Determine the nth term formula for the number of square tiles in the nth figure.
Answers
Answer:
the nth term is 2n
Step-by-step explanation:
notice how for each number of tiles, 2, 4, 6, 8, 10, they are all multiples of 2, so like ok 2 is definitely in the term, next check how n can fit. Well, since they are multiples, you multiply n by 2, now check to see if you dont need to add any values by the following method:
first number = 2, then 2(1) = 2 if n = 1
second = 4, then (2)(2) = 4 if n = 2
its all the same for the rest. Each new diagram or tile structures represents n, so if n =1, then there are 2 tiles, if n = 4 there are 8 tiles and so on, which explains us why the nth term is 2n
The nth term formula for the number of square tiles in the nth figure is aₙ=2n.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given sequence is 2, 4, 6, 8, 10,.....
Here, a=2 and d=4-2=2
Substitute a=2 and d=2 in aₙ=a+(n-1)d, we get
aₙ=2+(n-1)×2
aₙ=2+2n-2
aₙ=2n
Therefore, the nth term formula for the number of square tiles in the nth figure is aₙ=2n.
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Related Questions
GIVING BRAINLIEST & 30 POINTS!
(please do the math and don't use other sources I know answering this question means nothing to you other than points but just think about me and others who might get the question wrong if you other sources.) Ty!
−np − 5 = 4(c − 2)
Which of the following solves for n?
n = the quantity 4 times c minus 3 all over negative p
n = the quantity 4 times c minus 13 all over negative p
n = the quantity 4 times c plus 3 all over p
n = the quantity 4 times c plus 13 all over p
Answers
Answer:
n = the quantity 4 times c minus 3 all over negative p
Explanation:
Interpretation of answers to equation
n = the quantity 4 times c minus 3 all over negative p = [tex]\frac{4c-3}{-p}[/tex]
n = the quantity 4 times c minus 13 all over negative p = [tex]\frac{4c-13}{-p}[/tex]
n = the quantity 4 times c plus 3 all over p = [tex]\frac{4c+3}{p}[/tex]
n = the quantity 4 times c plus 13 all over p = [tex]\frac{4c+13}{p}[/tex]
Step-by-step:
[tex]-np-5=4(c-2)[/tex]
[tex]-np-5=4c-4(2)[/tex]
[tex]-np-5=4c-8[/tex]
[tex]-np-5+5=4c-8+5[/tex]
[tex]-np=4c-3[/tex]
Divide both side by -p
[tex]n=\frac{4c-3}{-p}[/tex]
n = the quantity 4 times c minus 3 all over negative p
Answer:
The answer is the option A, which is: A.) n ≥ − the quantity 4 times c minus 3 all over p.
Step-by-step explanation:
You have −np − 5 ≤ 4(c − 2)
When you solve for n, you obtain:
-np-5 ≤ 4(c-2)
-np≤4c-8+5
Therefore, you have:
n≤-(4c-3/p)
Hope it helps :) make me as Brainlest! Or Expert-Verified Answer!
Differentiate each function with respect to x.
I need the step. The answer is A
Answers
The differentiation for the given function is f'(x) = -27x⁸- 48x³. The correct option is (A).
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).
Geometric meaning of it is the slope of the function at a given point.
The given function is f(x) = (-x⁵ - 4). 3x⁴
It is in the form of u.v, the differentiation is given as below,
uv' + vu'
As per the above expression suppose (-x⁵ - 4) = u and 3x⁴ = v.
Now, the differentiation can be done as follows,
f'(x) = d(-x⁵ - 4)/dx × 3x⁴ + (-x⁵ - 4) × d(3x⁴)/dx
= -5x⁴ × 3x⁴ + (-x⁵ - 4) × 4 × 3x³
= -15x⁸ + 12x³(-x⁵ - 4)
= -15x⁸ - 12x⁸ - 48x³
= -27x⁸- 48x³
Hence, the differentiation is obtained as f'(x) = -27x⁸- 48x³.
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what is 1/9 divided by 7
Answers
1/63.
Step-by-step explanation:1. Write the expression.[tex]\frac{\frac{1}{9} }{7}[/tex]
2. Apply the fraction rules.Check the attached image below.
[tex]\frac{1}{9}*\frac{1}{7}[/tex]
3. Simplify.[tex]\frac{1}{9}*\frac{1}{7}=\\\\ \frac{1*1}{9*7} =\\\\ \frac{1}{63}[/tex]
4. Conclude.[tex]\frac{\frac{1}{9} }{7}=\frac{1}{63}[/tex]
Find the domain and range of the function represented by the graph.
