Answers
The domain and the range of the graph in interval notation are (-∝, ∝) and [-3, ∝) respectively
What is the domain and the range of a function?The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.
How to determine the domain and the range of the function?The graph represents the given parameter
Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph
On the graph, we can see that:
The x values extend indefinitely on the graph;
This means that the domain is (-∝, ∝)
While y values start from -3 and increases up
This means that the range is [-3, ∝)
Hence, the domain and the range of the function in interval notation are (-∝, ∝) and [-3, ∝) respectively
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Related Questions
My thermometer has a percent error of 3%. The actual temperature is 75°F.
Will the thermometer show the temperature at 72.00 °F or 78.00 °F?
Answers
The thermometer show the temperature at 73°F when there is a percentage error.
How to calculate the value?From the information, the thermometer has a percent error of 3% and the actual temperature is 75°F.
Therefore, the temperature down on the thermometer will be:
= 75 - (3% ×75)
= 75 - 2.25
= 72.75
= 73 approximately.
Therefore, the thermometer show the temperature at 73°F when there is a percentage error.
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What are the values of a and r of the geometric series?
2-2+2-2+2
Answers
The given geometric series, the first term is a₁ = 2 and the common ratio is r = -1
What are some examples of geometric series?
In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward illustration and converges to a sum of 2. (or 1 if the first term is excluded).We are given to find the values of a₁ and r of the following geometric series
2 - 2 + 2 - 2 + 2 - ........
We know that
a₁ is the first term and r is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
a₁ = 2
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio r of the given geometric series is
r = -2/2 = 2 / -2 = ...... = -1
Thus, for the given geometric series, the first term is a₁ = 2 and the common ratio is r = -1.
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Consider the sequence of real numbers
[tex] \rm a_1 = \frac{ log_{2}( {3}^{2} ) }{ log_{3}(2) } ,a_2 = \frac{ log_{ {3}^{3} }( {4}^{4} ) }{ log_{ {4}^3}( {3}^{4} ) } ,a_3 = \frac{ log_{ {4}^5 }( {5}^{6} ) }{ log_{ {5}^{5} }( {4}^{9} ) }, \dots[/tex]
In general, [tex] \rm a_k = \frac{ log_{(k + 1) ^{(2k - 1)} } ((k + 2 {)}^{2k}) }{log_{(k + 2) ^{(2k - 1)} } ((k + 1 {)}^{ {k}^{2} })} [/tex]
Let [tex] \rm P_n = \frac{ log_{ {(n + 1)}^{(2n - 1)} }( {2}^{2n} ) }{ log_{ {2}^{(2n - 1)} }((n + 1) {}^{ {n}^{2} } )} \cdot \prod \limits_{k = 1}^{n - 1} a_k[/tex] for integer n [tex]\geq [/tex] 2.
[tex] \rm Find \sum \limits_{n = 2}^{ \infty } P_n[/tex]
Answers
Use the change-of-base identity and the exponent property for logarithms.
[tex]\log_b(a) = \dfrac{\log_c(a)}{\log_c(b)} \implies \log_b(a) = \dfrac1{\log_a(b)}[/tex]
[tex]\log_c(a^b) = b \log_c(a)[/tex]
This lets us rewrite
[tex]\log_{(k+1)^{2k-1}} (k+2)^{2k} = \dfrac{2k}{\log_{k+2}(k+1)^{2k-1}} = \dfrac{2k}{(2k-1) \log_{k+2}(k+1)}[/tex]
[tex]\log_{(k+2)^{2k-1}} (k+1)^{k^2} = \dfrac{k^2}{\log_{k+1} (k+2)^{2k-1}} = \dfrac{k^2}{(2k-1) \log_{k+1}(k+2)}[/tex]
It follows that
[tex]a_k = \dfrac2k \dfrac{\log_{k+2}(k+1)}{\log_{k+1}(k+2)} = \dfrac2k \left(\ln^2(k+1)}{\ln^2(k+2)}[/tex]
so that the product of [tex]a_k[/tex] telescopes:
[tex]\displaystyle \prod_{k=1}^{n-1} a_k = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(2)}{\ln^2(3)}\cdot\frac{\ln^2(3)}{\ln^2(4)}\cdot\frac{\ln^2(4)}{\ln^2(5)} \cdots \frac{\ln^2(n-1)}{\ln^2(n)} \cdot \frac{\ln^2(n)}{\ln^2(n+1)} \\\\ ~~~~~~~~ = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(n+1)}{\ln^2(2)}[/tex]
