Answer:
(x + 5)=0 or (x - 17)=0
x=-5 or x=17
Discard the negative value
x=17 is considered.
Michael is 17yrs old
Answer:
[tex]\boxed{\textbf{He is 17 years old}}[/tex]Step-by-step explanation:
Let x = Michael's age.
Then x² = the square of his age
and x² - 12x = the square of his age – 12 times his age
and x² - 12x = 85
We must solve the quadratic for x.
1. Subtract 85 from each side.
x² - 12x - 85 = 0
2. Multiply the leading coefficient and the constant
1 × 85 = 85
3. Find two numbers that multiply to give -85 and add to give -12.
Possible pairs are 1, 85; 5, 17
Start with the numbers near the end of the list.
By trial and error, you will find that 5 and -17 work:
5 ×(-17) = -85
and 5 - 17 = -12
4. Rewrite -12x as 5x -17x
x² + 5x – 17x - 85 =0
5. Factor by grouping the first two and the last two terms
x(x + 5) - 17(x + 5) =0
(x + 5)(x - 17) = 0
6. Find the zeroe
[tex](x + 5)(x - 17) = 0\\\\\begin{array}{rlrl}x + 5 & = 0 & x - 17 & =0\\x & = -5 & x & = 17\\\end{array}\\\text{Michael can't have a negative age, so } \boxed{\textbf{he is 17 years old.}}[/tex]
Check:
[tex]\begin{array}{rcl}(-17)^{2} + 12(-17) & = & 85\\289 - 204 & = & 85\\85 & = & 85\\\end{array}[/tex]
OK.
This week, the art museum gave away 1,200 tickets to the Greco exhibit, which was 150 percent as many tickets as it gave away last week. Martin is trying to figure out how many tickets the museum gave away last week. His work is shown below.
Answer:
Step 1 1200/ ?
Step-by-step explanation:
There is a mistake in the very first step
He is writing par over whole
100% is the original amount of tickets x
150% is the 1200 tickets
150 1200
----- = ------------
100 ?
Answer:
a
Step-by-step explanation:
tab
cap
3. A cylindrical oil drum has a radius of 0.28 m and an altitude of 0.83 m. How many cubic meters of oil
can the drum hold?
A. 1 m3
B.0.2 m3
C. 1.2 m3
D. 0.5 m3
Answer:
B
Step-by-step explanation:
We basically want to find the volume of this cylinder.
The volume of a cylinder is given by the formula [tex]V=\pi r^2 h[/tex]
where r is the radius and h is the height.
We plug the info given and find the volume:
[tex]V=\pi r^2 h\\V=\pi (0.28)^2 (0.83)\\V=0.20[/tex]
Correct answer B
the volume of the a sphere whoes diameter is 18 cm is cubic cm . if it's diameter were reduced by half, it's volume would be of its original volume
Answer:
The new volume is 8 times smaller than the original volume
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x ----> the volume of the reduced sphere
y ----> the volume of the original sphere
so
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=1/2[/tex] ----> scale factor
substitute
[tex](1/2)^{3}=\frac{x}{y}[/tex]
[tex](1/8)=\frac{x}{y}[/tex]
[tex]x=\frac{y}{8}[/tex]
therefore
The new volume is 8 times smaller than the original volume
Verify
The volume of the original sphere is
[tex]r=18/2=9\ cm[/tex] ---> the radius is half the diameter
[tex]V=\frac{4}{3}\pi (9)^{3}=972\pi \ cm^{3}[/tex]
the volume of the reduced sphere is
[tex]r=9/2=4.5\ cm[/tex] ---> the radius is half the diameter
[tex]V=\frac{4}{3}\pi (4.5)^{3}=121.5\pi \ cm^{3}[/tex]
Divide the volumes
[tex]972\pi \ cm^{3}/121.5\pi \ cm^{3}=8[/tex]
The graph of f(x) = 2x is shown on the grid. The graph of g(x) = ()x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
Answer:
[tex]g(x)=-2x[/tex]
Step-by-step explanation:
A point reflected across the y-axis maintains its y-coordinate, but its x-coordinate switches signs. So, a positive x-coordinate becomes negative, and a negative x-coordinate becomes positive.
