Answer:
There would be no change in the standard deviation if each one of the numbers in the set was decreased by 4.
Step-by-step explanation:
We are given that the standard deviation of a set of numbers is 22.2.
And we have to check that what would be the standard deviation, if each one of the numbers in the set was decreased by 4.
For concluding this, we will take a simple example;
Suppose that there are three set of numbers : 6, 8 and 10
Firstly, we will calculate the standard deviation for these numbers;
X [tex]X - \bar X[/tex] [tex](X-\bar X)^{2}[/tex]
6 6 - 8 = -2 4
8 8 - 8 = 0 0
10 10 - 8 = 2 4
8
Here, the Mean of the three numbers is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{6+8+10}{3}[/tex] = 8
Now, standard deviation formula is given by;
Standard deviation, s = [tex]\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{8 }{3-1} }[/tex] = 2
Now, we will decrease each of the three numbers by 4, we get ;
X [tex]X - \bar X[/tex] [tex](X-\bar X)^{2}[/tex]
2 2 - 4 = -2 4
4 4 - 4 = 0 0
6 6 - 4 = 2 4
8
Here, the Mean of the three numbers is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{2+4+6}{3}[/tex] = 4
Now, standard deviation formula is given by;
Standard deviation, s = [tex]\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{8 }{3-1} }[/tex] = 2
From this, we observe that even after decreasing each number by 4, the standard deviation remains same.
SO, we can conclude that if each one of the numbers in the set was decreased by 4 , the standard deviation of a set of numbers will be 22.2 only.
A triangular prism is 4 millimeters long. It has a triangular face with a base of 13 millimeters. The volume of the prism is 416 cubic millimeters. What is the height of its triangular face? Height = millimeters
Answer:
16 millimeters
Step-by-step explanation:
Length of the Triangular Prism=4 millimetersBase Length of One Triangular Face=13 millimeters.Volume of the Prism =416 cubic millimeters.Now:
Volume of a Prism=Base Area X Prism Length
Since we have a triangular base:
Volume of the Prism=(0.5 X Base X Height) X Prism Length
Substituting the given values, we obtain:
416=(0.5 X 13 X Height) X 4
416=26 X Height
Divide both sides by 26
Height of its triangular face=16 millimeters
Answer:
h = 16 mm
Step-by-step explanation:
Th volume of the prism is:
[tex] V = A*l [/tex] (1)
Where:
V. is the volume of the triangular prism = 416 mm³
A. is the area of the prism = ?
l: is the large of the prism = 4 mm
The area of the triangular face of the prism is:
[tex] A = \frac{1}{2}bh [/tex] (2)
Where:
b: is the base of the triangular face = 13 mm
h: is the height of the triangular face = ?
From equation (1) we have:
[tex] V = A*l [/tex]
[tex] A = \frac{V}{l} = \frac{416 mm^{3}}{4 mm} = 104 mm^{2} [/tex]
Now, using equation (2) we can find the height of the triangular face:
[tex] A = \frac{1}{2}bh [/tex]
[tex] h = \frac{2A}{b} = \frac{2*104 mm^{2}}{13 mm} = 16 mm [/tex]
Therefore, the height of the triangular face is 16 mm.
I hope it helps you!
Use greatest common factor and the distributive property to write equivalent expressions in factored form. 2 +8
Answer:
2(x+4y)
Step-by-step explanation:
The greatest common factor would be 2. So 2/2 is 1 and then 8/2 is 4. Now if we plug back the variables, you should get 1x and 4y. To put it in distributive property, just put the greatest common factor outside and the variables inside. inside. That's your answer! Hope this helped and have a great dayyyyy!!!!
If y(x) = 2x^2 +sqr/5(x-2), complete the following statement:
f(6) =
Answer:
Step-by-step explanation:
Just plug in 6 as x.
[tex]f(6)=2(6)^2+\sqrt{5} *(6-2) \\or\\f(6)=2(6)^2+\sqrt{5(6-2)}[/tex]
Depending on how the equation is written (I got confused so I gave both answers of what I thought both versions were) this is the answer.
[tex]72+4\sqrt{5} =2(6)^2+\sqrt{5} *(6-2) \\or\\72+2\sqrt{5} =2(6)^2+\sqrt{5(6-2)}[/tex]
I need help on this question??
Answer:
Not sure what your choices are on the drop-down, but these expressions are equivalent to each other and include all solutions (all real numbers).
Edit:
1--Equivalent
2--29
3--Equivalent
4.
Find the range.
4.7 6.3 5.4 3.2 4.9
O
-3.1
-9.5
9.5
O
3.1
Answer:
[tex]3.1[/tex]
Step-by-step explanation:
Range = biggest no. - smallest no.
