Answer:
10.53
Step-by-step explanation:
hope it helps :)
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1?
1, –0.25, –1.5, –2.75, –4, . . .
1, 2.25, 3.5, 4.75, 6, . . .
4, 2.75, 1.5, 0.25, –1, . . .
4, 5.25, 6.5, 7.75, 8
The sequence that can be defined by the recursive formula is (c) 4, 2.75, 1.5...
How to determine the elements of the recursive definition of f?The function definition is given as
f(1) = 4
f(n + 1) = f(n) - 1.25 for n ≥ 1
Set n = 1
So, we have the following representation
f(1 + 1) = f(1) - 1.25
This gives
f(2) = f(1) - 1.25
So, we have
f(2) = 4 - 1.25 = 2.75
Set n = 2
So, we have the following representation
f(2 + 1) = f(2) - 1.25
This gives
f(3) = f(2) - 1.25
So, we have
f(3) = 2.75 - 1.25 = 1.5
So, we have
4, 2.75, 1.5...
The sequence that matches 2.75, 1.5... in the options is (c) 4, 2.75, 1.5...
Hence, the sequence is (c) 4, 2.75, 1.5...
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Answer:
C
Step-by-step explanation:
Because i got it right
how many ways are there to chose from a team of eleven soccer players: a captain and one alternate captain?
The number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55
A permutation is an act of putting things or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.
Given that soccer player = 11
We have to find in many ways we can choose a captain and one alternate captain from a team of eleven soccer players
Out of 11 player, we have to pick one captain and one alternate captain
nCr ways
nCr = n!/r!(n-r)!
Here n = 11 and r = 2
= 11C2
= 11!/2!(11-2)!
= 11! / 2!.9!
= ((11x 10 x 9!)/2!.9!)
= (11 x 10)/2
= 110/2
= 55
Therefore the number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55
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if the average *arithmetic mean) of 5,6,7 and w is 10 what is the value of w
Using the properties of arithmetic mean and average we get the value of 'w' is 22.
We know that mean is calculated by dividing the sum by the frequency.
Here n= 3
Sum = 5+6+7+w = 18+w
Now , (18+w )/4 = 10 which is the mean
or, 18 + w = 40
or, w = 40 - 18
or, w = 22
The value of w is 22.
By adding together all the observations and then dividing the sum by the same total sample sizes, the arithmetic mean of the supplied data can be calculated.
In order to determine the data's central tendency, an arithmetic mean formula computes the mean, or average, of the numbers. It can alternatively be described as the total number of observations multiplied by the sum of all the observations that were provided.
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Isosceles and Equilateral Triangles !
Study each equation, then solve.
8) 5 + r = 6 - r
9) z - 16 = - 16
10) 7n - 7 = 0
The solution for r in equation 5 + r = 6 - r, r =1/2
The solution for z in equation z - 16 = - 16, z= 0
The solution for n in equation 7n - 7 = 0 , n= 1
(8) 5 + r = 6 - r
Step 1: Rearrange the equation by collecting the like terms
r +r=6-5
Step 2: Simplify r +r=6-5
2r = 1
Step 3: Divide both sides by 2
2r/ 2 =1/2
r =1/2
9) z - 16 = - 16
Step 1; Add 16 to both sides
z-16 +16 = -16 +16
z= 0
10) 7n - 7 = 0
To solve for n
Step 1: Add 7 to both sides
7n - 7 +7 = 0+7
7n =7
Step 2: Divide both side by 7
7n/7 =7/7
n= 1
Therefore, the solution for r in equation 5 + r = 6 - r, r =1/2
The solution for z in equation z - 16 = - 16, z= 0
The solution for n in equation 7n - 7 = 0, n= 1
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you are constructing a cardboard box from a piece of cardboard with the dimensions 4 m by 8 m. you then cut equal-size squares from each corner so you may fold the edges. what are the dimensions (in m) of the box with the largest volume?
The dimensions (in m) of the cardboard box with the largest volume is obtained as 2 m length.
Define the term largest volume?Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.Dimensions of piece of cardboard;
Length = 8 mWidth = 4 m.Let the corner cut length be 'x',
New dimensions;
Length = 8 - 2x Width = 4 - 2xHeight = xVolume = length x width x height
Put the values;
V = ( 8 - 2x ) (4 - 2x) x
Find the solution of the obtained quadratic equation by quadratic formula.
x = 0, 2 and 4.
As, x ≠ 0 and 4.
Thus, x = 2.
Thus, the dimensions (in m) of the box with the largest volume is obtained as 2 m length.
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Members of a lacrosse team raised $1672.50 to go to a tournament. They rented a bus for $1068.50 and budgeted $37.75 per player for meals. Write and solve an equation which can be used to determine
x, the number of players the team can bring to the tournament.
Answer:
x = 16
Step-by-step explanation:
1: Put the numbers into an equation.
