The standard deviation exists as the positive square root of the variance.
So, the standard deviation = 4.47.
How to estimate the standard deviation?Given data set: 13 17 9 21
To calculate the mean of the data.
We know that mean exists as the average of the data values and exists estimated as:
Mean [tex]$=\frac{13+17+9+21}{4} \\[/tex]
Mean [tex]$=\frac{60}{4} \\[/tex]
Mean = 15
To find the difference of each data point from the mean as:
Deviation:
13 - 15 = -2
17 - 15 = 2
9 - 15 = -6
21 - 15 = 6
Now we have to square the above deviations we obtain:
4, 4, 36, 36
To estimate the variance of the above sets:
variance [tex]$=\frac{4+4+36+36}{4}$[/tex]
Variance [tex]$=\frac{80}{4}$[/tex]
Variance = 20
The standard deviation exists as the positive square root of the variance. so, the standard deviation [tex]$=\sqrt{20 }=4.47$[/tex].
To learn more about standard deviation refer to:
https://brainly.com/question/475676
#SPJ4
Answer:
4.4
Step-by-step explanation:
The answer above is correct.
A necklace calls for red, blue and white beads in the ratio of 5: 8:12. Ming has used
350 beads, how many of them are white in colour?
Answer:
168Step-by-step explanation:
find unity
350 : (5 + 8 + 12) =
350 : 25 = 14
multiply the units by the white ratio14 * 12 = 168
The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. on the bottom shelf are 3 fiction and 5 nonfiction books. choosing which 2 books describes a pair of dependent events?
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change. Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance. Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is. Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
Know more about probability here:
https://brainly.com/question/25870256
#SPJ4
Help me in thisssssss
Answer:
34
Step-by-step explanation:
(a + [tex]\frac{1}{a}[/tex] ) = 6← square both sides
(a + [tex]\frac{1}{a}[/tex] )² = 6² ← expand left side using FOIL
a² + 1 + 1 + [tex]\frac{1}{a^2}[/tex] = 36
a² + 2 + [tex]\frac{1}{a^2}[/tex] = 36 ( subtract 2 from both sides )
a² + [tex]\frac{1}{a^2}[/tex] = 34
Which word describes their measures? linear congruent complementary supplementary
A meson when at rest decays 2 μs after it is created. If moving in the laboratory at 0. 99C. Its lifetime according to laboratory clocks would be?
The lifetime of meson according to laboratory clocks would be 14 μs.
In this question,
Meson decay, Δt = 2μs
Velocity, y = 0.99C, where C is the speed of the light
Time measurement depends on the reference frame of clock.
Time dilation, Δt' = y Δt
⇒ [tex]\frac{\Delta t }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-\frac{(0.99c)^{2} }{c^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.99^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.9801 } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{0.0199} } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{0.1410} } }[/tex]
⇒ 14.18 × 10⁻⁶ ≈ 14 μs
Hence we can conclude that the lifetime of meson according to laboratory clocks would be 14 μs.
Learn more about lifetime at laboratory clocks here
https://brainly.com/question/23455167
#SPJ4
Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b to complete the solutions.
The roots of the given polynomials exists
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex]
What is the formula of the quadratic equation?For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Therefore by using the formula we have
[tex]$x^{2}-16 x+54=0[/tex]
Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get
[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]
simplifying the equation, we get
[tex]$x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1}[/tex]
[tex]$x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1}$[/tex]
[tex]$x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]
Therefore, the roots of the given polynomials are
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex].
To learn more about quadratic equations refer to:
https://brainly.com/question/1214333
#SPJ4
what is ratio (maths short definition)
Answer:
division
Step-by-step explanation:
ratio means those 2 nunbers are being divided
division is how the numbers are related or compared
much of it is describing some of all something
like 2 out 3 dentists like chrwing gum
Two 6-sided dice, one red and one green, are rolled. What is the probability that the red die shows a 2 and the green die shows a 5
The probability that the red die shows a 2 and the green die shows a 5 is 1/36
How to determine the probability that the red die shows a 2 and the green die shows a 5?The sample space of a die is
S = {1, 2, 3, 4, 5, 6}
This means that
Red die = {1, 2, 3, 4, 5, 6}
Green die = {1, 2, 3, 4, 5, 6}
On the dice, we have
P(Red = 2) = 1/6
P(Green = 5) = 1/6
The probability that the red die shows a 2 and the green die shows a 5 is
P = P(Red = 2) * P(Green = 5)
Substitute the known values in the above equation
P = 1/6 *1/6
Evaluate the product
P = 1/36
Hence, the probability that the red die shows a 2 and the green die shows a 5 is 1/36
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
The diameter of a sphere measures 10.4 inches. what is the surface area of the sphere?
