3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence.Formulas:
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A sequence is called arithmetic if the difference between two consecutives is a constant
In the first case we see a constant difference of 5
every two consecutives have difference of 5, for example 20-15, 30-25 and so on.
In the second case we see the division between two consecutives is a constant . That is called a GEOMETRIC sequence.
the constant in this case is 18/6 =3
lets return to the 1st case find the explicit
An = Ao +(n-1) d
An means the n term in the sucession
Ao means the first term
d means the constant
with that in mind we replace the values obtained
An= 5 + (n-1) •5
now for the recursive
a1= 5
An = An-1 + 5
Now lets go to the second part, the geometric sequence. Just is needed to replace the values in the ABOVE RIGHT formula
so then
An = A1 •(3)^(n-1)
An = 2• (3)^(n-1)
Related Questions
Make a tree diagramPlease be quick, I am in a hurry.
Answers
Explanation
The question wants us to obtain all the outcomes possible when a coin and a cube is tossed
A coin has two possible outcomes
[tex]\mleft\lbrace\text{Head, Tail}\mright\rbrace[/tex]A cube has 6 surfaces, so the outcomes are
[tex]\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Thus, we can have the diagram showing the outcomes to be
What function makes the HIV virus unique?
Answers
The function which makes the HIV virus unique is: B. It has viral DNA that is transmitted through indirect contact with infected persons.
HIV is an acronym or abbreviation for human immunodeficiency virus and it refers to a type of venereal disease that destabilizes and destroys the immune system of an infected person, thereby, making it impossible for antigens to effectively fight pathogens.
Generally, the high mutation or replication rate of the human immunodeficiency virus (HIV) owing to its enormous genetic diversity (deoxyribonucleic acid - DNA) makes it easily transmittable from an infected person to another.
This ultimately implies that, the HIV virus is unique among other viruses because it can be transmitted without having a direct contact with an infected person such as:
Sharing a hair clipper with him or her.
Using an object that has been infected by a HIV patient.
Additionally, it is extremely difficult to develop an effective and accurate vaccine against the HIV virus because it possesses a high error rate.
the Missing Angles (plus angle review)<8 of 16Whats the measure of each of the angle in degrees? Label the angles, then answer,Subm104056°
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A is angle opposite by the vertex with the angle of 104 degrees, that is why it also measure 104 degrees
The three inner angles of any triangle add 180 degrees, then 56 + A + B = 180
Solving for B: B = 180 - 56 - A = 180 - 56 - 104 = 20
assume the rate of inflation is 7% per year for the next 2 years. what will be the cost of goods 2 years from now adjusted for inflation if the goods cost $330.00 today? round to the nearest cent
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To find the cost of the goods after two years we are going to use the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the cost now, r is the inglation rate in decimal form, n is the number of times the interest is taken per year and t is the time.
In this case we have P=$300.00, r=0.07, n=1 (once per year) and t=2 (two years). Plugging this values we have:
[tex]A=330(1+\frac{0.07}{1})^{1\cdot2}=377.82[/tex]Therefore after two years the cost will be $377.82
Sketch the vectors u and w with angle θ between them and sketch the resultant.|u|=20, |w|=50, θ=80°
Answers
Vectors are represented by arrows, where the norm of a vector determinate its length.
Since θ = 80° is the angle between them, a sketch for our vectors is
The resultant of their sum is given by the parallelogram law. If we draw two vectors parallel to u and w, we're going to have a sketch of a parallelogram, and the diagonal connecting the angle between u and w to the opposite vertice represents the resultant.
Kyzell is traveling 15 meters per second. Which expression could be used to convert this speed to kilometers per hour.