(1672.50 - 1068.50) / 37.75x
2: Solve the equation in parentheses.
(604) / 37.75x
3: Divide.
16 = x
Only 16 players can be brought to the tournament
Dominique uses a car service company to travel to work and back home. She uses the same route each way. The company charges a ride fee of $3.00 and $1.25 per mile. Dominique pays $11.75 for transportation each way. Select all of the equations that model the total amount of money Dominique spends on travel each day if her route to work is x miles long.
The equation that model the total amount of money Dominique spends on travel each day if her route to work is x miles long is 3 + 1.25x = 11.75.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Dominique uses a car service company to travel to work and back home.
The company charges a ride fee of $3.00 and $1.25 per mile. The appropriate equation will be:
3 + 1.25(x) = 11.75
where x = number of miles
3 + 1.25(x) = 11.75
3 + 1.25x = 11.75
This illustrates the equation.
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Graph f(z)=-0.25z +4.
The graph of the function f(z) = - 0.25z + 4 is drawn.
What is a Graph?Drawing the graph (curve) of the appropriate function is the process of graphing a function. Although graphing simple functions like linear, quadratic, cubic, etc. is very straightforward, complicated functions like rational, logarithmic, etc. need some expertise and an understanding of certain mathematical principles.
Drawing a function's representation as a curve on a coordinate plane is known as graphing. Every point on a curve (or graph) that represents a function satisfies the function equation.
A collection of edges that are ordered pairings of vertices (also known as directed edges, directed links, directed lines, arrows, or arcs) is displayed
The graph of the function is drawn. On the x-axis, the z-variable variables and on the y-axis the f(z) values are shown.
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What is the slope for the line shown?
The answer choices are -1/3, 8, 3, and -3.
What was the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64
the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64 was $ 68.73
We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:
Xw= Cw/Cm * 100%
Where:
Cw: cost of coverage for a woman of 50 years.
Cm: coverage cost for a 30-year-old man.
Xw= 819.73/1192.64 *100%
= 68.73
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Simplify. (4i+1)^2
show all work
(4i+1)² can be simplified to 8i-15
What is Complex number?A complex number is a number of the form a + bi, where a and b are real numbers
Given expression is (4i+1)²
four times of i plus one whole square.
(4i+1)² can be expanded by using algebraic identity
(a+b)²=a²+b²+2ab
(4i+1)²
Now put a as 4i and b as 1
(4i+1)²=16i²+1+2(4i)(1)
Where i²=-1
=-16+1+8i
=8i-15
Hence (4i+1)² can be simplified to 8i-15
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Write the equation of the circle in standard form that has the following: Center (-5,7) and Radius = 4
Answer:
[tex](x+5)^{2}+(y-7)^{2} =16[/tex]
Step-by-step explanation:
The Standard Form of Circle Equation whose Center is at ( h , k) and Radius of r is given by
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
So for our Question
we have ( h , k ) = ( -5 , 7 ) and r = 4
By substitution
[tex](x-(-5))^{2}+(y-7)^{2} =4^{2}[/tex]
Simplify [tex](x+5)^{2}+(y-7)^{2} =16[/tex]
A certain airline charges a service fee of 7% for each plane ticket purchased. What is the total price the airline charges for a $320 plane ticket?
Answer: $342.40
Step-by-step explanation:
There are two ways you can solve this problem:
Simply turning the percentage to a decimal and multiplying it to the $320.
In the picture provided the method at the top represents you multiplying $320 x .07, You might be wondering “why .07 instead of 7%?” Well, if you were turning this number from a percent to a decimal you would shift the decimal point over to the left 2 times.
And so multiplying $320 x .07 = 22.4 or 22.40. Either way works but without the zero is the way you should write it. And you would add 22.4 to $320 and get $342.40.
Also in the picture provided I used the method of proportions.
Where the total is $320 in this case which you would put next to 100% as 100% means complete or the total. And you would put 7% above 100%. Then, proceed to cross multiply $320 by 7 and it will give you, 2240. Then, you divide it by 100. When you divide it you get 22.40. Then you would add it to $320 and get 342.40.
Answer each question below, showing all work.
A local movie theater is showing a new movie this weekend. The theater sold 144 tickets. Adult
tickets cost $9.00 each and a child's ticket costs $6.00 each. The theater collected $1164.00 from these
ticket sales. How many adult tickets and how many children's tickets were sold? Only an algebraic
solution will be accepted.
Answer:
a=100, c=44
Step-by-step explanation:
# of adult tickets is represented by a
# of child tickets is represented by c
C+A=144
9a+6c=1164
system of equations is solved by solving 1 equation for 1 variable first.
c=144-a
plug in c in the second equation
9a+6(144-a)=1164
9a+864-6a=1164
combine like terms
3a=300
a=300/3
a=100
now we know a is 100 we can plug it into the original equation of c=a=144
c+100=144
c=144-100
c=44
A baseball and softball facility offers batting lessons and fielding lessons to its members. There are 850 members, all of which are registered for at least one lesson. If 80% of members registered for a batting lesson and 56% registered for a fielding lesson, how many members registered for both batting and fielding?