Range = [tex]6.3-3.2[/tex]
Range = [tex]3.1[/tex]
Answer:
3.1
Step-by-step explanation:
Range is the difference between the highest and the least number in a set.
Out of all the numbers given, 6.3 is the highest and 3.2 is the least. When, I found the difference of those two numbers, the difference was 3.1. :)
2) Rearrange the Pythagorean Theorem to solve first for c and then y.
Answer:
[tex]x=z-\sqrt{-y} , or, x^2=z^2-y^2\\y=z-\sqrt{-x}, or, y^2=z^2-x^2[/tex]
Step-by-step explanation:
I can't do much except put the Pythagorean theorem in terms of y or x.
All I did was isolate x or y by subtracting the, x or y variable from each side.
[tex]-(y^2)+x^2 +y^2=z^2-(x^2)\\-(y^2)+x^2 +y^2=z^2-(y^2)[/tex]
Which tuns it into:
[tex]x^2=z^2-y^2\\y^2=z^2-x^2[/tex]
And I isolated further by squaring each side, but squaring negative number is difficult and causes imaginary numbers so I just think it should stay as all of them to the power of two.
WILL MARK BRAINIEST!!! 35 POINTS!!! The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 7 units, then what is the value of k? K=1/7 K=-1/7 k = 7 k = −7 Determine the equivalent system for the given system of equations. 4x − 5y = 2 10x − 21y = 10 4x − 5y = 2 3x − y = 4 4x − 5y = 2 24x − 47y = 22 4x − 5y = 2 10x + 3y = 15 4x − 5y = 2 14x + 26y = 12 PLZ SHOW WORK!!! I NEED THE HELP!!!!
Answer:
Step-by-step explanation:
First one is 7, since there is a minus sign by k, shifting the line 0.5x seven units down
the second one is too confusing due to spacing to find the answer
Answer:
the person that answer is correct
Step-by-step explanation:
Define the proper and improper subsets?
Answer: A proper subset is one that contains few elements of the original set whereas an improper subset, contains every element of the original set along with the null set.
Find the distance between (−5, 8) and (6, 8).
Answer:
11
Step-by-step explanation:
Since the y coordinates are the same, the distance is the values between the x coordinates
6 - -5
6+5
11
The right answer is 11 units.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
How to rearrange the Pythagorean theory
Can someone please explain to me how to find y=Mx+b? We’ve learned this a long time ago and I kinda forgot .. can’t find a solution anywhere else :/
Answer:
y = mx + b equals y = the slope of the line(x) + the y-intercept
First find the slope of the line using rise/run, which is 12/-2 so the slope is -6
To find the y-intercept, you need to look for the point where x = 0 (or the point that lies on the y-axis), which is when y = -4 so the equation is:
y = -6x - 4
It is worked out that if 3 ladles full of soup are given to each person,
150 people can be fed.
The customers have complained in the past that the portions are too small.
The cook decides to give 5 ladles full of soup to each person.
How many people can now be fed soup?
Answer:
it is worked out that if 5 ladles full soup are given to each person 300 at a time
Answer:
90 people
Step-by-step explanation:
Let's find the total number of ladels of soup.
1 person ----- 3 ladles
150 people ----- 3 ×150= 450 ladles
The amount of soup cooked does not change. Since now more soup is given to each person, the number of customers fed would decrease.
Number of people fed
= 450 ÷5
= 90
someone please help me, if i dont turn this in within less than 24 hrs, ill have to repeat my grade. how do i write an equation for the cost of a vacaton? the cost per night is 69$ and im staying for 5 days, it costs 1,079 to get there. PLEASE HELP ME
What is the nth rule of the quadratic sequence 4,15,30,49,72,99,130
Answer:
2(n²)+5n-3
Step-by-step explanation:
4,15,30,49,72,99,130
1st you find the difference between the numbers: (e.g. difference between 4 and 15 is 11) 11,15,19,23,27,31 Then you find the second difference between them. 4,4,4,4,4,4
If you divide the second difference by 2, you will get the value of a. 4 ÷ 2 = 2
So the first term of the nth term is 2n²
Then you have to do what do you do to get from 2n² to 4,15,30,49,72,99,130
part 1. Please show work. Please assist me with these math problems.
