Answer:
The variance of the given data is 106.9667
Step-by-step explanation:
The variance, S² of a sample is given by the expression;
[tex]S^2 = \dfrac{\sum \left (x_{i}-\bar{x} \right )^{2}}{n-1}[/tex]
Where:
[tex]x_{i}[/tex] = One of the observations
[tex]\bar{x}[/tex] = The mean of the observations
n = Number in the sample = 6
The mean = Σ[tex]x_{i}[/tex]/n = (26 + 32 + 29 + 16 + 45 + 19 )/6 = 167/6 = 27.833
Therefore, we have;
S² = ((26 - 27.833)²+(32 - 27.833)²+(29 - 27.833)²+(16 - 27.833)²+(45 - 27.833)²+(19 - 27.833)²)/(6 - 1) = 106.9667.
Solve: (8r + 9) + 7(4r + 3) ( 1 ) 2. Solve: (3f - 9) + (-7f + 4) ( 1 ) 3. Solve: -8(-g + 6) + 4(8g + 5) ( 1 ) 4. Solve: 5(2n + 3) + (4n - 7) ( 1 ) 5. Solve: 2(-4) + (-8m) ( 1 )
Answer:
1. 36r+30
2. -4f-5
3. 40g-28
4. 14n+8
5. -8-8m
Step-by-step explanation:
Solve: (8r + 9) + 7(4r + 3) ( 1 )
8r+9+28r+21
=36r+30
Solve: (3f - 9) + (-7f + 4) ( 1 )
3f-9-7f+4
= -4f-5
Solve: -8(-g + 6) + 4(8g + 5) ( 1 )
8g-48+32g+20
=40g-28
Solve: 5(2n + 3) + (4n - 7) ( 1 )
10n+15+4n-7
=14n+8
Solve: 2(-4) + (-8m) ( 1 )
= -8-8m
Frankie wants to build a path from one corner of his yard to the opposite corner. His yard measures 20 ft. x 32 ft. What will be the length of his path to the nearest tenth of a foot?
Answer:
≈37.7 feet
Step-by-step explanation:
I'm assuming he goes diagonally.
We can form a triangle with legs 20 feet and 32 feet.
Using the Pythagorean Theorem, we get:
[tex]20^2+32^2=c^2\\400+1024=c^2\\1424=c^2\\c^2=1424\\c=\sqrt{1424}\\[/tex]
c≈37.7
Answer: 37.7 ft
Step-by-step explanation:
20^2 + 32^2 = C^2 where c squared is the distance of the diagonal distance that he wants to walk.
20^2 +32^2 =c^2
400 +1024 =c^2
1424 = c^2
c= 37.7359 rounded to the nearest tenth of a foot is 37.7
Which of the following is the result of the equation below after completing the square and factoring?
Answer:
D) [tex](x + \frac{5}{2})^{2} = \frac{9}{4}[/tex]
Step-by-step explanation:
Step(i):-
Given equation
x² + 5 x + 8 = 4
⇒ [tex]x^{2} + 2 X \frac{5}{2} x + (\frac{5}{2} )^{2} - (\frac{5}{2} )^{2}+ 8 = 4[/tex]
Step(ii):-
By using (a + b)² = a² + 2 a b + b²
⇒ [tex](x + \frac{5}{2})^{2} - (\frac{5}{2} )^{2}+ 8 = 4[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = 4 + (\frac{5}{2} )^{2} -8[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = (\frac{25}{4} ) -4[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = (\frac{25-16}{4} )[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = \frac{9}{4}[/tex]
Final answer:-
[tex](x + \frac{5}{2})^{2} = \frac{9}{4}[/tex]
The stack on the left is made up of 15 pennies, and the stack on the right is also made up of 15 pennies. If the volume of the stack of pennies on the left is 390 mm3, what is the volume of the stack of pennies on the right in cubic millimeters? (Clue: only enter numerals in the answer blank)
Answer:
i am not good in maths sorry the answer is 6075
Triangle ABC has perimeter 20 cm.
AB = 7 cm.
BC = 4 cm.
By calculation, deduce whether triangle ABC is a right-angled triangle.
