Answer:
The first term is 10.
The second term is 16
The third term is 22.
We can see that the first term plus 6, is:
10 + 6 = 16
Then the first term plus 6 is equal to the second term.
And the second term plus 6 is:
16 + 6 = 22
Then the second term plus 6 is equal to the third term.
A) As we already found, the recursive rule is:
Aₙ = Aₙ₋₁ + 6
B) The explicit rule is:
Aₙ = A₁ + (n - 1)*6
Such that A1 is the first term, in this case A₁ = 10
Then:
Aₙ = 10 + (n - 1)*6
C)
Now we want to find A₅, then:
A₅ = 10 + (5 - 1)*6 = 34
There are 34 chairs in row 5.
D)
Here we have 17 rows, then we can have 17 terms, this means that the total number of chairs will be:
C = A₀ + A₁ + ... + A₁₆
This summation can be written as:
∑ 10 + (n - 1)*6 such that n goes from 0 to 16.
The formula for the sum of the first N terms of a sum like this is:
S(N) = (N)*(A₁ + Aₙ)/2
Then the sum of the 17 rows gives:
S(17) = 17*(10 + (10 + (17 - 1)*6)/2 = 986 chairs.
There are total 986 chairs in the considered auditorium and there are 34 chairs in the fifth row.
The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex]The explicit rule for this series is: [tex]T_n = 6n + 4[/tex]What is recursive rule?A rule defined such that its definition includes itself.
Example: [tex]F(x) = F(x-1) + c[/tex] is one such recursive rule.
For this case, we're provided that:
Seats in rows are 10 in front, 16 in second, 22 in third, and so on.
10 , 16 , 22 , .....
16 - 10 = 6
22 - 16 = 6
...
So consecutive difference is 6
If we take [tex]T_i[/tex] as ith term of the series then:
[tex]T_2 - T_1 = 6\\T_3 - T_2 = 6\\T_4 - T_3 = 6 \\T_5 - T_4 = 6\\\cdots\\T_{n} - T_{n-1} = 6[/tex]
Thus, the recursive rule for the given series is [tex]T_{n} - T_{n-1} = 6[/tex] or [tex]T_n = T_{n-1} + 6[/tex]
From this recursive rule, we can deduce the explicit formula as:
[tex]T_n = T_{n-1} + 6\\T_n = T_{n-2} + 6 + 6\\\cdots\\T_n = T_{n-k} + k \times 6\\T_n = T_1 + 6(n-1)\\T_n = 10 + 6(n-1) \: \rm (as \: T_1 = 10)\\[/tex]
Thus, the explicit rule for this series is [tex]T_n = 10 + 6(n-1)[/tex]
For 5th row, putting n = 5 gives us:
[tex]T_n = 10 + 6(n-1) = 6n + 4\\T_5 = 6(5) + 4 = 34[/tex]
If the auditorium has 17 rows, then total chairs are:
[tex]T = T_1 + T_2 + \cdots + T_{17} = \sum_{n=1}^{17} T_n\\\\T = \sum_{n=1}^{17} (10 + 6(n-1))\\\\T = \sum_{n=1}^{17} (6n + 4)\\\\T = 6\sum_{n=1}^{17} n + \sum_{n=1}^{17}4 = 6\sum_{n=1}^{17} n + 4 \times 17\\\\T = 6\left( \dfrac{17(18)}{2}\right) + 68 = 918 + 68\\\\T = 986[/tex]
(it is because [tex]\sum_{k=1}^n k = 1 + 2 + \cdots + n = \dfrac{n(n+1)}{2}[/tex] )
Thus, there are total 986 chairs in the considered auditorium. There are 34 chairs in the fifth row. The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex] The explicit rule for this series is: [tex]T_n = 6n + 4[/tex].
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Jim sliced a cylinder to create a cross section shaped like an oval. How did Jim slice the cylinder?
Answer:
He sliced it diagonally or at an angle.
Step-by-step explanation:
He sliced it diagonally (or at an angle) because the horizontal cross-section of a cylinder is a circle and the vertical cross-section of a cylinder is a rectangle, an oval is between a rectangle and a circle.
Given the following discrete probability mass function (f(x)): f(x) 1/4 1/8] 1/4 3/8 Find the following probabilities: a) P(x = 3) = b) P(x < 4) = c) P(x > 3) = d) P(2
These probabilities are calculated based on the given probability mass function and represent the likelihood of specific events occurring with the random variable x.
What is the probability of getting a sum of 7 when rolling two fair six-sided dice?P(x = 3) represents the probability of getting the value 3 from the random variable x. In this case, the probability is 1/4, which means there is a 1/4 chance of getting the value 3.
P(x < 4) represents the probability of getting a value less than 4 from the random variable x. Since all the values in the given probability mass function are less than 4, the probability is 1, indicating that it is certain to get a value less than 4.
