Answer:
The difference between two consecutive numbers in this sequence would be something like:
(2n + 1)^(2*k) - (2n)^(2k)
(or in the other order, but is essentially the same)
where n is an integer number.
Then:
2*n is an even number
2*n + 1 is an odd number.
(2n)^(2k) = 2*(2^(2k-1)*n^(2k)) this will be even for any natural number k.
(2n + 1)^(2k)
Let's suppose that k = 1.
Then we have:
(2n + 1)^(2) = (2n + 1)*(2n + 1) = (2n)^2 + 4n + 1 = 2*(2n^2 + 2n) + 1
If (2n^2 + 2n) is an integer (and it is) we can rename it as N
(2n + 1)^(2) = 2*N + 1
It is still odd.
Now if k = 2, we will have:
(2n + 1)^(2*2) = (2n + 1)^(4)
And using what we found above, we can rewrite this as:
(2*N + 1)^2
And we know that this will be odd.
Then we can already see that:
(2n + 1)^(2k) will be odd for any value of k (where k is a natural number)
Then:
(2n + 1)^(2k) - (2n)^(2k)
Is the difference between an odd number and an even number, and this will always be an odd number.
What is the base in the expression 4 superscript 5?
A)4 B)5 C)9 D)20
Answer:
A)4
Step-by-step explanation:
Expression 4 superscript pt 5=4^5
Answer:
A
Step-by-step explanation:
What is the value of the function at x=−2?
Answer:
y = 3
General Formulas and Concepts:
Reading a Cartesian PlaneReading and labeling coordinatesStep-by-step explanation:
The question is asking us what the y-value is when x = -2.
According to the graph, when x = -2, y = 3.
Therefore, y = 3.
What property was used to solve the equation?
O Property of opposites
O Division property of equality
* Addition property of equality
O Multiplication property of equality
Answer:
Multiplication sorry I late
Step-by-step explanation:
Answer: Multiplication property of equality
What is the equation of the line that passes through the point (5,2) and has a slope
of -3/5
Answer:y = -0.6x + 5
Step-by-step explanation:
Answer:
yessir the one on top is right btw
Step-by-step explanation:
hope this helped
your company purchased a twelve-month insurance policy for $36,000 in January
whats the entry to record the monthly insurance expense in march
Answer:
Debit Insurance expense for $3,000
Credit Prepaid insurance for $3,000
Step-by-step explanation:
Before the recording entry, the monthly insurance expense has to be calculated first as follows:
Monthly insurance expense = Prepaid insurance / n ............. (1)
Where;
Prepaid insurance = Insurance policy amount = $36,000
n = number of months = 12
Substituting the values into equation (1), we have:
Monthly insurance expense = $36,000 / 12 = $3,000
Since the monthly insurance expense is $3,000, it implies that the insurance expense for March is $3,000.
the entry to record the monthly insurance expense in March will therefore look as follows:
Month Account Title DR ($) CR ($)
March Insurance expense 3,000
Prepaid insurance 3,000
(To record monthly insurance expense for March)
you have a bill of $56.40. find a 15% tip?
Answer:
$8.46
Step-by-step explanation:
15%=0.15
56.40(0.15)
8.46
factor 5x^2 + 10x + 5
What value(s) of x will make x2 = 36 true?
Answer:
x²=36
x²=6²
equating both squares
x=6
so, b is correct answer
The solution of the given quadratic equation is x=6 and x=-6.
The given equation is x²=36.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given equation can be solved as follows
Now, x²=36
Square root on both the sides, we get
x=±√36
⇒ x=±6
So, x=6 and x=-6
Hence, the solution of the given quadratic equation is x=6 and x=-6.
To learn more about the solution of quadratic equation visit:
https://brainly.com/question/18305483.
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what type of angle is 2??
a. Alternate Exterior
b. Alternate Interior
c. Corresponding
d. Linear Pair
e. Same-Side Exterior
f. Same Side Interior
g. Vertical Angles
h. No Relationship
Answer:
Vertical Angles...............
What is the missing side? Round your answer to the nearest hundredth if necessary .
Answer:
20......................
f(x) = x g(x) = 1
What is the domain of (
g
f
) (x)?
Answer:
[tex]x\neq 0[/tex]
Step-by-step explanation: the domain[tex]0[/tex]⇒[tex]x{}[/tex]∈[tex]R[/tex]-{0}
A sample of n = 16 scores has a mean of M = 40 and a variance of s2 = 64. What is the estimated standard error for the sample mean?
