The correct response is option 3 i.e n = 6.
What is a Sequence?
A sequence is a list of items arranged in a stepwise order, with members coming either before or after.
We know that,
aₙ = a₁ + (n-1)×d .............................(Arithmetic sequence formulae)
here,
aₙ = -13
a₁ = 7
d = -4
Substituting the values we get,
-13 = 7 + (n-1)×(-4)
∵ (-4)×(n-1) = -20
=> n-1 = 5
=> n = 6
Thus, the final value of n is 6.
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The water usage at a car wash is modeled by the equation w(x) = 4x3 6x2 − 11x 7, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 4x3 4x2 − 11x 8 c(x) = 3x3 4x2 − 11x − 8 c(x) = 3x3 4x2 − 11x 8 c(x) = 4x3 4x2 − 11x − 8
A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
What is an equation?A relationship between two variables is defined as an equation; if we plot the graph of the linear equation, we will get a straight line.To find a function, C(x), to model the water used by the car wash on a shorter day:
Given information -
The water usage at a car wash is modeled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open.The amount of decrease in water used is modeled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.
We are trying to find:
C(x) = W(x) - D(x)C(x) = (4x³ + 6x²− 11x + 7) - (x³ + 2x² + 15)C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15C(x) = 3x³ + 4x² - 11x - 8Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
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The correct question is given below:
The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day
Out of the 50 students in Mrs. Green's class, 8 have a pet. What percent of the students in Mrs. Green's class have a pet?
The percent of students in Mrs. Green's class that have a pet is
%.
Answer:
4%
Step-by-step explanation:
In a right triangle, given are the
lengths of two sides. What should be
used to solve for the length of the
third side?
*
Answer:
bro you can find 3rd side by using pythogras thegrom
Step-by-step explanation:
1\(h ^{2} = p ^{2} + {p}^{2} \)Scarlett is deciding between two parking garages. garage a charges an initial fee of $11 to park plus $5 per hour. garage b charges an initial fee of $8 to park plus $6 per hour. let a a represent the amount garage a would charge if scarlett parks for t t hours, and let b b represent the amount garage b would charge if scarlett parks for t t hours. write an equation for each situation, in terms of t , t, and determine the hours parked, t , t, that would make the cost of each garage the same.
The number of hours parked for the cost of each garage to be the same is 3 hours.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let t represent the number of hours parked at either garage A or garage B. Hence:
Total charges at garage A (A) = 5t + 11
A = 5t + 11
Total charges at garage B (B) = 6t + 8
B = 6t + 8
If both garages have the same cost:
5t + 11 = 6t + 8
t = 3
The number of hours parked for the cost of each garage to be the same is 3 hours.
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test the null hypothesis: h0:(μ1−μ2)=0 versus the alternative hypothesis: ha:(μ1−μ2)≠0. using α=0.04, give the following: The test statistic Z ____
since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.
To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:
Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))
Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.
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Determine the Equation of the line Perpendicular to 2x -3y +5= 0 and passers through (-6,-3)
9514 1404 393
Answer:
3x +2y +24 = 0
Step-by-step explanation:
In general, the equation of a perpendicular line can be found by swapping the coefficients of x and y, then negating one of them. The value of the constant will be what is required to make the line pass through the given point.
The equation will be of the form ...
3x +2y +c = 0
At the given point, (x, y) = (-6, -3), we have ...
3(-6) +2(-3) +c = 0 . . . . substitute the given point coordinates
-18 -6 +c = 0 . . .simplify
c = 24 . . . . . . . . add 24
The general-form equation for the line is ...
3x +2y +24 = 0 . . . . . shown in blue in the attachment
State the horizontal asymptote of the rational function. F(x) = 5x + 1/ 9x -2
Answer:
\(y=\frac{5}{9}\)
Step-by-step explanation:
For the graph of \(y=f(x)\),
the horizontal asymptote becomes \(y=\frac{5}{9}\)
how many driving lessons do you need to do with a professioanl instructor before my parents could teach me
The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.
In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.
The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.
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A binomial has been partially factored, as shown below:
x2 − 36 = (x + 6)(_____)
Which of the following binomials represents the missing factor?
(x + 6)
(x − 6)
(x + 30)
(x − 30)
Answer:
(x-6)
Step-by-step explanation:
x² - 36 = (x+6)(x-6)
remeber that a negative and a positive = negative
and in this case 36 is negatice to verify your answer multiply brackets .
Answer:
b is correct
Step-by-step explanation:
5(4 + 6) - 72 and explain the answer thank you
Answer:
-22
Step-by-step explanation:
5(4+6)-72
5(10)-72
50-72
-22
Answer:
5(4+6)-72
5x10-72
50-72
-22
Step-by-step explanation:
If you use PEMDAS, the P is for parenthesis.
So first, you do the (4+6) and then multiply it by 5, when you get that answer, do the final step. Subtract 72.
Hope this helped!! <3
For National High Five Day, Ronnie’s class decides that everyone in the class should exchange one high five with each other person in the class. If there are 20 people in Ronnie’s class, how many high fives will be exchanged?
