If a₁ = 5 and an 5an-1 then The value οf a₄ is 625.
What is arithmetic sequence?An arithmetic sequence is a sequence οf numbers in which each term after the first is fοund by adding a fixed cοnstant number, called the cοmmοn difference, tο the preceding term. Fοr example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a cοmmοn difference οf 3, since each term after the first is fοund by adding 3 tο the preceding term.
The nth term οf an arithmetic sequence can be fοund using the fοrmula:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, and d is the cοmmοn difference. The sum οf the first n terms οf an arithmetic sequence can be fοund using the fοrmula:
Sn = n/2 (a1 + an)
We are given that a₁ = 5, and that the nth term is 5 times the (n-1)th term. We can use this infοrmatiοn tο find the value οf a₄ as fοllοws:
a₂ = 5a₁ = 5(5) = 25
a₃ = 5a₂ = 5(25) = 125
a₄ = 5a₃ = 5(125) = 625
Therefore, the value of a₄ is 625.
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what is the square root of 36 divided by 5 times 12 divided by the cube root of 343 rounded to the nearest 2 decimal point
Answer:
2.06
Step-by-step explanation:
You want the value of the numerical expression √36÷5×12÷∛343.
CalculatorThis is a straightforward calculator problem. Your pocket calculator, or any of numerous calculator apps, online calculators, or spreadsheets can evaluate this expression for you.
The attachment shows the result is 2.06.
__
Additional comment
As expressed in this problem statement, the expression is ...
[tex]\dfrac{\sqrt{36}\times12}{5\times\sqrt[3]{343}}=\dfrac{6\cdot12}{5\cdot7}=\dfrac{72}{35}[/tex]
If you mean something else, you need to identify the quantities that need to be considered as a unit.
Solve the triangle PQR(find m < P, m < Q, and the length of side r. See Attached.
The following are the values for the angles and side of the right triangle using the trigonometric ratio: P = 28.6137, Q = 61.3863, and r = 14.0112
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
tan P= 6.71/12.3 {opposite/adjacent}
P = tan⁻¹(6.71/12.3)
P = 28.6137
Q = 180 - (90 + 28.6137) {sum of interior angles of a triangle}
Q = 61.3863
sin P = 6.71/r {opposite/hypotenuse}
sin 28.6137 = 6.71/r
r = 6.71/sin 28.6137 {cross multiplication}
r = 14.0112
Therefore, the values for the angles and side of the right triangle using the trigonometric ratio are: P = 28.6137, Q = 61.3863, and r = 14.0112
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Let G
be a group. Say what it means for a map φ:G→G
to be an automorphism. Show that the set-theoretic composition φψ=φ∘ψ
of any two automorphisms φ,ψ
is an automorphism. Prove that the set Aut(G)
of all automorphisms of the group G
with the operation of taking the composition is a group.
a) An automorphism of a group G is a bijective map φ:G→G that preserves the group structure. That is, φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹ for all a, b ∈ G.
b) The set-theoretic composition φψ of any two automorphisms φ, ψ is an automorphism, as it preserves the group structure and is bijective.
c) The set Aut(G) of all automorphisms of G, with the operation of composition of maps, is a group. This is because it satisfies the four group axioms: closure, associativity, identity, and inverses. Therefore, Aut(G) is a group under composition of maps.
An automorphism of a group G is a bijective map φ:G→G that preserves the group structure, meaning that for any elements a,b∈G, we have φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹. In other words, an automorphism is an isomorphism from G to itself.
To show that the set-theoretic composition φψ is an automorphism, we need to show that it satisfies the two conditions for being an automorphism. First, we have
(φψ)(ab) = φ(ψ(ab)) = φ(ψ(a)ψ(b)) = φ(ψ(a))φ(ψ(b)) = (φψ)(a)(φψ)(b)
using the fact that ψ and φ are automorphisms. Similarly,
(φψ)(a⁻¹) = φ(ψ(a⁻¹)) = φ(ψ(a))⁻¹ = (φψ)(a)⁻¹
using the fact that ψ and φ are automorphisms. Therefore, φψ is an automorphism.
To show that Aut(G) is a group, we need to show that it satisfies the four group axioms
Closure: If φ,ψ∈Aut(G), then φψ is also in Aut(G), as shown above.
Associativity: Composition of maps is associative, so (φψ)χ = φ(ψχ) for any automorphisms φ,ψ,χ of G.
