Which best describes the graph of
f(x) = log₂(x + 3) + 2 as a transformation of the
graph of g(x) = log₂x?
A translation 3 units left and 2 units up best describes the graph of f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x
How to solve this problem?
f(x) = log2(x + 3) + 2 (given)
g(x) = log2x (given)
We need to describe the best statement for the graph
The graph is shown in the image
The following steps are shown to describe the graph.
The general equation of f(x) = log2(x-h)+k
When h > 0 (positive)
The graph of the base of the function shift to the right
When h < 0 (Negative)
The graph of the base function shifts to the left.
When k > 0 (Positive)
The graph of the base function shifts upward.
When k < 0 (Negative)
The graph of the base function shifts downward
Here h = 3 , k = 2
Hence , a translation 3 units left and 2 units up describes the graph.
Learn more about Translating the logarithm function more
brainly.com/question/12640727
#SPJ1
Which choice is equivalent to the quotient shown here when x > 0?
98x³+√72x²
O A. TV₂
OB. √26x
7x
O C. 7
6
OD. √98x3 - 72x²
Answer:
A.[tex] \frac{7}{6} \sqrt{x} [/tex]
Step-by-step explanation:
Solution Given:
[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]
Bye using indices formula
[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]
we get
[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]
[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]
[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]
[tex] \frac{7}{6} \sqrt{x} [/tex]
What values of x make the two expressions below equal?
(x-1)(x-6)_
4(x-1)
x-6
4
A. All real numbers except 1
B. All real numbers except 6
C. All real numbers
D. All real numbers except 1 and 6
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expressions are given below.
[(x - 1)(x - 6)] / [4(x - 1)] and (x - 6) / 4
Simplify the expression [(x - 1)(x - 6)] / [4(x - 1)], then we have
⇒ [(x - 1)(x - 6)] / [4(x - 1)]
⇒ (x - 6) / 4
But at x = 1, the expression [(x - 1)(x - 6)] / [4(x - 1)] is not defined.
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
More about the equivalent link is given below.
https://brainly.com/question/889935
#SPJ1
An aircraft is flying at altitude H when it begins its descent to an airport runway that is at a horizontal ground distance L from the airplane. Assume that the landing path is described by the cubic polynomial function y=ax3+bx2+cx+d where y(-L)= H and y(0)= 0.a. What is dy\dx at x= 0?b. What is dy\dx at x= -L?
a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]
b. [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]
a. The derivative of a cubic function
[tex]y=ax^3+bx^2+cx+d[/tex] is [tex]y'=3ax^2+2bx+c[/tex].
Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.
b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].
Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]
A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.
A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3
To learn more about sets, visit:
brainly.com/question/8053622
#SPJ4
what number is 16 2/3% more than 240
280 is the number which is 16 2/3% more than 240
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.
(1/6) th of 240 = 240/6 = 40
40 more than 240 = 280
So, 280 is the number which is 16 2/3% more than 240
To Learn more about the percentage form the link:
https://brainly.com/question/24304697
#SPJ1
please help meeeeeeee
Answer: B & A
Step-by-step explanation: I think?
A _______ is a set of input data in a relationship
The complete answer: A domain is a set of input data in a relationship.
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
An input value and an output value are matched in a relation.
A relation is a function where each input value yields one and only one output value.
Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,
while the range is the set of output values.
The domain of a function or relation is the set of all possible independent values that it can have.
Therefore, a domain is a set of input data in a relationship.
To learn more about the domain;
https://brainly.com/question/28135761
#SPJ1
according to wine-searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. random ratings of a pinot noir recently produced by a newly established vineyard in follow: excel file: data07-11.xlsx 87 91 86 82 72 91 60 77 80 79 83 96 a. develop a point estimate of mean wine score for this pinot noir (to decimals). 82.00 b. develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals). 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.
Below table showing calculation of Point Estimate of Mean and Standard Deviation:
Score X-X’ (X-X’)^2
87 5 25
91 9 81
86 4 16
82 0 0
72 -10 100
91 9 81
60 -22 484
77 -5 25
80 -2 4
79 -3 9
83 1 1
96 14 196
984 1022
Mean(X’) = Total Score/n
n = Total number = 12
X’ = 984/12 = 82
Standard Deviation (σ) = √∑(X-X’)^2/(n-1)
σ = √1022/(12-1)
σ = √1022/ 11
σ = 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389
To learn more about mean and standard deviation link is here
brainly.com/question/28108712
#SPJ4
Find f(x) where f'(x)=4x+7
Answer:
[tex]2x^2+7x+C[/tex]
Step-by-step explanation:
Find the antiderivative of f'(x)=4x+7
[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]
Helpp!! GIVING BRAINIEST
The value of the c in the function c = 19m - 15 when m=10 is 175.