Let's take a few points from the original function, f(x). Remember, if we know the function, we can find the y-coordinate for any x-coordiante by simply plugging it into the function's equation.
Generally, [tex]f(x)=2x[/tex]
So:
[tex]f(0)=2(0)=0\\f(1)=2(1)=2\\f(2)=2(2)=4[/tex]
Leading us to have the plot points (0,0), (1,2) and (2,4).
To reflect this across the y-axis for the g(x) equation, we just need to turn the x-coordinates negative, resulting in a set of (0,0), (-1,2), and (-2,4).
Since we know this is a linear function (because there are no exponents in the equation), we can calculate the slope of this new set of points by using just 2 of them. The slope will give us our equation, because since (0,0) is a point on our line, we know that the y-intercept is zero.
[tex]slope=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})} \\slope=\frac{(4-2)}{((-2)-(-1))} \\slope=\frac{2}{-1}\\slope=-2\\\\g(x)=-2(x)[/tex]
2x + 4y = 12
y= 2x-3
What is the solution to the system of equations?
• (-1,8)
(8, -1)
• (5. 3
Answer:
y=
−1
2
x+3
Step-by-step explanation:
is solved for y
Which of the following is graphed below?
Answer:
Step-by-step explanation:
Begin with process of elimination: As seen on the graph, there is a discontinuity at x=3. this means that x>=3. so we can eliminate B and C
Now you can see that at x = 3, two things happen. When moving to the left, x<3. when moving tot he right x>=3 so because of this you can eliminate D. The answer is A
Finding Intercepts of Quadratic FunctionsConsider the function f(x) = x2 + 12x + 11.
x-intercepts:
0 = x2 + 12x + 11
0 = (x + 1)(x+ 11)
y-intercept:
f(0) = (0)2 + 12(0) + 11
What are the intercepts of the function?
The x-intercepts are .
The y-intercept is .
Answer:
x1=-11 x2=-1 y=11
Step-by-step explanation:
you can see the explanation in the pics
A system of linear equations contains two equations with the same slope.
Select all of the correct statements.
I A. The system may have two solutions.
-
B. The system may have infinitely many solutions.
C. The system may have one solution.
O
D. The system may have no solution.
SUBMIT
Answer:
B. The system may have infinitely many solutions
D. The system may have no solution
Step-by-step explanation:
we know that
If a system of linear equations contains two equations with the same slope
then
we may have two cases
case 1) The two equations are identical, in this case we are going to have infinite solutions
case 2) The two equations have the same slope but different y-intercept, (parallel lines) in that case the system has no solution.
2. Find the value of x to the nearest tenth.
a. 4.5
b. 5.4
c. 6.3
d. 7.2
3. Find the value of x.
a. 7
b. 7.5
c. 8
d. 8.5
4. FG ⊥ OP, RS ⊥ OQ. FG=40, RS=40, OP=15. Find x.
a. 15
b. 17
c. 20
d. 21
5. Find the value of x to the nearest tenth.
a. 7.5
b. 7.9
c. 8.1
d. 8.9
Answer:
Part 2) Option b. 5.4
Part 3) Option c. 8
Part 4) Option a. 15
Part 5) Option d. 8.9
Step-by-step explanation:
Part 2) Find the value of x to the nearest tenth
we know that
x is the radius of the circle
Applying the Pythagoras Theorem
[tex]x^{2}=3.6^{2}+(8/2)^{2}[/tex]
[tex]x^{2}=28.96[/tex]
[tex]x=5.4\ units[/tex]
Part 3) Find the value of x
In this problem
x=8
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
Applying the Pythagoras Theorem
[tex]r^{2}=8^{2}+(15/2)^{2}[/tex]
[tex]r^{2}=120.25[/tex]
[tex]r=\sqrt{120.25}[/tex]
step 2
Find the value of x
Applying the Pythagoras Theorem
[tex]r^{2}=x^{2}+(15/2)^{2}[/tex]
substitute
[tex]120.25=x^{2}+56.25[/tex]
[tex]x^{2}=120.25-56.25[/tex]
[tex]x^{2}=64[/tex]
[tex]x=8\ units[/tex]
Part 4) Find the value of x
In this problem
x=OP=15
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
In the right triangle FPO
Applying the Pythagoras Theorem
[tex]r^{2}=15^{2}+(40/2)^{2}[/tex]
[tex]r^{2}=625[/tex]
[tex]r=25[/tex]
step 2
Find the value of x
In the right triangle RQO
Applying the Pythagoras Theorem
[tex]25^{2}=x^{2}+(40/2)^{2}[/tex]
[tex]625=x^{2}+400[/tex]
[tex]x^{2}=625-400[/tex]
[tex]x^{2}=225[/tex]
[tex]x=15\ units[/tex]
Part 5) Find the value of x
Applying the Pythagoras Theorem
[tex]6^{2}=4^{2}+(x/2)^{2}[/tex]
[tex]36=16+(x/2)^{2}[/tex]
[tex](x/2)^{2}=36-16[/tex]
[tex](x/2)^{2}=20[/tex]
[tex](x/2)=4.47[/tex]
[tex]x=8.9[/tex]
Which graph shows the solution to the system of linear inequalities below?
