The statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2 for n > 2
How to determine which of the following statements is the recursive definition of f?The function definition is given as
f(n) = -4 +2n for n > 1
Start by calculating f(2), f(3) and f(4)
So, we have
f(2) = -4 +2(2)
f(2) = 0
f(3) = -4 +2(3)
f(3) = 2
f(4) = -4 +2(4)
f(4) = 4
In the above computation, we can see that the sequence is an arithmetic sequence with a common difference of 2
So, we have
f(n) = f(n - 1) + 2
Also, we have
f(1) = -4 +2(1)
f(1) = -2
Hence, the statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2 for n > 2
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A set contains 23 elements set B contains 15 elements, and 13 elements are common to sets A and B how many elements are in set A
A contains 21 elements
Let's assume set A contains X elements ,
so , according to set theory , A ∪ B = 23
or, A + B - ( A ∩ B ) = 23
or ,X + 15 - 13 = 23
or, X + 2 = 23
or , X = 23 - 2
or, X = 21
So , there are 21 elements are present in set A .
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Solving the problem according to the set theory, we get that set A contains 21 elements.
A set is a well-defined collection of objects, whose elements remain fixed and do not vary. It means that set doesn't change from person to person and is invariable.
Let's assume that set A contains X elements,
So, according to the set theory, A ∪ B = 23
or, A + B - ( A ∩ B ) = 23
or ,X + 15 - 13 = 23
or, X + 2 = 23
or , X = 23 - 2
or, X = 21
From the above explanation, we get that there are 21 elements are present in set A .
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help pls its algebra quick
Answer:
B
Step-by-step explanation:
Graph is positive and y intercept is on negative 2.
joe and millie each have some baseball cards, and ¾ of the number of cards joe has is equal to 2/3 of the number of cards millie has. what is the least number of cards they could have altogether?
So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.
What is an integer?
A whole number that can be either positive, negative, or zero is known as an integer.Let Joe has x no. of cards,
then,
Millie has (3/4)x cards.
In that case, Let millie has a total y no. of cards,
then, Joe has (2/3) y cards.
This means that,
(3X)/4 = (2Y)/3
The alternate form shall be:
X = (8 Y)/9
(3 X)/4 - (2 Y)/3 = 0
Real solution:
Y=(9X)/8
Integer Solution shall be:
X=8n, Y=9n, n∈Z, where Z is the set of integers.
So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.
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Paul runs a small farm. After the last harvest, he weighed the amount of squash he collected. He had 42.2 total pounds of green and yellow squash. If yellow squash made up 1 5 of the harvest by weight, how many pounds of green squash did he have? Write your answer as a whole number, decimal, fraction, or mixed number. Simplify any fractions.
The weight of the green squash is 33.76 pounds.
What is the weight of the green quash?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/4. A decimal is a non-integer that is made up of integers and non-integers that are separated by a decimal point. An example of a decimal is 1.2.
The weight of the green squash can be determined by multiplying the fraction of the green quash by the total pounds of green and yellow squash.
Pounds of green squash = fraction of green squash x total pounds of squash
Fraction of green squash = 1 - 1/5 = 4/5
Pounds of green squash = 4/5 X 42.2 = 33.76 pounds
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PLEASE HELP ME ITS DUE IN 10 MINUTES (I'm in 5th BTW!!!)
Answer:
1st box: 2000
2nd box: 1
3rd box: 22.99
4th box: 0.11
5th box: 23
Step-by-step explanation:
It's simply splitting up the 2000 and 1, and then diving them by 87 each.
After that you can divide them and round to the nearest 10th, and add them to get 23.
coach ferguson uses a thermometer to measure the temperature (in degrees fahrenheit) at 20 different locations in the school swimming pool. an analysis of the data yields a mean of 77 degrees fahrenheit and a standard deviation of 3 degrees fahrenheit. recall that ∘c
1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.
2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.
1) Let, X be the temperature in Fahrenheit and Y be the temperature in Celsius.
Mean = 77° F
[tex]77^\circ \ F=\frac{5\times77}{9}-\frac{160}{9}[/tex]
[tex]= 25^{\circ}C[/tex]
Variance in Fahrenheit is [tex]3^2=9[/tex]
[tex]Var(aX+b)=a^2VarX[/tex]
Here, [tex]a=\frac{5}{9}[/tex] and [tex]b=-\frac{160}{9}[/tex]
[tex]Var(Y)=\frac{25}{81}\times9[/tex]
[tex]=2.77[/tex]
Standard deviation [tex]= \sqrt{Var(X)[/tex]
[tex]= \sqrt{2.77}[/tex]
[tex]= 1.66^{\circ}[/tex]
2) Let, X be the cost of them meal and Y be the tip he gives.
