Can someone pls help me find the equation for the arithmetic sequence and help me fill out the graph
Answers
Solution
- The question gives us the following arithmetic sequence:
[tex]t(n+1)=t(n)-4[/tex]- We are asked to write out the explicit function for the sequence.
- To do this, we simply write out the terms of the sequence. After this, we would determine the common difference of the sequence.
- We will use the common difference to find the first term of the sequence and then use the formula below to find the explicit form of the arithmetic sequence:
[tex]\begin{gathered} t(m)=a+(m-1)d \\ \text{where,} \\ a=\text{first term of the sequence} \\ d=\text{common difference} \\ m=\text{ number of terms} \\ \\ (\text{Note that: }m=n+1\text{, since the formula starts assumes that the sequence starts from the 1st term not zeroth term} \end{gathered}[/tex]- We have been given that the second term of the sequence is 10. We would also use this term to form our sequence.
[tex]\begin{gathered} \text{Let n=2} \\ \text{The formula becomes} \\ t(2+1)=t(2)-4 \\ t(3)=t(2)-4 \\ \\ \text{But we know that }t(2)=10 \\ \therefore t(3)=10-4 \\ t(3)=6 \\ \\ \text{Let n=3} \\ t(3+1)=t(3)-4 \\ t(4)=6-4 \\ t(4)=2 \\ \\ \text{Let n=4} \\ t(4+1)=t(4)-4 \\ t(5)=2-4 \\ t(5)=-2 \\ \\ \text{Thus, we can write out the terms of the sequence as follows:} \\ \ldots,t(2),t(3),t(4),t(5),\ldots=\ldots10,6,2,-2\ldots \\ \\ \text{ We can observe that the common difference is -4 since,} \\ 6-10=-4 \\ 2-6=-4 \\ -2-2=-4 \\ \text{And so on}\ldots \\ \\ \text{Thus, we can trace our sequence back to its first term as follows:} \\ t(2)-t(1)=-4 \\ 10-t(1)=-4 \\ \text{Subtract 10 from both sides} \\ -t(1)=-4-10 \\ \therefore t(1)=14 \\ \\ t(1)-t(0)=-4 \\ 14-t(0)=-4 \\ \text{Subtract 14 from both sides} \\ -t(0)=-4-14=-18 \\ \therefore t(0)=18. \\ \\ \text{Thus, the first term }t(0)=18 \end{gathered}[/tex]- Let us now apply the formula for the nth term of a sequence to find the explicit formula:
[tex]\begin{gathered} first\text{ term =}t(0)=a=18 \\ \text{common difference}=d=-4 \\ t(m)=a+(m-1)d \\ \\ t(m)=18+(m-1)(-4) \\ \text{Expand the bracket} \\ t(m)=18+m(-4)-1(-4) \\ t(m)=18-4m+4 \\ \\ \therefore t(m)=22-4m \\ \\ \text{Let us write the sequence in terms of n} \\ m=n+1 \\ t(n)=22-4(n+1) \\ t(n)=22-4n-4 \\ t(n)=18-4n \\ \\ \text{Thus, the explicit function is:} \\ t(n)=18-4n \end{gathered}[/tex]- With the above formula, we can proceed to populate the table. Let us use the formula to calculate all the terms for each value of n.
[tex]\begin{gathered} t(n)=18-4n \\ \\ \text{when n = 0} \\ t(0)=18-4(0) \\ t(0)=18 \\ \\ \text{when n= 1} \\ t(1)=18-4(1) \\ t(1)=14 \\ \\ \text{when n=2} \\ t(2)=18-4(2) \\ t(2)=10 \\ \\ \text{when n = 3} \\ t(3)=18-4(3) \\ t(3)=18-12=6 \\ \\ \text{when n = 4} \\ t(4)=18-4(4) \\ t(4)=2 \\ \\ \text{when n = 5} \\ t(5)=18-4(5) \\ t(5)=-2 \end{gathered}[/tex]- On the table, we have the values filled in below:
Final Answer
The explicit form of the sequence is:
[tex]t(n)=18-4n[/tex]
Related Questions
The mean height of women in a certain country ( ages 20 29) is 64.1 inches .A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches if the standard deviation is 2.52
Answers
The mean height is given as 64.1 . We want to obtain the probability that he mean height for the sample is greater than 65 inches if the standard deviation is 2.52.