Answer:
You have an obtuse, scalene triangle, so no :)
Step-by-step explanation:
Side a = 4
Side b = 9
Side c = 7
Angle ∠A = 25.209° = 25°12'32" = 0.43998 rad
Angle ∠B = 106.602° = 106°36'6" = 1.86055 rad
Angle ∠C = 48.19° = 48°11'23" = 0.84107 rad
Answer:
Triangle ABC is not a right-angle triangle.
Step-by-step explanation:
perimeter of the triangle: 20cm
AB=7cm and BC=4cm.
We can do the third length (AC) by subtracting the known lengths from the perimeter: 20 - 7 - 4 = 9
Therefore, the length AC is 9.If
ABC were a right angle triangle, we'd be able to use Pythagoras's Theorem to work out the length AC.
AC is the hypotenuse of the triangle because it is the longest length.
a2 + b2 = c242 + 72 = 16 + 49 = 65
Where AC = c, c2 = 65 If c = 9, then c2 = 81, however when using Pythagoras, c2 = 65.
I hope this helps. I am sorry if you get this wrong.
At a school carnival you pick a ball from two different containers. Each container has red balls and green balls. How many possible outcomes are there?
Answer:
4
Step-by-step explanation:
2^2
Answer:
4
Step-by-step explanation:
Simplify this expression 9v-v
Answer:
8v
Step-by-step explanation:
Match the information on the left with the appropriate equation on the right.
Answer:
See attachment below
Step-by-step explanation:
For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,
y = - 2 / 3x + 3,
y + 2 / 3x = 3,
2x + 3y = 9 - Option C
_______________________________________________________
Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.
- 1 = ( - 3 / 2 )( 4 ) + b,
b = 5,
Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,
y = - 3 / 2x + 5,
2y = - 3x + 10,
- 2y = 3x - 10 - Option A
_______________________________________________________
( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,
Slope = 3 - 1 / 6 - 3 = 2 / 3
Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,
3 = ( 2 / 3 )( 6 ) + b,
b = - 1,
y = 2 / 3x - 1 = Option D
Take a look at the attachment below for further help;
What is the value of X that makes A parallel to B? WILL GIVE BRAINLIEST!
Answer:
20
Step-by-step explanation:
To make these parallel, 2 and 5 would have to be corresponding angles, meaning that they have equal angle measure:
3x-20=x+20
3x=x+40
2x=40
x=20
Hope this helps!
Answer:
x= 20
Step-by-step explanation:
To make the lines parallel, angle 2 would equal angle 5
3x-20 = x+20
Subtract x from each side
2x -20 = 20
Add 20 to each side
2x-20 +20 = 20+20
2x = 40
Divide by 2
2x/2 = 40/2
x = 20
The mapping diagram shows a functional relationship.
Domain
Range
Complete the statements
f(4) is
f(x) = 4 when x is
4
8
2
3
11
3
NI-
Intro
Done
Answer:f(4)=1/2
f(x)=4 when x is 8
The complete statements would be as:
⇒ function f(4) is 1/2 and function f(x) = 4 when domain x is 8.
What are the domain and range?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
We have been given that the mapping diagram shows a functional relationship.
To determine the value of f(4)
As per the given functional relationship,
If the value of the domain is 4 then the value of the respective range would be 1/2.
Therefore, the function f(4) would be 1/2.
To determine the value of x, when f(x) = 4
As per the given functional relationship,
If the value of the range is 4 then the value of the respective domain would be 8.
Therefore, x would be 8 if function f(x) = 4 .
Hence, the complete statements would be as:
f(4) is 1/2 and f(x) = 4 when x is 8.
Learn more about the domain and the range here:
brainly.com/question/21027387
#SPJ7
Can I get help with understanding this?
Answer:
KG = Diameter
FH = Secant
KH = Chord
E = Tangent Point
A = not shown in picture
JG = Radius
HG = Chord
Step-by-step explanation:
Those are the basic parts of a circle.
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. (A) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
Answer:
See below
Step-by-step explanation:
When you roll an 8-sided die twice, the sample space is the set of all possible pairs (x,y) where x is the first outcome and y is the second outcome.
The sample space is:
[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]
The sample space of the product xy of each outcome forms the required possibility diagram.