Identity: The identity map id:G→G is an automorphism, since it clearly preserves the group structure and is bijective. It serves as the identity element in Aut(G), since φid = idφ = φ for any φ∈Aut(G).
Inverses: For any automorphism φ∈Aut(G), its inverse φ⁻¹ is also an automorphism, since it is bijective and preserves the group structure. Therefore, Aut(G) is closed under inverses.
Since Aut(G) satisfies all four group axioms, it is a group under composition of maps.
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can someone please!!! THANK YOU PLEASE!
Answer:
84 [cm³]
Step-by-step explanation:
if to imagine the given figure as parallelepiped, then the required volume can be calculated as V[1]-V[2], where V[2] is the additional part.
finally, V=10*2*7-7*2*4=84.
All the details are in the attachment.
the larger leg of a right triangle is 7cm more than the smaller leg the hypotenuse is 17cm find each leg
Answer:
So the lengths of the legs are approximately 8.6 cm and 15.6 cm.
Step-by-step explanation:
Let's call the smaller leg "x" and the larger leg "x + 7". According to the Pythagorean theorem, we know that:
x^2 + (x + 7)^2 = 17^2
Expanding the square on the left side and simplifying, we get:
2x^2 + 14x - 210 = 0
Dividing both sides by 2, we get:
x^2 + 7x - 105 = 0
Now we can solve for x using the quadratic formula:
x = (-7 ± sqrt(7^2 - 4(1)(-105))) / 2(1)
x = (-7 ± sqrt(649)) / 2
x ≈ -15.6 or x ≈ 8.6
Since we're dealing with lengths of sides in a triangle, we can't have a negative value for x. So we discard the negative solution and conclude that the smaller leg is approximately 8.6 cm.
To find the larger leg, we add 7 to x:
x + 7 ≈ 15.6 cm
Write the sentence as an equation. j plus 309 equals 313
Answer:j+309=313
Step-by-step explanation:
313-309=4
J=4
Using the data table, what is the probability that Baxter’s Shelties will NOT have a Tri-Color puppy this year? Justify your decision.
PLEASE ANSWER THIS QUESTION, 20 POINTS!!
Answer:
∠1 = 50
∠2 = 50
∠3 = 80
∠4 = 130
∠5 = 130
Step-by-step explanation:
∠1 = 180 - 130 = 50
∠2 = ∠1 = 50
∠3 = 180 - ∠1 - ∠2 = 180 - 50 - 50 = 80
∠4 = 180 - ∠2 = 180 - 50 = 130
∠5 = ∠4 = 130
8. A rectangle is inch longer
than it is wide.
Let w=width.
Let = length.
Graph=w+
l=w
By the values of w and l we can plot the graph as shown in figure.
Define the term graph?A graph in x-y axis plot is a visual representation of mathematical functions or data points on a Cartesian coordinate system. The x-axis represents the horizontal or independent variable, while the y-axis represents the vertical or dependent variable. A line or curve is drawn connecting the plotted points to show the relationship between the two variables.
Our equation is;
[tex]l = w +\frac{1}{2}[/tex]
Table between w and l can be draw as;
w l
1 [tex]1+\frac{1}{2}[/tex] = 1.5
2 [tex]2+\frac{1}{2}[/tex] = 2.5
3 [tex]3+\frac{1}{2}[/tex] = 3.5
4 [tex]4+\frac{1}{2}[/tex] = 4.5
By these values we can plot the graph as shown in figure.
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What type of exercise is ideal for a client who is new to strength training and learning new movement patterns
Answer:
For a client who is new to strength training and learning new movement patterns, it is ideal to start with bodyweight exercises and light resistance training. This will help them focus on proper form and technique without risking injury. Additionally, exercises that engage multiple muscle groups and involve functional movements, such as squats, lunges, and push-ups, are recommended as they provide a good foundation for overall strength and fitness. It is important to progress slowly and gradually increase resistance over time as the client becomes more comfortable with the movements and their strength improves. A certified personal trainer or strength coach can provide guidance and create a tailored program to meet the individual needs and goals of the client.
Vince is saving for a new mobile phone. The least expensive model Vince likes costs $225.90. Vince has saved $122.35. He used this solution to determine how much more he needs to save.