Answers
Given:
Kyzell is traveling 15 meters per second
we need to convert meters per second to kilometers per hours
As we know:
1 km = 1000 meters
So, 1 meters = 1/1000 kilometers
And, 1 Hour = 60 minutes = 3600 seconds
So, 1 seconds = 1/3600 Hours
So,
[tex]15\frac{meters}{\sec onds}=15\cdot\frac{1}{1000}\cdot3600\cdot\frac{kilometes}{\text{hours}}=54\frac{kilometrers}{hours}[/tex]So, the answer will be:
15 meters per second = 54 kilometers per hour
solve the inequality for 5x + 9 ≤ 24
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From the problem, we have an inequality of :
[tex]5x+9\le24[/tex]Subtract 9 to both sides of the inequality :
[tex]\begin{gathered} 5x+9-9\le24-9 \\ 5x\le15 \end{gathered}[/tex]Divide both sides by 5 :
[tex]\begin{gathered} \frac{5x}{5}\le\frac{15}{5} \\ x\le3 \end{gathered}[/tex]The answer is x ≤ 3
Factor each polynomial by factoring out the greatest common factorminimum steps please
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we are given the following expression:
[tex]12x^4+6x^3-8x^2[/tex]The greatest common factor between 12, 6, and 8 is 2. And the greatest common factor between the variables is:
[tex]\text{GCF(x}^4,x^3,x^2)=x^2[/tex]Therefore, the factorization is:
[tex]12x^4+6x^3-8x^2=2x^2(6x^2+3x-4)[/tex]An amusement park's owners are considering extending the weeks of the year that it is opened. The owners would like to survey 100 randomly selected families to see whether an extended season would be of interest to those that may visit the amusement park.What is the best way to randomly choose these 100 families? Have the owners of the amusement park ask the first 100 people they see.Choose a neighborhood near the amusement park and ask 100 families in this neighborhood.Ask the first 100 families that enter the amusement park on a busy weekend day.Allow a random number generator to come up with 100 families within a 50 radius of the amusement park.
Answers
Solution
Option 1:
- The owners asking the first 100 people they see would mean that they would see only those around them. This could be anyone at all from workers in the amusement park to people outside the park; these would not be random, and would not necessarily be a family but the survey is talking about randomly choosing 100 families. Because of these reasons, this is not the best way to randomly choose 100 families.
Option 2:
- Choosing a neighborhood near the amusement park would mean that they go to a neighborhood with families that might visit the amusement park and there would be many families to randomly choose from.
- This option seems like a good choice to randomly choose these 100 families that might visit the amusement park.
Option 3:
- Asking the first 100 families that enter the amusement park on a busy weekend would definitely bias the survey since families that you find in the amusement park are families that definitely want to be there and if they are there on a busy weekend, they certainly would not mind extending the season
if a driver drive at aconstant rate of 38 miles per hour how long would it take the driver to drive 209 mile
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In order to calculate how long would it take to drive 209 miles, we just need to divide this total amount of miles by the speed of the driver.
So we have:
[tex]\text{time}=\frac{209}{38}=5.5[/tex]So it would take 5.5 hours (5 hours and 30 minutes).
Determine whether the sequence is geometric. 160, 40, 10,2.5, ...
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Since the ratio is constant through the sequence, we conclude that it is geometric sequence.
Select all the situations in which a proportional relationship is described.
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
Robert spends $2 in the first 3 days of the week and $5 in the next 4 days.
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The situations that describe a proportional relationship are:
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
What is a proportional relationship?A relation is proportional if the rate of change of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.
Is Jackson's saving proportional?
Average of the amount saved in the next 3 months: $30 / 3 = $10
The relationship is proportional because the amount saved in the first month and the average is equal.
Is Mia's saving proportional?
Average of the amount saved in the first 2 months: $8 / 2 = $4
The relationship is proportional because the amount saved in the thir month and the average is equal.
Is Piyoli's spending proportional?
Average of the amount spent in the first 2 days: $2 / 2 = $1
Average of the amount spent in the next 5 days = $5 / 5 = $1
The relationship is proportional because the averages are equal.
Is Robert's spending proportional?