Area of the sphere ≅ 339.62 in².
What is Sphere?A sphere is a geometrical object in three-dimensional space that is the surface of a ball. Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space.
Area of sphere = 4[tex]\pi r^{2}[/tex]
diameter d = 2r
Given that,
diameter d = 10.4 , r =5.2 in
then, Area of sphere = 4[tex]\pi r^{2}[/tex]
= 4×3.14×5.2×5.2
≅ 339.62 in²
Learn more about sphere with the help of given link:
https://brainly.com/question/29241617
#SPJ4
Answer:
108.16 to the second power
Step-by-step explanation:
This design is made from 1 blue circle, 4 orange circles and 16 green circles. The circles touch each othe Given that the radius of each green circle is I unit, find the exact radius of a the orange circles, b the blue circle.
The radius of the orange circle is 1.5 unit and the radius of the blue circle is 2.25 units
How to determine the radii of the circles?The figure that completes the question is added as an attachment
The orange circle
The radius of the green circle is given as:
r = 1
One and half green circle make up the radius of the orange circle.
So, the radius of the orange circle is
R = 1.5 * r
This gives
R = 1.5 * 1
R = 1.5
Hence, the radius of the orange circle is 1.5 unit
The blue circle
The radius of the orange circle is given as:
r = 1.5
One and half orange circle make up the radius of the blue circle.
So, the radius of the blue circle is
R = 1.5 * r
This gives
R = 1.5 * 1.5
R = 2.25
Hence, the radius of the blue circle is 2.25 units
Read more about radius at:
https://brainly.com/question/14283575
#SPJ1
A and B are two cylinders that are mathematically similar.
The area of the cross-section
of cylinder A is 18 cm².
Work out the volume of cylinder B.
+
18 cm²
A
5 cm
1
B
61%
10 cm
The Volume of the Cylinder B is gotten as; 720 cm³
What is the Volume of the Cylinder?We are given 2 similar cylinders with;
ratio of heights = a : b
Thus;
ratio of areas = a² : b²
We are given that;
Height of A is 5cm.
Height of B is 10cm.
Thus;
Ratio of heights = 5 : 10 = 1 : 2
Therefore;
ratio of areas = 1² : 2² = 1 : 4
The cross sectional area of B is 4 times the cross sectional area of A. Thus;
Cross sectional area of B = 4 × 18 = 72 cm²
Volume of cylinder = cross section area × height
Volume of cylinder B = 72 × 10 = 720 cm³
The complete question is;
A and B are two cylinders that are mathematically similar.
The area of the cross-section of cylinder A is 18cm².
Height of A is 5cm.
Height of B is 10cm.
Work out the volume of cylinder B
Read more about Volume of Cylinder at; https://brainly.com/question/9554871
#SPJ1
pretty please what is g(x)
The value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x). This can be obtained by finding composite of (h ° g) (x) using the formula for composition.
Find the value of g(x):
Composition of a function : A composite function is created when one function is substituted into another.
f composite of g is denoted as (f ° g)
The formula to find the composite of a function,
(f ° g)(x) = f(g(x))For example,
f(x) = x + 2, and g(x) = 3x
(f ° g)(x) = f(g(x)) = g(x) + 2 = 3x +2 (g ° f)(x) = g(f(x)) = 3(f(x)) = 3(x+2) = 3x + 6
In the question,
Given that, f(x) = (8x³ - 1)³, h(x) = x³
f(x) = (h ° g) (x)
⇒ (8x³ - 1)³ = h(g(x))
⇒ (8x³ - 1)³ = (g(x))³
Taking cube roots on both sides,
⇒ ∛(8x³ - 1)³ = ∛(g(x))³
⇒ (8x³ - 1) = (g(x))
⇒ g(x) = 8x³ - 1
Hence the value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x).
Learn more about composite of a function here:
brainly.com/question/20379727
#SPJ1
Alonso brings \$21$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost \$2.50$2.50dollar sign, 2, point, 50. Then, he notices that the store only sells avocados in bags of 333 for \$5$5dollar sign, 5. He wants to buy as many avocados as he can with his remaining money.
How do u get 3 bags of avacodes or 9 avacadoes ??
Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
EquationAmount Alonso brings to the market = $21Cost of an egg = $2.50Cost of avocados in bags of 3 = $5Number of avocados bought = x21 = 2.50 + 5x
21 - 2.50 = 5x
18.50 = 5x
x = 18.50 / 5
x = 3.7 bags of avocados
To get 3 bags of avocados or 9 avocados
= $5 × 3
= $15
Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
Which of the following is a solution to the equation
3/4
x-12 = -18?