225.90 less-than-or-equal-to 122.35 + a. 225.90 minus 122.35 less-than-or-equal-to 122.35 minus 122.35 + a. 103.55 less-than-or-equal-to a.
Vince says that based on the solution, he should save a maximum of $103.55.
Is Vince correct?
Vince is correct because he found the correct solution to the inequality.
Vince is correct because he should save at least $103.55.
Vince is not correct because he wrote the wrong inequality to represent the situation.
Vince is not correct because he should have interpreted the solution as having to save a minimum of $103.55.
In light of the solution, Vince is correct in believing that he should only save up to $103.55.
How to determine with an example?1. a: to formally decide (something), particularly because of facts or evidence: to establish (something) precisely or with authority. Title of the land has now been determined by the town. The land's legal owner has been established by the town. A particular committee will choose the new policy.
Vince is accurate because he perceived the solution correctly.
The inequality 225.90 ≤ 122.35 + a show that the cost of a phone ($225.90) is lower than or equal to the sum of Vince's saved money ($122.35) plus the remaining amount he needs to save (a).
The inequity can be made simpler by taking 122.35 off of both sides to get 103.55 ≤ a. Hence, Vince now needs to put aside at least $103.55 in order to buy the cheapest phone he loves.
In light of the solution, Vince is correct in believing that he should only save up to $103.55.
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Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.
Important points to conduct a survey are; to gather information, make informed decisions, evaluate programs or services, identify trends, assess needs.
What is the need to conduct a survey?Surveys are conducted for a variety of reasons, including gathering information, making informed decisions, evaluating programs or services, identifying trends, and assessing needs. By using surveys, organizations can collect valuable data that can be used to inform decisions, improve programs or services, and better understand their target audience.
Surveys, also known as questionnaires, are used to gather information from a targeted group of individuals or a population. Surveys are an important tool for collecting data in a structured manner and can be used for a variety of reasons. Here are some of the reasons why surveys are conducted:
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Mr. Roy captures 15 snapping turtles near some wetland by his house. He marks them with a “math is cool” label and releases them back into the wild. 6 months later, he captures another 15 snapping turtles – 4 of which were marked. Estimate the population of snapping turtles in the area to the nearest whole number. Show your work.
Answer: 56
Step-by-step explanation:
One possible method to estimate the population of snapping turtles in the area is by using the mark and recapture method, also known as the Lincoln-Petersen index.
According to this method, the population size can be estimated by dividing the number of marked individuals in the second sample by the proportion of marked individuals in the combined sample. In other words:
Estimated population size = (Number of individuals in sample 1 × Number of individuals in sample 2) / Number of marked individuals in sample 2
Using the information provided in the problem, we can fill in the formula as follows:
Estimated population size = (15 × 15) / 4
Estimated population size = 56.25
Rounding to the nearest whole number, we get an estimated population size of 56 snapping turtles in the area.
A binomial probability experiment is conducted with the given parameters compute the probability of X successes in the N independent trials of the experiment an equals 10P equals 0.35 and X equals 3
Therefore, the probability of getting exactly 3 successes in 10 independent trials of a binomial probability experiment with probability of success 0.35 is approximately 0.213.
What is Probability?Probability is a branch of mathematics that deals with the measurement and analysis of random events. It is a way of quantifying the likelihood of an event occurring. Probability can be expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.
The concept of probability is used in a wide range of fields, including statistics, physics, engineering, economics, and finance. It helps us make predictions about the likelihood of future events and make informed decisions based on those predictions.
by the question.
To compute the probability of X successes in N independent trials of a binomial experiment, we use the following formula:
[tex]P(X = x) = (N choose x) * p^x * (1-p)^(N-x)[/tex]
where "N choose x" is the binomial coefficient, given by:
[tex](N choose x) = N! / (x!(N-x)!)[/tex]
In this case, we are given that:
N = 10 (number of independent trials)
p = 0.35 (probability of success in each trial)
X = 3 (number of successes)
Therefore, we can compute the probability of X successes as:
[tex]P(X = 3) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3)[/tex]
Using a calculator, we can calculate:
[tex](10 choose 3) = 120 / (3! * 7!) = 120 / (6 * 5040) = 0.1666666670.35^3 = 0.042875(1-0.35)^(10-3) = 0.338915[/tex]
Putting it all together:
[tex]P(X = 3) = 0.166666667 * 0.042875 * 0.338915 = 0.00240157[/tex]
Substituting these values into the formula, we get:
[tex]P(X = 3) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3)[/tex]
[tex]= (10! / (3! * 7!)) * 0.35^3 *0.65^7[/tex]
≈ 0.213
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assuming w1, w2, and w3 are 0-1 integer variables, the constraint w1 w2 w3 < 1 is often called a
The constraint w1 w2 w3 < 1, where w1, w2, and w3 are 0-1 integer variables, is often called a packing constraint. The packing constraint w1 w2 w3 < 1 limits the number of variables that can be set to 1 and is used to control the number of items that can be selected in integer programming problems.
