Answer:
Step-by-step explanation:
1. (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab
2. (a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab
3. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
4. (a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a + b)3 − 3ab(a + b)
5. (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a − b)3 + 3ab(a − b)
6. a2 − b2 = (a + b)(a − b)
7. a3 − b3 = (a − b)(a2 + ab + b2)
8. a3 + b3 = (a + b)(a2 − ab + b2)
9. an − bn = (a − b)(an−1 + an−2b + an−3b2 + ··· + bn−1)
10. an = a.a.a . . . n times
11. am.an = am+n
12. am
an = am−n if m>n
= 1 if m = n
= 1
an−m if m<n; a ∈ R, a 6= 0
13. (am)n = amn = (an)m
14. (ab)n = an.bn
15. a
b
n
= an
bn
16. a0 = 1 where a ∈ R, a 6= 0
17. a−n = 1
an , an = 1
a−n
18. ap/q = √q ap
19. If am = an and a 6= ±1, a 6= 0 then m = n
20. If an = bn where n 6= 0, then a = ±b
21. If √x, √y are quadratic surds and if a + √x = √y, then a = 0 and x = y
22. If √x, √y are quadratic surds and if a+ √x = b+ √y then a = b and x = y
23. If a, m, n are positive real numbers and a 6= 1, then loga mn = loga m+loga n
24. If a, m, n are positive real numbers, a 6= 1, then loga
m
n
= loga m−loga n
25. If a and m are positive real numbers, a 6= 1 then loga mn = n loga m
26. If a, b and k are positive real numbers, b 6= 1, k 6= 1, then logb a = logk a
logk b
27. logb a = 1
loga b where a, b are positive real numbers, a 6= 1, b 6= 1
28. if a, m, n are positive real numbers, a 6= 1 and if loga m = loga n, then
m = n
The sum of 6 times a number and 4 is 9
Geometry
please help if you can!
picture included
Answer:
x = 12.5
Step-by-step explanation:
Based on the interesting chords theorem, we would have the following:
2*x = 5*5
2x = 25
Divide both sides by 2
x = 25/2
x = 12.5
What is the total surface area of the pyramid below?
5 ft
-
6ft
6 ft
Please I need answer!
Answer:
17 ft that's the ans
I don't know if it is correct
A body starts from rest and
accelerates uniform at 5 ms2.
calculate the time taken
by the body to cover a
distance of
1km
what is the area of the figure above ?
Answer:
256m^2
Step-by-step explanation:
you can cut up the figure.
A1=bh
A1= 24x8
A1=192m^2
A2=bh
A2= bh
A2=8x8
A2=64m^2
A1+A2= Atotal
A=192+64
A=256m^2
The solution to the following system of linear equations lies in which quadrant?
-2x + 3y = 8
4x + y=-2
Select one:
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
At a football stadium 5% of the fans in attendance were teens. If there were 400 teens at the football stadium what was the total number of people
Answer: 8000
Step-by-step explanation:
Each 5% is 400.
10%= 800
10x10= 100% therefore
800x10 =8000.