Answers
Answer:
D = [1,5]
R= [0,4]
.........
Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
Answers
The volume of the composite solid is 5770.28ft³
How to determine the volume of the solid?The composite solid is made up of a cylinder and a hemisphere
The volume is the addition of the two solids
Volume=[tex]\pi[/tex]r²h +2/3πr²
The given parameters are
π=22/7
h=22 ft
r=9 ft
Input the values to get
(22/7*9*9*22) + (2/3*22/7*9*9)
Simplifying the terms to get
5600.57+169.71
The volume is = 5770.28c
ft³
In conclusion, the volume of the solid is 5,770.28ft³
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Roll a fair die twice. Let A be the even that the sum of the two rolls equals six, and let B be the even that the same number comes up twice. What is P(A/B)?
Answers
The value of P(A/B) will be = 1/4
As per the question,
As a fair six-sided die is rolled twice
So, the total number of outcomes will be N=6^2=36
A: sum of the two rolls is 5
[tex]$$\begin{aligned}& A=\{(1,4),(2,3),(3,2),(4,1)\} \\& n(A)=4 \\& P(A)=\frac{n(A)}{N}=\frac{4}{36}\end{aligned}$$[/tex]
B: The first roll results in a 2
[tex]B=\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\}$ \\$n(B)=6$ \\$P(B)=\frac{n(B)}{N}=\frac{6}{36}$ \\$B \cap A=\{(2,3)\}$ \\$\cap(B \cap A)=1$ \\$P(B \cap A)=\frac{n(B \cap A)}{N}=\frac{1}{36}$\\$P(B \mid A)=\frac{P(B \cap A)}{P(A)}=\frac{1 / 36}{4 / 36}=\frac{1}{36} \times \frac{36}{4}$$P(B \mid A)=\frac{1}{4}$[/tex]
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suppose that you want to describe the relationship between operating cost per hour and number of passenger
Answers
The operating cost per hour of a plane increases with the number of passengers it carries. More passengers require more fuel, maintenance, and staff, which all increase the overall cost of operating the plane per hour.
Additionally, if the plane is larger and designed to carry more passengers, the operating cost per hour may be higher than for smaller planes.The cost of operating an aircraft per hour is directly related to the number of passengers it carries. As the number of passengers increases, so too does the amount of fuel, maintenance, and personnel needed to safely operate the plane, resulting in a higher operating cost per hour. Additionally, larger planes that can carry more passengers also tend to have higher operating costs per hour than smaller planes.
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The students in a gym class measured the length of their longest jump (in feet). The results were tallied and are reported in the following histogram. How many students jumped greater than 8.5 but less than 11.5 feet?
Answers
On solving the provided question we can say that, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.
What is frequency?the frequency or reality that something occurs frequently or a great number of times within a specific time frame. The frequency of buses, for instance, has been the subject of more complaints in recent months.
Number of students jumped greater than 8.5 but less than 11.5= frequency of length of jump greater than 8.5 but less than 11.5
AND,
frequency of length of jump greater than 8.5 but less than 11.5 is -
Number of students jumped greater than 8.5 and less than 9.5 + Number of students jumped greater than 9.5 but less than 10.5 + Number of students jumped greater than 10.5 but less than 11.5=
3+3+1=7 ( since, sum of respective frequencies of the three class)
so, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.
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Find the value of x:
a)
b)
Answers
The value of x in first part = 16
The value of x in second part = 10
Part a
The angle U = angle Z = 54 degrees
Angle V = angle Y = 67 degrees
Therefore angle W = angle X
The sum of the angles in a triangle is 180 degrees
Then, the equation will be
54 + 67 + a = 180
121 + a = 180
a = 180 - 121
a = 59 degrees
Then
4x - 5 = 59
4x = 59 + 5
4x = 64
x = 64/4
x = 16
Part 2
Similarly the unknown angle as b
Sum of the the angles in a triangle is 180 degrees
58 + 74 + b = 180
132 + b = 180
b = 180 - 132
b = 48 degrees
Then the equation will be
5x - 2 = 48
5x = 48 + 2
5x = 50
x = 50/5
x = 10
Therefore, the value of x in the part a and part b are 16 and 10 respectively
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It’s number 14 btw, I swear this homework stresses me out so much
Answers
Answer:
m∠WYZ = 23°
Step-by-step explanation:
4) Describe the continuity or discontinuity of the graphed function.