Average of the amount spent in the first 3 days: $2 / 3 = $0.67
Average of the amount spent in the next 4 days = $5 / 4 = $1.25
The relationship is not proportional because the averages are not equal.
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The number of inequality’s and signs can be changed by the way
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Linear Optimization
It consists of finding the optimum solution to a problem where all the conditions are related as linear functions.
We'll use the graphic method to solve the problem.
The problem is as follows:
Ava sells burritos amd tacos. Let's call x to the number of tacos sold and y to the number of burritos sold.
The first condition we find is that she can only produce a maximum of 130 units between tacos and burritos. This gives us the first inequality:
x + y ≤ 130 (1)
She sells each taco for $3.75 and each burrito for $6. She must sell a minimum of $600 worth of both products, so:
3.75x + 6y ≥ 600
Multiply this inequality by 4:
15x + 24y ≥ 2400
And divide it by 3:
5x + 8y ≥ 800 (2)
We are given a final condition that she can sell a minimum of 80 burritos, thus:
y ≥ 80 (3)
There are two obvious conditions not explicitly said but they can be deducted by the wording of the problem. Both x and y must be greater or equal to zero:
x ≥ 0 (4)
y ≥ 0 (5)
Let's put this all together:
x + y ≤ 130 (1)
5x + 8y ≥ 800 (2)
y ≥ 80 (3)
x ≥ 0 (4)
y ≥ 0 (5)
The optimum solution must satisfy all the conditions. They form a feasible region in the x-y coordinates system. One of the corners of that region will eventually be the best solution, depending on the objective function (not given here).
We need to graph all five lines in one common grid. It's shown below.
According to the graph, one possible solution is to sell x=50 tacos and y=80 burritos
Find the value of this expression if x = 1 andy = -7x2y-9
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We are asked to evaluate the expression:
[tex]\frac{x^2y}{-9}[/tex]when x = 1 and y = -7
so we replace them as shown below, making sure we include them inside parenthesis to keep clear that the expressions in x and in y are multiplying each other:
[tex]\frac{x^2y}{-9}=\frac{(1)^2(-7)}{-9}=\frac{-7}{-9}=\frac{7}{9}[/tex]So we see that x^2 becomes 1 and the factor y stays as -7. The final expression cancels out the negative sign in numerator (from -7) and in denominator (from -9) and gives 7/9.
65+ (blank) =180
11x + (blank)=180
11x =
x =
Answers
The angle x has a measure of 13 degrees
What are angles?Angles are the measure of space between lines
How to determine the measure of the angle x?The figure represents the given parameter
On the figure, we have the following parameters:
Angle 1 = 54
Angle 2 = 11x - 7
Angle 5
From the figure, angles 1 and angle 5 are corresponding angles
Corresponding angles are congruent angles
So, we have
Angle 1 = Angle 5
This gives
Angle 5 = 54
Also, we have
Angle 5 and Angle 2 are supplementary angles
This means that
Angle 5 + Angle 2 = 180
Substitute the known values in the above equation
So, we have
54 + 11x - 17 = 180
Evaluate the like terms
11x = 143
Divide both sides by 11
x = 13
Hence, the value of x is 13 degrees
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how long is the hypotenuse of this right triangle?28 519023
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To calculate the hypotenuse of a right angled triangle as shown in the diagram, we can apply the Pythagoras theorem which states as follows;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (the longest side) 28 units, AB is one of the other two sides, 23 units and BC is the third side.
We can now re-write the formula as follows;
28^2 = 23^2 + BC^2
784 = 529 = BC^2
Subtract 529 from both sides of the equation
255 = BC^2
Add the square root sign to both sides of the equation and you have
BC = 15.9687
BC is approximately 16 units
The shaded triangle has an area of 4 cm?Find the area of the entire rectangleBe sure to include the correct unit in your answer.
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Given:
Area of a shaded region of a rectangle is given.