The members who have registered for both batting and fielding are 306.
What is percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
Total members = 850
Number of members registered for batting = 80%
Number of members registered for fielding = 56%
Members who participated in both,
80% of 850 + 56% of 850 - x = 850
680 +476 -x = 850
x = 1156 - 850
x = 306.
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What is the answer to this question?
We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.
Given that,
The linear equation is y=-9x-10.
We have to fill the table given in the question.
First,
Taking x value is -8
We get y value as,
y=-9(-8)-10 (multiply -9 and -8)
y=72-10 (Subtracting 72 and 10)
y=62
When x is -8 y is 62.
Taking y value is -73
We get x value as,
-73=-9x-10
-73+10=-9x
-63=-9x
63=9x
x=63/9
x=7
When y is -73 x is 7.
Taking x value is 3.
We get y value as,
y=-9(3)-10
y=-27-10
y=-37
When x is 3 y is -37.
Therefore, We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.
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18. Write three valid congruency statements given the triangles below.
The three valid congruency statements are; Triangle PQR = Triangle STU
What are congruent angles?Angles who are of same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of same measure, then
[tex]m\angle A = m\angle B[/tex] is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
Congruence statement states that a statement used in geometry that simply says that two objects are congruent, or has the same shape and size.
Also, we can make congruence statements in words or in symbols. Using symbols we use the congruence symbol i,e ≅ to indicate that two objects are congruent.
In the given triangles;
Angle T = Angle Q
QR = ST
TU = PQ
Triangle PQR = Triangle STU reason=ASA
Therefore, the three valid congruency statements are;
Triangle PQR = Triangle STU
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Otis made 1 3/5 cups of oatmeal. He put 2/3 cup of
oatmeal into each bowl. How many bowls of oatmeal
did Otis make? Use equations to solve the problem.
Show your work.
If Otis made [tex]1\frac{3}{5}[/tex] cups of oatmeal and he put 2/3 cup of oatmeal into each bowl, then he made 12/5 bowls of oatmeal
Total quantity of oatmeal that Otis made = [tex]1\frac{3}{5}[/tex] cups of oatmeal
Convert mixed fraction to simple fraction
[tex]1\frac{3}{5}[/tex] cups = 8/5 cups
The quantity of oatmeal in each bowls = 2/3 cup of oatmeal
Then the number of bowls of oatmeal that he made = Total quantity of oatmeal that Otis made ÷ The quantity of oatmeal in each bowls
Substitute the values in the equation
The number of bowls of oatmeal that he made = 8/5 ÷ 2/3
= 8/5 × 3/2
= 12/5 bowls
Hence, if Otis made [tex]1\frac{3}{5}[/tex] cups of oatmeal and he put 2/3 cup of oatmeal into each bowl, then he made 12/5 bowls of oatmeal
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Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Find CG.
Since Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Then CG is 6 in.
What guidelines govern a right triangle?The area of the square whose side is the hypotenuse (the side across from the right angle) in any right triangle equals the sum of the areas of the squares whose sides are the two legs, according to the Pythagorean theorem.
Note that from the question, A triangle's centroid, G, is located 2/3 of the way down one of its medians. We tend must determine the median C's length in order to find CG.
We require the use of Thale's Theorem to get the median length at C. According to this, a right triangle ABC can be encircled by a semicircle with the hypotenuse acting as the diameter.
Therefore, the median C is a point on the semicircle that connects to the diameter of the hypotenuse AB. Since it is connected to the center, median C is a radius. Half of its length, or 18/2, or 9 inches, makes it.
So:
CG is 2/3 down the median, which is:
9 x 2/3 = 6 inches.
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Which table represents an exponential function of the form y = b when 0
Second table represents an exponential function of the form y = b when 0
Define exponential function.A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered. In addition to many other applications, exponential functions are used to estimate populations, carbon date artefacts, assist coroners in determining the time of death, compute investments, and many more. Three of the most popular applications—population expansion, exponential decay, and compound interest—will be covered in this session.
Given,
Second table represents an exponential function of the form y = b when 0
Function: y = bˣ
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Rewrite the point-slope form equation into slope-intercept form.
y+4= -3(x-5)
The slope-intercept form of the equation is
(Type an equation. Use integers or fractions for any numbers in the equation.
The point slope and the intercept form is y = -3x + 11
What is the slope intercept form?One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
This written in the form of y = ax + b
where a is the slope and b is the intercept
We have the equation as
y + 4 = - 3 ( x - 5 )
we would have to open the bracket and then take the like term
this is going to be
y + 4 = -3x + 15
From here we would get the like term
y = -3x + 15 -4
y = -3x + 11
The slope is -3 and the intercept is 11.