Answers
This function is continuous at all values except x=-2 and x=-1. We know that it is discontinuous at these values because there is a hole discontinuity at x=-2 and a jump discontinuity at x=-1.
How many solutions does the following system of equations have? Show your reasoning.
4x+6y= 24
2x+3y=12
Answers
infinitely many solutions because these 2 lines are exactly the same line. If you multiply the 2nd equation by 2, you will get the 1st one, or if you divide the 1st equation by 2, you will get the 2nd one.
Calculate the p-value for each of the given hypothesis test scenarios below. Round p-values to four decimal places. • Find the p-value for a left-tailed test of hypothesis for a mean when the test statistic has been calculated as -1.03. Assume the population standard deviation is known. p-value • Find the p-value for a right-tailed test of hypothesis for a mean when the test statistic has been calculated as 2.58. Assume the population standard deviation is known. p-value • Find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as 1.91. p-value = Find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as - 1.16. p-value =
Answers
The p-value of ay distribution given can be calculated using the formula P(Z < X) where X is any sample data.
To find the p-value for a left-tailed test of hypothesis for a mean when the test statistic has been calculated as -1.03, you can use the following formula:
p-value = P(Z < -1.03)
Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is less than -1.03. The resulting p-value will be the probability that the test statistic is as extreme or more extreme than the observed value, given that the null hypothesis is true.
To find the p-value for a right-tailed test of hypothesis for a mean when the test statistic has been calculated as 2.58, you can use the following formula:
p-value = P(Z > 2.58)
Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is greater than 2.58. The resulting p-value will be the probability that the test statistic is as extreme or more extreme than the observed value, given that the null hypothesis is true.
To find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as 1.91, you can use the following formula:
p-value = 2 * P(Z > 1.91)
Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is greater than 1.91. The resulting p-value will be twice this probability, since the test is two-tailed and we need to consider both tails of the distribution.
To find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as -1.16, you can use the following formula:
p-value = 2 * P(Z < -1.16)
Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is less than -1.16. The resulting p-value will be twice this probability, since the test is two-tailed and we need to consider both tails of the distribution.
Note that in all of these cases, you need to assume that the population standard deviation is known. If the population standard deviation is not known, you will need to use a different test statistic and a different approach to calculate the p-value.
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The weight of a medium-size orange selected at random from a large bin of oranges at the local supermarket is a random variable with mean u = 12 ounces and standard deviation 0 = 1.2 ounces. Suppose we independently pick two oranges at random from the bin. The expected value of the sum of the weights of the two oranges, in pounds (1 pound = 16 ounces) is: a. 24. b. 1.5. c. 0.75. 24/16 = 1.5 lb. 4 4
Answers
Therefore, the probability that the probability that the difference in the weights of the two oranges exceeds 3 ounces is 0.0385 .
Describe probability.The study of numerical estimates of the likelihood that an event will occur or that a proposition is true is known as probability. The probability of an occurrence is a number between 0 and 1, where 0 often indicates that the event is impossible and 1 typically indicates that it will happen.
Here,
Let X1 and X2 represent the weights of the two oranges.
Let d=X1 - X2 represent the difference in weight.
We're given that
X1 ~ N(12, 1.2^2)
X2 ~ N(12, 1.2^2)
Then,
Then, d N(12-12, 1.22 +1.22) or N (0, 21.22)
So the standard deviation of this √2.1.22 = 1.6971
Let's find
=> P(d>3)
=> 1-(1891)
=> 1-0.9615 = 0.0385
Therefore the probability that the probability that the difference in the weights of the two oranges exceeds 3 ounces is 0.0385 .
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The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers.
What is the rate of change of y with respect to x for this line?
Answers
The rate of change of y with respect to x for this line is 4 / 5 .
Given :
The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers.
From the graph :
The marked coordinates are ( 5 , 7 ) and ( -5 , -1 ) .
slope m = rate of change of y / rate of change of x
= y2 - y1 / x2 - x1
= -1 -7 / -5 - 5
= -8 / -10
= 8 / 10
= 4 / 5
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3x-8=14 need help asap
Answers
[tex]3x-8=14[/tex]
Add 8 to both sides:
[tex]3x-8+8=14+8[/tex]
[tex]3x=22[/tex]
Divide both sides by 3:
[tex]\dfrac{3x}{3} =\dfrac{22}{3}[/tex]
[tex]\fbox{x = $\dfrac{22}{3} $ or 7.333333}[/tex]
A man buys a car worth 850,000 rupees. He agrees to pay 350,000 rupees immediately and the balance amount in 60 equal monthly installments with 12% p.a. compounded monthly. What is the amount of the monthly installments?