Answer:
Option B
The solution in the attached figure
Step-by-step explanation:
we have
Inequality A
[tex]y > -\frac{1}{3}x+1[/tex]
we know that
The solution of the inequality A is the shaded area above the dashed line
The equation of the dashed line is [tex]y=-\frac{1}{3}x+1[/tex]
The slope of the dashed line is negative [tex]m=-\frac{1}{3}[/tex]
Inequality B
[tex]y > 2x-1[/tex]
we know that
The solution of the inequality B is the shaded area above the dashed line
The equation of the dashed line is [tex]y=2x-1[/tex]
The slope of the dashed line is positive [tex]m=2[/tex]
therefore
The solution in the attached figure
The correct graph is:
Graph B
Step-by-step explanation:First inequality is given by:
[tex]y>\dfrac{-1}{3}x+1[/tex]
The inequality is a straight line that passes through (0,1) and (3,0) and also the line is dotted since the inequality is strict.
The shaded region is away from the origin since the inequality does not pass the zero point test.
Second inequality is given by:
[tex]y>2x-1[/tex]
The graph of this inequality is a dotted line (since the inequality is strict) and passes through (0,-1) and (1/2,0) and the shaded region is towards the origin
( since the line passes the zero point test )
Graph B represents the system of inequality.
Find the coordinates of P so that P partitions the segment AB in the ratio 1:7 if A(7,14) and B(−1,−2).
Answer:
P(6, 12 )
Step-by-step explanation:
Using the Section formula, then
[tex]x_{P}[/tex] = [tex]\frac{7(7)+1(-1)}{1+7}[/tex] = [tex]\frac{49-1}{8}[/tex] = [tex]\frac{48}{8}[/tex] = 6
[tex]y_{P}[/tex] = [tex]\frac{7(14)+1(-2)}{1+7}[/tex] = [tex]\frac{98-2}{8}[/tex] = [tex]\frac{96}{8}[/tex] = 12
Hence P(6, 12 )
Which best describes the transformation?
A. The transformation was a 90° rotation about the origin.
B. The transformation was a 180° rotation about the origin.
C. The transformation was a 270° rotation about the origin.
D. The transformation was a 360° rotation about the origin.
Answer:
Correct answer is "A"
Step-by-step explanation:
It is a tranformation about 90° in anti-clock wise direction
In geometry, transformations are used to move a point or points from one position to another. The transformation of [tex](x,y) \to (-y,x)[/tex] is a 90 degrees rotation about the origin.
Given that:
[tex]A(-1,1) \to A'(-1,-1)[/tex]
[tex]B(1,1) \to B'(-1,1)[/tex]
[tex]C(1,4) \to C'(-4,1)[/tex]
The transformation rule is:
[tex](x,y) \to (-y,x)[/tex]
When a point is rotated through [tex](x,y) \to (-y,x)[/tex]
Such point has undergone a 90 degrees counterclockwise rotation.
Hence, option (a) is correct.
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please help Ill mark brainliest -5/7 times 1/5
[tex]-\dfrac{5}{7}\cdot\dfrac{1}{5}=-\dfrac{1}{7}[/tex]
where would you put 5/2 on a number line
Answer:
Step-by-step explanation:
You would simplify 5/2, making it 2 and 1/2. this would go in between 2 and 3 on a graph.