Answer:
[tex]S.E = 2[/tex]
Step-by-step explanation:
Given
[tex]Mean = 40[/tex]
[tex]s^2 = 64[/tex] ----- variance
[tex]n = 16[/tex] ------------ sample
Required
Determine the S.E
The estimated standard error (S.E) for the sample mean is calculated using the following formula:
[tex]S.E = \frac{SD}{\sqrt n}[/tex]
Where
[tex]SD = Standard\ Deviation[/tex]
[tex]SD = \sqrt {s^2}[/tex]
[tex]SD = \sqrt {64}[/tex]
[tex]SD = 8[/tex]
So:
[tex]S.E = \frac{SD}{\sqrt n}[/tex]
[tex]S.E = \frac{8}{\sqrt{16}}[/tex]
[tex]S.E = \frac{8}{4}[/tex]
[tex]S.E = 2[/tex]
Hence: the estimated standard error for the sample mean is 2
Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are . If point D divides in the ratio 4 : 5, the coordinates of point D are .
Answer:10,-4 and 58/9,-2
Step-by-step explanation:
Plato users
what is the decimal expansion for 7 over 9
Answer:
0.77777777......
Step-by-step explanation:
You divide them. Hope I helped!
Please mark Brainliest!!!!
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years, while profits increased $30 million per year. Select the correct graph of this function. (2 points)
A)There is a graph of a line that has a y intercept that is approximately $80 million and passes through the point of approximately x equals 2 years and y equals $140 million.
B)There is a graph of a line that has a y intercept that is approximately negative $80 million and an x intercept that is approximately 2.7 years.
C)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 2 years.
D)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 0.6 years.
Answer:
I am not really good at this but...if I had to choose the ones that make sense
A and B
Step-by-step explanation:
Your are incresing the amount is going up, so if you go backwards you woild have to the negatuves.
Then again I woild not trust my math for the second answer cause I am no good at math.
{1.2.3.4.5} set builder
Step-by-step explanation:
A set-builder notation describes or defines the elements of a set instead of listing the elements. For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the elements. The same set could be described as { x/x is a counting number less than 10 } in set-builder notation.
Find the measures of the angles.
(8x-1)º
(3x + 4)º
(3x + 9)
°
95, 40, 45
90, 25, 65
80, 52, 48
70, 68, 42
Answer:
answer is - 95, 40, 45
Step-by-step explanation:
Since the interior angles of a triangle add up to be 180 degrees, I set up the equation like so:
(8x-1)+(3x + 4)+(3x + 9) = 180
=> 14x +12 = 180
=> 14x = 180-12
=> x = 168/14 = 12
now putting value of x = 12
we get---
8*12 -1 = 96-1 = 95
3*12 + 4 = 36+4 = 40
3*12 + 9 = 36 + 9 = 45
( Answer )
HELP PLZZZ i need it plz
What are 25 times by the same number then divide it by sixty
Solve this equation.
[tex]\frac{x + 4}{6x} = \frac{1}{x}[/tex]
A. x = -2
B. x = 0, -2
C. x = 2
D. x = 0, 2
In a survey of 2,300 people who owned a certain type of car, 1,150 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
65%
Step-by-step explanation:
To find percentage, take the number out of the whole number, and divide it by the whole number. In this case, 1495 out of 2300 said they are satisfied. To find the percent, we have to do 1495/2300=0.65, which is 65%.
Michelle works in the mall and her hours increase during busy shopping times of the year. Michelle has a plan to
save $45 each week for 7 weeks, and then increase that amount by $30 for the next 8 weeks during the busy time,
then go back to $45 per week. If Michelle's plan is to save $1185, how many weeks total will she need to save?
Show your work
12
II
Answer:
The total number of weeks Michelle needs to save is 29.
Step-by-step explanation:
Michelle plans to save $1185 in a number of weeks to determine later.
In the first 7 weeks, she will save $45 each week for a total of
$45 * 7 = $315
In the next 8 weeks, she will save $30 each week for a total of:
$30 * 8 = $240
During these 15 weeks, she has saved
$315 + $240 = $555
She still has a remaining $1185 - $555 = $630 to save.
Those $630 will be saved in a number of weeks at $45 per week, thus the number of weeks is:
$630 / $45 = 14 weeks
Total weeks = 15 + 14 = 29
The total number of weeks Michelle needs to save is 29.
Need HELP plz 45 points
Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a congruence statement.
If no, justify your answer.
Answer:
They are equal and we can prove this using the AAS Congruence Postulate.