To proceed we, find the z-score of 65 in the distribution, we make use of the formula;
[tex]z=\frac{x-\mu}{(\frac{\sigma}{\sqrt[]{n}})}[/tex]x = 65, mu = population mean = 64.1, sigma = standard deviation = 2.52, n = sample size = 70.
inserting these values, we have;
[tex]\begin{gathered} z=\frac{65-64.1}{\frac{2.52}{\sqrt[]{70}}} \\ z=0.043 \end{gathered}[/tex]The problem now boils down to finding the probability of the z-score greater than 0.043
From z-score tables. the probability of the z-score greater than 0.043;
[tex]Pr(z>0.043)=0.48285[/tex]Therefore, the probability that the mean height for the sample is greater than 65 inches is 0.48285
Translate to a system of equations and solve:Priam has a collection of nickels and quarters, with a total value of $9.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he have?
Answers
The value of a nickel is 5 cents
The value of the quarter is 25 cents
Since Priam has a total of 9.30 dollars = 930 cents, then
[tex]5n+25q=930[/tex]Simplify the equation by dividing all terms by 5
[tex]\begin{gathered} \frac{5n}{5}+\frac{25q}{5}=\frac{930}{5} \\ n+5q=186\rightarrow(1) \end{gathered}[/tex]Since he has 6 nickels less than 3 times the quarters, then
[tex]n=3q-6\rightarrow(2)[/tex]Substitute n in equation (1) by equation (2)
[tex](3q-6)+5q=186[/tex]Add the like terms on the left side
[tex]\begin{gathered} (3q+5q)-6=186 \\ 8q-6=186 \end{gathered}[/tex]Add 6 to both sides
[tex]\begin{gathered} 8q-6+6=186+6 \\ 8q=192 \end{gathered}[/tex]Divide both sides by 8
[tex]\begin{gathered} \frac{8q}{8}=\frac{192}{8} \\ q=24 \end{gathered}[/tex]The number of quarters is 24
Substitute q by 24 in equation 2 to find n
[tex]\begin{gathered} n=3(24)-6 \\ n=72-6 \\ n=66 \end{gathered}[/tex]The number of nickels is 66
He has 66 nickels and 24 quarters
What is the probability that a card drawn randomly from a standard deck of 52 cards is a red four? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
We have a deck of 52 cards.
We have to calculate the probability that when a card is randomly drawn from the deck, this cart is a red four.
There is only one red four in the deck. Then, if we calculate the probability of an event as the quotient between the number success events (getting a red four, in this case) and the total possible events (getting any card), we will get:
[tex]p=\frac{S}{N}=\frac{1}{52}[/tex]As there is only one card in the deck that gives a success event within the 52 cards, the probability is 1 in 52.
Answer: the probability is 1/52.
Explanation and answer for both Part A and B please
Answers
(2x - 21) + x = 90°
So after factorising:
(2x + x) -21 = 90°
And simplify:
3x -21 = 90°
Do some moving around:
3x = 90° + 21°
3x = 111°
Then divide by 3 on both sides:
x = 37°
Then, because we know what x is, we can substitute it into the formulas for each complimentary angle:
So:
(2x -21) = (2 times 37) - 21 = 53°
And:
x°= 37°
In the questions format:
∠SOT = 37 °
∠SOR = 53°
Hope this helps!
If you have any questions, ask them here!
