An arithmetic sequence is shown below. −7,−3,1,5,9,... Which represents an explicit formula for this sequence. A f(n) = -7 +4 (n-1) B f(n) = -4 +7 (n-1) C f(n) = -4 +7 (n-1) D f(n) = -11 (n-1)
Answers
Answer:
A. f(n) = -7 +4 (n-1)Step-by-step explanation:
\(a_1=-7\,,\ a_2=-3\,,\ a_3=1\,,\ a_4=5\,,\ a_5=9...\implies d=4\)
{-3-(-7)=4 and 1-(-3)=4 and 5-1=4 and 9-5=4}
An arithmetic sequence is: \(a_n=a_1+(n-1)d\)
\(a_1=-7\quad and\quad d=4\)
\(a_n=-7+(n-1)\cdot4\)
So:
\(f(n)=-7+4(n-1)\)
Related Questions
How many cups of sugar will he use if he makes 8 gallons of tea?
Answers
explanation:
triple of 38 is 38 × 3 = 114 gallon. using proportion to solve tgis question. 12 cups = 38 gallons.
Answer: 36
Step-by-step explanation: Multiplication
if 12 people are called for jury duty, what is the probability that all 12 will be available to serve on the jury? (round your answer to three decimal places.)
Answers
IXLl-Additive property of length
Answers
The value of x will be 1.
What is Line segment?
A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
Given that;
Point D is lie on the between C and E.
The value of CD = 4x
The value of DE = 19x - 12
The value of CE = 11
Now,
Since, D is lie is between C and E.
So, We can formulate;
CD + DE = CE
Substitute all the values, we get;
⇒ 4x + (19x - 12) = 11
Solve for x;
⇒ 4x + (19x - 12) = 11
Combine like term;
⇒ 23x - 12 = 11
Add 12 we get;
⇒ 23x = 11 + 12
⇒ 23x = 23
Divide by 23, we get;
⇒ x = 1
Therefore, The value of x will be 1.
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Draw four different triangles(drawings don't need to be shown) with side a=2cm and side b=5cm (you decide the length of side c). Look at the triangles you created. What do you notice about the different lengths of line c? Write an inequality that shows the possible lengths for line c (the triangle inequality theorem will help you):
Answers
Step-by-step explanation:
Triangle 1: c = 7 cm
Triangle 2: c = 4 cm
Triangle 3: c = 3 cm
Triangle 4: c = 6 cm
The lengths of line c vary and can be any value greater than 0 and less than (a + b) = (2 + 5) = 7 cm. Therefore, the inequality that shows the possible lengths for line c is 0 < c < 7.
the slope in a least-squares regression line of the form y = a bx is ______
Answers
The slope in a least-squares regression line of the form y = a bx is equal to the coefficient b. This coefficient represents the rate of change in the dependent variable (y) for every one unit increase in the independent variable (x).
Specifically, it represents the change in y divided by the change in x, as b is calculated as the covariance between x and y divided by the variance of x.
This slope is important in understanding the relationship between the variables being studied and can help to make predictions about future values of the dependent variable based on changes in the independent variable.
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Oltp systems are designed to handle ad hoc analysis and complex queries that deal with many data items.
a. true
b. false
Answers
Answer:
b) It is false
Prove the following statement using the given pieces of information.
Given: Line AB is parellel to Line DC and Line AD is parellel to Line BC.
Prove: Triangle ABC is congrent to Triangle CDA.
Answers
Triangle ABC is congruent to Triangle CDA using the SSS rule.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
SSS rule states that,
If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.
To prove:
ΔABC ≅ ΔCDA.
AB = DC ( given)
AD = BC (given)
AC = AC (common to both the triangles)
ΔABC ≅ ΔCDA ( By SSS rule )
Thus,
ΔABC ≅ ΔCDA by SSS rule.
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how to find absolute maximum and minimum on a graph
Answers
The absolute maximum is the highest point on the graph, while the absolute minimum is the lowest point.
To find the absolute maximum and minimum on a graph, we follow these steps:
1. Identify the critical points: These are the points where the derivative of the function is zero or does not exist. Critical points can occur at the endpoints of the interval as well.
2. Evaluate the function at the critical points: Plug in the x-values of the critical points into the function to obtain the corresponding y-values.