1) 4.5
2) -8
3) -22.5
4) -40
Answer: B) -8
Step-by-step explanation:
We add 12 both sides
3/4 x = -18 + 12Add −18 and 12 to get −6.
3/4 x = -6Multiply both sides by 3/4 by the reciprocal of 3/4.
x = -6 × (3/4)Express a -6 x (3/4) as a single fraction.
x = -6 × 4 / 3Multiply −6 and 4 to get −24.
x = -24 / 3Divide −24 by 3 to get −8.
x = -8Answer: Option "2" is correct. ✅
A trander an article at 10% loss. If he had sold it for Rs.540 more , he would have gain 5% . Find the cost price of the articles.
The answer is :3600
Answer:
3600
Step-by-step explanation:
Reason is because you put the answer in your question.
Answer:
Rs.10800
Step-by-step explanation:
loss of article(L%)=10%
s.p=?
c.p of an article (c.p)=c.p
Now,
s.p=100-L%×c.p
_____
100
= 100-10 ×c.p
_____
100
=90 ×c.p
___
100
=0.9 × c.p
if article sold with Rs. 540 more
Article profit =5%
s.p =c.p + 540 =100+p%×c.p
______
100
or, c.p +540=105×c.p
______
100
or, c.p +540=1.05×c.p
or,c.p +540=1.05c.p
or, 540=1.05c.p-c.p
or,540=0.05c.p
or, 540=c.p
____
0.05
Therefore, c.p =Rs. 10800
evaluate the expression: 7 - 3 + 9 x 8 ÷ 2
Answer:
40
Step-by-step explanation:
7 - 3 + 9 x 8 / 2
Multiplication and division left - right.
7 - 3 + 72 / 2
7 - 3 + 36
Add and subtract left to right.
4 + 36 = 40
PLEASE HELP IM STUCK
Answer:
If I'm not mistaken that is the answer
4.
Find the perimeter of the triangle.
A. 294 m
B. 119 m
C. 84 m
D. 168 m
Answer:
84m
Step-by-step explanation:
The perimeter of a triangle is the sum of the length of the external sides.
Therefore, the perimeter of the triangle = 21m + 28m + 35m = 84m.
Hey there!
What is the formula for finding the perimeter of a triangle?
a + b + c = perimeter
What does the labels mean?
a = side 1
b = base
c = side 2
What should the equation look like?
21m + 28m + 35m = perimeter
How do should it be solve?
21m + 28m + 35m = perimeter
49m + 35m = perimeter
84m = perimeter
What is the answer to the question?
84m
Good luck on your assignment and enjoy your day!
~Amphitrite1040
Evaluate the double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d
The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
What is the double integral 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d?Generally, the equation for is mathematically given as
The area denoted by the letter D that is bordered by y=0, y=x2, and x=7
The equation for the X-axis is y=0.
y=x² ---> (y-0) = (x-0)²
Therefore, the equation of a parabola is y = x2, and the vertex of the parabola is located at the point (0,0), and the axis of the parabola is parallel to the Y axis.
The equation for a straight line that is parallel to the Y-axis and passes through the point (7,0) is x=7.
[tex]\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA[/tex]
Integrating we have
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
If x equals zero, then we know that u equals zero as well.
When x equals seven, we know that u=72=49.
Therefore, by changing x2=u into our integral, it becomes from
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
[tex]7/2 \int^49_0 sin u dx[/tex]
Hence
=7/2(-cos49+1)
In conclusion,
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
Read more about integral
https://brainly.com/question/18125359
#SPJ1
What type of function is f(x) = 2 log5(3x)? exponential logarithmic polynomial rational
The type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
What kind of function is a given expression?
In this problem we must check the characteristics of an expression and conclude what kind of function is. First, we need to find if any trascendent operator, it not, then the function may be either polynomial or rational. If the function has a trascendent operator, then we must check if it is logarithmic or exponential.
At first glance, we see that the function includes only one trascendent operator, a "log" operator that creates a function of the form f(x) = A · ㏒ₙ (B · x). Therefore, the type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
RemarkThe statement is poorly formatted, correct form is shown below:
What type of function is f(x) = 2 · ㏒₅ (3 · x)? a) Exponential, b) Logarithmic, c) Polynomial, d) Rational.
To learn more on logarithmic functions: https://brainly.com/question/3181916
#SPJ1
Answer: Logarithmic
Step-by-step explanation: Got the question right on test.
To the nearest foot what is the length of a pendulum that makes one full swing in 1.9s
A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.
