Answer:
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
Step-by-step explanation:
[tex]4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536[/tex]
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
To prove this conjecture
[tex]4^1 = 4\\4^2 = 16[/tex] unit digit = 6
hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1 to 8 )
Use the inequality below to find the value of r .
150 - 5 r ≥ 87.5
a. r ≥ 12.5
b. r ≤ 12.5
c. r ≥ -(12.5)
d. r ≤ -(12.5)
Given the point and slope write the equation of the line (6, -6); slope = 5/6
Answer:
y=5/6x-11
Step-by-step explanation:
Slope intercept form: y=mx+b
With slope: y=5/6x+b
Replace x with 6 and y with -6
[To figure out which one is x or y remember (x,y) so if you compare (6,-6) then you will find that 6 is x and -6 is y]
-6=5/6(6)+b
Simplify:
-6=5+b
Subtract 5 on both sides:
-11=b or b=-11
Answer:y=5/6x-11 (Replace the b in y=5/6x+b with -11 since -11 is equal to b)
Hope this helps!
Brita has a monthly budget of x dollars. She spends $1,425 on her mortgage every month. One-third of her remaining budget is spent on recreational activities. Which equation below can be used to determine the amount, in dollars, spent on recreational activities?
Answer:
y = ⅓(x - 1425)
Step-by-step explanation:
Given
Budget = x
Mortgage = 1425
Required
Determine the amount spent on recreational activities.
First, we need to get the balance after she pays her mortgage.
Balance = Budget - Mortgage
Balance = x - 1425
From the question, we understand that she spends ⅓ of the balance on recreational activities.
Represent this with y.
y is calculated as thus:
y = ⅓ of Balance
y = ⅓ * (x - 1425)
y = ⅓(x - 1425)
Hence, the above equation y = ⅓(x - 1425) can be used to calculate the amount spent on recreational activities
Jessica has an account with a credit union. Her account earns 2.6% simple interest yearly. Exactly a year and a half ago, she opened her account with $900.
How much interest has she earned so far?
Answer:
$35.1
Step-by-step explanation:
2.6% of 900 = 23.4
Since it's a year and a half you might want to divide by two.
2.6/2 = 1.3
1.3% of 900 = 11.7
add them up,
23.4 + 11.7 = 35.1
It's asking for how much she EARNED not HAS in her bank account in 1.5 years. So include what she earned with interest, do not include the 900 dollars because she didn't earn it with interest, she already had that.
Help please! I’ll give brainliest if correct!
Answer:
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.
Step-by-step explanation:
Hope his helps!
write -90 in simplest radical form
please help or i’ll failll
2.2.PS-16
Challenge Schools A and B are competing in an academic contest. Correct answers earn 9 points.
Incorrect answers lose 2 points. In the final round, School A gives the same number of correct and
incorrect answers. School B gives no incorrect answers and the same number of correct answers as
School A. School A started the final round with 62 points. School B started with 24. The game ends
with the two schools tied. Let x represent the number of correct answers given by School A in the final
round. Write an equation that models the outcome of the contest. Then find the number of answers
that each school got correct in the final round.
Which equation models the scoring in the final round and the outcome of the contest?
OA. 9x + 2x - 62 = - 9x + 24
OB. 2x-9x + 62 = 9x + 24
OC. 9x - 2x - 62 = 9x + 24
OD. 9x - 2x + 62 = 9x + 24
Answer:
9x - 2x + 62 = 9x + 24
Number of correct answer each obtained = 19
Step-by-step explanation:
Given that:
Number of correct answers = x
POINTS for correct answers = 9
POINTS for incorrect answers = - 2
SCHOOL A:
Number of correct answers = x
Number of incorrect answers = x
Initial point = 62
Initial point + 9(number of correct answers) + - 2(number of incorrect answers)
62 + 9x - 2x
SCHOOL B :
Number of correct answers = x
Number of incorrect answers = 0
Initial point = 24
Initial point + 9(number of correct answers) + - 2(number of incorrect answers
24 + 9x
Since they end up tied :
School A = School B
62 + 9x - 2x = 24 + 9x
9x - 2x + 62 = 9x + 24
Number of correct answers gotten :
9x - 2x + 62 = 9x + 24
7x + 62 = 9x + 24
7x - 9x = 24 - 62
-2x = - 38
x = 19
Hence, Number of correct answers each obtained = 19
What are the answers and explain
Answer:
Step-by-step explanation:
answers to what
Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles.
