Given:
The rule for the sequence is
[tex]f(n)=3n^2+1[/tex]
Domain of the function is the set of whole numbers greater than 0.
To find:
The first 4 terms of the sequence defined by the given rule.
Solution:
We have,
[tex]f(n)=3n^2+1[/tex]
Domain of the function is the set of whole numbers greater than 0. So, domain for first four terms are 1, 2, 3 and 4 respectively.
For n=1,
[tex]f(1)=3(1)^2+1[/tex]
[tex]f(1)=3(1)+1[/tex]
[tex]f(1)=3+1[/tex]
[tex]f(1)=4[/tex]
For n=2,
[tex]f(2)=3(2)^2+1[/tex]
[tex]f(2)=3(4)+1[/tex]
[tex]f(2)=12+1[/tex]
[tex]f(2)=13[/tex]
For n=3,
[tex]f(3)=3(3)^2+1[/tex]
[tex]f(3)=3(9)+1[/tex]
[tex]f(3)=27+1[/tex]
[tex]f(3)=28[/tex]
For n=4,
[tex]f(4)=3(4)^2+1[/tex]
[tex]f(4)=3(16)+1[/tex]
[tex]f(4)=48+1[/tex]
[tex]f(4)=49[/tex]
Therefore, the first 4 terms of the sequence defined by the given rule are 4, 13, 28 and 49 respectively.
Jeffery wants to save the same amount of money each week to buy a new bike. He needs $224.If he wants the bike in 14 weeks, how much money should Jeffery save each week?
Answer:
16 dollars per week
Step-by-step explanation:
Divide 224 by 14
Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter "". a. What is ? b. What is ? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer. - Select your answer - , because - Select your answer - . d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem? - Select your answer -
Answer:
Explained below.
Step-by-step explanation:
The complete question is:
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.
What is P(A and B)?
What is P(A | B)?
Is P(A | B) equal to P(A)?
Are events A and B dependent or independent?
A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
Solution:
The probability of the two events A and B are:
P(A) = 0.30 and P(B) =0.40
(a)
Compute the value of P (A ∩ B) as follows:
[tex]P(A\cap B)=0[/tex]
This is because mutually exclusive events are those events that cannot occur together.
(b)
Compute the value of P (A | B) as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{0.40}=0[/tex]
Thus, the value of P (A | B) is 0.
(c)
No, P (A | B) is not equal to the P (A).
(d)
As mentioned in part (a), mutually exclusive events are those events which cannot occur together.
That is, [tex]P(A\cap B)=0[/tex].
Events A and B are independent if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.
That is, [tex]P(A\cap B)=P(A)\times P(B)[/tex].
The concepts of mutually exclusive events and independent events are not the same.
(e)
As the it is provided that A and B are mutually exclusive events, we know that [tex]P(A\cap B)=0[/tex].
Now compute the value of [tex]P(A)\times P(B)[/tex] as follows:
[tex]P(A)\times P(B)=0.30\times 0.40=0.12\neq 0[/tex]
Thus, the events A and B are not independent.
Thus, if two events are mutually exclusive events they cannot be independent.
Pls look at pic and pls help
Answer:Don´t know but hope ypu find someone who knows
Step-by-step explanation:
Answer:
5½
Step-by-step explanation:
1). Convert any mixed numbers to fractions. Then your initial equation becomes: ³⁄₂·¹¹⁄₃
3). Applying the fractions formula for multiplication: [tex]\frac{3*11}{2*3}[/tex] = [tex]\frac{33}{6}[/tex] = [tex]5\frac{1}{2}[/tex]
A data analytics firm hired by a Republican candidate running for political office wants to test whether its practices were successful in increasing voter turnout among registered Republicans. The firm collected data in a random selection of cities before the candidate ran for office and then after the election. Find the test statistic and the number of degrees of freedom for an appropriate hypothesis test using the data set below. Let the difference d for each city be computed as d=after−before. Assume that the populations are normally distributed. Round the test statistic to three decimal places.
Answer:
The practices were successful in increasing voter turnout among registered Republicans.
Step-by-step explanation:
The missing data is attached below.
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
In this case a paired t-test is used to determine whether the practices were successful in increasing voter turnout among registered Republicans.
The hypothesis for the test can be defined as follows:
H₀: The practices were not successful in increasing voter turnout among registered Republicans, i.e. d ≤ 0.
Hₐ: The practices were successful in increasing voter turnout among registered Republicans, i.e. d > 0.
Use Excel to perform the paired t-test.
Go to Data → Data Analysis → t-Test: Paired Two Sample for Means
A dialog box will open.
Select the variables.