Solve the system of equations below to find it's solution. List the x-coordinate and y-coordinate.y = 2x - 56x - 2y= 20
Answers
y = 2x - 5 Eq(1)
6x - 2y= 20 Eq(2)
We are going to use the elimination method to solve the system.
y-2x = -5 Transpose x to the othe side in Eq(1)
2y - 4x = -10 Multiply all terms of Eq(1) by 2. Then add Eq(1) to Eq(2)
2y - 4x = -10
+ -2y +6x= 20
----------------------
2x = 10 Operating like terms
x= 10/2 Isolating x
x = 5
Replacing x in Eq(1)
y = 2*(5) -5
y= 10 - 5 = 5
The answer is the point with coordinates ( 5 (x-coordinate) , 5(y-coordinate)).
Find the missing value.Hint: Use the number line to find the missing value.-(-5) = -7A-15-10-5051015
Answers
Given:
The expression is ___-(-5) = -7.
The objective is to find the missing value using number line.
Consider the missing value as x.
Now, the expression can be rearranged as,
[tex]\begin{gathered} x-(-5)=-7 \\ x+5=-7 \\ x=-7-5 \end{gathered}[/tex]So, we have to solve -7-5 on number line, which means starting from -7 subtract 5 in the number line.
Hence, the missing value is -12.
find the equation of the line that contains the point (6,4) and is perpendicular to the line y=3x-5
Answers
The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
What is a equation of line?The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that,
equation of given line with a slope of m = 3
y=3x-5
A line perpendicular to that line will have a slope that is the negative reciprocal of 3.
The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.
Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).
y = mx + b
4 = (-1/3)(6) + b
(we've set up the equation with only one unknown, b, that we can now solve for)
4 = -2 + b
b = 6
With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:
y = (-1/3)x + 6
Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
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Nina has 19.50 to ride the subway around New York it will cost her 0.75 every time she rides identify the dependent variable and independent variable in this scenario
Answers
The independent variable is the cost of riding the subway.
The dependent variable is the number of times she can ride the subway.
What is independent variable and independent variable?The independent variable is the variable whose value is given. It is the value of the independent variable that determines the dependent variable. The dependent variable is the variable whose value is determined by changes in the independent variable.
In this question, the cost of each ride is given. There is little or nothing Nina can do to change the price of the subway ride. Thus, it is the independent variable. The total amount of rides Nina can go on is dependent on the cost per ride and the total amount she has. Thus, it is the dependent variable.
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a salad dressing recipe calls for 3/4 cup of olive oil for every 1/2 cup of vinegar is needed for 2 cups of olive oil?
Answers
the answer is 1 1/4 cups of vinegar
Step-by-step explanati
Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
Answers
Answer:
I don't know if it is the answer
Solve Step by step
8 = x/7 + 9
Answers
Answer:
[tex]x=\frac{-1}{7}[/tex]
Step-by-step explanation:
[tex]8=x/7+9\\[/tex]
Subtract 9 from both sides
[tex]-1=x/7[/tex]
Multiply both sides by 7
[tex]\frac{-1}{7} =x[/tex]
Swap the order because you're a smart person
[tex]x=\frac{-1}{7}[/tex]
24. Write the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5
Answers
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
[tex]y-y_1=m(x-x_1)[/tex]where m = slope.
[tex]\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}[/tex]Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
Step-by-step explanation:
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
y-y_1=m(x-x_1)y−y
1
=m(x−x
1
)
where m = slope.
\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}
y−(−13)=
2
1
(x−0)
y+13=
2
1
(x)
y=
2
1
x−13
Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
A table is on sale for $589, which is 24% less than the regular price.
What is the regular price?
Answers
$589 + $141.36 = $730.36
Regular price was $730.36
There are 175 students enrolled in Blue Bear High School. Twenty-five students train in Karate (T) and 35 students compete with other schools in Karate (C). One hundred students practice martial arts, but not Karate. How many students qualify for a Karate tournament if they train and compete at Blue Bear High School? A. 0 B. 15 C. 60 D. 115
Answers
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
As given in the question,
Total number of students enrolled in Blue Bear High School =175
Number of students train in karate = 25
Number of students compete with other school in karate =35
Number of students practice martial arts but not karate=100
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School
= 25 + 35
= 60
Therefore, number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
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The table below represents the snacks that Sidney and Erica purchased at the movies last month. Write a system of equations to determine the price of each candy and each drink.