P(x > 3) represents the probability of getting a value greater than 3 from the random variable x. In the given probability mass function, there are 3 values greater than 3 (1/4 + 3/8), so the probability is 3/8.
P(2 < x < 4) represents the probability of getting a value between 2 and 4 (exclusive) from the random variable x. In the given probability mass function, there are two values within this range (1/8 + 1/4), so the probability is 3/8.
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A few times a week, Scott treats himself to a small latte from his favorite coffee shop. Each latte costs $3.55. If Scott bought 15 lattes last month, how much did he spend?
$
Answer:
Scott spent $53.25 on lattes last month.
Step-by-step explanation:
To find how much Scott spent in total, multiply the number of lattes bought by the cost of each latte:
15 × 3.55
53.25
The polygon shown is regular and has 9 sides. It is a regular nonagon.
Type in your answer to complete the sentence.
What is the measure of ∠F
∠
F
?
The measure of ∠F in the regular nonagon is 140 degrees.
In a regular nonagon, all angles have the same measure since it is a regular polygon. To find the measure of ∠F, we need to divide the sum of the interior angles of a nonagon by the number of sides.
The sum of the interior angles of a polygon can be found using the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n represents the number of sides.
For a nonagon with 9 sides, the sum of the interior angles is:
Sum of interior angles = (9 - 2) * 180 degrees = 7 * 180 degrees = 1260 degrees.
Since all angles in a regular nonagon have the same measure, we can find the measure of ∠F by dividing the sum of the interior angles by the number of sides:
Measure of ∠F = Sum of interior angles / Number of sides = 1260 degrees / 9 = 140 degrees.
Therefore, the measure of ∠F in the regular nonagon is 140 degrees.
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What’s an equivalent expression of 24a-16
Answer:
24 A-(8+8)
Step-by-step explanation:
Answer: 4(6a-4) This is one equivalent expression of 24a-16.
5. Andrea ate half as many crackers as Darnell. Darnell ate 3 more crackers than Ziyah. If Ziyah ate 21 crackers, how many did Andrea eat?
A. 24 crackers
B. 18 crackers
C. 10 crackers
D. 63 crackers
E 7 crackers
F. 12 crackers
The object below is made of solid plastic. It is a cylinder with an indentation at the top in the shape of a cone. What is the volume of the object (in cubic inches)? *
Answer:
97.6 cm³
Step-by-step explanation:
Volume of plastic object :
Volume of cylinder - volume of cone
From. The diagram. :
Radius, r = diameter /2 = 4/2
Volume of cylinder = pi*r²h
V = 22/7 * 2² * 8 = 100.53096 cm³
Volume of cone = 1/3*pi*r²h
V = 1/3 * 22/7 * 2² * 8
V = 2.9321531 cm³
(100.53096 - 2.9321531) cm³
= 97.598 cm³
= 97.6 cm³
Plzzzzz i need help!!!!!
Step-by-step explanation:
here is the anewer then change in fractionWhat is the slope of the line graphed in this grid? Help.
Answer:
A slope of 2/3
Step-by-step explanation:
if you look at the line, starting at the y axis, then just count up 2 and over three, in other graphed lines, just start at the y axis and try to find where the line crosses a specific point, then calculate the rise/run.
What are the angles in degreees
Answer: A is 70 B is 45 and C is 50
Step-by-step explanation:
Hi can someone help me understand how to work this problem out? I'll mark brainliest. Thanks:)
It costs $.001 per hour for electricity to run a light bulb. Find the cost per month.
Answer:
0.73001
Step-by-step explanation:
1 month = 730.01 hours
730.01 * $0.001
= 0.73001
Approximately 0.73 or 0.7.
HELPPPPPPPPPPPPP
In a bag of marbles there are 3 blue marbles, 3 red marbles, and 3 green marbles. You pick three marbles out of a bag one at a time without replacement. How many ways can you pick two green marbles first and one red marble last?
Answer:
separating
Step-by-step explanation:
separate the colors and if u separate the green from the red u can easily pick the marbles out
EXTREMELY IMPORTANT! HELP SOMEONE CORRECT!!!!
Answer: 891ft just did this
Step-by-step explanation:
Answer: 891ft I think.
Step-by-step explanation:
¿Porque crees que es importante tener conocimientos sobre el cálculo de área de polígonos y circunferencias?
Step-by-step explanation:
En la vida diaria estamos rodeados de figuras geométricas como los polígonos y las circunferencias;alguno ejemplos son los siguientes: las ventanas,las puertas,el reloj de pared,un balón,los vasos de cocina,las llantas de una bicicleta,un automóvil,etc.
Si necesitamos pintar la sala de nuestra casa,debemos saber exactamente la cantidad de pintura que vamos a necesitar ,para eso debemos calcular el área exacta del tramo de pared.
Si necesitamos acabar con la maleza de nuestra jardin ,debemos saber exactamente cual es el área de nuestro jardín ,para aplicar el volumen o la proporción exacta del plaguicida.
Conocer el área de un terreno o lote nos da una idea de lo grande que es y del valor que tiene, por eso es importante saber cómo obtener el área.
Are the expressions 3(x + y) + 2y + 10 and x + 5y + 2(x + 5) equivalent?
.
PLEASE HURRY.
SHOW WORK
Answer: x^5/x^1 = x^4
y^2/y^2 = 1
so
x^4
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1. the height of a water bottle in a bathtub, w, is a function of time, t. Let P represent this function. Height is measured in inches and time is in minutes.
match each statement in function with a description.
A: P(0)=0
1. after 20 minutes, the bathtub is empty
2. the bathtub starts out with no water
3. the height of the water is 4 inches
4. the height of the water is 10 inches after 4 minutes.
3. After 10 minutes, the height of the water is 4 inches
Answer:
1) P(20) = 0
2) P(0) = 0
3) P(10) = 4
4) P(4) = 10
Step-by-step explanation:
We are told that the function P(t) denotes the height of the water in the bath tub.
At P(0) = 0, it means that after 0 minutes, there is no water in the bath tub.
1) If after 20 minutes, the bathtub is empty, then we can depict the function as; P(20) = 0
2) The bath tub starts out with no water. It means at 0 minutes, there was no water in the tub. Thus;
P(0) = 0
3) If after 10 minutes, the height of the water is to be 4 inches, then;
P(10) = 4
4) If the height is 10 inches after 4 minutes, then;
P(4) = 10
Simplify. Simplify.
62+15
Answer:
62+15= 77
Step-by-step explanation:
Answer:
77
Can I have brain list
Step-by-step explanation:
PRE-CALC no links.
How much should be deposited in an account paying 3% interest, compounded monthly, in order to have a balance of $9,000 after 17 years and 3 months?
Answer:
$5367.54
Step-by-step explanation:
9000 = P(1 + .03/12)^207*
9000 = P×1.676744643
P = 5367.54
*207 = 12 x 17.25
Please i need help. Thank you!
write a letter to your friend in another school telling her why you like your school
Answer:
I hope this helps but I do not really know what your school is like.
Step-by-step explanation:
Dear Friend,
I wish you could be here at my school, it is really a great school. Here everyone is so helpful, and you are sure to find lots of friends. The teachers don't care of your race, gender, or backround, or anyone. Everyone is so nice and caring. Also, their food is healthy and delicious, and they have different varieties of food each day so that you have to pick from. Did I also tell you that, safety is the number one thing that is on the list, they help remind you what you can do to stay safe, and they have top security with guards, cameras, locked gates, and drills. Also, during lunch or recess or lunch they have plenty of things you do, like they have benches for relaxing, basketball courts, and a big soccer field. Finally, bullying is not tolerated here. But, if there is anything that is bothering you, we beautiful amazing counselors that will help you through anything. So, I help this makes you want to come over here.
-Sincerely,
Your friend.
Please help me with this.
20
94
Find the value of the missing angle
Answer:
x = 74°
Step-by-step explanation:
supplementary angle to 94° = 86°
x = 180° - 20° - 86° = 74°
in triangle ABC with the right triangle at vertex C, sin a=35/7
Evaluate the line integrals.
a. C is the line segment from (-1.0.2) to (1,-3,8) ∫_{c} yz ds
The line integral is -165/7.
The given line integral is ∫ ds, where is the line segment from (−1,0,2) to (1,−3,8).
The line integral is given by the following formula:
∫ (,,) ds = ∫_^ ((),(),()) ||'()|| d
Here,() = 2 − 1, () = −3, () = 6 + 2and a = 0 and b = 1.
We know that ds = ||'()|| d.
Let us find '() first.'() = 〈2,−3,6〉,
therefore, ||'()|| = √(2² + (−3)² + 6²) = 7
So, ds = 7dt.
We need to find the value of (,,) at each of the parameterizations, so let us find those next.
(,,) = = (−3)(6 + 2) = −18² − 6
Now we can compute the integral:
∫ ds=∫0^1(−18² − 6)7=−162/7 - 3/7= −(165/7)
Therefore, the value of the line integral is -165/7.
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help needed for this question please
Answer:
11.72sq.m
Step-by-step explanation:
Area of the shaded region = Area o triangle - Area of the semicircle
Area of triangle = 1/2 * base * height
Area of triangle = 1/2 * 6 * 6
Area of triangle = 3 * 6
Area of triangle = 18sq. m
Area of semicircle = πr²/2
r is the radius = 2m
Area of semicircle = π(2)²/2
Area of semicircle = 2(3.14)
Area of semicircle = 6.28sq. m
Area of the shaded region = 18 - 6.28
Area of the shaded region = 11.72sq.m
validity coefficients greater than _________ are considered in the very high range.