Set the Hypothesized mean difference as 0.
Press OK.
The output is attached below.
The test statistic value is, t = 5.409.
The degrees of freedom is, df = 9.
The p-value for he one-tailed test is, p-value = 0.00021.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Thus, concluding that the practices were successful in increasing voter turnout among registered Republicans.
Which of the following is NOT a possible root of the function? (Hint: Use the rational root theorem, write out all the possible roots, and see which one is NOT on your list.) Please use any sources to help you.
f(x)= 3x^3+2x^2+x+4
A. +4/3
B. +1
C. +3/4
D. +2
Given:
The function is
[tex]f(x)=3x^3+2x^2+x+4[/tex]
To find:
The value from the given options that is NOT a possible root of the function.
Solution:
According to rational root theorem, all possible roots are in the form of
[tex]x=\dfrac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}[/tex]
We have,
[tex]f(x)=3x^3+2x^2+x+4[/tex]
Here,
Leading coefficient = 3.
Constant term = 4
Factors of 3 are ±1, ±3.
Factors of 4 are ±1, ±2, ±4.
Using rational root theorem, all possible roots of given functions are
[tex]\pm 1,\pm 2,\pm 4,\pm \dfrac{1}{3}, \pm \dfrac{2}{3},\pm \dfrac{4}{3}[/tex]
Clearly, [tex]\dfrac{4}{3},1,2[/tex] are possible roots but [tex]\dfrac{3}{4}[/tex] is not the possible root.
Therefore, the correct option is C.
What are the solutions to this quadratic equation?
x2+13=8x+37
Answer:
x = 4 + 2 sqrt(10) or x = 4 - 2 sqrt(10)
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + 13 = 8 x + 37
Subtract 8 x + 37 from both sides:
x^2 - 8 x - 24 = 0
Add 24 to both sides:
x^2 - 8 x = 24
Add 16 to both sides:
x^2 - 8 x + 16 = 40
Write the left hand side as a square:
(x - 4)^2 = 40
Take the square root of both sides:
x - 4 = 2 sqrt(10) or x - 4 = -2 sqrt(10)
Add 4 to both sides:
x = 4 + 2 sqrt(10) or x - 4 = -2 sqrt(10)
Add 4 to both sides:
Answer: x = 4 + 2 sqrt(10) or x = 4 - 2 sqrt(10)
The base of a building is 5 feet tall , the first floor and every floor about it is 11 feet tall. Which equation represents the total hight of the building
Answer:
5+11x= total height
x is the number of floors
The animal shelter requires 1 pound of food for every 3 animals. This directly proportional relationship is represented by the equation y = (1/3)x, where x represents the number of animals and y represents pounds of food. If y varies directly with x, which graph represents the situation?
A graph has number of animals on the x-axis and food (pounds) on the y-axis. Points are at (0, 1), (2, 2), (4, 3), (6, 4), (8, 5), and (10, 6).
A graph has number of animals on the x-axis and food (pounds) on the y-axis. Points are at (0, 0), (3, 1), (6, 2), (9, 3).
A graph has number of animals on the x-axis and food (pounds) on the y-axis. Points are at (0, 3), (3, 2), (6, 1), and (9, 0).
Answer:
It is graph B or the second graph!
Step-by-step explanation:
Answer:
Its graph B.
Step-by-step explanation:
I just got it right on Edge.
Darius and Matthew have 3 fruit bars.They are both hungry after playing football and decide to split the fruit bar evenly.How much fruit bar will each boy get ?
Answer:
1 1/2 or 1.5
Step-by-step explanation:
If they split 1/2 of the bar with each other
3 bars x 1/2 split bar = 1.5 or 1 1/2 of the shared amount
3 *1/2=1.5 or 1 1/2
What is 4/5 x 2/5? I need help
Answer:
8/25
Step-by-step explanation:
200m - 100m + 48,250 = 50,250 – 150m
200m - 100m + 48,250 = 50,250 - 150m
(Add or subtract common variables)
100m + 48,250 = 50,250 - 150m
(Add 150m to both sides)
250m + 48,250 = 50,250
(Subtract 48,250 to both sides)
250m = 2000
(Divide 250 to both sides to isolate m)
m = 8
In this table what is the domain of the function?
Answer:
c. D: {1, 2, 3, 4, 5}
Step-by-step explanation:
The domain of a function includes values of x that are in the given table of values of the given function.
The range, on the other hand, includes all set of values of y, given in the table of values.
Thus, for the table of values above:
Domain would be [1, 2, 3, 4, 5]
Range would be [a, b, c, d, e]
The domain of the function can be represented as:
D: {1, 2, 3, 4, 5}
Find the slope of the line.