Answer: 1) 2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784
2) 2,490,924
3) Neither
Step-by-step explanation:
[tex]S_n=S_{n-2}\cdot (S_{n-1}-1)\quad \\\\S_1=2\quad given\\S_2=3\quad given\\S_3=S_1(S_2-1)\quad =2(3-1)\quad =4\\S_4=S_2(S_3-1)\quad =3(4-1)\quad =9\\S_5=S_3(S_4-1)\quad =4(9-1)\quad =32\\S_6=S_4(S_5-1)\quad =9(32-1)\quad =279\\S_7=S_5(S_6-1)\quad =32(279-1)\quad =8,896\\S_8=S_6(S_7-1)\quad =279(8896-1)\quad =2,481,705\\S_9=S_7(S_8-1)\quad =8896(2481705-1)\quad =22,077,238,784[/tex]
[tex]\sum^8_{k=1}S_k\\\\=S_1+S_2+S_3+S_4+S_5+S_6+S_7+S_8\\\\= 2,490,924\\[/tex]
Neither
Not arithmetic because the difference between each of the terms is not the same.
S₂ - S₁ S₃ - S₂ S₄ - S₃
3 - 2 = 1 4 - 3 = 1 9 - 4 = 5
Not geometric because the ratios between each of the terms is not the same.
[tex]\dfrac{S_2}{S_1}=\dfrac{S_3}{S_2}\qquad \rightarrow \dfrac{3}{2}=\dfrac{4}{3}\qquad \rightarrow \text{cross multiply to get}: 9\neq 8[/tex]
Find the area of the shape.
Answer: 12.56 / 4 = 3.1416 =9.4248
Step-by-step explanation: pi by the 2 squared gives u the area of all the circle but u need to fin 3/4 of the circle so divide by 4 and the result of the dividion x 3 gives u the answer
Please help me it’s geometry
Answer:
(-5,4)
Step-by-step explanation:
A: (5,4)
Reflect it across the y axis would mean you negate the x value
So if you reflect it across the y axis, 5 would become -5
Answer:
B
(-5,4)
Step-by-step explanation:
square 1 (+,+) square 2 (-,+) square 3 (-,-) square 4 (+,-) Find the coordinates is (5,4) but reflect the y-axis so it goes to square 2 where the x-axis turns in to a negative
during a practice sash drank 2 1/2 pints of water and on the way home she drank 1/2 cup of water how much water did she drank in total
Answer:
5 1/2 cups
Step-by-step explanation:
1 pint = 2 cups
(2 1/2)(2) = 5
5 + 1/2 = 5 1/2
What are the solutions of x2 +6x-6= 10?
O x=-11 or x=1
O X=-11 or X=-1
O X=-8 or X=-2
O X=-8 or X= 2
Answer:
x= -8 x=2
Step-by-step explanation:
x^2 +6x-6= 10
Subtract 10 from each side
x^2 +6x-6-10= 10-10
x^2 +6x-16 = 0
What 2 number multiply to -16 and add to 6
8 * -2 = -16
8 -2 = 6
(x+8) (x-2)=0
Using the zero product property
x+8=0 x-2=0
x= -8 x=2
Answer:D
Step-by-step explanation:
Patty Cake and Jim Nasium are flying a kite. Patty is 200 m away from Jim who is holding the kite. Facing Jim, Patty finds the angle of elevation of the kite is 40 degrees . If the kite string makes an angle of 85 degrees with the ground, find the amount of string let out by Jim.
Answer:
Amount of string let out by Jim will be 156.9 m.
Step-by-step explanation:
Distance between Jim and Patty = 200 m
Angle of elevation of the kite from Jim = 85°
Angle of elevation of the kite from Patty = 40°
Angle between the lines joining Jim and kite and Patty and the kite = 180° - (85 + 40)° = 55°
By applying Sine rule in the triangle formed by the kite, Jim and Patty,
[tex]\frac{\text{sin}55}{200}=\frac{\text{sin}40}{x}[/tex]
x = [tex]\frac{200\times \text{sin}40}{\text{sin55}}[/tex]
x = 156.94
≈ 156.9 m
Therefore, amount of string let out by Jim will be 156.9 m.
Solve the inequality.
2(4+2x)25x+5
estimate the line of best fit using two points on the line (2,8) (8,5)
Answer:
y= -1/2x +9
Step-by-step explanation:
The line equation of best fit is y = (-1/2)x+9 if the two points on the line are (2,8) and (8,5) option (C) is correct.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
We have two points (2, 8) and (8, 5)
To find the line of best fit using these two points:
[tex]\rm (y-y_1)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex]\rm (y-8)=\frac{5-8}{8-2} (x-2)[/tex]
[tex]\rm (y-8)=-\frac{3}{6} (x-2)\\\\\rm (y-8)=-\frac{1}{2} (x-2)[/tex]
[tex]\rm y = - \frac{1}{2} x +9[/tex]
Thus, the line equation of best fit is y = (-1/2)x+9 if the two points on the line are (2,8) and (8,5) option (C) is correct.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
The shapes below are drawn on a centimetre grid
show that these shapes have the same area
Answer: See the explanation to understand.