We can similar reduce the coefficient of [tex]P_n[/tex] to write
[tex]\log_{(n+1)^{2n-1}}(2^{2n}) = \dfrac{2n}{(2n-1) \log_2(n+1)}[/tex]
[tex]\log_{2^{2n-1}}(n+1)^{n^2} = \dfrac{n^2}{(2n-1)\log_{n+1}(2)}[/tex]
[tex]\implies \dfrac{\log_{(n+1)^{2n-1}}(2^{2n})}{\log_{2^{2n-1}}(n+1)^{n^2}} = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)}[/tex]
Then the expression for [tex]P_n[/tex] reduces significantly to
[tex]P_n = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)} \cdot \dfrac{2^{n-1}}{(n-1)!} \dfrac{\ln^2(n+1)}{\ln^2(2)} = \dfrac{2^n}{n!}[/tex]
and we ultimately find
[tex]\displaystyle \sum_{n=2}^\infty P_n = \sum_{n=0}^\infty \frac{2^n}{n!} - \frac{2^1}{1!} - \frac{2^0}{0!} = \boxed{e^2 - 3}[/tex]
where we recall the power series
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]
xy + 8
Click on the correct answer.
monomial
binomial
trinomial
Answers
Answer:
Binomial
Step-by-step explanation:
There are only 2 terms
The circumference of a circle is 30. What is its area?
Answers
2 pi r is circumference.
a =c^2 / 4pi = 30^2 / 4 * pi = 71.619
Answer:
71.62
Step-by-step explanation:
[tex]A = \frac{C^2}{4 \times \pi }\\A = \frac{30^2}{4 \times 3.14 }\\A = 71.62[/tex]
PLEASEEEE HELPPP!!!! THIS IS DUE ON WEDNESDAY
Jeri bought 32 cookies and 56 slices of pizza for his sisters birthday. Each guest will receive the same number of cookies and pizza, with nothing left over. If Jeri wants to invite the greatest number of guests, how many cookies will each guest receive?
Answers
Reason:
32 = 8*4
56 = 8*7
We see that 8 is the largest common factor, aka GCF, of 32 and 56
So this is the greatest number of guests possible.
Each guest will get 32/8 = 4 cookies and 56/8 = 7 slices of pizza.
WILL GIVE BRAINLIEST
Answers
Answer:
a. = 1
b. = 0
c. = 2
d. = 7
Hopefully this helps
Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s =
Answers
The required value of the standard deviation is 0.04.
Given that,
1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers is to be determined. Where s = 5
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
1 miles = 1.60934 Km
Given
1 mile = 1.6
Standard deviation = 1.60934 - 1.6000
= 0.00934
S = 5
Standard deviation = 5 * 0.00934
= 0.04670
Thus, the required value of the standard deviation is 0.04.
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You are saving for a skateboard. Your aunt gives you $45 to start, and you save $3 each week. The expression 45 + 3w gives the amount of money you save after w weeks. How much will you have after six weeks?
Answers
Answer: $63
Step-by-step explanation:
so you put 6 where the w is to find out the answer
45+3(6)=45+18=63
The midpoint of AB is M (2, -2). If the coordinates of A are (8, 1), what
are the coordinates of B?
Answers
b. Write the set of natural numbers greater than 22 using the most concise method.
(Use a comma to separate answers as needed.)
A. The set of numbers is {}
B. The set of numbers is {x|XEN and x> }}
C. The set of numbers is {x|XEN and x< }
D. The set of number is {xXEN and x =}
Answers
The set of numbers is S = { x ∈ N ; x > 22 }.
We have the statement:
Set of natural numbers greater than 22.
We need to make the set from it.
A set is a collection of different things objects or elements that are used to represent a situation or a function in a concise form.
For example a set of real numbers can be denoted by x ∈ R.
There can be finite or infinite sets. In finite sets, the number of elements are limited whereas in infinite sets it is not limited.
Here, the set that will be formed can be written as:
S = { x ∈ N ; x > 22 }
Therefore, the set of numbers is S = { x ∈ N ; x > 22 }.