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(xy)7 (exponent 7)
—————————
(x²y³)²
please solve quickly!!
i have 2 answers i think it is ,, is it x3y or x6y6?
Answer: (X^3)*y
:) Hope this helps, I spent a lot of time on it!
A store manager instructs some new trainees that a barbecue grill priced at $700 winds up costing a customer $714 once the sales tax is included. What is the sales tax percentage?
Write your answer using a percent sign (%).
Answer:
0.02 or 2%
Step-by-step explanation:
$700(x)=$714
$700(0.02)=14
700+14=714
Simplify the radical expression (3+√6)(3-√6)
Applying the distributive property, the given radical expression can be represented by 15.
Properties of Multiplication
The properties of multiplication are:
Distributive: a(b±c)= ab±ac Commutative: a . b = b. a Associative: a(b+c)= c(a+b) Identity: b.1=bThe question gives [tex](3+\sqrt{6} )(3-\sqrt {6} )[/tex]. Therefore, you should analyze the properties presented previously, and after that, you should identify which was used.
Here, it is possible to see that you can apply the distributive property. See below.
[tex](3+\sqrt{6} )(3-\sqrt {6} )\\ 9-3\sqrt {6} +3\sqrt {6}+6[/tex]
9+0+6=15
Then, the radical expression (3+√6)(3-√6)=15
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DUE TOMORROW PLS HELP!!
does anyone know how to solve the area and perimeter for this parallelogram pls help!!! In details !!!
Answer:
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example
You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).
Step-by-step explanation:
1. (a) What does probability convey about an event's
occurrence? (b) What is the probability of a
random event based on?
a) In any given experiment or trial, there is a probability that either an event occurs or it does not. The probability of the occurrence of an event lies between 0 and 1.
The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. However if the outcome ω is such that, ω ∉ E we say that the event has not occurred.
Let us take the example of playing cards. Here the event E is drawing a face card. If you draw a king of spades, we say the event E has occurred. However, if you draw an eight of clubs, we say the event E has not occurred.
b) The probability of an event is equal to the events relative frequency in the population of possible events that can occur.
An event’s relative frequency is a number between 0 and 1, so the event’s probability is from 0 to 1.
For example, when someone says that the probability it raining today is high, you understand that they mean that there is a high chance that it will rain.
But what if someone says that the probability of something happening is very low? You understand that the person means that the event may not occur at all. In mathematics, we define probability in a similar sense.
What is Probability?
Probability is the measure of uncertainty of any event (any phenomenon happened or bound to happen).
What is event?
In probability, the set of outcomes from an experiment is known as an Event.
What is random events?
An event with a probability of occurrence determined by some probability distribution.
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Find the values of the variables. Then find the side length of the square 
Answer:
x = 4y = 8side length = 4Step-by-step explanation:
You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.
SetupAll sides of the square are the same length. Equating two different y-expressions, we get ...
y -4 = 2y -12
We can use the solution to that to find x:
y -4 = 3x -8
SolutionAdding 12-y to the first of these equations gives us ...
8 = y
Using this value in the second equation, we have ...
8 -4 = 3x -8
12 = 3x . . . . . . add 8
4 = x . . . . . . . . divide by 3
The side length is ...
y -4 = 8 -4 = 4
The values of the variables are x = 4, y = 8, and the side length of the square is 4.
The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.8w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown. graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 1.6 Which of the following statements is true about the graph shown?
The correct statement regarding the proportional relationship c = 0.8w is given as follows:
The equation c = 0.8w is correctly represented by the graph.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
When the two variables x and y are direct proportional, the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k, as follows:
y = kx.
In this problem, the equation is given as follows:
c = 0.8w.
In which:
c is the cost in dollars -> output -> y-axis of the graph.w is the weight in ounces -> input -> x-axis of the graph.For a input of 2, the output is given as follows:
c = 0.8 x 2 = 1.6.
Hence point (1,0.8) is in the graph, along with point (2,1.6).
Missing InformationThe statements are given as follows:
The equation c = 0.8w is correctly represented by the graph.The graph is incorrect and the line should go through the point (0.8, 1).The x-axis and y-axis are labeled incorrectly.The graph does not show a proportional relationship.More can be learned about proportional relationships at https://brainly.com/question/10424180
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a jar contains 4 red marbles numbered 1 to 4 and 8 blue marbles numbered 1 to 8. a marble is drawn at random from the jar. find the probability of the given event. write your answers as reduced fractions. (a) the marble is red your answer is : (b) the marble is odd-numbered your answer is : (c) the marble is red or odd-numbered your answer is : (d) the marble is blue and even-numbered your answer is :