Answer:
[tex]n = 8[/tex]
Step-by-step explanation:
Given
[tex]3(^nP_2 + 24) = ^{2n}P_2[/tex]
Required
Find n
To do this, we simply apply permutations formula
[tex]nP_r = \frac{n!}{(n -r)!}[/tex]
So, we have:
[tex]3 * [\frac{n!}{(n -2)!} + 24] = \frac{2n!}{(2n -2)!}[/tex]
Expand
[tex]3 * [\frac{n * (n - 1) * (n - 2)!}{(n -2)!} + 24] = \frac{2n * (2n - 1) * (2n - 2)}{2n - 2}[/tex]
[tex]3 * [n * (n - 1) + 24] = 2n * (2n - 1)[/tex]
[tex]3 * [n^2 - n + 24] = 4n^2 - 2n[/tex]
Open bracket
[tex]3n^2 - 3n + 72 = 4n^2 - 2n[/tex]
Collect like terms
[tex]3n^2 - 4n^2- 3n+2n + 72 = 0[/tex]
[tex]-n^2- n + 72 = 0[/tex]
Expand
[tex]-n^2 -9n + 8n + 72 = 0[/tex]
Factorize
[tex]-n(n +9) - 8(n + 9) = 0[/tex]
Factor out n + 9
[tex](-n -8)(n + 9) = 0[/tex]
Split
[tex](-n -8)= 0 \ or\ (n + 9) = 0[/tex]
Solve for n
[tex]n =8\ or\ n = -9[/tex]
The positive value is [tex]n = 8[/tex]
Under which transformation can the image be a different size than the original
figure?
A. translation
B. rotation
C. dilation
D. reflection
C. Dilation.
Dilation can resize the image.
Translation will shift the imagine's position but won't change its actual size.
Rotation will mangle with image's orientation but also won't change its size.
Reflection is just a type of rotation which as established, also won't change its size.
Hope this helps.
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!! THIS IS NOT A TEST OR AN ASSESSMENT!!! Please help me answer these questions. Chapter 12 part 1
1. What is a recursive formula?
2. What is a factorial?
3. What is the relationship between sequences, series and sigma notation?
Answer:
1. What is a recursive formula?
A recursive formula is a formula that defines each term of a sequence using preceding terms of the sequence.
2. What is a factorial?
factorial the product of all positive integers less than or equal to n:
3. What is the relationship between sequences, series and sigma notation?
A series can be represented in a sigma notation.
A series can be represented in a sigma notation.A series is a sum of a sequence of terms.
Can someone possibly help me?
Answer:
72
Step-by-step explanation:
To be divisible by 4, the number must be even, so we can eliminate 63 and 73 (There are other restrictions for 4, we just want to eliminate answers that cannot be true)
We have only 2 answers left
64 and 72
To be divisible by 3, the sum of the digits must be divisible by 3
6+4 = 10 which is not divisible by 3
7+2 = 9 9/3 =3
Please someone help I need help been stuck on this for the longest
Answer:
a.) 16
b.) 8
Step-by-step explanation:
a. how much lower was the 6am temperature in Nome than in Wyoming
Essentially this question is asking us to find the difference of the temperatures of Nome and Wyoming at 6am
Temperature of Nome at 6am: -31
Temperature of Wyoming at 6am: -15
Difference between two temperatures: -31 - (-15)
The two negative signs cancel out and the sign changes to +
-31 + 15 = -16
The temperature in Nome was 16 degrees lower then in Wyoming
b. At noon the temperature of Boston had risen by 14 degrees. what was the temperature of boston at noon.
All we have to do for this one is add 14 to the temperature of Boston at 6am. ( This is because the question tells us the temperature has risen 14 degrees by noon )
-6 + 14 = 8
At noon the temperature would be 8 degrees in Boston.
What is the equation of the following line? Be sure to scroll down first to see
all answer options
Answer:
y=1/4x
Step-by-step explanation:
Just did the math ;D
Use the limit comparison test to determine whether ∑n=19∞an=∑n=19∞8n3−2n2+196+3n4 converges or diverges.
(a) Choose a series ∑n=19∞bn with terms of the form bn=1np and apply the limit comparison test. Write your answer as a fully simplified fraction. For n≥19,
limn→∞anbn=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞ as infinity and −∞ as -infinity. If the limit does not exist, enter DNE.
limn→∞anbn =
(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive?