Answer:
Slope = 4/3
Step-by-step explanation:
Slope= (y2-y1)/(x2-x1)
Let's say (0,1) is x2 and y2. That means (-3,-3) is x1 and y1.
(1 - -3) / (0 - -3)
(1 + 3) / (0 + 3)
4 / 3
A restaurant customer left $0.90 as a tip. The tax was 6 percent and the tip was 10% of the after-tax cost. What was the total bill?
which is the same as 10^-3
A. 0.0001
B.0.001
C.3
D.1000
Answer:
B. 0.001Step-by-step explanation:
Your answer is B. 0.001.Thank you ☺️☺️
its answer is option B
0.001
please help me!!! I am just a meme poster... :c
Suppose X has an exponential distribution with lambda equals 5. Determine the following. Round the answers to 3 decimal places.a) Upper P left-parenthesis Upper X less-than-or-equal-to 0 right-parenthesis equalsb) Upper P left-parenthesis Upper X greater-than-or-equal-to 2 right-parenthesis equalsc) Upper P left-parenthesis Upper X less-than-or-equal-to 1 right-parenthesis equalsd) Upper P left-parenthesis 1 less-than Upper X less-than 2 right-parenthesis equalse) Find the value of x such that Upper P left-parenthesis Upper X less-than x right-parenthesis equals 0.05.
Answer:
Explained below.
Step-by-step explanation:
The random variable X follows an exponential distribution with λ = 5.
The probability density function of X is:
[tex]f_{X}(x)=\lambda\cdot e^{-\lambda\cdot x};\ 0<x<\infty[/tex]
[tex]P(X\leq x)=1-e^{-\lambda\cdot x}\\\\P(X\geq x)=e^{-\lambda\cdot x}[/tex]
(a)
Compute the value of P (X ≤ 0) as follows:
[tex]P(X\leq 0)=1-e^{-\lambda\cdot x}[/tex]
[tex]=1-e^{-5\times 0}\\\\=1-1\\\\=0[/tex]
Thus, the value of P (X ≤ 0) is 0.
(b)
Compute the value of P (X ≥ 2) as follows:
[tex]P(X\geq 2)=e^{-5\times 2}=4.54\times 10^{-5}\approx 0[/tex]
Thus, the value of P (X ≥ 2) is approximately 0.
(c)
Compute the value of P (X ≤ 1) as follows:
[tex]P(X\leq 0)=1-e^{-\lambda\cdot x}[/tex]
[tex]=1-e^{-5\times 1}\\\\=1-0.00674\\\\=0.99326[/tex]
Thus, the value of P (X ≤ 1) is 0.99326.
(d)
Compute the value of P (1 ≤ X ≤ 2) as follows:
[tex]P(1<X<2)=\int\limits^{2}_{1} {5\times e^{-5x}} \, dx \\\\=5\times [\frac{e^{-5x}}{-5}]^{2}_{1} \\\\=5\times [\frac{0-0.00674}{-5}]\\\\=0.0067[/tex]
Thus, the value of P (1 ≤ X ≤ 2) is 0.0067.
(e)
Compute the value of x such that P (X < x) = 0.05 as follows:
[tex]P(X<x)=0.05\\\\\int\limits^{x}_{0} {5\times e^{-5x}} \, dx =0.05\\\\5\times [\frac{e^{-5x}}{-5}]^{x}_{0} =0.05\\\\1-e^{-5x}=0.05\\\\-e^{-5x}=0.95\\\\-5x=\ln(0.95)\\\\-5x=-0.05\\\\x=0.01\\\\[/tex]
Thus, the value of x is 0.01.
a pair of socks cost $18.50 the markup is 5% the taxes
Answer:
I'm pretty sure the answer is 19.425
You have to round up or down because it is money.
The answer is $19.43
Step-by-step explanation:
I really hope this is correct.
Answer:
$19.43
Step-by-step explanation:
At first you get 19.425
But money only has 2 decimal places and the 5 tells to to round the 2 up to 3
Snow play ski park cost $35 entry fee and then $5 per hour. If you have $60, how long can you be at snow play ski park
For $60, you may spend four hours at Snow Play Ski Park.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Snow plays ski park costs a $35 entry fee and then $5 per hour. If you have $60
Let "x" be the hours you can play in the ski park
Since,
Addition charges = 35
Thus your total expenses to play x hours in the park = 5*x + 35
Since We have only 60$
So,
60 = 5x + 35
=> 5x = 25
=> x = 5
therefore, You can be at a snow play ski park for four hours for $60.
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Which inequality represents all the solutions of 8(6x - 7) < 5(9x - 4)?