What is a function?A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.
Given the function;
c = 19m - 15,
where m represents the number of months and c represents the total number of car sent to New York.
To find the value of c:
when m = 10,
Substitute the value of m to the function;
c = 19 (10) - 15
c = 190 - 15
c = 175.
Therefore, the value of c is 175.
To learn more about the function;
brainly.com/question/28303908
#SPJ1
Your school is planning a fundraising dinner. The expense for this event must not exceed $2,475.00. The team organizing the event has calculated that the cost per adult guest will be $18.00 and the cost per child guest will be $9.00. The venue can hold no more than 150 guests.
The two inequalities that describe the total cost and no. of guests are
18a + 9c ≤ 2475 and
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let 'a' be the no. of adults and 'c' be the no. of children.
The expense for this event must not exceed $2,475.00.
Therefore, 18a + 9c ≤ 2475...(i)
The venue can hold no more than 150 guests.
Therefore, a + c ≤ 150...(ii)
learn more about inequalities here :
https://brainly.com/question/20383699
#SPJ1
let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)
The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.
Given :
Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,
Let g(x) = f(x) − 5.
g(x) = (x−p)(x−q)(x−r)(x−s)h(x)
The condition f(t) > 5 translates to g(t) > 0.
Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :
the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }
The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.
Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have
f(x)=x(x−1)(x−3)(x−4)+5
Learn more about the polynomial here:
https://brainly.com/question/11536910
#SPJ4
Full question ;
Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?
a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]
Given that,
Length of the ladder is, [tex]l=9ft[/tex]
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
[tex]h^{2} +b^{2} =l^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = 81 (Equation-1)
Differentiating the above equation with respect to time, 't'.
So,
We can write,
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0
[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0
[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0 (Equation-2)
In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.
Let us assume,
h = 3 ft and db/dt = 3 ft/s
We can substitute values in equation-1,
[tex]3^{2} +b^{2}[/tex] = 81
9 + [tex]b^{2}[/tex] = 81
[tex]b^{2}[/tex] = 81-9
[tex]b^{2}[/tex] = 72
b = [tex]\sqrt{72}[/tex]
b = 8.48 ft
Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]
3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0
3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0
3*[tex]\frac{dh}{dt}[/tex] = - 25.44
[tex]\frac{dh}{dt}[/tex] = -25.44/3
[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s
Therefore,
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
To learn more about Pythagoras theorem visit :
brainly.com/question/28022959
#SPJ4
Polly borrowed $285 for a new floor lamp. She will make 5 monthly payments of $62 to repay the loan. How much will she pay in interest?
Interest is the price you pay to borrow money or the cost you charge to lend money.
How do you calculate interest on a loan?Divide your interest rate by the number of payments you'll make that year. If you have a 6 percent interest rate and you make monthly payments, you would divide 0.06 by 12 to get 0.005. Multiply that number by your remaining loan balance to find out how much you'll pay in interest that month.If the payment plan is $62 per month for 5 months, then the whole payment will be: $310To calculate simple interest on a loan, take the principal (P) times the interest rate (R) times the loan term in years (T), then divide the total by 100. To use this formula, make sure you're expressing your interest rate as a percentage, not a decimal (i.e., a rate of 4% would go into the formula as 4, not 0.04).So, $10$ percent per annum means that $10$ percent interest will be charged yearly or annually over a principal amount or a loan. Note: If the rate of interest is $10$ percent per annum, then the interest calculated will be $10$ percent of the principal amount.To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.
310-285 = 25
So, Polly will pay $25 in interest.
To learn more about interest refer to:
https://brainly.com/question/29369088
#SPJ1
Select all of the lines of reflection that will carry the rectangle back onto itself.
The lines that carry the rectangle onto itself are x = 0 and y = 1
How to determine the lines that carry the rectangle onto itself?The graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The rectangular graph
The coordinates of one end of the graph are
(-3, 3) and (-3, -1)
Next, we calculate the midpoint of these ends
So, we have
Midpoint = 1/2(x₁ + x₂, y₁ + y₂)
Substitute the known values in the above equation, so, we have the following representation
Midpoint = 1/2(-3 + 3, -1 + 3)
Evaluate the like terms
Midpoint = 1/2(0, 2)
So, we have
Midpoint = (0, 1)
So, we have
x = 0 and y = 1
Hence, the reflection lines are x = 0 and y = 1
Read more about reflection at
https://brainly.com/question/27224272
#SPJ1
57. Center: (0, 0); Radius: 3
A scientist began measuring the temperature of a solution when it was 100 °F. The temperature of the solution
decreased at a constant rate of 1.5 °F per hour.