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4. Communicate Precisely What does it mean for a figure to have 60° rotational symmetry?
Answers
It means that if you rotated the figure 60 degrees (clockwise or counterclockwise) about its center, then the figure does not change.
The "before" and "after" are identical. In other words, the preimage and image are the same.
Apple weights in an orchard are normally distributed. From a sample farmer Fred determines the mean weight of a box of apples to be 270 oz. with a standard deviation of 10 oz. He wonders what percent of the apple boxes he has grouped for sale will have a weight less than 255 oz.
Answers
Carl calculates the z-score corresponding to the weight 255oz= -1.5.
Now, Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.
Given that,
In an orchard, apple weights are typically distributed. Fred the farmer concludes from a sample that the average weight of a box of apples is 270 ounces, with a standard deviation of 10 ounces.
He is interested in knowing what proportion of the apple boxes he has gathered for sale will weigh less than 255 oz.
Mean is 270
Standard deviation is 10
x = 255
Formula for z-score,
z = (x - mean)/SD
z = (255 - 270) / 10
=> z = -15 / 10
=> z = -1.5
Hence, by using z-table,
-1.5 equates to 0.0668, which suggests that 0.07
Therefore, 7% of Apple boxes weigh less than 255 oz.
The ratio of boxes is between 255 oz and 270 oz,
Calculating the proportion
Now,
50% - 7% = 43%.
Therefore, Carl calculates the z-score corresponding to the weight 255oz= -1.5.
Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.
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For some linear relationships, doubling the independent variable results in doubling the function value. For example, doubling the number of steps in a staircase doubles the height of the staircase. Does this doubling property hold for every linear relationship?
Answers
Using linear function concepts, it is found that this doubling property does not hold for every linear relationship.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.One example of function is:
y = 4x + 3.
When x = 1:
y = 4 + 3 = 7.
When x = 2:
y = 8 + 3 = 11.
The input did not double, meaning that this doubling property does not hold for every linear relationship, it doubles only for a linear function with a slope of 2 and intercept of 0.
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Jim gross pay for the week. wad $987.00 how much was taken from his check for FICA taxes?
Answers
The amount taken from Jim's check for FICA taxes is $75.51.
What are FICA taxes?FICA (Federal Insurance Contributions Act) taxes are of two types: Social Security tax and Medicare tax.
FICA taxes simply mean United States federal payroll (or employment) taxes imposed on both employees and employers. The purpose of FICA taxes is to fund Social Security and Medicare.
These two federal programs benefit retirees, the disabled, and the children of deceased workers.
The rate for the Social Security tax is 6.2% of the taxpayer's gross pay.
The rate for the Medicare tax is 1.45% of the income earner's gross pay.
The FICA taxes rate is 7.65%.
Data and Calculations:Gross pay for the week = $987
FICA taxes = 7.65%
FICA taxes in dollars = $75.51 ($987 x 7.65%)
Thus, the amount Jim paid in FICA taxes is $75.51.
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Need help with This assignment asap will mark brainless
Answers
Answer:
Hello,
Answer: B : y=(m-3)*(x+1)²3
Step-by-step explanation:
The parabola with vertex (-1,3)
is y=k(x+1)²+3
(0,m) is a point of the parabola:
m=k*(0+1)²+3 ==> k=m-3
So, y=(m-3)*(x+1)²+3 is the correct equation.
What do you call a row of large animals separating two yard
Answers
Answer: The answer is play on words, or a pun - a row of large animals separating two yards is called an elefence.
Step-by-step explanation: The first part of the word, ele-, obviously refers to elephants, which are large animals. The second part is a fence, which separates two yards. So this is intended to have a humorous effect (I got this from go.ogle....)
If two out of every fifteen trick-or-treaters that came to your house last Halloween were dressed as Spiderman, what proportion of trick-or-treaters were not dressed as
Spiderman?
Answers
The proportion of trick-or-treaters that were not dressed as Spiderman will be 131/15.
How to calculate the value?From the information, two out of every fifteen trick-or-treaters that came to the house last Halloween were dressed as Spiderman.
Therefore the fraction is represented as 2/15.
Therefore, the proportion of trick-or-treaters that were not dressed as Spiderman will be:
= 1 - 2/15
= 13/15.
