and equation. Since the line passes through (1,n), we can substitute these values into the equation y=kx to get n=k(1) or n=k. Similarly, substituting the values (n,16) into the equation gives us 16=k(n). By equating these two equations, we can solve for k and n.
Using substitution, we have n=16/n. Solving this equation by multiplying both sides by n, we get n^2=16. Taking the square root of both sides, we have n=±4. Therefore, the value of n that could be possible is 4.
Learn more about Equations and Variables here:https://brainly.com/question/29209545
#SPJ3
A sporting goods store is offering a 10% discount on in-line skates that normally cost $110.99. How much will the in-line skates cost with the discount, not including tax?
The in-line skates will cost $99.891 with the discount.
Explanation:To find the cost of the in-line skates with the discount, we need to calculate the amount of the discount first. The discount is 10% of the original price, which is $110.99. To calculate the discount amount, we can multiply the original price by 0.10. The discount would be $110.99 x 0.10 = $11.099. The discounted price would be the original price minus the discount amount, so the discounted price would be $110.99 - $11.099 = $99.891.
Which system below has no solution?
y = 4x and y = 2x - 3
y = -4x and y = 2x - 3
y = -4x and y = 2x + 3
y = -4-x and y = 2x - 3
it is multiple choice
The system of equations with y = -4x and y = 2x + 3 has no solution.
Explanation:The system of equations with y = -4x and y = 2x + 3 has no solution. To determine this, we can set the two equations equal to each other and solve for x:
-4x = 2x + 3
Adding 4x to both sides, we get:
0 = 6x + 3
Subtracting 3 from both sides, we get:
-3 = 6x
Dividing both sides by 6, we get:
-1/2 = x
Substituting x = -1/2 back into either equation will result in a false statement, indicating that the system has no solution.
Learn more about No solution to a system of equations here:https://brainly.com/question/30127282
#SPJ12
What is the missing reason in the proof?
Prove –(–y – x) – x = y
–(–y – x) – x = –[–y +(–x)] – x
Definition of subtraction
–[–y +(–x)] – x = y + x – x
Opposite of a sum property
y + x – x = y + x + (–x)
Definition of subtraction
y + x + (–x) = y + [x + (–x)]
Associative property of addition
y + [x + (–x)] = y + 0
Additive inverse property
y + 0 = y
(blank)
Answer options for (blank):
A. Symmetric Property
B. Additive Inverse Property
C. Additive Identity Property
D. Opposite of a Sum Property
Answer:
Option C is correct.
Step-by-step explanation:
The last step is y+0 =y
This represents additive identity property.
This property states if zero is added to any number we get the same number.i.e if 0 is added to y then we get y (y+0=y)
So, Option C is correct
Final answer:
The missing reason in the proof that demonstrates –(–y – x) – x equals y is the Additive Identity Property, which indicates adding zero to a number does not change its value.
Explanation:
The question refers to a series of algebraic manipulations with the aim of proving the equation –(–y – x) – x = y. The final step in the proof involves the simplification of y + 0 to y. The correct reason for this step is the Additive Identity Property, which states that adding zero to any number does not change the value of that number. Therefore, the missing reason in the proof is option C.
find the total area for the regular pyramid
(please follow the answer set up in the picture)
Answer:
T.A. = 144 + 36√3
Step-by-step explanation:
The pyramid has a regular triangle for a base. The other three faces are isosceles triangles.
The height of base can be found by dividing it into two right triangles. We can either use properties of a 30-60-90 triangle, or use Pythagorean theorem.
h = 6√3
So the area of the base is:
A = 1/2 bh
A = 1/2 (12)(6√3)
A = 36√3
Similarly, the height of the three isosceles triangles can be found by dividing them into two right triangles and using Pythagorean theorem.
h = √(10² - 6²)
h = 8
So the area of the isosceles triangles is:
A = 1/2 bh
A = 1/2 (12)(8)
A = 48
So the total surface area of the pyramid is:
T.A. = 3(48) + 36√3
T.A. = 144 + 36√3
For what value of x is P|| BC?
A. 5
B. 6
C. 7
D. 8
Answer:
Option C. x=7
Step-by-step explanation:
we know that
If PQ is parallel to BC
then
triangles APQ and ABC are similar
Remember that
If two figures are similar them the ratio of its corresponding sides is proportional
so
[tex]\frac{AP}{AB}=\frac{AQ}{AC}[/tex]
substitute the values
[tex]\frac{x}{x+7+x}=\frac{x-3}{x-3+x+1}[/tex]
Solve for x
[tex]\frac{x}{2x+7}=\frac{x-3}{2x-2}\\ \\x(2x-2)=(2x+7)(x-3)\\ \\2x^{2}-2x=2x^{2}-6x+7x-21\\ \\3x=21\\ \\x=7\ units[/tex]
Kris has 4 yards of ribbon. it takes 2/3 yard to wrap one package. How many packages can Kris wrap?