What is the length of a pendulum?A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.
Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".
Given the equation:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
where L is the length in feet and T is the time in seconds.
Given that T = 1.9sec,
Hence:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
L = 2.93 feet
A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.
Learn more about Length of a pendulum here: https://brainly.com/question/8168512
#SPJ4
Solve for x: 12x2 – 6 (a2 + b2)x + 3a2b2 = 0
Answer:
x:12×2−6(a2+b2)x+3a2b2=0
Step-by-step explanation:
equation
Find all subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2•
All subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2 is
{( 0,1) (-1,1)}
{(1,0)(0,1)}
{(1,0)(-1,1)}
A fixed A is a subset of some other set B if all elements of set A are factors of set B. In other phrases, set A is contained within set B. The subset relationship is denoted as A⊂B.
Subsets are a part of one of the mathematical ideas known assets. a hard and fast is a set of items or factors, grouped within the curly braces, consisting of {a,b,c,d}. If a set A is a set of even numbers and set B includes {2, 4,6}, then B is stated to be a subset of A, denoted by B⊆A and A is the superset of B.
In mathematics, set A is a subset of a fixed B if all factors of A are also elements of B; B is then a superset of A. It's far possible for A and B to be equal; if they may be unequal, then A is a proper subset of B. The relationship of one set being a subset of every other is known as inclusion.
A set which is (is linearly independent andoil generates/ spans the space (like R) is called a baris.
S= (1,0), (0,1), (-1))}
option-1
As, dimension of R²=2, so, Ary set
conists of three vectors cannot be baris for R²
so, option-1 is wrong.
option-2
As, dimention of R2-2.
{(10), (-11)} is a linearly independent
subset of S. so And as, this subset
has 2 vectors so it will as also
span R se, it will be a baris
of IR?
So, option-6 is correct
{(0,1)} is linearly independent subset
option-7
As (LO) has one vector. So, it cannot
Span/generate R so, it also cannot be balis
for R2
of S.
But it cannot span R²
So ut cannot
be a baris of R2
se, option-2 is wrong.
Option-3
AS, {(0,1), (-1,1)} is linearly independent
So, option -7, is wrong.
Answer
[as fox amy KER, (-1,1) K (0,1)] subset of s
And also as dim {(0,1), (-11)}=2
which is same as the dimention of IR2
so {(0,1), (-11)} forms a baris of R2
{(1,0), (0,1), (-11)}
{(1,0)}
So, option-3 is
Connect
option-4
{(1,0), (3, 1)} is standard balis of R2
which is subset of S.
10
[{(1,0), (0,1)}]
So, option-4 is correct.
option-5
{(-11)}
consists of one vertex,
so, ut cannot span R², so, ut cannot
be a baris of R²
9090
LO {(1,0), (-1,1)}]
Learn more about subsets here https://brainly.com/question/2000547
#SPJ4
Which expression is equivalent to?
Answer: [tex]\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{\frac{16}[81}} \sqrt[4]{\frac{x^{11}y^{8}}{x^{7}y^{6}}}\\\\=\frac{2}{3} \sqrt[4]{x^{4}y^{2}}\\\\=\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
Darren wins a coupon for $4 off the lunch special for each of 5 days. He pays $75 for his 5 lunch specials. Write and solve the equation to find the original price p for one lunch special.
Answer:
19
Step-by-step explanation: (75/5) + 4= p
15+4=p
19=p
The original price for one lunch meal is $19
p = $15 + $4
p = $19
can someone help me pls
Explanation:
The sector is the pizza slice. We subtract off the area of the triangle to find the yellow shaded area.
78.6794 - 70.4956 = 8.1838
c= 6x+100 and c=10x+80
what number does x have to be for c to be the same on each equation?
Answer:
x= 5 , for c to be same on each eqn
Luigi is navigating a maze. He gets to a junction and has 3 directions he can go in. For each of these choices, he eventually gets to another junction where he has 6 choices of direction.
How many different possible paths are there?
PLEASE HELP, I THINK IT’S EITHER B OR C.
(09.01 LC)
A function is shown in the table.
x g(x)
-2 2
-10
02
1 8
Which of the following is a true statement for this function? (5 points)
The function is decreasing from x = 0 to x = 1.
The function is decreasing from x = -1 to x = 0.
The function is increasing from x = 0 to x = 1.
The function is increasing from x = -2 to x = -1.
its c! there isnt a decrease between x = -1 and x = 0, as when x = -1 y = 0 and when x = 0 y = 2, showing an increase of +2.
67 is the difference of Gail’s height and 16.