8000 total fans
Fewer young people are driving. In 1995, 63.9% of people under years old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to in . Suppose these results are based on a random sample of people under years old who were eligible to have a driver's license in and again in . a. At confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver's license in
Answer:
A. 0.0272
B. 0.0278
C. No
Step-by-step explanation:
a. Calculation for the margin of error and the interval estimate of the number of eligible people who had a driver’s license in 1995u
First step is to calculate the Standard error using this formula
Standard error(SE)= √(pcap * (1 - pcap)/n)
Where,
pcap represent sample proportion = 0.639
n represent sample size = 1200
Let plug in the formula
Standard error (SE)= √(0.639 * (1 - 0.639)/1200)
Standard error(SE)= 0.0139
Second step is to find Zc using this formula
Zc = Z(α/2)
Where,
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
Zc = Z(α/2) = 1.96
Now let calculate the Margin of Error using this formula
Margin of Error= zc * SE
Let plug in the formula
Margin of Error = 1.96 * 0.0139
Margin of Error = 0.0272
Therefore the Margin of Error is 0.0272
b. Calculation for the margin of error and the interval estimate of the number of eligible people who had a driver’s license in 2016
First step is to calculate the Standard error using this formula
Standard error(SE)= √(pcap * (1 - pcap)/n)
Where,
pcap represent sample proportion = 0.417
n represent sample size = 1200
Let plug in the formula
Standard error (SE)= √(0.417 * (1 - 0.417)/1200)
Standard error(SE)= 0.0142
Second step is to find Zc using this formula
Zc = Z(α/2)
Where,
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
Zc = Z(α/2) = 1.96
Now let calculate the Margin of Error using this formula
Margin of Error= zc * SE
Let plug in the formula
Margin of Error = 1.96 * 0.0142
Margin of Error = 0.0278
Therefore the Margin of Error is 0.0278
c. Based on the above calculation for both (a) and (b) the MARGIN OF ERROR are NOT the same reason been that (a) Margin of Error is 0.0272 while (b) Margin of Error is 0.0278 which simply shows that the proportion in parts (a) and are different.
Plz plz plz, HELP!!!! I will give u brainlylist
There are 20 pieces of fruit in a bowl and 8 of them are bananas. What percentage of the pieces of fruit in the bowl are bananas?
**choose your answer from the choices on Slide 5, but you must show how you got your answer on the chart, blank drawing space below, or explain in words**
Show how you found the slope and y-intercept
Answer:
Slope: [tex]\frac{5}{2}[/tex]
y-intercept: 0
Step-by-step explanation:
First, find the slope. Use two points given to you. In this case, I will use the following:
(x₁ , y₁) = (2 , 5)
(x₂ , y₂) = (4 , 10)
Use the following equation:
slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the corresponding numbers to the corresponding variables:
slope (m) = [tex]\frac{10 - 5}{4 - 2}[/tex] = [tex]\frac{5}{2}[/tex]
Note the slope intercept form:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Plug in the slope into m for the equation:
[tex]y = \frac{5}{2} x + b[/tex]
Choose a point to use to find b. In this case, I will use (2 , 5). Plug in 2 for x, and 5 for y:
[tex]5 = \frac{5}{2}(2) + b[/tex]
Simplify. Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other:
[tex]5 = \frac{5}{2}(2) + b\\5 = 5 + b\\5 (-5) = 5 (-5) + b\\b = 5 - 5\\b = 0[/tex]
Y-intercept: 0
If Mario drives at a rate of 70 miles per hour, how long will it take him to drive 700 miles?
Answer:
dam mario u trying get a speeding ticket
bu the answer is 10 if im not mistaken
Step-by-step explanation:
Please help me with this! Picture is provided and only answer is you know it!
Answer:
Option A
Step-by-step explanation:
Number of components assembled by the new employee per day,
N(t) = [tex]\frac{50t}{t+4}[/tex]
Number of components assembled by the experienced employee per day,
E(t) = [tex]\frac{70t}{t+3}[/tex]
Difference in number of components assembled per day by experienced ane new employee
D(t)= E(t) - N(t)
D(t) = [tex]\frac{70t}{t+3}-\frac{50t}{t+4}[/tex]
= [tex]\frac{70t(t+4)-50t(t+3)}{(t+3)(t+4)}[/tex]
= [tex]\frac{70t^2+280t-50t^2-150t}{(t+3)(t+4)}[/tex]
= [tex]\frac{20t^2+130t}{(t+3)(t+4)}[/tex]
= [tex]\frac{10t(2t+13)}{(t+4)(t+3)}[/tex]
Therefore, Option A will be the answer.
Question
Is the statement below true or false?
A sampling error is the situation in which not all members of the population are equally likely to be selected.
Answer:
I think it's true sorry if I get it wrong
Answer: it is false, I hope this helps you out!