To determine the number of high fives that will be exchanged, we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person .
To calculate the number of unique pairs, we can use the formula for combinations, which is nC2, where n is the number of people .So, for Ronnie's class with 20 people, the number of high fives exchanged is:20C2 = (20 * 19) / (2 * 1) = 190.Therefore, a total of 190 high fives will be exchanged in Ronnie's class on National High Five Day. we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person needs to give a high five to every other person, excluding themselves.
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Gina is making bags of trail mix for hiking club. She will use 20 ounces of walnuts, 11.2 ounces of almonds, and 28.3 ounces of cashews. This amount makes 25 bags of trail mix. How many ounces are in each bag?
Answer:
Step-by-step explanation:
20 oz walnuts = 20/25 = 0.8 ounces of walnuts per bag. / bag
11.2 oz of almonds = 11.2 / 25 = 0.448 ounces of almonds / bag
28.3 oz of cashews = 28.3 / 25 = 1.132 oz of cashews / bag
5.03, 5.00, 4.97, 4.94, __, 4.88 description
HELP FAST
The population density of Lemonland is 15 lemon trees per acre. Exactly 795 lemon trees grow in Lemonland. How many acres are in Lemonland?
A.40
B.44
C.53
D.66
HELP PLSSSSSSSS!!! TY!!! If the sum of four consecutive numbers is 1998, what is the third number? The third number is ?
Answer:
500
Step-by-step explanation:
Hello!
Let the smallest number be x. The next number would be x + 1, then the next would be x + 2, then x + 3.
The sum of these four is 1998.
Solve for x:
x + (x + 1) + (x + 2) + (x + 3) = 19984x + 6 = 19984x = 1992x = 498The third number is (x + 2), so simply add 2 to 498 = 500
The third number is 500.
All 4 numbers are 498, 499, 500, and 501.
Aditi bought 20 apples at Rs 25 each and sold them at Rs 32 each. What is her total profit?
Answer: 140
Step-by-step explanation: 25x20=500
32x20=640
640-500= 140!!
use newton's method to approximate the indicated root of the equation correct to six decimal positive root of 4 cos x = x4
The positive root of the equation \(4cos(x) - x^4\) using Newton's method is 0.866966.
We begin with an initial guess \(x_{0}=1\), and we can iteratively define the calculation using the formula:
\(x_{i+1}= x_{i} - \frac{ f(x_{i})}{f'(x_{i})}\)
where \(f(x)=4cos(x) - x^4\)and f'(x) is the derivative of f(x).
So, \(f'(x) = -4sin(x) - 4x^3.\)
We repeat this process, using the previous approximation to find the next one, until we reach the desired accuracy.
In each iteration, we substitute the current approximation into the formula to refine our estimate.
Iteration 1: \(x_{1}= x_{0}- f(x_{0})/f'(x_{0})= 1 - \frac{ (4cos(1) - 1^4)}{(-4sin(1) - 4(1)^3)}= 1.576\)
Iteration 2: \(x_{2}= x_{1} - f(x_{1})/f'(x_{1}) = 1.1576 - \frac{(4cos(1.1576) - 1.1576^4)}{(-4sin(1.1576) - 4(1.1576)^3)} = 1.2055\)
Iteration 3: \(x_{3}= x_{2} - f(x_{2})/f'(x_{2}) = 1.2055 - \frac{4cos(1.2055-(1.2055)^4)) }{(-4sin(1.2055) - 4(1.2055)^3)} = 1.2080\)
After several iterations, we get that the positive root of the equation \(4cos(x) - x^4\) is approximate x ≈ 0.866966, accurate to six decimal places.
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A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to
buy each player a bottle of water and an energy bar. The price of one energy bar is $2.
Let w equal the price of a bottle of water. Write an equation that
represents the situation.
Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50
Step-by-step explanation: i dont know what to write??
It took Ruthene 1/4 an hour to run 2 mi. What was her average speed?
Answer:
8
Step-by-step explanation:
Answer:
8mph
Step-by-step explanation:
Because it took Ruthene 1/4 of an hour or 15 minutes to run two miles, if she were to run for an entire hour she would go 4 times as far, or 8 miles. This means that Ruthene had an average speed of 8mph.
In reference to line items, how many permutations are possible with the letters "ABC"?
So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.
Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.
In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:
3! = 3 x 2 x 1 = 6
This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:
ABC
ACB
BAC
BCA
CAB
CBA
To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:
3 x 2 x 1 = 6
In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.
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9511961
4. Analyze and Persevere What is the
measurement of the longest line segment
in a right rectangular prism that is
4.8 inches long, 1.4 inches wide, and
8 inches tall? Round to the nearest tenth of
an inch.
9.43 inches is the measure of the longest segment
How to solve for the longest segment
We are aware that the diagonal connecting the two opposing corners at the top and bottom will be the longest segment.