Therefore, the proportion of trick-or-treaters that were not dressed as Spiderman will be 131/15.
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Which set of points represents a nonlinear function?
A (-3,-6) (0,1) (3,8)
B (-2,2) (0,0) (2,2)
C (0,4) (3,3) (6,2)
D (8,0) (9,1) (10, 2)
Answers
Answer:
The answer would be B.
Step-by-step explanation:
(-2,2)(0,0)(2,2) represents a nonlinear function.
Find the circumference and the area of a circle that has a
diameter of 14 centimeters. For each, give the exact answer
and an approximation to the nearest hundredth.
[Section 9.8]
Answers
Answer:
circumference=44cm
44cn
Area=154cm
200cm
A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets.
Answers
The equation that states the sum of the tickets sold is -
30x + 45y = 60900.
We have concert promoter.
We have to write an equation that states that the total amount received from the sale, which is 60,900 dollars.
What is Equation Modelling ?The equation modelling is a process of writing a mathematical equation from a mathematical statement involving variables, constants etc.
According to the question -
Money earned from $30 tickets = $30x
Money earned from $45 tickets = $45y
Total money from 1780 tickets = $60,900
Therefore -
30x + 45y = 60900
Hence, the equation that states the sum of the tickets sold is -
30x + 45y = 60900.
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[ The given question is incomplete, the complete question is
A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets. Write an equation that states that the total amount received from the sale is 60900 dollars.]
please help
please hurry
Answers
PLA HELP I WILL GOVE BRAINLIEST
Find the x-intercept and the y-intercept of each line. Express the answers as ordered
pairs.
y = 5x-10
x-intercept is
y - intercept is
Answers
Answer:
the answer is x intercept is 8 and the y intercept is 10
what Robert decided to buy half a dozen mangoes priced at $0.15 each.he gives $20 to the cashier.how much change should he receive
Answers
The profit or loses change should he receive is $19.5
Given,
The price of Dozen of mangoes is $.15
Robert gives $20
The change should be is $20-$.15 =$19.5
When a person buys an item at one price and later sells it at a different one, he either earns a profit or loses money. There are several phrases that are involved with the complete transaction procedure. For instance, cost price (C.P. ), selling price (S.P. ), discount, marked price, profit, and loss. Let us go through the definitions of these terminologies one by one.
Price Cost
For example, if Neil purchased an umbrella for $8, the cost price of the umbrella is $8. The abbreviation is C.P.
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You have a drawer with 7 different pencils. Each pencil is a different color (red, blue, white, green, pink, black, and yellow). If you take a pencil out of the drawer, it is green, and do not put it back, what is the probability that the next pencil is pink?
Answers
Answer:
1 in 6
Step-by-step explanation:
The probability of getting the original green is 1 in 7 (1 green pencil and 7 total)
If you take it out, there will be 6 pencils left
Hello can you help me with this please
Answers
Answer:
Q1: Plane
Q2: Point
Q3: line
I hope this helps!
I’m stuck in this one
Answers
Answer:
Step-by-step explanation:
90 - 65 = 25
x = 25 degrees
90 - 25 = 65
y = 65 degrees
AB=[1+4.5]=5.5 describe and correct
Answers
The required solution is correct. AB = 5.5.
Given that,
AB=[1+4.5]=5.5
To describe the expression and to determine whether the expression is correct or not.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
Simplifying the given expression, AB = 1 + 4.5
AB = 1 + 4.5
Addition property of alike terms
AB = 1.00 + 4.50
AB = 5.50
AB = 5.5
Thus, the required solution is correct. AB = 5.5
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Which of the following is true about parallel lines? Select all that apply.
*
They will never cross.
They have the same slope.
Their slopes are opposite reciprocals.
They will cross at a right angle.
They are in the same plane.
Answers
The statements which are true about parallel lines are;
They will never cross.They have the same slope.They are in the same plane.What are parallel lines?Parallel lines in their simplest description are lines which would never meet or cross each other under any circumstance.
Also, It follows from line geometry that such lines have the same slope and are coplanar, exist in the same plane.
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Please help me is this problem <, >, or =
Answers
[tex] \sqrt{15} \approx3.873\\ \\ \sqrt{15} < 3.9[/tex]
since 15 square root equals 3.87 it is less than 3.9