Step-by-step explanation:
Well first off you have to understand the area concept. The area is shown on the grid clearly fir the square, 4cm (2x2). Now it might be a little tricky for the triangle but don’t worry, take it slowly, count the areas of the base of the triangle, the correct answer for that is 2cm so the base of the triangle is 2cm. Now go to highest point of the triangle and count down all the way to the base. The number you should get is 4. So now we know that the base is 2cm and the height is 4cm. Using the triangle Area formula which is base times height divided by two: bh/2 , substituting the values we have 2x4 is 8. 8 divided by two is 4cm. Now we know that the areas are the same by checking using the formula.
Hope this makes sense!
Brainliest question please help please help me and plz show your work
Answer:
A
Step-by-step explanation:
since the radius is 12, the most the circle expands out towards is 15 for x and 15 for y. (-6,-5) easily fits inside it.
The library is located 1.8 miles west of Callie’s house. The grocery store is located 2.4 miles south of the library. What is the length of a straight line between Callie’s house and the grocery store?
Answer:
0.6 is the answer
Step-by-step explanation:
Answer:
[tex]3[/tex] Miles
Step-by-step explanation:
[tex]1.8^2+2.4^2=c^2[/tex]
[tex]9=c^2[/tex]
[tex]9-c^2=c^2-c^2[/tex]
[tex]-c^2+9=0[/tex]
[tex]-c^2+9-9=0-9[/tex]
[tex]-c^2=-9[/tex]
[tex]\frac{-c^2}{-1} = \frac{-9}{-1}[/tex]
[tex]c^2=9[/tex]
[tex]c=+\sqrt{9}[/tex]
[tex]c=3[/tex]
I can’t figure out the answer to this, does anybody know?
Answer:
Option (2).
Step-by-step explanation:
Let f(x) and g(x) are the two functions with domain A and B.
Then (fg)(x) will be the function with domain A∩B
(fg)(x) = f(x)g(x) Domain : A∩B
In this question two functions are,
c(x) = [tex]\frac{5}{(x-2)}[/tex] and d(x) = (x + 3)
Domain : (x - 2) > 0 ⇒ x > 2
and (x - 2) < 0 ⇒ x < 2
Or domain of (cd)(x) will be C = (-∞, 2)∪(2, ∞).
Similarly, d(x) = x + 3
Domain : All real numbers
: D = (-∞, ∞)
(cd)(x) = c(x)d(x)
= [tex]\frac{5}{(x-2)}\times (x+3)[/tex]
Domain of (cd)(x) will be,
Domain : C∩D = (-∞, 2)∪(2, ∞) ∩ (-∞, ∞)
: (-∞, 2) ∩ (2, ∞)
Therefore, domain of (cd)(x) will be all real values except 2.
Option (2) will be the answer.
Which of the following describes the graph of y=3\sqrt[3]{27x-54}+5 compared to the parent cube root function?
Horizontal translation: 2 units right.
Vertical translation: 5 units up
Stretch/compression: stretched by a factor of 3.
Reflection: not reflected.
what is 6 times 12 + 5
Answer:77
Step-by-step explanation:
6*12+5
72+5
77
the answer is simply 77
does anyone know how to do this
Answer:
Six over Seven
Step-by-step explanation:
Answer:
six sevenths
Step-by-step explanation:
6/7 in words is six sevenths
I need to know how to do the following equation for system of equations (Aka Alegbra) I need to know how to do this: 5x+9y=23 -2X+y=23 I have a test tomorrow so if someone can help me I'd really appreciate it I need a step by step explanations please! Will 100% give brainlist!
Answer:
(-8,7)
Step-by-step explanation:
5x+9y=23
-2x+y=23
Step 1. When looking at the equation you need to find out what method you must use and a good way to find out if you use subtraction is to look for a variable of 1
just like -2x+y=23 has the variable 1y
Step 2. solve for y in the second equation
-2x+y=23
+2x +2x
y=2x+23
Step 3. rewrite your equation
5x+9y=23
y=2x+23
Step 4. replace your y variable with the expression you just made
5x+9(2x+23)=23
Step 5. Distribute the 9 and solve
5x+18x+207=23
23x+207=23
23x=-184
x=-8
Step 6. enter your x value into the equation you solved in step one
y=2(-8)+23
y=-16+23
y=7
Step 7. determine if consistent or inconsistent
Because you have a x and y you have an consistent
...you can also graph it