A. x> 12
B. x< 12
C. x> 20
D. x < 20
Answer:
A. x>12
Step-by-step explanation:
8(6x - 7) < 5(9x - 4)
Distribute:
48x-56<45x-20
Move like-terms together:
48x-45x<-20+56
Subtract/add:
3x<36
Divide both sides by 3
x<12
Answer:
B. x< 12
Step-by-step explanation:
Mr. Witherspoon's fifth grade class was on the
playground. Billy was told to stand still.
Mr. Witherspoon had Rosey stand 10 feet from
Billy. The rest of the class was also told to stand
10 feet from Billy. What shape did the positions of
the class form in relation to Billy?
The location of the circumference of a circle is the set of points that are equidistant from a given point
The shape formed by the rest of the class in relation to Billy is the shape of a circleReason:
Given information;
The distance of Rosey from Billy = 10 feet
The distance of the rest of the class from Bill = 10 feet
Required:
The shape the positions of the class formed in relation to Billy
Solution;
The distance from Billy to each pupil in the class is equal, (10 feet), therefore, Billy is at a central position to the rest of the class
Therefore, the shape that the rest of the class form in relation to Billy is a figure that has Billy as the center or centroid
If the number of pupils in the class is sufficiently, large, the shape formed will be a circle, given that a circle is formed by the set of points that have equal distance from a particular points
Therefore, the shape formed by the rest of the class in relation to Billy is the shape of a circle
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f(x)=|3x+5|+6
g(x)=7
find (f+g) (x).
Answer:
[tex](f+g) (x)=\mid 3x+5\mid+13[/tex]
Step-by-step explanation:
Operation of Functions
Given:
[tex]f(x)=\mid 3x+5\mid+6[/tex]
[tex]g(x)=7[/tex]
The sum of (f+g) (x) is:
[tex](f+g) (x)=\mid 3x+5\mid+6+7[/tex]
We cannot operate with the expression inside the absolute bars, thus:
[tex]\boxed{(f+g) (x)=\mid 3x+5\mid+13}[/tex]
A scanner scanned 56 photos in 7 minutes. If it scans photos at a constant rate, it can scan
photos in 27 minutes.
Answer:
56 photos-7 minutes
X photos-27 minutes
X=1 512 :7= A scanner will scan 216 photos
Step-by-step explanation:
Ethan is using his compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is he in the process of constructing?
1. An equilateral triangle
2. A square
3. A regular pentagon
4. A regular hexagon
Answer:
A
Step-by-step explanation:
Cuz Im just right
(A) An equilateral triangle.
Circle:All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.Polygon:In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).Triangle:A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Therefore, Ethan is in the process of constructing (A) an equilateral triangle.
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convert
32 ½ meters to feet
Answer: 32 1/2 meters = 106.63 ft
Step-by-step explanation: 1 meter is 3 ft and 3.37 inches, or 39.37 inches :)
Rolling a fair six-sided die is supposed to randomly generate the numbers 1 through 6. Explain what random means in this context? Choose the correct answer below.
a. That if a 1 is rolled it that means that each other number was not rolled.
b. That the only possible outcomes are 1, 2, 3, 4, 5, and 6.
c. That each result will not be influenced by the previous result of the die roll.
d. That in the long run, a fair die will produce roughly equal amounts of the numbers 1 through 6 when rolled. But for each roll each value 1 through 6 is equally likely.
Answer: D.
Step-by-step explanation: It explains the definition of random in particular with the die.
Random means in this context is
d. That in the long run, a fair die will produce roughly equal amounts of the numbers 1 through 6 when rolled. But for each roll each value 1 through 6 is equally likely.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, Rolling a fair six-sided die is supposed to randomly generate the numbers 1 through 6.
Random means here is that in the long run, a fair die will produce roughly equal amounts of the numbers 1 through 6 when rolled. But for each roll each value 1 through 6 is equally likely.
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what is the sum of 3/4 and 4/5
Answer:
31/20
Step-by-step explanation:
just cross multiply and add
(3x5 + 4x4) / 4x5
Answer: 31/20 or 1.55
yo you guys think you could help me find the sum
Answer:
4m + 8n -4p
Step-by-step explanation:
Im pretty sure its that. Hope its right!
2/3 + 2/3 please answer
Answer:
4 over 3
Step-by-step explanation:
this is beause you add the numertior and not the divend
Answer:
4/3 or 1 1/3 or 1.333 repeating
Step-by-step explanation:
Since 2/3 + 2/3 has the same denominator you can just add the top numerators together and keep the same denominator.
Given the area and perimeter find the length and width