[tex]\text{Area of the triangle=}4cm^2[/tex]Area of the rectangle is twice the area of the triangle given.
[tex]\begin{gathered} \text{Area of a rectangle=2}\times Area\text{ of a triangle} \\ =2\times4 \\ =8cm^2 \end{gathered}[/tex]which answer is the right one according to the image below
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To do that, we have to do the following:
[tex]\begin{gathered} t(s(x))=t(x\text{ -}7) \\ =4(x\text{ - }7)^2\text{ - }(x\text{ - }7)+3 \\ \\ \end{gathered}[/tex]So, that would be the equivalent expression, because x is s(x), which is x - 7, so you have to replace every x value with (x - 7)
Graph the line with slope -2 passing through the point (3,5)
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To graph the line, you need to know at least two points of it.
Knowing its slope and one point you can determine the equation of the line by using the point-slope form:
[tex]y-y_1=m(x-x_1_{})[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line
For m=-2 and (x₁,y₁)=(3,5) the equation of the line is:
[tex]y-5=-2(x-3)[/tex]Next, replace the equation for any value of x and solve for y, for example, use x=2
[tex]y-5=-2(2-3)[/tex]-Solve the difference within the parentheses then the multiplication
[tex]\begin{gathered} y-5=-2(-1) \\ y-5=2 \end{gathered}[/tex]-Add 5 to both sides of the equation
[tex]\begin{gathered} y-5+5=2+5 \\ y=7 \end{gathered}[/tex]The coordinates for the second point are (2,7)
Plot both points and link them with a line
Can someone please help me with this problem? I’ve been struggling with it
Answers
Consider the following table for interval notation:
First row:
x<0 is the same as:
[tex]-\inftyThen, the graph of that interval looks like:And the interval notation for that inequality is:
[tex](-\infty,0)[/tex]Second row:
-2
The graph of this inequality is:
The interval notation is:
[tex](-2,1\rbrack[/tex]Third row
The inequality that is represented by that interval is:
[tex]-3\le x[/tex]Its graph is:
Fourth row
The interval represented in that graph is:
[tex]\lbrack0,6)[/tex]The inequality represented by that interval is:
[tex]0\le x<6[/tex]A chocolate factory has a goal to produce10121012pounds of chocolate frogs per day. If the machines operate for712712hours per day making215215pounds of chocolate frogs per hour, will the chocolate factory make it’s goal?The chocolate factory meet their goal with the total being10121012pounds of chocolate frogs produced.
Answers
First, rewrite all the mixed fractions as impropper fractions:
[tex]\begin{gathered} 10\frac{1}{2}=10\times\frac{2}{2}+\frac{1}{2}=\frac{20}{2}+\frac{1}{2}=\frac{21}{2} \\ \\ 7\frac{1}{2}=7\times\frac{2}{2}+\frac{1}{2}=\frac{14}{2}+\frac{1}{2}=\frac{15}{2} \\ \\ 2\frac{1}{5}=2\times\frac{5}{5}+\frac{1}{5}=\frac{10}{5}+\frac{1}{5}=\frac{11}{5} \end{gathered}[/tex]Next, multiply the rate of chocolate production over time by the the operating time of the machines to find the total amount of pounds of chocolate frogs produced in one day:
[tex]7\frac{1}{2}\times2\frac{1}{5}=\frac{15}{2}\times\frac{11}{5}=\frac{15\times11}{2\times5}=\frac{3\times11}{2}=\frac{33}{2}=16\frac{1}{2}[/tex]Then, the chocolate factory can produce 16 1/2 pounds of chocolate frogs per day.
Since 16 1/2 is greater than 10 1/2, then the chocolate factory will meet their goal with the total being over 10 1/2 pounds of chocolate frogs produced.
Refer to attached image.
213 and 131 are incorrect.
Answers
Answer:
P(X<16) = 0.64P(X>12) = 0.64Step-by-step explanation:
Given a graph of a probability density function, you want the probabilities ...