3. Determine the y-values at the endpoints: Evaluate the function at the endpoints of the interval under consideration.
4. Compare the y-values: Compare the y-values obtained from steps 2 and 3. The highest y-value corresponds to the absolute maximum, and the lowest y-value corresponds to the absolute minimum.
It is important to note that the above steps assume that the function is continuous over the interval being considered. If the function is not continuous, the concept of absolute maximum and minimum may not apply.
Additionally, it is crucial to check for any local maximum or minimum within the interval to ensure that the identified points are indeed the absolute maximum and minimum on the graph.
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find the area of the circle r = 3 ft
Answers
Answer:
9π ft² or approximately 28.26 ft²
Step-by-step explanation:
The area of a circle is A=πr².
Plug 3 in for the radius.
A=π(3²)
A=9π ft²,
or using 3.14 for pi,
Approximately 28.26 ft².
Find the area of the square
The radius is 10
Answers
Since half of the diagonal of the square is 10, that means the whole diagonal is 20.
Area of the square = \(\frac{1}{2} *(20)^{2} =200\)
Thus the area is 200. Hope that helps!
Solution:
Given:
Half of diagonal: 10 unitsTo find the diagonal, multiply half the diagonal by 2.
=> Diagonal = 2(Half of diagonal)=> Diagonal = 2(10) = 20 unitsWe also know that the sides of the square are equal. Let's use Pythagoras theorem to solve for the side length (c).
=> 20² = c² + c²=> 400 = 2c²=> 200 = c²=> c = √200 = 10√2Square the side length to obtain the area of the square.
=> (10√2)² = Area of square=> (10√2) x (10√2) = Area of square=> 100 x 2 = Area of square=> 200 units² = Area of squareThe area of the square is 200 units²
Compare the expressions if a is less than b
-12.7a...-12.7b
What sign should be between -12.7a and -12.7b?
Answers
The required sign between -12.7a and -12.7b should be greater than sign (>).
If a is less than b, then -12.7a will be greater than -12.7b, because multiplying a smaller number by a negative constant (-12.7 in this case) will result in a larger negative value than multiplying a larger number by the same constant.
To see this, suppose we have two positive numbers x and y such that x < y. Then, multiplying both by a negative constant c will result in two negative numbers with magnitudes that are greater for x:
cx < cy, because c is negative and (x < y)
Therefore, if a is less than b, then:
-12.7a > -12.7b
So the sign between -12.7a and -12.7b should be greater than sign (>).
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Solve the system by graphing, then state the solution as an ordered pair
HELP ASAP!!!!!
Answers
Step-by-step explanation:
Simply graph the two equations....the intersection of the two graphs is the solution
plss answer asap i will give brainliest
Answers
Answer:
g(-4)=2.5
g(1)=0
Step-by-step explanation:
g signifies the line, ad the number in parenthesis is the x value. so for other problems like this, just find the y value of the graphed object at the x value listed. hope this helped :)
Apollo traveled 84 leagues in 6 days. Then he tripled his rate. How long would it take him to travel 462 leagues at
this new speed?
Answers
It would take him 11 days to travel 462 leagues
How long would it take him to travel 462 leaguesFrom the question, we have the following parameters that can be used in our computation:
Apollo traveled 84 leagues in 6 days.
So, the speed is
Speed = 84/6
When tripled, we have
New speed = 84/6 * 3
Evaluate
New speed = 42
For 462 leagues, we have
Time = 462/42
Evaluate
Time = 11 days
Hence, teh time taken is 11 days
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Find the equation of a line that passes through the point (0,5) and has a gradient of 3.
Leave your answer in the form y = mx + c
Answers
Gradient = m
when x= 0, y=5
5=3(0) + 5
Determine whether (3,2) is a solution of y = 3x +2.
Answers
Answer:
This point is not a solution to the equivalence
Step-by-step explanation:
Becouse if we put x= 3 then y= 11
\(y = 3 \times 3 + 2 = 11\)
jogging burns 21 calories in 10 minutes determine how many calories are burned per hour?
Answers
Answer:
126 burned calories per hour
There are 60 minutes in 1 hour, so ir you multyply 21 x 6 your answer will be 126.