[tex]Y=2+0.1X[/tex]
[tex]E[X]=9, Var[X] = 9[/tex]
Therefore,
[tex]E[Y]=E[2+0.1X][/tex]
[tex]=0.1E[X]+2[/tex]
[tex]=0.1\times9+2[/tex]
[tex]=1.1[/tex]
[tex]Var[Y] = 0.12Var[X] = 0.01\times9=0.09[/tex]
Standard deviation of [tex]Y = \sqrt{Var[Y]}[/tex]
[tex]= \sqrt{0.09}[/tex]
[tex]= 0.3[/tex]
Therefore,
1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.
2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.
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"Your question is incomplete, probably the complete question/missing part is:"
Coach Ferguson uses a thermometer to measure the temperature (in degrees Fahrenheit) at 20 different locations in the school swimming pool. An analysis of the data yields a mean of 77 degrees Fahrenheit and a standard deviation of 3 degrees Fahrenheit. Recall that [tex]C^{\circ}=\frac{5^{\circ}F}{9} -\frac{160}{9}[/tex]. What is the mean temperature reading in degrees Celsius? What is the standard deviation of the temperature readings in degrees Celsius? When Sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. If Sam's distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of his tip distribution?
The man has 2 he loses one how many does he have left
Answer:
1
Step-by-step explanation:
If a person has 2 apples and gives someone 1 which is 2-1=1
how to solve if 5a=6 and 7b=8, 35ab=
(please explain, i need explaination)
Answer:
35ab = 48
Step-by-step explanation:
given
5a = 6 ( divide both sides by 5 )
a = [tex]\frac{6}{5}[/tex]
and
7b = 8 ( divide both sides by 7 )
b = [tex]\frac{8}{7}[/tex]
substitute these values for a and b into the expression and simplify
35ab
= 35 × [tex]\frac{6}{5}[/tex] × [tex]\frac{8}{7}[/tex] ( divide 35 and 5 by 5 )
= 7 × 6 × [tex]\frac{8}{7}[/tex]
= 42 × [tex]\frac{8}{7}[/tex] ( divide 42 and 7 by 7 )
= 6 × 8
= 48
Which equation represents a line through (4, -6) and (0, 2)?
Answer: C
Step-by-step explanation: Substitute four and zero in each of the choices and see if the sum becomes negative six and two, respectively. If it does, then the equation represents the line.
Third equation substitution:
x = 4
y = -2(4) + 2
y = -8 + 2
y = -6
x = 0
y = -2(0) + 2
y= 0 + 2
y = 2
Therefore, the answer is C.
Note: I skipped to the third equation because the other equations are false.
PLS HELP
ANSWER QUESTION QUICK
PLEASE SHOW WORK
Which expression is equivalent to 1/3 (2x + 12) - 14/15
A: 1 3/5x + 4
B: 4/15x - 4
C: -4/15x - 4
D: -4/15x + 4
Answer:
D.
Step-by-step explanation:
First distribute:
2/3x + 4 -14/15x
2/3 = 10/15
10/15-14/15=
-4/15
-4/15 + 4
4(4 – 12x) – 2(x – 12) + 5x = –50?
The value of x of the given equation is 2.
What is equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The given equation is
4(4 – 12x) – 2(x – 12) + 5x = –50
We have to find the value of x.
According to given question we have
4(4 – 12x) – 2(x – 12) + 5x = –50
Rearrange terms we get,
4(– 12x+4) – 2(x – 12) + 5x = –50
Distribute we get,
-48x+16-2x+24+5x=-50
Compare the like terms we get,
-45x=-50-40
-45x=-90
x=2
Therefore, the value of x of the given equation is 2.
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cos x + sin x tan x = sec x
Answer:
Dear Friend
To prove the given equation
2. If freezing rain is falling, then the air temperature is 32°F or less.
Converse:
Inverse:
Contrapositive:
Answer:
Converse: If the air temperature is 32°F or less, then freezing rain is falling.
Inverse: If freezing rain is not falling, then the air temperature is not 32°F or less.
Contrapositive: If the air temperature is not 32°F or less, then freezing rain is not falling.