Step-by-step explanation:
Use the diagram to solve. What is 260% of 6? Percent Total 100% 100% 20% 20% 20% 260% 3.6 9.6 15.6 21.6
Answer:
To find this, multiply 6 by the decimal value of the percent.
6*2.6=15.6
Final answer: 15.6
Step-by-step explanation:
Answer:
15.6 or c
Step-by-step explanation:
Please help me with this.
Answer:
-4 ≤ x ≤ 4
Step-by-step explanation:
The domain is essentially the range of values x can take. In the figure, the highest value is 4 and the lowest is -4.
Given: ΔABC
m∠1=m∠2
D∈ AC , BD = DC
m∠BDC=100°
Find: m∠A, m∠B, m∠C
Answer:
m∠A = 60°, m∠B = 80°, m∠C = 40°Step-by-step explanation:
Since BD = DC, the triangle BDC is isosceles, so
m∠C = m∠2Having m∠BDC = 100°, we can find m∠C
m∠C = 1/2(180° - 100°) = 1/2(80°) = 40°Finding angle B
m∠B = m∠1 + m∠2 = 2*m∠2= 2*40° = 80°Finding angle A
m∠BDA = 180° - m∠BDC = 180° - 100° = 80°m∠A = 180° - (m∠1 + m∠BDA) = 180° - (40° + 80°) = 180° - 120° = 60°Answer:
m<A=60 degrees, m<B=80 degrees, m<C=60 degrees.
Step-by-step explanation:
heyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
A recent study reported that the prevalence of hyperlipidemia (defined as total cholesterol over 200) is 30% in children 2-6 years of age. If 12 children are analyzed.
Required:
a. What is the probability that at least 3 are hyperlipidemic?
b. What is the probability that exactly 3 are hyperlipidemic?
c. How many would be expected to meet the criteria for hyperlipidemia?
Answer:
(a) 0.7472
(b) 0.2397
(c) 3.6
Step-by-step explanation:
Let X denote the number of children who are hyperlipidemic.
The proportion of children who are hyperlipidemic is, p = 0.30.
A random sample of n = 12 children are analyzed.
Every child is independent of the others to be expected to meet the criteria for hyperlipidemia.
The random variable X follows a binomial distribution with parameters n = 12 and p = 0.30.
(a)
Compute the probability that at least 3 are hyperlipidemic as follows:
[tex]P(X\geq 3)=1-P(X<3)\\\\=1-\sum\limits^{2}_{0}{{12\choose x}(0.30)^{x}(0.70)^{12-x}}\\\\=1-0.25282\\\\=0.74718\\\\\approx 0.7472[/tex]
Thus, the probability that at least 3 are hyperlipidemic is 0.7472.
(b)
Compute the probability that exactly 3 are hyperlipidemic as follows:
[tex]P(X=3)={12\choose 3}(0.30)^{3}(0.70)^{12-3}\\\\=220\times 0.027\times 0.040353607\\\\=0.23970042558\\\\\approx 0.2397[/tex]
Thus, the probability that exactly 3 are hyperlipidemic is 0.2397.
(c)
Compute the expected number of children who would meet the criteria for hyperlipidemia as follows:
[tex]E(X)=np=12\times 0.30=3.6[/tex]
Thus, 3.6 children would be expected to meet the criteria for hyperlipidemia.
A farm lets you pick 3 pints of raspberries for $12.00.
a. What is the cost per pint?
b. How many pints do you get per dollar?
c. At this rate, how many pints can you afford for $20.00?
d. At this rate, how much will 8 pints of raspberries cost?
Answer:a.4 dollars per pint
b.4th a pint/ 1 cup per dolllar
c. 5 pints
d.32 dollars
Step-by-step explanation:
2p(9p − 1) pls help will give brainiest
Answer:
18p^2-2p
Step-by-step explanation:
You need to distribute
2*9= 18, p*p= p^2 so 18p^2
Then
2*-1= -2 and you need to include the p so -2p
if l || m,find the value of x, (8x + 20) (11x-31)
Answer:
x=17
Step-by-step explanation:
8x+20=11x-31
We simplify the equation to the form, which is simple to understand
8x+20=11x-31
We move all terms containing x to the left and all other terms to the right.
+8x-11x=-31-20
We simplify left and right side of the equation.
-3x=-51
We divide both sides of the equation by -3 to get x.
x=17
Answer:
17
Step-by-step explanation:
8x + 20 = 11x - 31
-8. -8
20 = 3× - 31
+31. +31
51 = 3x
/3. /3
x = 17