Answers
SOLUTION:
Case: System of equations
Given: A table of value of snacks and drinks for Sidney and Erica
Required: Write a system of equations to determine the price of each candy and each drink.
Method:
Step 1: Assume the price of snacks be represented by s and drinks by d
Step 2: Equation for Sidney
[tex]\begin{gathered} 2s+1d=13.50 \\ 2s+d=13.50.........equation(1) \end{gathered}[/tex]Step 3: Equation for Erica
[tex]\begin{gathered} 3s+1d=12.85 \\ 3s+d=12.85.......equatiion(2) \end{gathered}[/tex]Final answer:
The system of equations is:
[tex]\begin{gathered} 2s+d=13.50 \\ 3s+d=12.85 \end{gathered}[/tex]you deposit $3,300 in account with an annual interest of 3.3% for 20 years. what is the amount of money you'll have at the end of the 20 years?
Answers
Given data:
The given principal is P=$3,300.
The given rate of interest is r=3.3%.
The given time is t=20 years.
The expression for the final amount of money is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=(3,300)+\frac{3,300\times3.3\times20}{100} \\ =3,300+2,178 \\ =5,478 \end{gathered}[/tex]Thus, the final amount after 20 years is 5,478.
can someone please help me find the value of x to this equation
Answers
SOLUTION
This is a right-triangle problem.
We will use the SOHCAHTOA principle.
In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \cos \theta=\frac{5}{18} \\ \cos \theta=0.27778 \\ \theta=\cos ^{-1}(0.27778) \\ \theta=73.872^o \\ \theta=73.87^o \end{gathered}[/tex]The final answer is 73.87 degrees.
I need help on this also could you check if the first 3 questions are correct
Answers
We have two parallel lines intersected by other line.
We have to relate the angles.
We will take the angle with measure 17° as reference (red angle).
The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.
[tex]m\angle1=180-17=163\degree[/tex]It has no direct relationship with the red angle.
The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).
The relationship with the red angle is that they are alternate exterior angles.
Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.
Angle <4 and the red angle are corresponding angles.
They have the same measure, so they are congruent.
Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.
Angle <6 and the red angle are vertical angles, so they have the same measure.
Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.
Answer:
Angle <1:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <2:
Measure = 17°
Relationship: Alternate exterior and congruent.
Angle <3:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <4:
Measure = 17°
Relationship: Corresponding and congruent.
Angle <5:
Measure = 163°
Relationship: Linear pair and supplementary.
Angle <6:
Measure = 17°
Relationship: Vertical and congruent.
Angle <7:
Measure = 163°
Relationship: Linear pair and supplementary.
what is the median value?if another 5 is added, which statement must be true the mean would increase the mean would decrease the median would increaseboth the median and mean will stay the samehow many people made 3 or less trips to the movie
Answers
Solution
We have the following data:
0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5
And the mean would be:
Mean = 2.958
And the median
Median = 4
Then if we add a 5 then the median would be the same 4
And the mean = 3.04
then the solution is:
The mean would increase
And for the other part of the question
we have:´
4+3+1+2 = 10 people made 3 or less trips to the movie
Find the length of the hypotenuse if the length of the legs are 6 inches and 9 inches. Round to two decimal places.The length of the hypotenuse is ___ inches.
Answers
The hypotenuse (longest side) of a right angled triangle can be derived using the Pythagoras' theorem as shown;
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ \text{Where AC is the hypotenuse, you now have;} \\ AC^2=6^2+9^2 \\ AC^2=36+81 \\ AC^2=117 \\ \text{Add the square root sign to both sides} \\ AC=\sqrt[]{117} \\ AC=10.8166 \\ AC=10.82\text{ (To 2 decimal places)} \end{gathered}[/tex]The answer is 10.82 inches, to 2 decimal places
In null hypothesis significance testing, if a result is unlikely under the hypothesis, then we infer
support for the _______ hypothesis.