Answer:
Diverges
General Formulas and Concepts:
Algebra I
Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Series Convergence Tests
P-Series: [tex]\displaystyle \sum^{\infty}_{n = 1} \frac{1}{n^p}[/tex]Direct Comparison Test (DCT)Limit Comparison Test (LCT): [tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex]
Step 2: Apply DCT
Define Comparison: [tex]\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{n^3}{n^4}[/tex][Comparison Sum] Simplify: [tex]\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n}[/tex][Comparison Sum] Determine convergence: [tex]\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n} = \infty , \ \text{div by P-Series}[/tex]Set up inequality comparison: [tex]\displaystyle\frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \geq \frac{1}{n}[/tex][Inequality Comparison] Rewrite: [tex]\displaystyle n(8n^3 - 2n^2 + 19) \geq 6 + 3n^4[/tex][Inequality Comparison] Simplify: [tex]\displaystyle 8n^4 - 2n^3 + 19n \geq 6 + 3n^4 \ \checkmark \text{true}[/tex]∴ the sum [tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex] is divergent by DCT.
Step 3: Apply LCT
Define: [tex]\displaystyle a_n = \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}, \ b_n = \frac{1}{n}[/tex]Substitute in variables [LCT]: [tex]\displaystyle \lim_{n \to \infty} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \cdot n[/tex]Simplify: [tex]\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4}[/tex][Limit] Evaluate [Coefficient Power Rule]: [tex]\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4} = \frac{8}{3}[/tex]∴ Because [tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} \neq 0[/tex] and the sum [tex]\displaystyle \sum^{\infty}_{n = 19} a_n[/tex] diverges by DCT, [tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex] also diverges by LCT.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
Malingo read 3/8 of a book on Friday, 1/4 on Saturday and the rest on Sunday. what fraction did he read on Sunday?
Answer:
3/8
Step-by-step explanation:
We can write the entire book with the number 1. Now we can write this operation
3/8 + 1/4 + x = 1
3 + 2 + 8x = 8
5 + 8x = 8
8x = 3
x = 3/8
James, Aimee and Zack have
weighed their suitcases. Each
weighs a prime number of
kilograms and the total weight
is 40kg.
an
What's the difference between
the lightest and heaviest
suitcase?
Answer:
29Kg
Step-by-step explanation:
P1=2Kg
P2=7Kg
P3=31Kg
P3-P1=29Kg
To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.
I was lucky and I got the result after few steps :-)
Subtract 7 pounds 3 ounces from 10 pounds
Need help with the answers that have been left Blank don’t understand how to do them
Step-by-step explanation:
d=20 J.
E=2,N,J
this is your answer
f(x) = x ^ 2 - x - 6; g(x) = 2x ^ 2 + 5x + 2 Find: (f/g)(X)
Answer:
[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]
Step-by-step explanation:
Given
[tex]f(x) =x^2 -x - 6[/tex]
[tex]g(x) = 2x^2 + 5x + 2[/tex]
Required
[tex](\frac{f}{g})(x)[/tex]
This is calculated as:
[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]
So, we have:
[tex](\frac{f}{g})(x) = \frac{x^2 - x - 6}{2x^2 + 5x + 2}[/tex]
Expand
[tex](\frac{f}{g})(x) = \frac{x^2 +2x - 3x - 6}{2x^2 + 4x+x + 2}[/tex]
Factorize
[tex](\frac{f}{g})(x) = \frac{x(x +2) - 3(x + 2)}{2x(x + 2)+1(x + 2)}[/tex]
Factor out x + 2
[tex](\frac{f}{g})(x) = \frac{(x- 3)(x + 2)}{(2x + 1)(x + 2)}[/tex]
Cancel out x + 2
[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]
Refer to the values described below, then identify which of the following is most appropriate: discrete random variable, a. Responses to the survey question "How many pets do you have?" b. Exact heights of the next 100 babies born in a region c. Responses to the survey question "What is your eye color?" d. Exact foot length of humans e. Number of people in families a. Since the outcomes are b. Since the outcomes are countable, this is this is a discrete random variable. random variable.
Answer:
Exact heights of the next 100 babies born in a region.
Step-by-step explanation:
A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.
I’m honestly not the best at math, can someone help?
Answer:
1/8
Step-by-step explanation:
Using the factor tree, we see that there is 8 possible outcomes ( right hand side)
There is only 1 way to go from left to right and have 3 wins
P(3 wins) = good outcomes / total
=1/8
How many gallons each of 25% alcohol and 5% alcohol should be mixed to obtain 20 gal of 16% alcohol?
Answer:
✓ x gal of 25% 20-x gal of 5% pure alcohol is x(.25)+(20-x)(.05)=20*.16=3.2 so .25x+1-.05x=3.2 gallons of 25% .20x=2.2 gallons of 5% x=11 gallons of 25%.
Step-by-step explanation:
Hope this helps~ ;D
Which equation has a constant of proportionality equal to 2?
Answer:
[tex]{ \tt{y = 2x}}[/tex]
Answer:
2y=x
Step-by-step explanation:
The hypotenuse of a right triangle is 16 units and the length of one of the legs is 12 units. What is the length of the other leg in simplest radical form?
A. 2√13
B. 4√11
C. 2√17
D. 4√7
Answer:
D, 4√7
Step-by-step explanation:
Answer:
Step-by-step explanation:
c = 16
a = 12
b = ?
a^2 + b^2 = c^2
12^2 + b^2 = 16^2
144 + b^2 = 256
b^2 = 256 - 144
b^2 = 112
b^2 = 16 * 7
sqrt(b^2) = sqrt(16)*sqrt(7)
b = 4 * sqrt(7)
Selena's gross annual salary as the Content editor of a fashion Magazine is Rs 40000 she contribute 10% of her salary. before she pays taxes to a retirement account 25% of her remaining salary is then consumed in state and federal taxes. what is the selenas annual in take home salary if she also has to pay Rs 30 for health Insurance each month.
Answer:
Selena's annual intake home salary is $ 26,640.
Step-by-step explanation:
Since Selena's gross annual salary as the content editor of a fashion Magazine is $ 40,000, and she contributes 10% of her salary before she pays taxes to a retirement account, and 25% of her remaining salary is then consumed in state and federal taxes, To determine what is Selena's annual intake home salary if she also has to pay $ 30 for health Insurance each month, the following calculation must be performed:
40,000 - (40,000 x 0.1) - (40,000 x 0.9 x 0.25) - (30 x 12) = X
40,000 - 4,000 - 9,000 - 360 = X
26.640 = X
Therefore, Selena's annual intake home salary is $ 26,640.
Kids with cell phones: A marketing manager for a cell phone company claims that the percentage of children aged 8-12 who have cell phones differs from 52%. In a survey of 832 children aged 8-12 by a national consumers group, 449 of them had cell phones. Can you conclude that the manager's claim is true? Use the a 0.10 level of significance and the P-value method. 1. State the appropriate null and alternate hypotheses.2. Compute the test statistic.
Answer:
Low-value method
Step-by-step explanation:
consumers group
Help please
Please help
9514 1404 393
Answer:
4. True
5. False
Step-by-step explanation:
4. The number of x-intercepts produced by the quadratic formula may be 0, 1, or 2. It will be 0 if the two roots are complex. It will be 1 if the two roots lie in the same place (one root with multiplicity 2). It is true that there may be only one x-intercept.
__
5. The value of 'b' in the quadratic formula is the coefficient of the linear term. In the given quadratic, it is -5, not 5.
If anyone can give me the answer that will be greatly appreciated :)
42-x=58
or, -x=58-42
with change in side sign also chamges we change sides to make like terms in one side and unlike in amother side.
or, -x= 16
or,x=-16.
therefore x=-16...
Hope this helps you.
Find the percentile rank for each test score in the data set. 12, 28, 35, 42, 47, 49, 50 What value corresponds to the 60th percentile
Answer:
Percentile rank:
12 = 7th
28 = 21st
35 = 36th
42 = 50th
47 = 64th
49 = 79th
50 = 93rd
- Vth number i.e. 47 is the value that corresponds to the 60th percentile.
Step-by-step explanation:
As we know,
Percentile rank = [(Number of values below x) + 0.5]/total number of values * 100
For 12,
Percentile rank = [0 + 0.5]/7 * 100
= 7th
For 28,
Percentile rank = [1 + 0.5]/7 * 100
= 21st
For 35,
Percentile rank = [2 + 0.5]/7 * 100
= 36th
For 42,
Percentile rank = [3 + 0.5]/7 * 100
= 50th
For 47,
Percentile rank = [4 + 0.5]/7 * 100
= 64th
For 49,
Percentile rank = [5 + 0.5]/7 * 100
= 79th
For 50,
Percentile rank = [6 + 0.5]/7 * 100
= 93rd
Now,
n = 7
60th percentile = 60% of n
So,
60% of n = 60/100 * 7
= 0.6 * 7
= 4.2
After rounding it off,
5th value is the 60th percentile i.e. 47.
The circumference of a circle with radius r can be found using the formula C=2πr
Find the circumference of a circle with radius 15.4 feet . Round your answer to two decimal places.