Answer:
Is there a picture?
Step-by-step explanation:
What does 0.05 x 300 represent?
Answer:
15
Step-by-step explanation:
Your friend and her parents are visiting colleges. They leave their home in Enid, Oklahoma, and drive to Tulsa, which is 107 mi east and 18 mi south of Enid. From Tulsa, they go to Norman, 83 mi west and 63 mi south of Tulsa. Where is Norman in relation to Enid?
Brainliest Answer
(has to be right for brainliest)
Answer:
it is 0.7x0.4=0.28
Step-by-step explanation:
Answer:
3627514
Step-by-step explanation:
3)m I really need help
====================================================
Explanation:
We'll use the angle addition postulate. This is basically the idea where we can break any angle into smaller parts, or go in reverse to build up larger angles based on smaller pieces.
In this case, we can see that the smaller angles KLU and ULM combine to form the largest angle KLM. Think of it like puzzle pieces.
Let x be the measure of angle ULM
We can say the following
(angle KLU) + (angle ULM) = angle KLM
(36) + (x) = 156
36 + x = 156
To solve for x, we subtract 36 from both sides
36+x-36 = 156-36
x = 120
Angle ULM is 120 degrees.
-------------------
As a check,
(angle KLU) + (angle ULM) = 36 + 120 = 156
which matches with angle KLM, so the answer is confirmed.
17 times the sum of a number, n, and 31 is 300. Write as an equation.
Answer:
17(n+31)=300
Step-by-step explanation:
17 times the sum of a number, n and 31 is 17(n+31)
and then set that equal to 300
What is the value of k in the equation k/3-5=34
Answer: What is the value of k in the equation k/3-5=34
Step-by-step explanation: Solution for k/3-5=34 equation: k in (-oo:+oo) k/3-5 = 34 // - 34 k/3-34-5 = 0 1/3*k-39 = 0 // + 39 1/3*k = 39 // : 1/3 k = 39/1/3 k = 117 k = 117
Answer:
k = 117
Step-by-step explanation:
I was just learning this in class...
So basically you need to get the variable k by itself so you add 5 to -5 in the equation and leave k/3 alone and then you add 5 to the other side of the equation also so you add 34+5 and you get 37 so you get k/3=37 and now you multiply 3 by 3 to cancel it out and then you once again do it on the other side of the equation 37 x 3=117 soo that leads you too k=117 YAYYY!!
the pic the pic this is it
Answer:
yes I agree with you
Step-by-step explanation:
thanks for the free question
Answer: mmmmmm Otae?
Step-by-step explanation:
Erasers cost 45 cents a piece. Notebooks cost 90 cents a piece . Karla spent $18 for a total of 28 erasers and notebooks . How many did she buy ?
Answer:
12 Notebooks And 16 Erasers
Step-by-step explanation:
Let x represent the number of notebooks and y represent the number of erasers. (x+y=28) Then, input the cent numbers into the equation. (90x+45y=1800) The 1800 represents the amount of dollars spent. Then simplfy the equation, which gives you 12 notebooks and 16 erasers.
Problem
What is the constant of proportionality in the equation y=3xy
Answer:
-3
Step-by-step explanation:
y=3xy and subtract y on both sides that gives u -1 and then you have -1=3x and then divide 3 on both sides you are left with -3 =x
An ice cream factory makes 310 quarts of ice cream in 5 hours. How many quarts can they make per hour?
Celeste wants to have her hair cut and
permed and also go to lunch. She knows
she will need $95. The perm costs twice
as much as her haircut and she needs $5
for lunch.
How much does the perm cost?
Answer:
the perm will cost $60
Step-by-step explanation:
take away $5 from the total because Its a set amount that's already known
which leaves 90 which if you take 30 away you are left with 60 its twice the amount of the haircut, I didn't really do any math techniques so I'm sorry that my explanation is weird, I hope this helped
Write the letters of the expressions that are equivalent to the given expression.