Answer:
126
Step-by-step explanation:
there are 60 minutes in an hour so divide 60 by 10 to get 6 and multiply by 21 to get 126
Find the product of (x − 8)2 and explain how it demonstrates the closure property of multiplication.
A. x2 − 64; is a polynomial
B. x2 − 16x + 64; is a polynomial
C. x2 − 64; may or may not be a polynomial
D. x2 − 16x + 64; may or may not be a polynomial
Answers
Answer:
B
Step-by-step explanation:
(x-8)^2=(x-8)(x-8)=x^2-8x-8x+64=x^2-16x+64
Answer:
x2 − 16x + 64; is a polynomial
A new bank customer with $4000 wants to open a money market account the bank is offering a simple interest rate of 1.5% how much interest with a customer in 20 years
Answers
Answer:
$1200
Step-by-step explanation:
Given data
Principal=$4000
Rate=1.5%
Time= 20years
The expression for simple interest is
SI= PRT/100
Substitute
SI= 4000*1.5*20/100
SI=120000/100
SI=$1200
Hence the interest is $1200
on a fair die whose faces are numbered consecutively starting from 1, the probability of rolling an even number is less than twice the probability of rolling a multiple of 3. which could be the number of sides on the die?
Answers
Answer:
iam sorry
i don't know the answer
A teacher writes the expression shown on the board.
12.2
x
+
50.6
y
+
3
(
1.4
x
−
2.6
y
)
Part A
A student writes the two expressions shown.
Expression 1:
4
(
4.1
x
+
10.7
y
)
Expression 2:
2
(
6.1
x
+
25.3
y
+
2.1
x
−
3.9
y
)
The student claims that both of the expressions are equivalent to the expression written on the board. Explain why the student’s claim is true. Show your work for both expressions.
Enter your work and explanation in the space provided.
Answers
The students' claim is true for both algebraic expressions 1 and 2 because they are equivalent to the teachers expression on the board.
How to find the Equivalent expression?The algebraic expression that the teacher wrote on the board was;
12.2x + 50.6y + 3(1.4x − 2.6y)
Expanding the bracket gives us;
12.2x + 50.6y + 4.2x - 7.8y
16.4x + 42.8y
Factorizing this gives;
4(4.1x + 10.7y)
This is same as the expression 1 by the student
The expression 2 is written as;
2(6.1x + 25.3y + 2.1x − 3.9y)
= 2(8.2x + 21.4y)
= 16.4x + 42.8y
This is same as the original expression
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Help me answer this please quickly!
Answers
Answer:
Step-by-step explanation:
When two lines intersect, the non adjacent angles formed are called vertical angles and they are congruent.
∠FZG = ∠HZJ {Vertical angles are congruent.
∠FZG = 38°
the average rate of change of the height of water in a vase with respect to the volume of water in the base as the volume changes from 2.5 cups to 3.25 cups is inches per cup? what does the average rate of change tell you in this context?
Answers
The average rate of change tell you in this context the volume of water in the base as the volume changes from 2.5 cups to 4.25 cups.
The average rate of change is a mathematical concept used to describe how a change in one quantity affects another quantity.
To calculate the average rate of change, we need to know the height of water in the vase at two different volumes. Let's call the height of water at a volume of 2.5 cups "h1" and the height of water at a volume of 3.25 cups "h2". Then, the average rate of change over the interval from 2.5 cups to 3.25 cups is calculated as:
=> (h2 - h1) / (3.25 - 2.5) = (h2 - h1) / 0.75
This average rate of change tells us how much the height of water changes, on average, for every one cup increase in the volume of water in the vase.
In other words, the average rate of change provides us with a measure of the "slope" of the relationship between the height of water and the volume of water in the vase over the interval from 2.5 cups to 3.25 cups.
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Could someone please answer these 2
Answers
Answer:
A. 1/6
B. 1
Step-by-step explanation:
A. 9/j x j/54= 9/54 = 1/6
B. 6k/8m : 3k/4m = 6k/8m : 4m / 3k = 2/2 =1
Answer:
a. 3/2
b. 1
Step-by-step explanation:
A. To simplify the expression, we can cancel out the common factor of j:
9/j * j/54 = (9/1 * 1/6) = 3/2
Therefore, 9/j * j/54 simplifies to 3/2.
B. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. That is,
(a/b) ÷ (c/d) = (a/b) x (d/c)
Using this rule, we can simplify the given expression as follows:
6k/8m ÷ 3k/4m = (6k/8m) x (4m/3k)
= (6/8) x (4/3)
= 2/2
= 1
the lengths of fish in a neighborhood pond are normally distributed with a mean of 5 inches and a standard deviation of 1.2 inches. what is the probability that a sample of 10 randomly selected fish will have a mean length of of over 6 inches?
Answers
According to the given standard deviation, the probability that a sample of 10 randomly selected fish will have a mean length of over 6 inches is 0.0188 or 1.88%.
In this problem, we want to find the probability of the sample mean being greater than 6 inches. We can calculate this by standardizing the sample mean using the formula:
z = (x - μ) / (σ / √n)
Where z is the standard normal variable, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values in the formula, we get:
z = (6 - 5) / (1.2 / √10)
z = 2.10
Now, we can use a standard normal table or calculator to find the probability of z being greater than 2.10. The probability of z being greater than 2.10 is approximately 0.0188 or 1.88%.
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Put the following steps for executing a stock trade in order. What is the order? 2,4,1,3?
1. Person submits order to buy/sell stock to broker
2. Online broker contacts representative at exchange
3. Person receives confirmation of sale/purchase
4. Sell order is matched with buy order
Answers
Answer:
The answer would be 1,2,4,3
Step-by-step explanation:
I just took a quiz with this same question :)
Consider an isosceles trapezoid rotated about an axis of symmetry that passes through the midpoint of the bases. the minor base of the trapezoid is 10 cm and the major base is 13 cm. what is the perimeter of the horizontal cross section if the cut is made at the middle of the height of the trapezoid?
Answers
Based on the calculation, the perimeter of the horizontal cross-section is equal to 36.13 cm.
How to calculate the perimeter?In this scenario, the resulting geometrical shape formed when the cut is made at the middle of the height of the trapezoid and then rotated is a circle.
Given the following data:
Minor base = 10 cm.Major base = 13 cm.From the middle, the diameter of this circle is given by:
D = 1/2 (10 + 13)
D = 11.5 cm.
Now, we can calculate the perimeter:
Perimeter = πD
Perimeter = 3.142 × 11.5
Perimeter = 36.13 cm.
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Sam's bill at the restaurant came to $36.45 he wants to leave a 20% tip What is the total cost?
Answers
Answer:
Here you go!
Step-by-step explanation:
The answer is a 7.29 dollar tip.
Answer:
The total cost will be $43.74
Step-by-step explanation:
To solve the problem we first have to find what is 20% of $36.45.
To do this, multiply 36.45 by .20
36.45 x .20 = 7.29
now that we know how much is the tip, we add that to the bill
36.45 + 7.29 = 43.74
your final answer will be $43.74
There are 505050 workers onsite at a large construction project. Six of them are left-handed, and the rest are not. Suppose that the project manager randomly selects 222 workers (without replacement). What is the probability that neither of the workers selected are left-handed? round your answer to two decimal places.
Answers
There are 50 workers, 6 of them are left-handed. If 2 workers are selected randomly, the probability neither of the workers selected are left-handed is 0.77
The conditional probability can be computed as:
P(A∩B) = P(B |A) P(A)
Where:
P(B |A) is read is the probability of B given A occurs.
In the given problem:
number of right-handed = 44
Let P(R) denote the probability that a selected worker is right-handed, then:
P(R) = 44 / 50
Now the remaining workers = 49, suppose the first selected worker is right-handed, the remaining right-handed one is 43. Hence,
P(R | R) = 43/49
Therefore, the probability that both selected workers are right handed is:
P(R, R) = 44/50 x 43/49 = 0.77
Correct question:
There are 50 workers onsite at a large construction project. Six of them are left-handed, and the rest are not. Suppose that the project manager randomly selects 2 workers (without replacement). What is the probability that neither of the workers selected are left-handed? round your answer to two decimal places.
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find the product 5^56 × 5^22 × 5^-96
Answers
Answer:
5^-18
Step-by-step explanation:
here is the answer please mark me as the brainliest