Answers
Answer:
The monthly installment amount for this loan is approximately
142956.575 rupees.
Step-by-step explanation:
To determine the amount of the monthly installments, we need to calculate the total interest on the loan and add it to the principal amount. The total interest can be calculated using the formula for compound interest, which is:Total Interest = Principal x (1 + Interest Rate/Compound Frequency)^(Compound Frequency x Number of Years) - PrincipalIn this case, the principal is 850,000 rupees, the interest rate is 12% per year, the compound frequency is monthly (12/1), and the number of years is 5 (60/12). Plugging these values into the formula, we get:Total Interest = 850,000 x (1 + 0.12/12)^(12 x 5) - 850,000
= 850,000 x (1 + 0.01)^60 - 850,000
= 850,000 x 1.01^60 - 850,000
= 850,000 x 1.675837 - 850,000
= 850,000 x 0.675837
= 573569.45
To determine the monthly installment amount, we add the total interest to the principal and divide the result by the number of months in the loan period:Monthly Installment = (Principal + Total Interest) / Number of Months= (850000 + 573569.45) / 60
= 142956.575
Therefore, the monthly installment amount for this loan is approximately 142956.575 rupees.If you have any question let me know.
The number 21 is 3.5% of what?
Answers
Answer:
The number 21 is 3.5% of 600---------------------------
Let the number be x.
Set equation for x and solve:
3.5% of x is 21x*3.5/100 = 21x = 21*100/3.5x = 600The hypotenuse of a 30°-60°-90° triangle has a length of 12 cm. Which could be the length of a leg of the triangle?
A. 8 cm
0
B. 10 cm
C. 6 cm
OD 6√3 cm
Answers
Answer:
C and D are correct.
Step-by-step explanation:
In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
What is the measure of
A. 116°
B. 25°
C. 62°
D. 54°
Answers
Answer:
62 degrees
Step-by-step explanation:
(3x-13)+(2x+4)+(180-116)=180
5x-9+64=180
5x+55=180
-55. -55
5x=125
/5. /5
x=25
3(25)-13
75-13
62
hopes this helps
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.62 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are at least 3.48? Please do not round your answer.
Answers
The percentage of students that have grade point averages that are at least 3.48 is of:
2.5%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.Considering the mean of 2.62 and the standard deviation of 0.43, a grade point average of at least 3.48 is at least two standard deviations above the mean.
100 - 95 = 5% of the measures are at least two standard deviations of the mean. Considering the symmetry of the normal distribution, we have that:
2.5% of the measures are at least 2 standard deviations below the mean.2.5% of the measures are at least 2 standard deviations above the mean. -> At least 3.48.More can be learned about the Empirical Rule at brainly.com/question/10093236
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The histogram shows a distribution of average daily steps in a gym class.
Which statement best describes the distribution?
A. The data is positively skewed because the majority of the data is clustered to the left of the center.
B. The data is negatively skewed because the majority of the data is clustered to the left of the center.
C. The data is normally distributed because the majority of the data is in the center.
D. The data does not support any distribution trend.
Answers
The statement that best describes the distribution is C. The data is normally distributed because the majority of the data is in the center.
What is the histogram about?A histogram is a graphical representation of data points organized into ranges that the user specifies. The histogram, which resembles a bar graph in appearance, condenses a data series into an easily interpreted visual by grouping many data points into logical ranges or bins.
Because the majority of the data is in the center, the data is normally distributed.
Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are identical.
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Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected. 31. {(x, y) | 0
Answers
This set {(x, y) | 0 is (a) open, (b) connected, and (c) not simply-connected.
(a) Open: This set is open because all points within the set have a neighborhood that is also within the set.
(b) Connected: This set is connected because there is a path between any two points in the set that does not leave the set.
(c) Not simply-connected: This set is not simply-connected because it contains a hole in the center, which is not a simply-connected space.
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I NEED HELP ASAP PLS
Answers
For the given circle the value of cotθ is -√30/√19.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The terminal side of an angle θ.
The standard position intersects the unit circle at (√30/7, -√19/7).
We need to find the value of cotθ.
Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (√30/7, -√19/7)
cotθ=x/y
=-√30/7/√19/7
=-√30/7×7/√19
=-√30/√19
Hence, the value of cotθ is -√30/√19 for the given circle.