HELP THIS WAS DUE THREE DAYS AGO!!!!!!!!!!
Answer:
Step-by-step explanation:
2. 2c(7c + 1)
3. stays as is
4. 2x^3y^4(4 - 11x^2y^2)
5. ab(10ab + 9b - a)
6. 3m^2(7m^4n^2+2m^2n+5)
7. (a - 8)(a + 8)
8. (y - 17)(y + 17)
9. stays as is
10. (1 - 5n)(1 + 5n)
11. (4x - 7y)(4x + 7y)
12. (w^2 - 10)(w^2 + 10)
13. (c - 9d)(c + 9d)
14. (14a - b)(14a + b)
Can someone helppp!!?
Answer:
angle 3 is 132
angle 2 is 48
Step-by-step explanation:
Section B
Solve the problems. Show your workings clearly in the spaces provided.
(10)
Paul was given $2760 to buy toys for a group of children.
(a) What would be the greatest number of toys Paul could buy if each toy
cost $9?
(b) How much money would be left after buying the toys?
If f(x) = x + 2x - 3, what is the value of f(1 + 2)?
Answer:
6
Explanation:
substituting- f(x)= (1+2) + 2(1+2) -3
3 + 2(3)-3
3+6-3
=6
HOPE IT HELPS
m∠IJK=155° and m∠ZJK=35°. Find m/∠IJZ
The reciprocal of 7/2 is 2/7. What does that mean?
Answer:2/7
Step-by-step explanation: A reciprocal is the "mirror image" of a fraction so the reciprocal is the fraction upside down.
Which one is the answer I think it’s four or five
Answer:
The answer is 4 (B)
Step-by-step explanation:
Hope this Helped
I don't know how to do this, please help
Answer:
m7=80º
m8=100º
Step-by-step explanation:
How do you do long divisions for 2 divided by 3339
Answer:
3339/2=1669.5
Step-by-step explanation:
Is x2+8x+16 a perfect square?
Answer:
yes, it's factors are (x+4)²
Step-by-step explanation:
Answer:
It is a perfect square.
Step-by-step explanation:
can you help me please
Answer:
1000 = n
Step-by-step explanation:
Write an equation that is equivalent to 1/4 plus 1 plus 3/4 minus 2/3 minus 1/2
Answer:1/4 + 1/4 = 1/2 = 0.5
For a given arithmetic sequence, the 75th term, a75, is equal to 342, and the 4th term, 24, is equal to - 13.
nd
Find the value of the 32
term, 232
Answer:
The 32th term is 127.
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same. The general equation for an arithmetic sequence is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which d is the common difference.
It can also be written as:
[tex]a_n = a_m + (n - m)d[/tex]
75th term is equal to 342, and the 4th term, 24, is equal to - 13.
This means that [tex]a_4 = -13, a_75 = 342[/tex]. We use this to find d. So
[tex]a_{75} = a_4 + (75 - 4)d[/tex]
[tex]342 = -13 + 71d[/tex]
[tex]71d = 355[/tex]
[tex]d = \frac{355}{71}[/tex]
[tex]d = 5[/tex]
Find the value of the 32th term:
[tex]a_n = a_m + (n - m)d[/tex]
[tex]a_{32} = a_{4} + (32 - 4)d[/tex]
[tex]a_{32} = -13 + 28(5) = -13 + 140 = 127[/tex]
The 32th term is 127.
1. Select all of the true statements.
A. Pi is the area of a circle of radius 1.
B. Pi is the area of a circle of diameter 1.
C. Pi is the circumference of a circle of radius 1.
D. Pi is the circumference of a circle of diameter 1.
E. Pi is the constant of proportionality relating the diameter of a circle to its circumference.
F. Pi is the constant of proportionality relating the radius of a circle to its area.
Which graph shows a dilation?
Help and show work please
Answer:
11111111 111 1 1 1 11
Step-by-step explanation:
Answer:
ok 1+1= 25 and add 3000 and you get 1
Step-by-step explanation: