HELP ME PLEASE
Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.
an = 8(1/2)n − 1; average rate of change is −3
an = 10(1/2)n − 1; average rate of change is 3
an = 8(1/2)n − 1; average rate of change is 3
an = 10(1/2)n − 1; average rate of change is −3
Answer:
Option A
Step-by-step explanation:
To find nth term we use the given options.
[tex]a_n= 8(\frac{1}{2})^{n-1}[/tex]
Lets pick any point from the graph and plug it in the given option
LEts pick (1,8) and (2,4)
[tex]a_n= 8(\frac{1}{2})^{n-1}[/tex], n=1, an=8
[tex]8= 8(\frac{1}{2})^{1-1}[/tex]
[tex]8= 8(\frac{1}{2})^{0}[/tex]
8=8 True
LEts check with (2,4), n=2 and an=4
[tex]4= 8(\frac{1}{2})^{2-1}[/tex]
4=4 True
Average rate of change from n=1 to n=3= [tex]\frac{a_3-a_1}{3-1} =\frac{2-8}{2} =-3[/tex]
Average rate of change from n=1 to n=3 is -3
the perimeter of Jared's property is 56 yards. how many feet of fence will Jared need if he wants to enclose the whole property?
Marcus painted 1/3 of his bedroom in 4/5 of an hour. at this rate how long will it take him to paint his entire room
Answer:
So it took him 4/5 of an hour to paint 1/3
that means there is still 2/3 to go
so that means that he will have two times that time to paint the rest of the room
4/5 = ?
1/3 2/3
using cross multiplication
(4/5)(2/3) = (1/3) (?)
8/15 = 1/3 ?
divide both sides by 1/3
so that will be 8/5
that means it will take 8/5 of an hour to complete the rest
or 12/5 total to do entire room
Hope this helps ;)
Step-by-step explanation:
In each round of a game show, a contestant answers a multiple-choice question that has three answer choices. The contestant advances to the next round by answering the question correctly. What is the probability of advancing to the seventh round if the contestant randomly guesses the answer to each question? Write your answer as a fraction in simplest form.
The probability of advancing to the seventh round by randomly guessing on a game show with three answer choices per question is 1/729.
The probability of advancing to the seventh round if the contestant randomly guesses the answer to each multiple-choice question with three answer choices is calculated by raising the probability of guessing one question correctly to the power of six, since the contestant needs to guess correctly six times in a row to reach the seventh round.
The probability of guessing one question correctly is 1/3, as there are three possible choices and only one correct answer. Thus, the probability of guessing six questions correctly in a row is (1/3)⁶.
Simplifying this, we get:
(1/3)⁶ = 1/729.
Therefore, the probability is 1/729.
What is the volume of the cylinder below?
Answer:
C) 288π units³
Step-by-step explanation:
When the height of an oblique cylinder is given, the formula for volume is
V = π×r²×h
Our radius is 6 and our height is 8:
V = π(6²)(8) = π(36)(8) = 288π
The volume of the cylinder is [tex]\boxed{288\pi {\text{ unit}}{{\text{s}}^3}}[/tex].Option (C) is correct.
Further explanation:
Given:
Theheight of the cylinder is [tex]{\text{8 units}}[/tex] and the radius of the cylinder is [tex]{\text{6 units}}.[/tex]
The options of the volume are given as follows.
A. [tex]{\text{216}}\pi {\text{uni}}{{\text{t}}^3}[/tex]
B. [tex]324\pi {\text{uni}}{{\text{t}}^3}[/tex]
C. [tex]288\pi {\text{uni}}{{\text{t}}^3}[/tex]
D. [tex]432\pi {\text{uni}}{{\text{t}}^3}[/tex]
Explanation:
The formula for the volume of the cylinder can be expressed as,
[tex]\boxed{{\text{Volume}} = \pi {r^2}h}[/tex]
‘r” is the radius of the cylinder and “h” is the height of the cylinder.
