The standard deviation of both sets of data is the same, at 3.67,and adding the same constant c to each data value results in the standard deviation remaining the same.
Define Standard deviation?
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
We have a data set:
14, 12, 16, 8, 6
As we know the standard deviation formula is :
σ = √[∑(xi-X)/n]
σ = population standard deviation
Here ,
xi = value from the data set
X = mean of the data set
n = number of observation in data set.
X = (14+12+16+8+6)/5
X = 56/5
Where, n = 5
After calculating the standard deviation will be:
σ = 11.2
Add 8 to each data value to get the new data set 14, 12, 16, 8, 6.
We can write,
14+8=22
12+8=20
16+8=24
8+8=16
6+8=14
Then,
New data set is ⇒ 22,20,24,16,14
New standard deviation:
σ(new) = 11.2
Since both sets of data have the same standard deviation, we can conclude that adding a constant to each data value has no effect on the standard deviation.
Adding the same constant c to each data value results in the standard deviation remaining the same.
Thus, the standard deviation of both the data are the same which is 11.2 and adding the same constant c to each data value results in the standard deviation remaining the same.
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:52:26 ATI
f(x) =
wer.
-(x+8)² + 4 for
for
Find f(-5)
x < -5
x ≥ 3
The value of f(-5) when we solve the function f(x) is -5.
What does the mathematical function mean?A function is a statement, tenet, or rule that creates a correlation between two variables. In mathematics, functions are used often and are required to build complicated connections.
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The function can be solved as:
[tex]f(x) = -(x+8)^{2} +4[/tex]
[tex]=-(-5+8)^{2}+4[/tex]
[tex]=-(3)^{2}+4[/tex]
[tex]=-9+4[/tex]
[tex]=-5[/tex]
Hence, f(-5) = -5
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[tex] \rm If \: \beta = \lim_{x \to0} \frac{ {e}^{ {x}^{3} } - (1 - {x}^{3} {)}^{ \frac{1}3 } + ((1 - {x}^{2} {)}^{ \frac{1}{2} } - 1) \sin x}{x \sin^{2} x} ,\\ [/tex]
then the value of [tex]6 \beta [/tex] is
Expand the limand as
[tex]\dfrac{e^{x^3} - (1 - x^3)^{1/3} + \left((1-x^2)^{1/2} - 1\right) \sin(x)}{x \sin^2(x)} \\\\ ~~~~~~~~ = \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} \cdot \dfrac{x^2}{\sin^2(x)} + \dfrac{(1-x^2)^{1/2} - 1}{x^2} \cdot \dfrac{x}{\sin(x)}[/tex]
Recall that for [tex]a\neq0[/tex],
[tex]\displaystyle \lim_{x\to0} \frac{\sin(ax)}{ax} = 1[/tex]
Then
[tex]\displaystyle \beta = \lim_{x\to0} \left( \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} + \dfrac{(1-x^2)^{1/2} - 1}{x^2}\right)[/tex]
Rationalize the numerators.
[tex]\dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} = \dfrac{e^{3x^3} - (1 - x^3)}{x^3 \left(e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}\right)} \\\\ ~~~~~~~~~~~ = \left(\dfrac{e^{3x^3} - 1}{x^3} + 1\right) \cdot\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}}[/tex]
and observe that
[tex]\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}} \to \dfrac13[/tex]
[tex]\dfrac{(1-x^2)^{1/2}-1}{x^2} = \dfrac{(1-x^2) - 1}{x^2 \left((1-x^2)^{1/2} + 1\right)} \\\\ ~~~~~~~~ = -\dfrac1{(1-x^2)^{1/2} + 1} \to -\dfrac12[/tex]
This leaves us with
[tex]\displaystyle \beta = \lim_{x\to0} \frac{e^{3x^3} - 1}{3x^3} - \frac16[/tex]
The remaining limit is the derivative of [tex]e^{3x^3}[/tex] at [tex]x=0[/tex], so its value is 1, and we find
[tex]\beta = 1 - \dfrac16 = \dfrac56 \implies 6\beta = \boxed{5}[/tex]
If m∠3 = 4x + 10 and m∠4 = 5x, find x.
The value of x is 10.
Given m∠3 = 4x+10 and m∠4 = 5x
Now, we need to determine what value of x it is.
We know that in quadrilateral four angles are there in that two angles are equal it is said to be as Rhombus.
Two angles are given in this question. We assume those are equal angles.
∴ m∠3 = m∠4
By substituting the values of two angles, we get
4x+10 = 5x
By deducting '4x' on both sides, we get
4x+10-4x = 5x - 4x
10 = x
∴ x = 10
The final value for x is 10.
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I need help with 4 and 5
4. The two triangles are similar by virtue of the AAA triangle congruence theorem as a result of the corresponding angles which have equal measures.
5. The length of segment CE to the nearest tenth is; 46.7 in.
What is the length of segment CE as required in the task content?4. The ∆CBD and ∆CAE are similar (congruent) following the fact that angle C is common to both triangles and the angles A and E have equal measures as E and D respectively by virtue of corresponding angles theorem. Ultimately, the two triangles; ∆CBD and ∆CAE are congruent since all three angle measures are the same in the triangles.