A.Kris can wrap 5 packages
B.Kris can wrap 4 Packages
C.Kris can wrap 6 packages
Answer:
C. 6 packages
Step-by-step explanation:
4 divided by 2/3
=>4x3/2=6
mark me as the brainliest plz
Given 4 yards of ribbon and each package requires 2/3 yard, Kris can wrap 6 packages.
Explanation:This question is about dividing total resources, in this case, ribbon, by the amount needed for each unit, in this case, a package. Kris has 4 yards of ribbon, and each package requires 2/3 yard of ribbon to wrap. To find out how many packages Kris can wrap, we need to do a division: total yards of ribbon ÷ yards of ribbon per package.
The equation for this would be: 4 ÷ 2/3. When we divide by a fraction, we multiply by its reciprocal. The reciprocal of 2/3 is 3/2, so we set up the equation like this: 4 x (3/2).
The answer to this equation is 6. Hence, Kris can wrap 6 packages with 4 yards of ribbon.
Learn more about Dividing total resources here:https://brainly.com/question/32245134
#SPJ3
Find the area of a square whose perimeter is equal 36m
Answer: Area of Square = 81m^2
Step-by-step explanation:
To find the area of a square you just need to know the side length on one side, and since we know that the perimeter is 36, and all sides of a square are equal we can divide 36/4, to get 9 is your side length.
Now to actually find the area you can just square your side length, so basically 9x9, which gives you 81, your answer!!
Answer:
Area = 81m^2
Step-by-step explanation:
Square has 4 equal sides so 36/4 = 9
9(9) = 81
Hope this helps :)
(20 Points)
Perform the indicated operations.
Answer:
5x-8/12y
Step-by-step explanation:
x+1
3y
+
x−2
4y
−(
x+3 /6y
=
30xy2−48y2
72y3
=
30x−48/72y
=
5x−8 /12y
if f(x)= 5 ^ x + 2x and g(x)= 3x - 6, find (f+g)(x)
Answer:
(f+g)(x) is 5^x + 5x - 6
Step-by-step explanation:
To find (f + g)(x), we are merely adding up all the terms present in both
f(x)= 5^x + 2x and g(x)= 3x - 6. 5^x is unique and cannot be combined with any other term. 2x and 3x can be combined to obtain 5x. -6 is unique.
Thus, the sum (f+g)(x) is 5^x + 5x - 6.
Answer:
[tex]5^x+5x-6[/tex]
Step-by-step explanation:
[tex]f(x)=5^x + 2x[/tex]
[tex]g(x)= 3x - 6[/tex]
[tex](f+g)(x)[/tex]
[tex]f(x) + g(x)[/tex]
[tex]5^x+2x+3x-6[/tex]
[tex]5^x+5x-6[/tex]
A regular convex polygon has eight sides. What is the measure of an exterior angle?
Answer:
The measure of one exterior angle is 45 degrees.
Step-by-step explanation:
The formula to find exterior angle of and shape is 360 degrees divided by n (number of sides the shape has). 360 divided by 8 = 45 degrees.
Answer:
Exterior angle = 45°
Step-by-step explanation:
We know that the sum of exterior angles of a polygon is 360 degrees.
Since here we a regular polygon with eight sides (which makes it an octagon) so this means that the interior angles each would be equal to:
[tex]\frac{(n - 2) \times 180}{n} \\ \frac{(8 - 2) \times 180}{8}\\ \frac{6 \times 180}{8} \\ \frac{1080}{8} [/tex] = 135 degrees
We know that each interior angle is supplementary to the exterior angle at the vertex.
So each exterior angle = [tex]180-135[/tex] = 45 degrees
Same question as the previous one but forgot to show the answer choices
Answer:
C
Step-by-step explanation:
x apples cost 80
1 apple costs 80/x
5 apples costs 80*5/x = 400/x
The same calculation works for the oranges.
y oranges cost 75
1 orange = 75/y
6 oranges = 75*6/y
6 oranges = 450/y
The total cost is 450/y + 400/x which is C
Drag the tiles to the correct boxes to complete the pairs.
Using the properties of integer exponents, match each expression with the correct equivalent expression.