The volume of the right cylinder can be obtained as follows,
[tex]\begin{aligned}{\text{Volume}} &= \pi {r^2}h\\&= \pi\times {\left( 6 \right)^2} \times 8\\&= \pi\times 36 \times 8\\&=288\pi \\\end{aligned}[/tex]
The volume of the cylinder is [tex]36\pi {\text{ unit}}{{\text{s}}^3}.[/tex]
The volume of the cylinder is [tex]\boxed{288\pi {\text{ unit}}{{\text{s}}^3}}[/tex].Option (C) is correct.
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Learn more about inverse of the functionhttps://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497Answer details:
Grade: High School
Subject: Mathematics
Chapter: Mensuration
Keywords: Cylinder, surface area of the cylinder, volume of the cylinder, right cylinder, height, radius depth.
Need help on this question
Simplify. x-2/(x^2+4x-12)
James has 16 balloons.1/4 of his balloons are red.How many red balloons does he have?
A survey was conducted on 800 students regarding the number of automobiles in their household. A sample mean of 2.7 automobiles was determined, with a standard deviation of 0.7 automobiles. Assuming a 95% confidence level, which of the following statements holds true?
The statement that holds true with a 95% confidence level is true population mean of the number of automobiles in households of students is between 2.6524 and 2.7476."
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
To determine which of the following statements holds true, we need to use the confidence interval formula:
Confidence Interval = sample mean ± (critical value x standard error)
where the critical value is determined by the confidence level and the standard error is calculated using the formula:
standard error = standard deviation / sqrt(sample size)
With a 95% confidence level, the critical value is 1.96. Plugging in the values given in the question, we get:
standard error = 0.7 / sqrt(800) = 0.0247
Confidence Interval = 2.7 ± (1.96 x 0.0247) = (2.6524, 2.7476)
Therefore, the statement that holds true with a 95% confidence level is:
"The true population mean of the number of automobiles in households of students is between 2.6524 and 2.7476."
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Solve the system of equations using any method. 6x + 4y = −8 4x − 2y = 2 A) ( 11 7 , 2 7 ) B) ( 2 7 , 11 7 ) C) (− 2 7 , 11 7 ) D) (− 2 7 , − 11 7 )
What is the distance between the points (14, 29) and (14, 58) in the coordinate plane?
Steve is turning half of his backyard into a chicken pen. His backyard is a 24 meter by 45 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?
I dont inderstand this at all
How is commission calculated?
Commission is typically a percentage of sales paid to an agent or employee, and it can be calculated by multiplying the percentage rate by the sale amount. Real estate agencies and stock brokers have different structures for commission, which can significantly affect agents' earnings and motivation. Properly designed sales commission structures balance salary and commissions for optimum sales and customer satisfaction.
Commission is a fee paid to an employee or agent for conducting a transaction or service, typically a percentage of the sale made. Real estate agencies often pay agents a combination of salary and commission, with the intent to motivate them to achieve higher sales and provide satisfactory service to clients. For instance, agencies like RE/MAX pay almost 100% commission, attracting agents who are confident in their sales abilities and prefer a high-reward structure, though this may come at a cost to agency-wide cooperation.
The calculation of commission generally involves multiplying the sale amount by the commission percentage agreed upon. If a real estate agent sells a house for $200,000 and has a commission rate of 5%, their commission would be $200,000 * 0.05 = $10,000. While most agencies operate on average commission rates of about 50%, RE/MAX's near-100% commission structure can be very lucrative for highly skilled agents.
In the stock market, since May 1, 1975, when the SEC abolished fixed commissions, commission rates have been competitive and are typically lower for 'round lots' (buying or selling 100 shares) compared to 'odd lots'. It is also a common practice for firms to add a flat brokerage charge to the transaction.
To design an effective compensation plan incorporating commission along with a fixed salary, companies must carefully balance the two to ensure that they achieve an optimum balance between sales volume, profitability, and customer satisfaction. This balance is critical to attract and retain talented agents and salespeople who are motivated to perform well.
the main difference between secured and unsecured loans is that the secured loan ___.