The corresponding angles in discuss is due to the fact that the lines ED and AE are parallel lines.
5. Also, upon establishing the congruence of the two triangles, it follows that the ratio of their corresponding sides is same for all three sides.
Therefore, we can establish that;
BD/AE = CD/CE
6/14 = 20/CE
CE = (14 × 20)/6
CE = 140/3
CE = 46.667 in.
Ultimately, the length of segment CE to the nearest tenth is; 46.7 in.
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Biff earned $45 working at Happy Days Drive-In. He spent 1/3 of the money on gas for his car and 1/5 of it on flowers . How much money does he have left
Biff has $12 left out of the money
How to calculate the amount of money left ?Biff earned $45 at happy days drive-in
He spent 1/3 of the money on gas
He also spent 1/5 of the money flowers
The money he has left can be calculated as follows
45 × {1-(1/3+1/5)}
= 45× (1-8/15)
= 45 × 7/15
= 3 × 7
= 21
Hence Biff has $12 left
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Which translation(s) will take Triangle T to Triangle U? Explain your answer
For Triangle T to translate Triangle U
1. Translate (-3, 0) to (1, 2).
2. Translate (-2, -1) to (2, 1) .
3. Translate (-4, -3) to (0, -1).
Options A and C
This is further explained below.
What is translation?Generally, A translation is a kind of geometric transformation that is used in Euclidean geometry. This type of transformation involves moving each point of a figure, shape, or space by the same distance in a certain direction.
In conclusion, for Triangle T to translate Triangle U
1. Translate (-3, 0) to (1, 2).
2. Translate (-2, -1) to (2, 1) .
3. Translate (-4, -3) to (0, -1).
Therefore, Options A and C are valid
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Please answer asap
is -√49 a rational number
from the knowledge of square and square root of numbers√49=7
-√49
-√7^2
-7
what the mean of 1,3,5,5, 1, 3, 0, 0, 5
1+3+5+5+1+3+5+0+0
4+5+5+1+3+5
9+5+1+3+5
14+1+3+5
15+3+5
18+5
23
23/9
the mean is 2 and 5/9
A copy machine makes 91 copies in 3 minutes and 15 seconds. How many copies does it make per minute?
copies per minute
X
5
-6(w +5 ) +9<-51
Solve the inequality
Answer:
w>5
Step-by-step explanation:
Go onto symbolab it's a website good for solving math problems like this
How to find the slope intercept form of the line that passes through (-4,1) and perpendicular to y = 2x - 3
Hope this helps, make sure to follow me! <3
PLEASE HELP! DUE IN LESS THAN 2 HOURS! IM STUCK! PLEASE HELP ME! YOU WILL GET 100 POINTS! THANKS QUESTION DOWN BELOW!!! PLEASE SHOW THE WORK!
Answer:
Do you want the equation?
y = [tex]x^{2}[/tex]
Step-by-step explanation:
Answer:
1. One square
2. Four squares
3. Nine squares
4. Sixteen squares
5. Twenty-five squares
6. Thirty six squares
7. 49 squares
8. 64 squares
9. 81 squares
10. 100 squares
Step-by-step explanation:
The pattern is add six squares to the image before the one you’re working.
Solve for x.
6/9=x/12
Simplify as much as possible
- - - - - - - - - - - - - - - - - - - - - - - -
Find common denominators :)
6/9
Divide by 4 (the common factor of 9 and 12)
2/3
Multiply by 4
8/12
8/12 = 8/12
Now, simplify.
2/3
- - - - - - - - - - - - - - - - - - - - - - - -
Have a great day/night! :)
(Please consider leaving a Brainliest!)
~pinetreee
What is the horizontal asymptote of f(x)=-2x/x+1
O y = -2
O y = -1
O y = 0
O y = 1
-2x
X+1?
The horizontal asymptote of the given function f(x) is y = –2.
What is defined as the horizontal asymptote?A horizontal asymptote is a straight line that is not part of a function's graph but guides it for x-values. "far" to a right and/or left.If a numerator and denominator have the same degree, this same horizontal asymptote is simply the fraction from the coefficient of their leading term.The numerator does have a degree one, and so does the denominator.
The foremost term in the numerator has a coefficient of -2.
In the denominator, the coefficient again for leading term is 1.
At y = -2/1, the horizontal asymptote exists.
Thus, the horizontal asymptote of the function is found as -2.
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Find the value of X then find the measure of each labeled angle.
The value of the angle x is 108 degree.
According to the statement
We have to find that the value of the x in the adjacent angle.
So, For this purpose, we know that the
The adjacent angles is the two angles are said to be adjacent angles when they share the common vertex and side.
From the given information:
When we extend line AB to E
Then ∠EBC is created
Since BC is parallel to AD
So, ∠EBC =∠BAD = x° (corresponding angles are equal )
Linear pair : Two angles are said to be linear if they're adjacent angles formed by two intersecting lines. The measure of a angular unit is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Now With the linear pair property
x+(x-36) = 180
2x - 36 = 180
2x = 180+36
2x = 216
x = 216/2
x = 108.