This is given as:
[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]
Please help me with this math problem, urgent please
Answer:
(1/2) y^5
Step-by-step explanation:
1/( 2y^-5)
1/2 * 1/ y^-5
We know that 1/ a^-b = a ^ b
(1/2) y^5
Simplify x^2÷x^-5. What is the exponent?
Answer:
[tex]7[/tex]
Step-by-step explanation:
[tex]x^2 \div x^{-5}[/tex]
[tex]x^{2-(-5)}[/tex]
[tex]x^{2+5}[/tex]
[tex]x^7[/tex]
I had $5.00. My mom gave me $10.00 while my Dad Gave me $30.00. My aunt and uncle gave me $100.00. I had another $5.00. How much did I have? I won against Tada Yazhe
Answer:
Is it $150?
Step-by-step explanation:
Step 1: Add it all together
5 + 10 + 30 + 100 + 5
All adds up to 150.
Probably got it wrong though haha.
Help!!! ASAP!! :3 Will Givve BRAINLIEST!!
Answer:
V = 672 cm³ (Option 3)
Step-by-step explanation:
Volume of Rectangular Prism = [tex]Length * Width * Height[/tex]
Where L = 14 cm, W = 6 cm and H = 8 cm
V = 14 * 6 * 8
V = 672 cm³
WILL GIVE BRAINLIEST! 7th GRADE MATH
Answer:
Third option is the right choice.
Step-by-step explanation:
The intersection point of both lines is [tex](-2, 2)[/tex].
Area of triangle [tex]\Rightarrow 12.5 = \frac{5\times x}{2}[/tex]
[tex]\Rightarrow x=5[/tex]
This represents the height of the triangle.
So, the y-coordinate of C, will be y-coordinate of point of intersection plus height of triangle.
y = 5+2 = 7
Best Regards!
Will grant you brainliest :) True or false?
Answer:
The answer is true
Step-by-step explanation:
Hope this Helps!
To find the amount of interest Jesse will pay to borrow money, you can use the formula I = PRT. I = interest; P = principal; R = Rate; and T=time. How much interest will Jesse pay if he borrows $5,000 for 5 years with an interest rate of 8%? A. $2,000.00 B. $20,000.00 C. $200.00 D. $2,500.00
Answer: A $2000
Step-by-step explanation:
Interest = prt / 100
= 5000 x .08 x 5
= 2000
Answer:
Its A I just took the quiz
Step-by-step explanation:
No rush. :) I really need help on this. Thxx Explanation needed. :D
Answer:
B' (16,14)
Step-by-step explanation:
Find the coordinates of the vertex B.
M is the midpoint of the diagonal AC.
A(2,7) and C(8,1), the center has coordinates Point M which is the midpoint of the diagonal BD.
Let B has coordinates (x,y),
B(8,7).
(x,y)→(2x,2y)
B(8,7)→B'(16,14).
Answer:
(16, 14)
Step-by-step explanation:
If there was no dilation, the fourth coordinate would be (8, 7)
Dilation of 2: (2x, 2y)
(16, 14)
Five minutes after midnight of 25 April 2016 there was a heavy rain in Adelaide. 144 hours later, what is the probability that it would be sunny over there? Justify your answer.
Answer:
0
Step-by-step explanation:
144 h = 6 days
Six days later would be midnight on May 1.
That's autumn in Australia, so sunset was probably around 8 pm. By midnight it would be completely dark.
The probability of Adelaide being sunny at midnight is zero.
how to solve this problem
Answer:
PR = 180 cm
Step-by-step explanation:
Given PQ : QR = 7 : 3 = 7x : 3x ( x is a multiplier )
PQ - QR = 72, substitute values
7x - 3x = 72
4x = 72 ( divide both sides by 4 )
x = 18
Thus
PR = PQ + QR = 7x + 3x = 10x = 10 × 18 = 180 cm
Answer:
180
Step-by-step explanation:
PQ:QR= 7:3
PQ-QR=72
7x- 3x= 724x= 72x= 72/4x=187x= 126, 3x= 3*18= 54PQ= 126 cm, QR= 54 cm
PR= PQ+QR= 126+54= 180 cm
What type of number is -2343 a)whole number b)integer c)rational d)irrational
Answer: B and C
Step-by-step explanation:
-2343 is an integer and also a rational number since it can be expressed as a fraction.
An integer is whole number and its opposite so -2343 is an integer because its opposite is 2343.