A) has a higher interest rate
B) requires a cosigner
C) offers protection against identity theft
D) includes a pledge of collateral
Apex.
It includes a pledge of collateral.
6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives
Answer with Step-by-step explanation:
6x – 2y = 10
2x + 3y = 51
Solving the first equation above for y:
6x-2y=10
⇒ 2y=6x-10
dividing both sides by 2
y=3x-5
Putting value of y in second equation
2x + 3(3x-5) = 51
2x+9x-15=51
11x=51+15
11x=66
⇒ x=6
y=3×6-5
=18-5
= 13
Hence, solution is: x=6 and y=13
and Solving the first equation above for y gives: y=3x-5
Factor the polynomial completely.
x2 + 16
A) (x + 4)(x + 4)
B) (x - 4)(x - 4)
Which statement follows from the given theorem? Theorem: The diagonal of a parallelogram divides it into two congruent triangles.
A. Diagonals of a parallelogram bisect opposite angles.
B. Consecutive sides of a parallelogram are congruent.
C. Consecutive angles of a parallelogram are congruent.
D. Consecutive angles of a parallelogram are supplementary.
Answer:
Opposite sides of a parallelogram are congruent.
Step-by-step explanation:
The correct answer is A. Diagonals of a parallelogram bisect opposite angles.
The theorem states that the diagonal of a parallelogram divides it into two congruent triangles. This means that the two triangles have the same corresponding side lengths and angles. Since the diagonal is a common side to both triangles, the opposite angles must also be congruent.
Option B, "Consecutive sides of a parallelogram are congruent," is not always true. For example, in a rectangle, which is a type of parallelogram, the consecutive sides are not congruent.
Option C, "Consecutive angles of a parallelogram are congruent," is also not always true. For example, in a rectangle, which is a type of parallelogram, the consecutive angles are not congruent.
Option D, "Consecutive angles of a parallelogram are supplementary," is not always true. For example, in a square, which is a type of parallelogram, the consecutive angles are not supplementary.
Therefore, the only statement that follows from the given theorem is A. Diagonals of a parallelogram bisect opposite angles.
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7,24,25. 7 , 23,24 7, 25,26
Which of the following will form a right triangle
Answer:
7, 24, 25
Step-by-step explanation:
7^2=49
24^2 = 576
25^2 = 625
576 + 49 = 625.
therefore, its a right angle
Need help asap for this math problem !!!!!!
i believe the answer is d
Whats the average cost to put wood floors in a 12 ft x 16 ft room?
Harry was given an assignment. He had 32 days to get 256 tasks done at work.Which operation would he use to figure out how many tasks he needs to complete each day?
Answer:
d
Step-by-step explanation:
A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown below. After how many seconds will the grasshopper land on the ground? Round to the nearest tenth.
h(t) = -t^2 + 4/3t + 1/4
A. -0.2 seconds
B. 0.5 seconds
C. 1.5 seconds
D. 0.7 seconds
The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function , which is
[tex] h(t) =-t^2+\frac{4}{3}t+ \frac{1}{4} [/tex]
When the grasshopper land on the ground,
[tex] h(t)=0 [/tex]
that is,
[tex] -t^2+\frac{4}{3}t+ \frac{1}{4}=0 [/tex]
Multiplying whole equation by 12 to get rid of denominators 3 and 4
[tex] -12t^2+16t +3=0 [/tex]
[tex] (3-2t)(6t+1)=0
\\
3-2t=0 , 6t+1=0
\\
t= \frac{3}{2} , \frac{-1}{6} [/tex]
And time cant be negative, so the correct option is
[tex] t = \frac{3}{2}=1.5 seconds [/tex]
Correct option is C .
The correct option is (D) 0.7 seconds.To determine when the grasshopper lands on the ground based on its height function, solve the quadratic equation and round to the nearest tenth for the time in seconds.