Then one angle is of 108 degree and second angle is 72 degree.
So, The value of the angle x is 108 degree.
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A square window has an area of 9 square feet. What is the perimeter of the window?
Answer:
12
Step-by-step explanation:
A turtle was swimming 2 feet below the surface of a pond. While looking for food, he went down 7 more feet
help me do this plroblem
Answer: $640
Step-by-step explanation:
Answer:
640
Step-by-step explanation:
Look for acute, obtuse, and right angles in your environment or find one of each online. Post an image of each. Can you find all three in one spot?
Identify the acute, obtuse, and right angles in your image or images.
Answer: Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.
Step-by-step explanation:
the graph shows two points from the table representing a proportional relationship. Which point corresponds to the last entry in the table?
Answer:
Step-by-step explanation: second point correspond to the last entry in the table
HELP PLEASE? THE PICTURE IS ATTACHED FOR ANYONE THAT WANTS TO HELP, I’D APPRECIATE IF SOMEONE HELP ME ANSWER THIS
Answer:
$32.00
Step-by-step explanation:
The easiest way of calculating discount is, in this case, to multiply the normal price $80 by 40 then divide it by one hundred. So, the discount is equal to $32. To calculate the sales price, simply deduct the discount of $32 from the original price $80 then get $48 as the sales price.
HELP PLEASE? THE PICTURE IS ATTACHED FOR ANYONE THAT WANTS TO HELP, I’D APPRECIATE IF SOMEONE HELP ME ANSWER THIS
Answer:
40% Of 80 is 32
h(x) = 3x - 5, find h(-2).
Answer:
h= 3x/x −5
Step-by-step explanation:
hx=3x−5
Step 1: Divide both sides by x.
hx/x = 3x/x −5
h= 3x/x −5
x
Answer:
h= 3x/x −5
An angle measures 124° less than the measure of its supplementary angle. What is the
measure of each angle?
Answer:
56°
Step-by-step explanation:
Supplementary angles are = to 180° so you have to subtract 124 from 180 which gives you 56°
The leg of a right triangle is 8 ft in length while
the hypotenuse is 15 ft in length. Find the missing
side of the triangle. Write the answer in simplified
radical form
Answer:
[tex]\sqrt{161}[/tex] ft
Step-by-step explanation:
According to the pythagorean theorem, in a right-angle triangle, the sum of of the squared legs is equal to the hypotenuse squared.
In simpler words, if we have legs [tex]a[/tex] and [tex]b[/tex], as well as hypotenuse [tex]c[/tex], then [tex]a^2 + b^2 = c^2[/tex].
In our case, we know that [tex]a = 8[/tex] and [tex]c = 15[/tex], therefore, we should try and find b.
[tex]8^2 + b^2 = 15^2\\\to 64 + b^2 = 225 \text{ // Subtract by 64}\\\to b^2 = 161 \text{ // Take the square root of both sides}\\\to b = \sqrt{161}[/tex]
Find the area of the semicircle. (Take pi=22/7) Diameter=14
Area of semicircle is 77.
What is semicircle?
A semicircle is defined as half circle formed by cutting the circle into two halves.
Given that;
Diameter of semicircle = 14
Radius of semicircle = 14/2 = 7
Now, Area of semicircle = 1/2 (πr²)
Substitute π = 22/7 and r = 7, we get;
Area of semicircle = 1/2 (πr²)
= 1/2 × (22/7) × 7 × 7
= 77
So, Area of semicircle is 77.
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solve 6/58 x -1 2/5 -371/40 -6 1/4 1 1/2 371/40
The simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
6 5/8 x -1 2/5
Convert the mixed fractions to improper fractions
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/8 x 1/5
Evaluate the product of the denominators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/40
Hence, the simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
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16. Vocabulary A number written in
expanded form is written as the sum
of each …..
.Write 39,005
in expanded form...
There is a pair of parallel sides in the following shape.
What is the area of the shape?
If there is a pair of parallel sides in the following shape. the area of the shape is: 21 unit².
Area of the shapeUsing this formula to determine or find the area of the shape
Area = (1/2)× (Area+ breadth )height
Where:
Area= 9
Breadth= 5
Height = 3
Now Let plug in the formula so as to find the area
Area of the shape = (1/2)× (9 + 5) ×3
Area of the shape = (1/2)× (14)×3
Area of the shape = (1/2)× 42
Area of the shape= 21 unit²
Therefore If there is a pair of parallel sides in the following shape. the area of the shape is: 21 unit².
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[ne
How many solutions for x does the following equation have?
(6x + 6) = 4x + 4
O A. 0
OB. 1
O C. infinite
OD. 4
the area A of a rectectangle is represented by the formula A=Lw where I is the length and W is the width. write an equation that would make it easy to find the length of the rectangle
Answer: L=A/W
Step-by-step explanation: If you do this then you will find the length because L x W = A. So if the area is determined by l and w then you could divide A by the width to find the length because you multiply length and width to find the area