P(X < 16)P(X > 12)Probability from PDFThe probability of a given range of values of X is the area under the density curve for those values of x.
P(X < 16)The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:
A = 1/2bh
A = 1/2(16)(0.08) = 0.64
The probability is P(X<16) = 0.64.
P(X > 12)The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...
A = 1/2(b1 +b2)h
A = 1/2(0.06 +0.10)(8) = 0.64
The probability is P(X>12) = 0.64.
The graph of a function is shown below. find the following, g(10), g(-3)
Answers
According to the graph, the value of the function g(-3) is 4 and g(10) is out of view
What are graphs?Graphs are graphical representations of equations, ordered pairs, tables of a relation
How to evaluate the function?From the question, the function is represented by the attached graph
Also from the question, the function to calculate is given as g(10) and g(-3)
This means that we calculate the values of the function, when x = 10 and -3
i.e.
We calculate g(x), when x = -3
We calculate g(x), when x = 10
So, we look at the graph for this function value
From the graph of values, we have
When x = -3, g(x) = 4
When x = 10, g(x) = not visible
This means that
g(-3) = 4
g(10) = out of view
Hence, the function g(-3) has a value of 4 and g(10) is out of view
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Chloe deposits $2,000 in a money market account. The bank offers a simple interest rate of 1.2%. How much internet she earn in 10 years?
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Given data:
deposits = $2,000
simple interest rate =1.2%
time =10 years
The formula to find the amount is,
[tex]A=\frac{\text{p}\cdot\text{n}\cdot\text{r}}{100}[/tex][tex]\begin{gathered} A=\frac{2000\cdot10\cdot1.2}{100} \\ A=\frac{24000}{100} \\ A=\text{ 240} \end{gathered}[/tex]The intrest she earn in 10 years is $240.Which of the following is NOT a factor of x3 + x2 - 4x - 4?x + 1x + 2x - 1x - 2
Answers
Answer: (x - 1)
Explanation
Given:
[tex]x^3+x^2-4x-4[/tex]To factor a third-degree polynomial, we can do it by grouping:
[tex]=(x^3+x^2)+(-4x-4)[/tex]Then, we have to find the common factor between groups:
[tex]=x^2(x+1)-4(x+1)[/tex]Now, we can get the common factor of (x+1):
[tex]=(x^2-4)(x+1)[/tex]Finally, the differences of squares equal the following:
[tex](x^2-a^2)=(x-a)(x+a)[/tex]Then, applying this rule to our factor we get:
[tex]=(x+2)(x-2)(x+1)[/tex]Thus, the only factor that is not correct is (x - 1)
RATIOS, PROPORTIONS, AND PERCENTSCalculating income taxTeresa made $20,000 in taxable income last year.Suppose the income tax rate is 10% for the first $7500 plus 16% for the amount over $7500.How much must Teresa pay in income tax for last year? I need help with this math problem.
Answers
We need find the tax on the first 7500
7500 * 10%
7500 * .10 = 750
Now we find the tax on what is over 7500
20000 -7500 =12500
The tax rate for this amount is 16%
12500 * 16%
12500 * .16
2000
Add the tax for both amounts together
750 + 2000
2750
The total tax paid is 2750
Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 4 in, x =6 in, y = 6 in, z = 2 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.
Answers
EXPLANATION:
Given;
We are given two ice cream cups in the shapes of a cone and a cylinder.
The dimensions are;
[tex]\begin{gathered} Cone: \\ Radius=4in \\ \\ Height=6in \\ \\ Cylinder: \\ Radius=3in \\ \\ Height=2in \end{gathered}[/tex]Required;
We are required to determine which of the two cups will hold the most ice cream.