5(2x + 3)
a. 10x + 15
b. 5x + 15x + 5x
c. 10x + 8
Answer: A.) 10x + 15
Step-by-step explanation:
You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.
Therefore, 10x + 15 is your answer.
Please help someone last one
Answer:
a in table → b on number line
b in table → c on number line
c in table → a on number line
Step-by-step explanation:
Here, we see the points are square roots. A square root of a number is a value, that when multiplied by itself, gives the number. For example, 4 × 4 = 16, so the square root of 16 is 4.
We can apply this logic easily by simplifying the square root, or multiplying integers with each other (aka "squaring" the integers) and seeing which result is closest to the value inside the square root.
Simplifying the square root won't help here, if we don't know basic values such as √3 or √2. So, we can just multiply an integer with itself and see if that value is closer to the value inside the square root.
For point a, we see the number inside the root is 27. We can start multiplying:
1×1 = 12×2 = 43×3 = 94×4 = 165×5 = 256×6 = 3625 is the closest value to 27 here. So, we know the point is somewhere around 5, and since 27 is slightly larger than 25, the point is slightly larger than 5. So, point a in the table is most likely point b on the number line.
For point b, we see the number inside the root is 32. We can start multiplying:
1×1 = 12×2 = 43×3 = 94×4 = 165×5 = 256×6 = 3636 is the closest value to 32 here. So, we know the point is somewhere around 6, and since 32 is smaller than 36, the point is lesser than 6. So, point b in the table is most likely point c on the number line.
For point c, we see the number inside the root is 16. We can start multiplying:
1×1 = 12×2 = 43×3 = 94×4 = 1616 is right on the dot! That means that the square root of 16 is 4, which leaves us with point a on the number line.
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonable) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).
In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.6%. Describe the conclusion about p using an absolute value inequality.
The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that too ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥.
Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).
Answer:
|0.254 ≤ p ≤ 0.286|
Step-by-step explanation:
Given that:
In a made up poll :
Proportion of people who like dark chocolate than milk chocolate (p) = 27%
Margin of Error = 1.6%
Hence,
p ± margin of error
27% ± 1.6%
(27 - 1.6)% ; (27 + 1.6)%
25.4% ; 28.6%
0.254 ; 0.286
Therefore ;
Lower bound = 0.254
Upper bound = 0.286
Expressing p as an absolute value Inequality ;
|0.254 ≤ p ≤ 0.286|
both the domain and range of the graph shown above is all real numbers.
true or false
DUE IN 10 MINUTES!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
1/4
Step-by-step explanation:
Solve this 2 step equation 3x-7=20
Answer:
x=9 if thats what your asking
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
3x-7=20
3x=20+7
3x=27
X=27/3
X=9
So the value of X is 9
What is the first step needed to solve 2 over 5 multiplied by x minus 6 equals negative 16?
Subtract 16 from both sides
Add 6 to both sides
Divide both sides by 5
Multiply both sides by 2
Answer:
The correct answer is D.
Step-by-step explanation:
A linear function contains the following points. (-2,8) (0,6) What are the slope and y-intercept of this function?
Answer:
slope= -1
y-intercept is 6
Step-by-step explanation:
slope = y2-y1/ x2-x1
slope = 6-8/ 0-(-2) = -1
y-intercept is 6 because of (0,6), where the points cross y-axis
A box that measures 15 inches by 5 inches by 3 inches.
What are the units of the volume of the figure?
square inches
cubic inches
square centimeters
cubic centimeters
Answer: cubic inches.
Step-by-step explanation: When calculating volume, all of the units must be cubed. And all of the measurements are in inches.
Find the midpoint of the segment with the following endpoints.
(-4,-9) and (4, -1)
Answer:
[tex](0,-5)[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point (-4, -9)
Point (4, -1)
Step 2: Find midpoint
Substitute: [tex](\frac{-4+4}{2},\frac{-9-1}{2})[/tex]Add/Subtract: [tex](\frac{0}{2},\frac{-10}{2})[/tex]Divide: [tex](0,-5)[/tex]