We know how to find the diagonal of a right triangular prism using the following formula:
d = \(\sqrt{w^2 + l^2+h^2} \\\\\)
where w = width = 1.4
l = length = 4.8
h = height = 8
We would put these values in the formula above
\(d = \sqrt{1.4^2 + 4.8^2+8^2} \\\\\)
d = \(\sqrt{1.96+23.04+64}\)
d = 9.43
The measure of the longest line segment is given as 9.43 inches
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t
H
2
5
3
7.5
5
12.5
10 25
write an equation that represents the relationship
An airliner carries 50 passengers and has doors with a height of 70 in. Heights of men are normally distributed with a mean of 69. 0 in and a standard deviation of 2. 8 in. Complete parts (a) through (d). A. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is 0. 6406. (Round to four decimal places as needed. ) b. If half of the 50 passengers are men, find the probability that the mean height of the 25 men is less than 70 in. The probability is 0. 9633. (Round to four decimal places as needed. )
The probability is 0.6480.
The probability is 0.9629.
How to solve for the probability1. This can be computed using the standard normal distribution as follows:
z = (70 - 69.0) / 2.8 = 0.357
Using a standard normal table or calculator, we find that P(Z ≤ 0.357) ≈ 0.6480. Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.6480.
2. = 2.8/√25 = 0.56 inches.
We want to find P(x < 70), which is the probability that the mean height of the 25 men is less than 70 inches. This can be standardized using the standard normal distribution as follows:
z = (70 - 69.0) / 0.56 = 1.79
Using a standard normal table or calculator, we find that P(Z < 1.79) ≈ 0.9629. Therefore, the probability that the mean height of the 25 men is less than 70 inches is approximately 0.9629.
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Ayoooo please help What's the sum to 0. 061 + 0. 43
SHESHHHHHHHH
Answer:
0.491
Step-by-step explanation:
(4x + 5)
Quadrilateral ABCD is inscribed in a
circle.
What is the measure of angle A?
(x + 15)
Enter your answer in the box
mZA=
Answer:
<A = 133degrees
Step-by-step explanation:
Find the diagram attached
Using the theorem that "the sum of opposite angle of a cyclic quadilateral is 180 degrees, hence;
m<A + m<C = 180
4x+5 + x + 15 = 180
4x+x+5+15 = 180
5x+20 = 180
5x = 180 - 20
5x = 160
x = 160/5
x = 32degrees
Get the measure of angle A
<A = 4x+5
<A = 4(32)+5
<A = 128+5
<A = 133degrees
#6 write it in y=MX+B
Please help me!!!!! I will give 15 points
Answer:
Step-by-step explanation:
all of them could be made into a difference of squares since they all have a minus sign in the expression, but maybe the question is if they can easily be made into a difference of squares.
with that said
\(y^{4}\) -2 => \((y^{2}) ^{2}\)- \((\sqrt{2}) ^{2}\) could be a difference of squares but not easy
25\(m^{2}\)\(n^{4}\) - 1 => (5m\(n^{2}\))^2 - \(1^{2}\) yes and pretty easy
\(p^{8}\) - \(q^{4}\) => \((p^{\sqrt{8} } )^2\)-\((q^{2})^2\) could be but not easy
16\(x^{2}\) - 24 => \((4x)^{2}\) -\((\sqrt{24}) ^{2}\) could be but not easy
A line passes through the point (6, - 3) and has a slope of -2.
Write an equation in slope-Intercept form for thls line.
To find the equation of the line passing through the point (6, -3) with a slope of -2, we can use the point-slope form of the equation of a line:y - y1 = m(x - x1)where (x1, y1) is the given point and m is the slope.Substituting the given values, we get:y - (-3) = -2(x - 6)Simplifying, we get:y + 3 = -2x + 12Subtracting 3 from both sides, we get:y = -2x + 9So, the equation of the line is y = -2x + 9
9 cans of paint are needed to
paint 4 rooms. Exactly how
many cans of paint are needed to
paint 10 rooms? How many cans
of paint should be purchased?
PLEASE HELP!! DUE REALLY SOON (LINK)
Answer:
youngest=115
middle=150
elder=230
Step-by-step explanation:
let the youngest be x
the middle will be x+35
the oldest will be 2x
x+x+35+2x=495
4x+35=495
4x=495-35
4x=460
x=115
since the youngest is x,the money he will receive is $115.
the middle will be x+35 which is equal to 115+35=$150.
lastly the oldest will be 2x which is equal to 2×115=$230.
Answer:
Defined variables:
Y - amount the youngest son gets
M - amount the middle son gets
O - amount the oldest son gets
Y got $115
M got $150
O got $230
Step by Step explaination:
If Y is the youngest, then the middle son, M = Y + $35 since the middle child gets $35 more than the youngest gets. The oldest son, O = 2Y since it’s twice the amount the youngest gets.
If you add each of those up, the equation you get is 2Y + (Y+$35) + Y = $495. Now you can solve for Y, the youngest son.
2Y + (Y+$35) + Y = $495
4Y + $35 = $495
4Y = $460
Y = $115
If Y gets $115 and M gets $35 more, M gets $150.
If Y gets $115 and O gets twice that amount, O gets $230.
To double check my work add 230 + 115 + 150. This equals $495. Hope this helps!