Step-by-step explanation:
5/2 = 2.5
see attached to find where 2.5 is located on the number line.
Which is another way to name ZUST?
•
ZTSR
ZTSU
ZUSR
LUTS
Answer:ZTSU
Step-by-step explanation:
Another way to name ∠UST is ∠TSU.
Option B is correct.
We have,
Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Angles are usually measured in degrees or radians.
The angle mentioned in the figure is at the point S.
This angle is the smaller angle formed at the point S.
An angle can be represented in two ways, from left to right or from right to left.
Suppose, an angle is ∠ABC.
We can represent this as ∠CBA.
So, the angle represented is ∠TSU.
Hence the angle is ∠TSU.
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Manuela solved the equation below.
What is the solution to Manuela’s equation?
For this case we have the following equation:
[tex]2 (x + 2) = x-4[/tex]
Applying distributive property to the terms within the parentheses on the left side of the equation we have:
[tex]2x + 4 = x-4[/tex]
Subtracting "x" on both sides of the equation we have:
[tex]2x-x + 4 = -4\\x + 4 = -4[/tex]
Subtracting 4 on both sides of the equation we have:
[tex]x = -4-4\\x = -8[/tex]
Answer:
[tex]x = -8[/tex]
Answer:
x = -8
Step-by-step explanation:
We are given that Manuela solved following equation and we are to find its solution:
[tex] 2 ( x + 2 ) = x - 4 [/tex]
Expanding the left side of the equation by multiplying the terms inside the bracket by 2:
[tex]2x+4=x-4[/tex]
Arranging the equation in a way such that like terms are on each side (variables on the left and constants on the right):
[tex]2x-x=-4-4[/tex]
x = -8
Which best describes a system of equations that has no solution?
-consistent, independent
-inconsistent, dependent
-consistent, dependent
-inconsistent
Answer:
Inconsistent equations describes a system of equations that has no solution.
Step-by-step explanation:
Inconsistent equations have no solutions and contain no further classes.
Inconsistent equations are defined as two or more equations that can never be solved, based on using one set of values for the variables.
Find the Area
i need help?
Check the picture below.
What is the product?
(x − 3)(2x2 − 5x + 1)
2x3 − x2 + 16x + 3
2x3 − 11x2 + 16x + 3
2x3 − 11x2 + 16x − 3
2x3 − x2 + 16x − 3
Answer:
Third option: 2x^3-11x^2+16x-3
Step-by-step explanation:
The product to be found is:
[tex](x-3)(2x^2-5x+1)[/tex]
Distributive property will be used for the product:
[tex]x(2x^2-5x+1)-3(2x^2-5x+1)\\[/tex]
Multiplication will give us:
[tex]=2x^3-5x^2+x-6x^2+15x-3\\Combining\ alike\ terms\\=2x^3-5x^2-6x^2+x+15x-3\\=2x^3-11x^2+16x-3[/tex]
The product is: 2x^3-11x^2+16x-3
Hence, third option is the correct answer ..
Answer:
The product is 2x³ - 11x² + 16x - 3 ⇒ 3rd answer
Step-by-step explanation:
* Lets explain how to find the product of binomial by trinomial
- If (ax² ± bx ± c) and (dx ± e) are trinomial and binomial, where
a , b , c , d , e are constant, their product is:
# Multiply (ax²) by (dx) ⇒ 1st term in the trinomial and 1st term in the
binomial
# Multiply (ax²) by (e) ⇒ 1st term in the trinomial and 2nd term in
the binomial
# Multiply (bx) by (dx) ⇒ 2nd term the trinomial and 1st term in
the binomial
# Multiply (bx) by (e) ⇒ 2nd term in the trinomial and 2nd term in the binomial
# Multiply (c) by (dx) ⇒ 3rd term in the trinomial and 1st term in
the binomial
# Multiply (c) by (e) ⇒ 3rd term the trinomial and 2nd term in
the binomial
# (ax² ± bx ± c)(dx ± e) = adx³ ± aex² ± bdx² ± bex ± cdx ± ce
- Add the terms aex² and bdx² because they are like terms
- Add the terms bex and cdx because they are like terms
* Now lets solve the problem
∵ The binomial is (x - 3) and the trinomial is (2x² - 5x + 1)
∴ (x)(2x²) = 2x³
∵ (x)(-5x) = -5x²
∵ (x)(1) = x
∵ (-3)(2x²) = -6x²
∵ (-3)(-5x) = 15x
∵ (-3)(1) = -3
∴ (x - 3)(2x² - 5x + 1) = 2x³ + -5x² + x + -6x² + 15x + -3
- Add the like terms
∵ -5x² and -6x² are like term
∴ Their sum is -11x²
∵ x and 15 x are like terms
∴ Their sum = 16x
∴ (x - 3)(2x² - 5x + 1) = 2x³ - 11x² + 16x - 3
* The product is 2x³ - 11x² + 16x - 3
At this same time in 2010, 78% of people said they went out dancing at least one night a month. Recently, this number has increased by only 2%. What is the recent percentage of people that go out dancing once a month?