----------------------ft
Answer:
96.72
Step-by-step explanation:
Answer:
96.77
Step-by-step explanation:
pi is 3.142
radius = 15.4ft
c = 2*3.142*15.4
Slope=6and passes through (4,-1)
Answer:
Step-by-step explanation:
If you need the equation:
point slope form is:
y-y1 = m(x-x1)
m is the slope and (x1,y1) is a point on the line.
y- (-1) = 6(x-4)
If you want standard form:
y= 6x -24 -1
y=6x-25
2-[6÷2+{6×1/2+(7/2-3/2)}]
Answer:
-6
Step-by-step explanation:
2 - [6 ÷ 2 + {6 × 1/2 + (7/2 - 3/2)}] =
Follow the correct order of operations.
Do one step at a time and copy everything else each time, so you don't lose track of any operation.
= 2 - [6 ÷ 2 + {6 × 1/2 + 4/2}]
= 2 - [6 ÷ 2 + {6 × 1/2 + 2}]
= 2 - [6 ÷ 2 + {3 + 2}]
= 2 - [6 ÷ 2 + 5]
= 2 - [3 + 5]
= 2 - 8
= -6
Answer:
-6
hope this helps
Step-by-step explanation:
2_(6÷2+(6*1/2+(7/2-3/2))) solve the ones in bracket first
(7/2-3/2)=2
2-(6÷2+(6×1/2+2))
6×1/2+2
6×1/2=3
3+2=5
2-(6÷2+5)
6÷2=3
3+5=8
2-8
=-6
Morgan puts $3,200 into an investment account that earns compound
interest at a rate of 0.6% per month. Calculate the accumulated amount in
Morgan's account at the end of the 15th month.
Answer:
3500.416
Step-by-step explanation:
Compound interest formula
A = A0(1 + r/n)^nt
3200(1 + 0.6%)^15
3200(1 + 0.006)^15
3200(1.006)^15
(c³d)a(cd⁷)a
Simplify
Answer:
= c^4 d^8 a^2
Step-by-step explanation:
Apply exponent rule: aa= a^2
= c^3 da^2 cd^7
= c^4 da^2 d^7
= c^4 d^8 a^2
Which is the correct calculation of the y-coordinate of point A? 0 (0 - 0)2 + (1 - y2 = 2 O (0 - 1)² + (0- y2 = 22 (0-0)² + (1 - y2 = 2 (0 - 1)2 + (0-y2 = 2
Answer:
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
Step-by-step explanation:
The equation of the circle is represented by the following expression:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.
[tex]r[/tex] - Radius of the circle.
If we know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]r = 2[/tex], then the equation of the circle is:
[tex]x^{2} + y^{2} = 4[/tex] (1b)
Then, we clear [tex]y[/tex] within (1b):
[tex]y^{2} = 4 - x^{2}[/tex]
[tex]y = \pm \sqrt{4-x^{2}}[/tex] (2)
If we know that [tex]x = 1[/tex], then the y-coordinate of point A is:
[tex]y = \sqrt{4-1^{2}}[/tex]
[tex]y = \sqrt{3}[/tex]
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
During a certain 9-year period, the Consumer Price Index (CPI) decreased by
45%, but during the next 9-year period, it decreased by only 5%. Which of
these conditions must have existed during the second 9-year period?
A. Deflation
B. Stagnation
C. Conflation
D. Inflation
Answer:
deflation ,,,,
Step-by-step explanation:
I hope it's helpful for you ☺️Deflation must have existed during the second 9-year period.
What is deflation?Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.
The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.
Given data ,
Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.
In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.
Hence , the process is deflation in the second year
To learn more about deflation click :
https://brainly.com/question/30060490
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Multiply the complex numbers: (1∕2 + 4i)2
Question 10 options:
A)
–153∕4 + 4i
B)
153∕4 + 8i
C)
–153∕4 + 8i
D)
153∕4 + 4i
Step-by-step explanation:
153∕4 + 8i is the correct answer
[I'm supposing that you have to find the value of (1/ 2 + 4i)²]
Answer:
[tex] = \frac{ - 63}{4} + 4i[/tex]
Step-by-step explanation:
we must know that
(a + b)² = a² + b² + 2ab[tex] {( \frac{1}{2} + 4i) }^{2} = { (\frac{1}{2} })^{2} + {(4i)}^{2} + 2 . \frac{1}{2} . 4i[/tex]
[tex] = \frac{1}{4} + 16 {i}^{2} + 4i[/tex]
since i²= -1[tex] = \frac{1}{4} - 16 + 4i[/tex]
[tex] = \frac{1 - 64}{4} + 4i[/tex]
[tex] = \underline{ \frac{ - 63}{4} + 4i} [/tex]
[I'm also assuming that instead of -153/4 + 4i option A says -63/ 4 + 4i.]
so the answer is option A.
Someone help please
66 because you have to solve the problem next time