Answer:
1. [tex](-2^2)^{-6}[/tex] ÷ [tex](2^{-5})^{-4} \implies 2^{-32}[/tex]
2. [tex]2^4 . (2^2)^{-2} \implies 1[/tex]
3. [tex](-2^{-4}).(2^2)^0 \implies -2^8[/tex]
4. [tex](2^2).(2^3)^{-3} \implies 2^{-5}[/tex]
Step-by-step explanation:
1. [tex](-2^2)^{-6}[/tex] ÷ [tex](2^{-5})^{-4}[/tex] :
[tex] = \frac{ ( - 2 ^ 2 ) ^ { - 6 } } { ( 2 ^ { - 5 } ) ^ { - 4 } } = \frac{2^{-12}}{2^{20}} = 2^{-12-20}=2^{-32}[/tex]
2. [tex] 2 ^ 4 . ( 2 ^ 2 ) ^ { - 2 } [/tex] :
[tex]= 2^4 \times \frac{1}{2^4} = 1[/tex]
3. [tex](-2^{-4}).(2^2)^0[/tex] :
[tex]= (-2^4)^2 \times 1 = -2^8[/tex]
4. [tex](2^2).(2^3)^{-3}[/tex] :
[tex]= 2^4 \times \frac{1}{2^9} =\frac{1}{2^5} =2^{-5}[/tex]
Answer:
The answer is 1-2 2-4 3-4 and 4-3
Step-by-step explanation:
What is the common ratio for this geometric sequence?
27, 9, 3, 1,...
Answers:
A. 1/3
B. 6
C. 1/6
D. 3
PLEASE HELPPPP!
Answer:
The common ratio is 1/3.
Step-by-step explanation:
Divide each term after the first by the previous one.
9/27 = 1/3
also 3/9 = 1/3 and 3 / 3 = 1/3.
Answer:
A. 1/3Step-by-step explanation:
[tex]\text{The common ratio of a geometric sequence}\ a_n:\\\\r=\dfrac{a_{n+1}}{a_n}\\\\\text{We divide next term by the previous one.}\\\\r=\dfrac{9}{27}=\dfrac{9:9}{27:9}=\dfrac{1}{3}\\\\r=\dfrac{3}{9}=\dfrac{3:3}{9:3}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}\\\vdots[/tex]
You need to put oil into the gearbox of a rebuilt machine tool. The gearbox holds 16.3 liters of oil but the only oil you have is in 1-quart containers. How many of the one quart containers of oil will you need to fill the gearbox with 16.3 liters of oil
Answer: You will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.
Step-by-step explanation:
Knowing that you have 1-quart containers, you need to make the conversion from quarts to liters. This is:
[tex]1\ quart=0.946\ liters[/tex]
Now, since the gearbox holds 16.3 liters of oil, you can divide the volume of oil the gearbox holds by the volume of a container (which is 0.946 liters or 1-quart) to calculate how many containers of 1-quart you will need to fill the gearbox with 16.3 liters of oil.
[tex]number\ of\ containers=\frac{16.3\ liters}{0.946\ liters}=17.2[/tex]
Based on the result, you will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.
You will need 17 one-quart containers of oil to fill the 16.3-liter gearbox.
Explanation:To determine how many 1-quart containers of oil you will need to fill the 16.3-liter gearbox, we can convert the 16.3 liters to quarts by using the conversion factor of 1 liter = 1.05668821 quarts. So, 16.3 liters would be approximately 17.229 quarts. Since each 1-quart container holds exactly 1 quart of oil, you will need 17 of the 1-quart containers to fill the gearbox with 16.3 liters of oil.
Learn more about Converting liters to quarts here:https://brainly.com/question/29195599
#SPJ3
Complete the missing parts of the table for the following function
The missing parts of the table for [tex]\( x = 0 \)[/tex] and [tex]\( x = 3 \)[/tex] are 1 and 216, respectively.
Let's solve for the missing values step by step.
The function given is [tex]\( y = 6^x \)[/tex]. This means that for each value of [tex]\( x \)[/tex], [tex]\( y \)[/tex] will be [tex]\( 6 \)[/tex] raised to the power of [tex]\( x \)[/tex].
Step 1: Solve for [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]
The exponent law states that any number raised to the power of 0 is 1. Therefore:
[tex]\( y = 6^0 = 1 \)[/tex]
Step 2: Solve for [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex]
To find [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex], we simply raise 6 to the power of 3:
[tex]\( y = 6^3 = 6 \times 6 \times 6 = 216 \)[/tex]
So, the completed table should look like this:
[tex]$\begin{array}{rrrrrrr}x & -2 & -1 & 0 & 1 & 2 & 3 \\ y & \frac{1}{36} & \frac{1}{6} & 1 & 6 & 36 & 216\end{array}$[/tex]
The solution set of 2x+1 = 8 is
B. (2)
C. (3)
D. (4)
Answer:
This answer isn't there, but it's correct: 3.5
Step-by-step explanation:
Subtract 1 from both sides of the equation.
2x = 7
Divide both sides of the equation by 2.
x = 7/2
x = 3.5
Final answer:
The solution to the equation 2x + 1 = 8 is x = 3.5, but this option is not listed among the provided answers, suggesting a possible error in the options listed.
Explanation:
The question seeks the solution set for the equation 2x + 1 = 8. To find the value of x, we begin by subtracting 1 from both sides of the equation, resulting in 2x = 7. Next, we divide both sides by 2 to isolate x, yielding x = 3.5. However, it's important to note that the options provided do not seem to match this solution. It's possible there was an error in the transcription of the options since none of them include 3.5.