Explanation:
Statement: If p, then q.
Converse: If q, then p.
Inverse: If not p, then not q.
Contrapositive: If not q, then not p.
50 points mathamatics last question for the day
10² = 100
28.007 × 100 / 2800.7
third option = 2,800.7
Answer: The answer is within the picture!
Step-by-step explanation:
an image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor.the actual book is 10.5 inches wide.what scale is being used on the image?
The scale that is being used on the image is 1:7
Calculating scaleFrom the question, we are to determine the scale that is being used on the image.
From the given information,
The image of the book shown on the website is 1.5 inches wide and 3 inches tall
Also, we have that
The actual width of the book is 10.5 inches
The scale = Width of the book on the website / Actual width of the book
Thus,
Scale = 1.5 inches / 10.5 inches
Scale = 1/7
∴ Scale = 1 : 7
Hence, the scale that is being used on the image is 1:7
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Which number is Irrational?
a
square root 9
b
0.123123123....
c
5/9
d
0.2535455565....
Answer:
Step-by-step explanation:
d. Square root of 9
you’re welcome :)
The irrational number is 0.2535455565.....
The correct option is D.
Given, that identify the irrational number.
Irrational number : Irrational numbers are non terminating and non repeating.
1) Square root of 9: √9
= 3
It is rational number.
2) Number : 0.123123123....
It is Non terminating but repeating thus it is not an irrational number.
3) Fraction : 5/9
5/9 = 0.555555..
It is a repeating number thus its is not an irrational number.
4) Number: 0.2535455565....
The number is non terminating as well as non repeating. Thus it is an irrational number.
Therefore option D is correct.
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WRITING A quadratic function is increasing on (- ∞ ,2) and decreasing on (2, ∞). Is the vertex the highest or lowest point on the parabola? Explain.
The vertex of the parabola of the quadratic function that is increasing in the interval (-∞, 2), and decreasing in the interval (2, ∞), is the highest point on the parabola.
How can the type of vertex be found from the description of the quadratic function?The given description of the quadratic function is presented as follows;
The interval the function is increasing = (-∞, 2)
The interval the function is decreasing = (2, ∞)
The graph of the function is therefore increasing from -∞ up to the point just before 2.
The graph of the function is decreasing from the point just after 2 to infinity.
The point 2 is therefore the highest point of the graph and also, the vertex of the quadratic function.
Therefore;
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the greatest of the 21 positive integers in a certain list is 16. the median of the 21 integers is 10. what is the least possible average (arithmetic mean) of the 21 integers?
The least possible average (arithmetic mean) of the 21 integers is 6.
Let the list be arranged in ascending order.The median of the list, i.e., the 11th term in the list, is 10.The greatest number in the list, i.e., the 21st term, is 16.We need to minimize the mean, so we will choose the smallest numbers.For the first 10 elements, we can choose the smallest positive integer, i.e., 1.The first 10 terms are all equal to 1.We must choose numbers greater than or equal to 10 for elements 12 to 20. We will choose 10 in order to keep the average at its minimum.The terms from the 11th to the 20th position are equal to 10.The 21st term is 16.The sum of all the terms is (1*10) + (10*10) + 16.The sum of all the terms is 10 + 100 + 16.The sum of all the terms is 126.The mean is calculated as the sum of all terms divided by the total number of terms.The mean is 126/21.The mean is 6.To learn more about the arithmetic mean, visit :
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Dana saved 450 for food for her upcoming vacation. the breakfast was included with their hotel, but lunch and dinner are not. when dana cooks lunch or dinner it costs on average 10 . when the family goes to a restaurant for lunch or dinner it costs on average 40 . what is the maximum number of meals the family can eat at a restaurant.
The maximum number of meals the family can eat at the restaurant is 11
Amount saved by Dana for her upcoming vacation = 450
Average cost when Dana cooks lunch or dinner = 10
Average cost when the family goes to a restaurant for lunch or dinner = 40
Maximum number of meals the family can have at the restaurant = Amount saved by Dana/Average cost of a meal when the family goes to a restaurant
=450/40
= 11.25 or 11
So, the maximum number of meals the family can eat at the restaurant is 11 with a budget of 450.