The height of the grasshopper above the ground is given by the function h(t) = -t² + 4/3t + 1/4. To find when the grasshopper lands on the ground, set h(t) = 0 and solve for t.
By setting -t² + 4/3t + 1/4 = 0 and solving the quadratic equation, you'll find the solutions for t. Round to the nearest tenth to get the time when the grasshopper lands.
The correct answer is 0.7 seconds (D).
A company is looking to design a new cover for their smartphone. The scale drawing of the design is shown below. The coordinates of the actual cover are: R' (12, 0); S' (0, 0); T' (0, 16); U' (12, 16). Is the design of the cover similar to the actual cover?
Rectangle RSTU is shown. Point R is at 3,0. S is at 0,0. T is at 0,4. U is at 3,4.
Yes; the corresponding sides are proportional.
No; the corresponding sides are not proportional.
Yes; the corresponding angles are proportional.
No; the corresponding angles are not proportional.
A holding pen for cattle must be square and have a diagonal length of 84 84 meters.
a. find the length of a side of the pen.
b. find the area of the pen.
To find the length of a side of the pen, we can use the Pythagorean Theorem. The area of the pen can be calculated by multiplying the length of a side by itself.
Explanation:To find the length of a side of the pen, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal of the pen acts as the hypotenuse.
Let's let s represent the length of a side of the pen. Using the Pythagorean Theorem, we have:
s^2 + s^2 = 84^2
Simplifying the equation, we get:
2s^2 = 7056
Dividing both sides of the equation by 2, we get:
s^2 = 3528
Taking the square root of both sides, we get:
s ≈ 59.46 meters
To find the area of the pen, we can multiply the length of a side by itself. So, the area is:
s * s = 59.46 * 59.46 = 3536.8516 square meters
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A man has 14 coins in his pocket, all of which are dimes and quarters. if the total value of his change is $2.60, how many dimes and how many quarters does he have?
The area of a rectangle is 56 cm. The length is 2cm more than x and the width is 5 cm less than twice x.Solve for x
TIMED, need the answer
Determine whether the graph of the quadratic function y = –x2 – 10x + 1 opens upward or downward. Explain.
a. Because a > 0, the parabola opens downward.
b. Because a < 0, the parabola opens upward.
c. Because a < 0, the parabola opens downward.
d. Because a > 0, the parabola opens upward.
When a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards and from the given equation a < 0 that is why the graph of the quadratic equation is a parabola that opens downward.
Given :
Quadratic Function --- [tex]y = -x^2-10x + 1[/tex]
The graph of the quadratic equation is in the shape of the parabola. The generalized quadratic equation is given by:
[tex]ax^2 + bx +c = 0[/tex]
Now, compare the given equation ([tex]y = -x^2-10x + 1[/tex]) with the generalized quadratic equation which is given above.
[tex]a = -2[/tex]
b = -10
c = 1
According to the rules of the graph, when a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards.
Therefore, the correct option is c).
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Given:In quadrilateral WXYZ , WY and XZ bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram.
Given that the diagonals WY and XZ in a quadrilateral WXYZ bisect each other, we can confidently say that quadrilateral WXYZ is a parallelogram. This is based on the property of a parallelogram which states that its diagonals bisect each other.
Explanation:To prove that a quadrilateral is a parallelogram given that the diagonals bisect each other, we'll apply the properties of a parallelogram. According to the properties of a parallelogram, the diagonals bisect each other. That is to say, if WY and XZ bisect each other at point A (i.e., WA=AY and AZ=ZX), then WXYZ is a parallelogram. This satisfies the condition for the given quadrilateral and hence WXYZ is a parallelogram.
We use this information along with the parallelogram rule and the Pythagorean theorem to prove the quadrilateral is, in fact, a parallelogram. The rule states that if a quadrilateral has diagonals that bisect each other then it is a parallelogram.
In this case, since WY and XZ bisect each other at point A, we know that the lengths WA = AY and XA = AZ. Hence, quadrilateral WXYZ is indeed a parallelogram.
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