Step-by-step solution;
Take note that the radius of the cylinder was derived as follows;
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \\ radius=\frac{6}{2}=3 \end{gathered}[/tex]The volume of the cone is given by the formula;
[tex]\begin{gathered} Volume=\frac{1}{3}\pi r^2h \\ \\ Therefore: \\ Volume=\frac{1}{3}\times3.14\times4^2\times6 \\ \\ Volume=\frac{3.14\times16\times6}{3} \\ \\ Volume=100.48 \end{gathered}[/tex]Rounded to the nearest tenth, the volume that the cone can hold will be;
[tex]Vol_{cone}=100.5in^3[/tex]Also, the volume of the cylinder is given by the formula;
[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=3.14\times3^2\times2 \\ \\ Volume=3.14\times9\times2 \\ \\ Volume=56.52 \end{gathered}[/tex]Rounded to the nearest tenth, the volume will be;
[tex]Vol_{cylinder}=56.5in^3[/tex]ANSWER:
Therefore, the results show that the CONE will hold the most ice cream.
5+10+15+...+100 write the series using summation notation
Answers
The Solution.
To determine that the series is an arithmetic progression,
[tex]\begin{gathered} T_{2_{}}-T_1=T_3-T_2=d \\ \text{Where d = common difference} \end{gathered}[/tex][tex]d=10-5=15-10=5[/tex]The sum of n terms of an arithmetic progression is given as
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ \text{Where S}_n=\sum ^{\square}_{\square} \\ n=n\text{ umber of terms}=\text{?} \\ a=\text{first term=5} \\ l=\text{last term=100} \end{gathered}[/tex]But we need to first find the number of terms (n), by using the formula below:
[tex]\begin{gathered} l=a+(n-1)d \\ \text{Where a = 5, l=100, d = 5 and n =?} \end{gathered}[/tex]Substituting the values, we get
[tex]\begin{gathered} 100=5+(n-1)5 \\ 100=5+5n-5 \\ 100=5n \\ \text{Dviding both sides by 5, we get} \\ n=\frac{100}{5}=20 \end{gathered}[/tex]Substituting into the formula for finding the sum of terms of the series, we get
[tex]\begin{gathered} S_{20}=\frac{20}{2}(5+100) \\ \text{ } \\ \text{ = 10(105) = 1050} \end{gathered}[/tex]Therefore, the correct answer is 1050.
A dilation with a scale factor of 4 is applied to the 3 line segment show on the resulting image are P'Q', A'B', And M'N'. Drag and drop the measures to correctly match the lengths of The images
Answers
Given:
Scale factor = 4 (Dilation)
PQ = 2 cm
AB = 1.5 cm
MN = 3 cm
Find-:
[tex]P^{\prime}Q^{\prime},A^{\prime}B^{\prime}\text{ and }M^{\prime}N^{\prime}[/tex]Explanation-:
Scale factor = 4
So,
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ A^{\prime}B^{\prime}=4AB \\ \\ M^{\prime}N^{\prime}=4MN \end{gathered}[/tex]So the value is:
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ P^{\prime}Q^{\prime}=4\times2 \\ \\ P^{\prime}Q^{\prime}=8\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} A^{\prime}B^{\prime}=4AB \\ \\ A^{\prime}B^{\prime}=4\times1.5 \\ \\ A^{\prime}B^{\prime}=6\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} M^{\prime}N^{\prime}=4MN \\ \\ M^{\prime}N^{\prime}=4\times3 \\ \\ M^{\prime}N^{\prime}=12\text{ cm} \end{gathered}[/tex]find the slope that goes through the points (1, -4) and (-3, 8)
Answers
Given the points:
(x1, y1) ==> (1, -4)
(x2, y2) ==> (-3, 8)
To find the slope, use the slope formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m\text{ = }\frac{8-(-4)}{-3-1} \\ \\ m=\frac{8+4}{-3-1} \\ \\ m=\frac{12}{-4} \\ \\ m\text{ = -3} \end{gathered}[/tex]Therefore, the slope is -3.
ANSWER:
-3