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The Daily Smile store sells bouquets in which 2 out of 5 are white. How many total daisies are there if 8 daisies are white?
a state park charges $5 per car plus $1 per person as an admission fee. the total charged for a car with x people is f(x)
Answer:
the total charged for a car is f(x)=x+5
Step-by-step explanation:
because ther is only on car the value 5 could be constant. but because there could be a number of people in the car that is described by x and is multiplied by the cost which is 1
Brooke and her mom are 21 years apart in age. The sum of their ages I'd 49. How old are Brooke and her mom
Answer: her mom is 35 and she is 14.
find the area of a cylinder with a height of 8 inches and base radius of 4 inches
A recipe had 4 tablespoons of seasoning to 6 cups of flour. So there is _____ of a tablespoon of seasoning for each cup of flour.
Answer:
Step-by-step explanation:
The ratio of seasoning to flour is 4:6.
This can also b re-written as a fraction. The fraction would be 4/6.
If you want to find the amount of seasoning per cup of flour, you must divide.
4/6 Divide the denominator (bottom number) by 6 to get a 1 on the bottom. Now divide the numerator (top number) be the same amount. This gives you a 0.66 on the top. Now you have 0.66/1.
0.66 is equivalent to 2/3, so for every 1 cup of flour, there is 2/3 a tablespoon of seasoning.
Hope this helps!
ill give uu crown if you answer this for me
Answer:
Given,points (0,3)and(10,8)
Step-by-step explanation:
slope(m)=
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
=
[tex] \frac{8 - 3}{10 - 0} [/tex]
=
[tex] \frac{5}{10} [/tex]
=
[tex] \frac{1}{2} [/tex]
The slope is 1/2.
If the answer is correct please mark brainliest
A bag of oranges costs 6.40 dollars there are 16 oranges in each bag what would be the cost of 48
Answer:
Step-by-step explanation:
bag of oranges = $6.40
each bag = 16 oranges
48 divided by 16 = 3 (bags)
$6.40 x 3= $19.20
The cost of 48 oranges would be $19.20 when the each cost 6.4
Given:
- Cost of a bag of oranges = $6.40
- Number of oranges in each bag = 16
First, let's find the cost per orange:
Cost per orange = Cost of a bag / Number of oranges in the bag
Cost per orange = $6.40 / 16 = $0.40
Now, the cost per orange is $0.40.
To find the cost of 48 oranges, multiply the cost per orange by the number of oranges:
Cost of 48 oranges = $0.40 * 48 = $19.20
Therefore, the cost of 48 oranges would be $19.20.
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0.6244 in scientific notation
Answer:
6.244 x 10^-1
Step-by-step explanation:
The sum of three lengths of a fence ranges from 45 to 60 inches. Two side lengths are 9 and 18 inches. If the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side.
a. 9 ≤ x ≤ 18
b. 18 ≤ x ≤ 33
c. 36 ≤ x ≤ 42
d. 45 ≤ x ≤ 60
The solution to a compound inequality to show the possible lengths of the third side is 18 ≤ x ≤ 33.
What is Compound Inequality?Two or more inequalities are connected together with or or and to form a compound inequality (also known as a combined inequality).
A value must only make one aspect of an inequality true in order to be the solution to an or inequality. An inequality's solution must make both portions true in order to be effective.
According to the given values;
given parameters are
Range = 45 to 60 inches
Sides = 9, 18 and x
The sum of the three sides is
sum=9 + 18 + x
Evaluate
Sum = 27 + x
Recall that
Range = 47 to 60 inches
So, we have
45 ≤ 27 + x ≤ 60
Subtract through by 27
So, we have
18 ≤ x ≤ 33
Hence, the solution to a compound inequality to show the possible lengths of the third side is 18 ≤ x ≤ 33.
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consider the question: what is the probability of getting a 7-card poker hand (order doesn’t matter) that contains at least two 3-of-a-kind (3-of-a-kind means three cards of the same rank). for example, this would be a valid hand: ace of hearts, ace of diamonds, ace of spaces, 7 of clubs, 7 of spades, 7 of hearts and queen of clubs. (note that a hand consisting of all 4 aces and three of the 7s is also valid.)
The probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013
For given question,
We need to find the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind.
Total number of cards = 52
If a 7-card poker hand contains at least two 3-of-a-kind,
3-of-a-kind means the three cards of the same rank.
The expression for the probability is,
[tex]P=\frac{ ^7C_3}{ ^{52}C_4} +\frac{ ^7C_2}{ ^{52}C_5} +\frac{ ^7C_1}{ ^{52}C_6}\\\\P=0.0013[/tex]
So, the required probability is 0.0013
Therefore, the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013
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