Which function can be used to find y, the temperature of the solution in degrees Fahrenheit after x hours?
Ay 1.5x - 100
By 1.5x + 100
y 100x1.5
Oy - 100x + 1.5
Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.
The required details for Conditional problems in given paragraph
This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.
For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.
The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.
what are conditional problems?
Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.
To learn more about conditional problems
https://brainly.com/question/27839142
#SPJ1
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2. (Let x, y, and z be the dimensions of the rectangular box.)(x, y, z) =
The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
Given that:
Total surface area of the rectangular box or cuboid = 100 cm²
A rectangular box with largest volume is a cube.
The total surface area of a cube = 6 times square of one edge length.
Let the edge length = given dimensions; x, y, z
So,
x = y = z
6x^2 = 100
x^2 = 100 / 6
x = √ 100 / 6
x = 10 / √ 6 cm
x = 2.449 cm
Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
Learn more about cube surface area at: https://brainly.com/question/13789496
#SPJ4
The area of ground A is given by 12x^2y sq. units and the area of ground B is given by 6xy^2sq Units
where x>0 and y> 0. Tiles of the same size need to be installed on both the grounds. What should
be the maximum tile area so that it can be used for both the grounds?
The maximum area of the tile to contain both grounds is 12x²y²
How to determine the maximum area of the tile?From the question, we have the following parameters that can be used in our computation:
Area of ground A = 12x^2y sq. units
Area of ground B = 6xy^2sq units
Rewrite these areas properly
So, we have the following representation
Area of ground A = 12x²y sq. units
Area of ground B = 6xy² sq units
Express the areas as the products of their prime factors
This gives
Area of ground A = 2 * 2 * 3 * x * x * y
Area of ground B = 2 * 3 * x * y * y
From the above products, we have
Least common multiple = 2 * 2 * 3 * x * x *y * y
Evaluate the products
Least common multiple = 12x²y²
This represents the greatest area
Hence, the greatest area is 12x²y²
Read more about LCM at
https://brainly.com/question/16407111
#SPJ1
Write the equation of the line that has the slope of 7/3
and goes through the point (7,-9) in standard form.
****
The equation of the line that has the slope of 7/3 is: y = (7/3) x - 27/49
What is equation of the line?Finding the slope and y-intercept is necessary to express the equation of a graphed line in y-intercept (y=mx+c) form, which can then be used to get the equation of the line. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.
Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
Given that,
slope (m) = 7/3
Putting (7,-9) into the equation: y =mx+c
or, -9 = (7/3) × (7) + c
or, -9 = 49 /3 + c
or, c = (-9) × (3/49)
or, c = -27/49
Thus, the equation becomes:
or, y = (7/3) x + -27/49
or, y = (7/3) x - 27/49
To know more about equation of the line refer to:
https://brainly.com/question/25969846
#SPJ1
Help with this plsssss !!!
Answer:
58
Step-by-step explanation:
There are 5 lines between 50 and 60
60 - 50 = 10
10 / 5 = 2
This means that each increment is 2.
We see the end of the box plot is above the fourth increment above 50.
4 x 2 = 8
50 + 8 = 58
Solve for x. Triangle stuff
Answer:
x=9
Step-by-step explanation:
these 2 angles are supplementary angles meaning added together they will equal 180 degrees
so we can add them together and set it equal to 180
(8x-3)+(16x-33)=180
combine like terms
(8x+16x)+(-3-33)=180
24x-36=180
+36. +36
24x=216
/24. /24
x=9
hopes this helps
emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28% sophomores: 26% juniors: 24% seniors: 22% according to the information emily has gathered, which of the following statements are true? choose all that are correct. responses more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15.
The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
Given :
emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 % .
Freshmen = 0.85
sophomores = 0.80
it is clearly visible that the freshmen or sophomores is greater than the 40 % .
Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
Learn more about the statements here:
https://brainly.com/question/29582805
#SPJ4
Find the volume of a cone with a radius of 3 feet and a height of 7 feet. Enter
the answer in terms of pie
The function f(x)=9.25x + 3 represents the amount radda earns dog walking for X hours
Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.
How to write a linear function for the total amount of money Radda earns?In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;
T = mx + b
Where:
T represents the total amount of money earned.m represents the rate of change (slope) per hour.x represents the number of hours or time.b represents the y-intercept or initial amount.Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;
f(x) = T = 9.25x + 3
When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;
f(1) = T = 9.25(1) + 3
f(1) = T = 9.25 + 3
f(1) = T = $12.25.
In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.
Read more on linear function here: brainly.com/question/27325295
#SPJ1
Complete Question:
The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?