The recent percentage of people that go out dancing at least one night a month, considering an initial percentage of 78% in 2010 and a recent increase of 2%, is 80%.
Explanation:The percentage of people who went out dancing at least once a month in 2010 was 78%. If the number has recently increased by 2%, we need to add these two percentages together to find the recent percentage. In mathematics, when an increase is given in percentage, it's added to the original.
So, let's do the calculation:
78% (percentage in 2010) + 2% (recent increase) = 80% (recent percentage).
So, the recent percentage of people who go out dancing at least once a month is 80%.
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Prism A is similar to Prism B with a scale factor of 6:5. If the volume of Prism B is 875 m2, find the volume of Prism A.
Answer:
[tex]\large\boxed{V_A=1512\ m^3}[/tex]
Step-by-step explanation:
[tex]\text{If a prism A is similar to a prism B with a scale k, then:}\\\\\text{1.\ The ratio of the lengths of the corresponding edges is equal to the scale k}\\\\\dfrac{a}{b}=k\\\\\text{2. The ratio of the surface area of the prisms is equal}\\\text{to the square of the scale k}\\\\\dfrac{S.A._A}{S.A._B}=k^2\\\\\text{3. The ratio of the prism volume is equal to the cube of the scale k}\\\\\dfrac{V_A}{V_B}=k^3[/tex]
[tex]\text{We have}\\\\k=6:5=\dfrac{6}{5}\\\\V_B=875\ m^3\\\\V_A=x\\\\\text{Substitute to 3.}\\\\\dfrac{x}{875}=\left(\dfrac{6}{5}\right)^3\\\\\dfrac{x}{875}=\dfrac{216}{125}\qquad\text{cross multiply}\\\\125x=(875)(216)\qquad\text{divide both sides by 125}\\\\x=\dfrac{(875)(216)}{125}\\\\x=\dfrac{(7)(216)}{1}\\\\x=1512\ m^3[/tex]
Prism A is similar to Prism B with a scale factor of 6:5. If the volume of Prism B is 875 m2. The volume of prism B is 1512 meter square.
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and the new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called the scale factor.
Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Thus, the scale factor is the ratio of the new measurement to the old measurement.
Prism A is similar to Prism B with a scale factor of 6:5.
If the volume of Prism B is 875 m2, find the volume of Prism A.
scale factor = 6/5
The ratio of the surface area of the prism A to the prism B
A1 / A2 = k^2
The ratio of the prism is equal to the cube of the scale k.
V1 / V2 = k^3
Let x be the volume of Prism A.
x / 875 = (6/5)^2
x / 875 = 216 / 125
x = 875 * 216 / 125
x = 1512
Therefore, the volume of prism B is 1512 meter square.
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Using the digits 3, 4, 5, 6 and 7, without repetitions, calculate the
number of 4-digit numbers that are greater than 5 000 that can be
formed.
Jawapan:
Answer:
[tex]1\cdot4\cdot3\cdot2+2\cdot4\cdot3\cdot2=24+48=72[/tex]
Answer:
72
Step-by-step explanation:
There are five possible digits to choose from: 3, 4, 5, 6, and 7.