The 3 by 3 grid below shows nine 1 cm × 1 cm 1 cm×1 cm squares and uses 24 cm 24 cm of wire. What length of wire is required for a similar 20 by 20 grid?
Answer:
Length of wire is required = 840 cm
Step-by-step explanation:
Given:
20 by 20 grid
Find:
Length of wire is required.
Computation:
We know that 20-20 grid required 21 lines.
20 cm vertical and horizontal.
⇒ Length of wire is required = (21 + 21)20 cm
⇒ Length of wire is required = (42)20 cm
⇒ Length of wire is required = 840 cm
Which equations are equivalent to Negative one-fourth (x) + three-fourths = 12 Select all that apply.
(StartFraction negative 4 x over 1 EndFraction + three-fourths = 12
Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12
StartFraction negative x + 3 over 4 EndFraction = 12
One-fourth (x + 3) = 12
(StartFraction negative x over 4 EndFraction + three-fourths = 12
Answer:
Step-by-step explanation:
Negative one-fourth (x) + three-fourths = 12
-1/4(x)+3/4=12
-x/4 + 3/4 =12
-x+3/4=12
1. Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12
-1(x/4)+3/4=12
-x/4+3/4=12
2. (StartFraction negative x over 4 EndFraction + three-fourths = 12
-x/4+3/4=12
3. StartFraction
negative x + 3 over 4 EndFraction = 12
-x+3/4=12
Answer:
B, C, & E
Step-by-step explanation:
-1(x/4) + 3/4
-x + 3 /4 = 12
(-x/4) +3/4 = 12
Hope this helps ^^
Model the situation with the sum of polynomials. Then simplify the sum.
4. The width of a rectangle is represented by 4x, and its length is
represented by (3x + 2). Write a polynomial for the perimeter of the
rectangle
3x + 2
4x
O
Answer:
[tex]perimeter= 14\,x\,+ \,4[/tex]
Step-by-step explanation:
Recall the formula for the perimeter rectangle (the addition of all rectangle\s sides): That is: twice the width ( 4x) plus twice the length (3x+2);
[tex]perimeter=2\,*\,width \,+\,2\,*\,length\\perimeter = 2\,(4\,x)+2\,(3\,x+2)\\perimeter= 8\,x+6\,x+4\\perimeter= 14\,x\,+ \,4[/tex]
A car travels 0.75 miles every minute explain how you could use proportional reasoning to find how far the car travels in one hour
Answer:
A car can travel 45 miles every hour, because I multiply 3/4 (0.75) by 60. Because of this, 60 minutes is an hour.
Step-by-step explanation:
Please help urgently!
Answer:
[tex]a=-6\quad and \quad b=8[/tex]
Step-by-step explanation:
[tex]\frac{8-\sqrt{18}}{\sqrt{2}}=\frac{\sqrt{2}}{\sqrt{2}}\times \frac{8-\sqrt{18}}{\sqrt{2}}\\\\=8\sqrt{2}-\sqrt{2}\cdot \sqrt{18}\\\\=8\sqrt{2}-\sqrt{36}\\\\=-6+8\sqrt2[/tex]
By comparing the last expression with [tex]a+b\sqrt{2}[/tex], we get:
[tex]a=-6\quad and \quad b=8[/tex]
Best Regards!
When a metal is placed in an a........ there is a chemical reaction. lol this is not maths
Step-by-step explanation:
you are my 7 year old are the only ones 6th in a world to make it to make a simple decision about you are you fresh out there in the United kingdom of America you have a great life in a country in the United kingdom of the world and inventor of the world is a good thing to be a great person but you can also find the right to be able and the way of the freash
p inversely as( m + 1 ). when p = 4, m = 8 . (a)Find a equation connecting P and ( m + 1 ). (b)calculate the value of p when m = 11
Answer:
a. p= 36/(m + 1)
b. p = 3
Step-by-step explanation:
If p varies inversely as (m + 1)
then p = k × 1/(m + 1). {Where k is the constant}
when p = 4, m = 8, that means 4 = k/(8 + 1)
4 × 9 = k and k = 36
a. Therefore the equation is p= 36/(m + 1)
b. When m = 11,
p = 36/(11 + 1)
p = 36/12
p = 3