NO LINKS!! Please help me with this problem. Part 8ff
Answer:
[tex]\dfrac{1}{36n^2+6n}[/tex]
Step-by-step explanation:
Given factorial expression:
[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]
[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]
Apply the factorial rule to the numerator and denominator of the given rational factorial expression:
[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]
[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]
Answer:
[tex]\cfrac{1}{6n(6n+1)}[/tex]--------------------------------
We know that:
n! = 1·2·3·4·...·nTherefore:
(6n + 1)! = (6n - 1)!·6n·(6n + 1)Therefore:
[tex]\cfrac{(6n-1)!}{(6n+1)!} =\cfrac{(6n-1)!}{(6n-1)!(6n)(6n+1)} =\cfrac{1}{6n(6n+1)}[/tex]A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 414 gram setting. Based on a 8 bag sample where the mean is 407 grams and the standard deviation is 18, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
Question #2:
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 26 samples is 4.6 ppm with a standard deviation of 1.2. Does the data support the claim at the 0.025 level? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
A)
A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.
So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414
It is believed that the machine is underfilling the bags.
So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414
Given,
n= 8
Population standard deviation (б) = 18
x= 407
We will use the t-test since n > 8 and we are given the population standard deviation.
t=x-μ / (б/[tex]\sqrt{n-1}[/tex])
t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]
t= -1.028
Use the t table to find p value
p-value = 12.706
Level of significance α = 0.025
p-value>α
It is a two-tailed test.
So, we fail to reject the null hypothesis.
So, its bag-filling machine works correctly at the 414-gram setting.
B)
Let μ be the population mean amount of ozone in the upper atmosphere.
As per the given, we have
[tex]H_{0}[/tex] : μ = 4.8
[tex]H_{1}[/tex] : μ ≠ 4.8
Sample size: n= 26
Sample mean = 4.6
Standard deviation = 1.2
Since population standard deviation is now given, so we use a t-test.
t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]
t= -0.2/0.24
t= -0.833
It is a two-tailed test.
We are accepting the null hypothesis.
To learn more about hypothesis testing visit: brainly.com/question/17099835
#SPJ4
A random sample of 75 students at the University of Minnesota spend an average of $614 per month in rent
with a standard deviation of $219. The distribution is moderately skewed to the high end. Which of the
following statements are true?
i. 95% of students at the university spend $564 to $664 on rent.
ii. We are 95% confident that the average rent for students at the university is between $564 and $664.
iii. Because we cannot examine other characteristics of the students in the random sample, it is not
advisable to construct a confidence interval.
Oi only
O ii only
O iii only
Oi and ii
Oi, ii, and iii
Check Answer
The correct option is b) ii only
From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.
What is meant by distribution?
The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.
What are the 3 types of distribution?
The Three Types of Distribution
Intensive Distribution: As many outlets as possible. The goal of intensive distribution is to penetrate as much of the market as possible.Selective Distribution: Select outlets in specific locations. ...Exclusive Distribution: Limited outlets.What are the 5 factors of distribution?
Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.
To know more about distribution:
https://brainly.com/question/29062095
#SPJ1
your ultra modern store is one story round. your square footage is 31,415. what is your he diameter of your store? area of a circle =
The solution is D = 200 feet
The diameter of the circular store is = 200 feet
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
Let the diameter of the circle be represented as = D
Let the radius of the circular store be = r
D = 2r
Now , the area of the circular store be = A
The value of A = 31,415 feet²
The area of the circular store is given by the formula
Area of the circle = πr²
Substituting the values in the equation , we get
31415 = 3.1415 x r²
Divide by 3.1415 on both sides of the equation , we get
r² = 10000
Taking square roots on both sides of the equation , we get
r = 100 feet
Now , the diameter of the store = 2 x radius of the store
Diameter of the store D = 2 x 100 feet
Therefore , diameter of the store D = 200 feet
Hence , The diameter of the circular store is = 200 feet
To learn more about circle click :
https://brainly.com/question/28391204
#SPJ1
Given a binomial experiment with the probability of success on a single trial p = 0.80, find the probability that the first success occurs on trial number n = 3. (Round your answer to three decimal places.)
The probability that the first success occurs on trial number n = 3 is 0.032
How to find the probability that the first success occurs on trial number n = 3?Given:
probability of success on a single trial p = 0.80
trial number, n = 3
Recall the formula for the Geometric Probability Distribution
P(n) = p(1 - p)ⁿ⁻¹
where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial
P(n) = p(1 - p)ⁿ⁻¹
P(3) = 0.8(1-0.8)³⁻¹
P(3) = 0.8(0.2)²
P(3) = 0.032
Learn more about binomial probability on:
brainly.com/question/29220138
#SPJ1