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David saves money from his teaching job to buy a new boat when he retires in 20 years. The boat will cost $30,000. He has $12,000 in his simple interest savings account. To reach his goal by retirement, David should
Answer: move his money to a compound interest account
Answers
David ought to keep saving money in his simple interest account regardless of his current age.
He will be able to purchase his 30,000 USD boat at that rate each year. David would need to put at least 5 to 10 percent of his income into a savings account with simple interest.
Your initial investment as well as any interest that has already been accrued will earn interest in a compound interest account. The "compounding" factor is the appreciation of interest based on interest that occurs over time. On the other hand, simple interest accounts only pay interest on the initial principal.
Can a compound interest account result in a loss of funds?Both guaranteed and non-guaranteed substances benefit from compounding. You might lose all of your money or some of it. Stocks, income trusts, real estate, mutual funds, and gold are all examples.
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If the system of the linear equations above has infinitely many solutions, and c is a constant, what is the value of c?
A) - 6
B) - 3
C) - 2
D) - 1
Answers
Option D is the correct answer. The value of 'c' for the given system of linear equations with infinitely many solutions is - 1.
A linear equation is an equation in which the highest power of the variable is always 1 and the equations are the equations of degree 1. It is the equation for the straight line.
The standard form of the linear equation is ax+by+c =0
where a ≠ 0 and b ≠ 0.
Given a system of linear equations are
1. 3x-9y=-6
⇒ x-3y=-2
Therefore,
a1=1, b1=-3, c1=-2
2. [tex]\frac{x}{2} -\frac{3y}{2} =c\\[/tex]
⇒ x-3y=2c
Therefore,
a2=1, b2=-3, c2=2
For the system of linear equations with infinitely many solutions,
compare c1=c2
2c=-2
⇒ c=-1
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A dolphin dives down into the ocean and resurfaces along a path that is modeled by x2 – 16x – 8y = 0, where the distances are in feet. How many feet is the dolphin from its starting point along the water's surface? (5 points)
Answers
Answer:
approx 17 ft
Step-by-step explanation:
You need to find the 'zeroes' of this equation......where the depth is zero
x^2 - 16x - 8 = 0 You will need to use the Quadratic Formula
with a = 1 b= -16 c = -8
to find x = 8 +- 6 sqrt 2
the distance between these zeroes is 12 sqrt2 = 16.97 = ~ 17 feet
Suppose △ABC has coordinates A(2, 3), B(5, 1), C(4, 4), and △ABC is mapped to △A′B′C′ by a reflection across the line y = 5 followed by a translation 1 unit down. select all the statements that are true about the coordinates of △A′B′C′.
Answers
The coordinates of A' = (1, 7)
The coordinates of B' = (4, 9)
The coordinates of C' = (3, 6)
What is a reflection?There are two ways of translation.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
ΔABC:
Coordinates:
A = (2, 3)
B = (5, 1)
C = (4, 4)
Reflection across y = 5.
So,
A = (2, 5)
There are two units between y = 5 and y = 3.
We add 2 units with the y-coordinate of A = (2, 5)
5 - 3 = 2
So,
A = (2, 5 + 2)
A = (2, 7)
Similarly,
5 - 1 = 4
B = (5, 5 + 4) = (5. 9)
5 - 4 = 1
C = (4, 5 + 1) = (4. 6)
Translation of 1 unit down.
A = (2 - 1, 7) = (1, 7)
B = (5 - 1, 9) = (4, 9)
C = (4 - 1, 6) = (3, 6)
Thus,
The coordinates of ΔA'B'C' are (1, 7), (4, 9), and (3, 6).
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WRLD ...Need Help....999
Lillian has a rectangular garden with an area of 10x2 +33x – 7 square feet. Find the expressions that would represent the length and width of the garden. Make sure you show all your work for full credit.
Answers
The expressions representing the length and width of the garden is (5x-1)(2x+7)
What are expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given that, Lillian has a rectangular garden with an area of 10x²+33x-7 square feet.
To find the expressions that would represent the length and width of the garden, we will factorize the expression representing the area of the garden,
10x²+33x-7
= 10x²+35x-2x-7
= 5x(2x+7)-1(2x+7)
= (5x-1)(2x+7)
Hence, The expressions representing the length and width of the garden is (5x-1)(2x+7)
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a circular spinner is divided into 10 sectors of equal area: 2 red sectors, 3 blue, 4 yellow, and 1 green. find p(blue) on a single spin.
Answers
Answer:
3/10
Step-by-step explanation:
There are 3 blue sectors out of the total 10.