The number must be greater than 5000, so there are 3 possibilities for the first digit: 5, 6, or 7.
There's no repetition, so the second digit is one of 4 remaining possible digits.
That leaves 3 possible digits for the third digit. And 2 possible digits for the fourth digit.
So the number of possible four-digit numbers that can be formed is:
3 × 4 × 3 × 2 = 72
which choice is equivalent to the expression below?
4 to the power of negative 2.
A. 1/6
B. 1/8
C. -1/16
D. -8
Answer:
1/16
Step-by-step explanation:
You need to know the following property
[tex]a^{(-b)} = \frac{1}{a^b}[/tex]
That means
[tex]4^{-2} = \frac{1}{4^2} = \frac{1}{4*4} = \boxed{\frac{1}{16}}[/tex]
if f(x)=-x^2+6x-1 and g(x)=3x^2-4x-1,find(f+g)(x)
Answer:
2x^2 +2x-2
Step-by-step explanation:
f(x)=-x^2+6x-1
g(x)=3x^2-4x-1
(f+g)(x)= -x^2+6x-1 +3x^2-4x-1
= 2x^2 +2x-2
What is the square root of ab2?
Answer:
sqrt.(a) * absolutevalue(b)
Step-by-step explanation:
You do abs value when you have an even exponent with an odd exponent result from b^2 to b^1.
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
Answer: Hello there!
Well, the square root is the inverse function of the square potential.
This is if you have [tex](\sqrt{x} )^{2} = x[/tex] and [tex]\sqrt{x^{2} } = +-x[/tex]
A interesting part of the square root is that (-4)*(-4) = 16, and 4*4 = 16, so the solutions for [tex]\sqrt{16}[/tex] are -4 and 4. For this is that you see a +- symbol in the second equation.
Now, if you have the number [tex](a*b)^{2}[/tex]
Now, we put this inside a square root: [tex]\sqrt{(a*b)^{2} } = +-a*b[/tex]
So the solutions for the square root of (a*b)^2 are a*b and - a*b.
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE = 11x -3 and CE = 12 - 4x. find x.
Answer: The value of x = 1
Step-by-step explanation:
Given : Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
[tex]AE = 11x -3 \text{ and} CE = 12- 4x.[/tex]
We know that the diagonal of a parallelogram bisects each other.
Therefore , we have the following equation :-
[tex]11x -3= 12- 4x\\\\\Righatrrow11x+4x=12+3\\\\\rightarrow\ 15x=15\\\\\Rightarrow\x=\dfrac{15}{15}=1[/tex]
Hence, the value of x = 1
what is the difference between -5 and 2?
Answer:
2 is the bigger number
Step-by-step explanation:
Answer:7
Step-by-step explanation:
Think about it this way your looking at a number line and at this point your looking at number -5 and then do bunny hops from -5 to 2 and however many hops you took is the difference between
what is (24x-35q) (56q+78x)
Answer:
= 1872x^2 - 1960q^2 - 1386xq
Step-by-step explanation:
First you should distribute.
(24x * 56q), (24x * 78x), (-35q * 56q), (-35q * 78x)
=1344xq + 1872x^2 - 1960q^2 - 2730xq
Now you combine like terms.
= 1872x^2 - 1960q^2 - 1386xq
**NOTE that (^2) means "squared"
Since there are no more like terms that is your final answer. I hope this helps love! :)
Heather, Sarah, Nicky, and Jill each have nine markers. How many markers do they have in all?
in total: thirty-six (36) markers.
If the variance of the ages of the people who attended a rock concert is 38, what is the standard deviation of the ages? Round your answer to two decimal places
Answer:
[tex]\sigma=6.16[/tex]
Step-by-step explanation:
By definition, the variance V of a population is defined as:
[tex]V = \sigma^2[/tex]
Where [tex]\sigma[/tex] is the standard deviation
We know that [tex]V = 38[/tex], then we can solve the equation for the standard deviation [tex]\sigma[/tex]
[tex]38 = \sigma^2[/tex]
[tex]\sigma^2=38[/tex]
[tex]\sigma=\sqrt{38}[/tex]
[tex]\sigma=6.16[/tex]
Finally the standard deviation is: [tex]\sigma=6.16[/tex]