When a validity coefficient exceeds 0.90, it is considered to be in the very high range.
Validity coefficients greater than 0.90 are considered in the very high range.
Validity coefficients measure the strength of the relationship between a test or measurement and the construct it is intended to assess. The coefficients range from -1.00 to +1.00, where higher values indicate stronger validity.
When a validity coefficient exceeds 0.90, it is considered to be in the very high range. This suggests that the test or measurement has a high degree of accuracy in assessing the intended construct, demonstrating a strong relationship between the two. Validity coefficients in this range provide strong evidence that the test is measuring what it is intended to measure.
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Suppose a random sample of eight students is chosen from the student body of a community college consisting of 40 % males. What is the probability that among the students in the sample no more than 7 are female ?
The probability that among the students in the sample no more than 7 are female is approximately 0.982 or 98.2%.
To calculate the probability that no more than 7 students in the sample are female, we need to consider the binomial distribution.
The community college student body consists of 40% males, which means 60% are females.
We have a random sample of 8 students.
To get the probability, we can use the binomial probability formula:
P(X ≤ k) = Σ (n choose x) * p^x * (1-p)^(n-x)
Where:
n is the number of trials (sample size)
k is the number of successes (female students)
p is the probability of success (proportion of females in the population)
(n choose x) is the binomial coefficient
In this case:
n = 8 (sample size)
p = 0.6 (proportion of females in the population)
k can take the values 0, 1, 2, 3, 4, 5, 6, or 7
We need to calculate the sum of probabilities for each value of k:
P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)
Calculating each term using the binomial probability formula and summing them will give us the desired probability.
Note: The binomial probability formula assumes independent and identically distributed (i.i.d.) trials and a fixed probability of success.
The community college student body consists of 40% males, which means 60% are females.
We have a random sample of 8 students.
Let's calculate the probability:
P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)
To calculate each term, we use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Where:
n is the number of trials (sample size) = 8
k is the number of successes (female students)
p is the probability of success (proportion of females in the population) = 0.6
Let's calculate each term and sum them up:
P(X = 0) = (8 choose 0) * (0.6^0) * (0.4^8) = 0.1678
P(X = 1) = (8 choose 1) * (0.6^1) * (0.4^7) = 0.3579
P(X = 2) = (8 choose 2) * (0.6^2) * (0.4^6) = 0.3020
P(X = 3) = (8 choose 3) * (0.6^3) * (0.4^5) = 0.1463
P(X = 4) = (8 choose 4) * (0.6^4) * (0.4^4) = 0.0410
P(X = 5) = (8 choose 5) * (0.6^5) * (0.4^3) = 0.0068
P(X = 6) = (8 choose 6) * (0.6^6) * (0.4^2) = 0.0006
P(X = 7) = (8 choose 7) * (0.6^7) * (0.4^1) = 0.00003
Summing up the probabilities:
P(X ≤ 7) = 0.1678 + 0.3579 + 0.3020 + 0.1463 + 0.0410 + 0.0068 + 0.0006 + 0.00003 ≈ 0.982
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Factor the expression:
x2-1x-56
Write the quadratic equation in standard form:
4x2 + 5x + 10 = 2x
The quadratic equation 4x² + 5x + 10 = 2x in standard terms can be written as 4x² + 3x + 10 = 0.
A quadratic equation is of the form ax² + bx + c = 0, where a is the coefficient of x², b is the coefficient of x and c is the constant term. Such equations are called quadratic because the degree of the equation is 2 as the highest power of the polynomial is 2. Such equations have 2 roots, whose sum equals [tex]-\frac{b}{a}[/tex] and their product is equal to [tex]\frac{a}{c}[/tex].
Some examples of quadratic equations are 2x² + 3x - 1, 4x² + 16x + 4, etcectra.
The given quadratic equation is 4x² + 5x + 10 = 2x.
4x² + 5x + 10 = 2x
4x² + 5x - 2x + 10 = 2x - 2x
4x² + 3x + 10 = 0.
Hence, in the standard form, the quadratic equation 4x² + 5x + 10 = 2x can be written as 4x² + 3x + 10 = 0.
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Using the information from the previous question, find the equation in standard form for the area of the fenced-in section in terms of the length of the field.
(area = length • width)
Answer:
y = x2 − 500x + 60,000
Step-by-step explanation:
area of the fenced-in section = length • width
y = (x − 200)(x − 300)
= x² − 300x − 200x + 60,000
= x² − 500x + 60,000