Answers
Answer:
Step-by-step explanation:
A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis.
Give the name (monomial,binomial, trinomial etc.) anddegree of the polynomial.
Answers
12x^3
Name: Monomial , because it has only 1 term
Degree: 3, exponent of the monomial
The table below represents the total weight, in pounds, of a set ofstone blocks.<
Answers
k=12
1) Gathering the data, and setting this table:
Blocks | Pounds
5 60
6 72
7 84
8 96
2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx
Then we can write:
y =12x
3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.
5 x 12 = 60
6 x 12 =
A phone company offers two monthly plans. Plan A costs $19 plus an additional $0.07 Tor each minute of calls. Plan B costs $12 plus an additional $0.11 for each minute of calls. For what amount of calling do the two plans cost the same? minutes What is the cost when the two plans cost the same? Х Submit AS
Answers
Explanation
Step 1
let x represents the number of minutes.
hence:
Plan A costs $19 plus an additional $0.07 for each minute of calls
[tex]A=19+0.07x[/tex]Plan B costs $12 plus an additional $0.11 for each minute of calls
[tex]B=12+0.11x[/tex]Step 2
there is a number of minutes x, such both plnas cost the same,so
[tex]undefined[/tex]which expression would be easier to simplify if used the associative property to change the group.A.4+(1.2 +(-0.2)b. 85+(120+80)c. (2+3/7)+4/7d. [-40+(60)] +52
Answers
The easiest expression to simplify by using the associative property is expression "b", since there is an addition already set (120 + 80 =200) to be performed.
'The other expressions involve more steps.
(｀・ω・´) thx for answering
Answers
Answer:
3nd one
Step-by-step explanation:
Hope I helped!
If I got it incorrect, please tell me, so I can at least try and see what I did wrong.
Assessment
Time Remaining: 2:33:21 | Question 16
Charmaine spent $21 on fruit at the grocery store. She spent a total of $70 at the store. What percentage of the total did she spend on fruit?
%
Answers
The slope of a line which passes through the vertex and the y-y− intercept of the quadratic equation x^2 + 10x - 5x
2
+10x−5 is
Answers
The slope of the line passing through the y intercept and the vertex of the quadratic x²+10x-5 is 5.
The provided quadratic equation is,
y = x²+10x-5
The vertex of a quadratic equation,
(-b/2a, -D/4a)
Where,
a = 1,
b = 10,
c = -5,
D = (b²-4ac)
D = (10²-4(-5)(1))
D = 100+20
D = 120,
Putting all the values to find the vertex of the equation,
(-10/2,-120/4)
(-5,-30)
So, the vertex are now known,
To find the y intercept, putting x = 0 and solving the equation for y,
y = (0)²+10(0)-5
y = -5
The y intercept is,
(0,-5)
If there are two points on the line, let say (a,b) and (c,d), then the slope of the line is,
M = (d-b)/(c-a)
Now, we know two points,(-5,-30) and (0,-5).
We can now find the slope of line,
M = (-5+30)/(0+5)
M = 25/5
M = 5
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Write the equation of the quadratic with a directrix of y=-5 and vertex of (-2,-3).
answer step by step, please
Answers
The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3
How to write the equation of parabola with directrix of y = -5 and vertex of (-2,-3)Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (-2,-3)
h = -2
k = -3
P in this problem, is the distance between the vertex and the directrix
P = -3 - -5 = -3 + 5 = 2
p = 2
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -2)² = 4 * 2 (y - -3)
(x + 2)² = 8 (y + 3)
rearranging the equation
8 (y + 3) = (x + 2)²
y + 3 = 1/8 (x + 2)²
y = 1/8 (x + 2)² - 3 (standard vertex form)
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What mathematical symbol goes between the two parentheses to show that you will be using the distributive property?
8 x 57 = (8 x 50) _______ (8 x 7)
Answers
Answer: The Answer is the addition symbol
Step-by-step explanation:
8 x 50 = 400
8 x 7 = 56
400 + 56 = 456
8 x 57 = 456