A packing constraint is a type of constraint used in integer programming that limits the number of items that can be selected from a set of items. In this case, the constraint limits the number of variables that can take the value 1 to be less than 1.
The term "packing" comes from the idea of packing items into a container. In the context of integer programming, packing constraints are used to limit the number of items that can be "packed" into a container (i.e., set to 1), while ensuring that the total value of the packed items meets certain requirements or constraints.
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the math method that returns the nearest whole number that is greater than or equal to its argument is
The math method that returns the nearest whole number that is greater than or equal to its argument is the "ceiling" function, denoted by ⌈x⌉ in mathematics.
The Ceiling function is denoted by ⌈x⌉, is a mathematical function that takes a real number x as an input and returns the smallest integer that is greater than or equal to x.
The ceiling function takes a real number x as an argument and returns the smallest integer that is greater than or equal to x.
For example, if x = 3.7, then ⌈x⌉ = 4, since 4 is the smallest integer that is greater than or equal to 3.7.
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10 POINTS!! ASAP please help me find the area and also the outer perimeter!!!
Answer:
area of semi circle =pi r^2/2
3.14*6*6/2=56.2
area of rectangle=lb
=20*12=240
240+56.2=296.2
rounding it it will become 300 ft sqr
perimeter of rectangle without including 4th side=20+12+20=52
perimeter of semicircle=pi r+d (d is not needed here)
3.14*6=18.84
so total perimeter=52+18.84=70.84ft
Step-by-step explanation:
can you help me to solve this question?
The asymptotes of the function f(x) = (2x² - 5x + 3)/(x - 2) are given as follows:
Vertical asymptote at x = 2.Oblique asymptote at: y = 2x - 3/2.How to obtain the asymptotes of the function?The function for this problem is defined as follows:
f(x) = (2x² - 5x + 3)/(x - 2)
The vertical asymptote is the value of x for which the function is not defined, hence it is at the zero of the denominator, and thus it is given as follows:
x - 2 = 0
x = 2.
The oblique asymptote is at the quotient of the two functions, hence:
(mx + b)(x - 2) = 2x² - 5x + 3
mx² + (b - 2m) - 2b = 2x² - 5x + 3.
Hence the values of m and b are given as follows:
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A calico cat named Lucy has a favorite place to nap. It's a soft Matt located in front of a sunny window the mat is 12 total square feet and 4 ft long what is the width of Lucy's mat
Solve the following equations graphically (a) .12x - 4y = 12
Answer:
12x-4y=12
-4y= -12x+12
___________ [divide everything by -4]
-4
Y=3x+3
Step-by-step explanation:
on the y axis is 3 and the slope is 3
9. find the second decile of the following data set 24, 64, 25, 40, 45, 34, 14, 26, 28, 24, 58, 51 d2
The second decile of the given data set, "24, 64, 25, 40, 45, 34, 14, 26, 28, 24, 58, 51" is 24.
To find the second decile of a data set, we first need to arrange the data in order from lowest to highest, that is :
⇒ 14, 24, 24, 25, 26, 28, 34, 40, 45, 51, 58, 64
The second decile represents the value that divides the data into two parts, where 20% of the data is below the value and 80% of the data is above the value.
Since there are 12 data points in this set,
So, 20% of the data is equal to 0.2 × 12 = 2.4.
Since we cannot have a fractional data point, we round up to 3.
So, the second decile is the third value in the ordered data set.
which is 24.
Therefore, The second decile is 24.
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Given that x + 1/2 = 5, what is 2*x^2 - 3x + 6 - 3/x +2/x^2
pls help me soon
Sure, let's solve this step-by-step:
First, we need to solve for x in the equation x + 1/2 = 5.
We can do this by subtracting 1/2 from both sides, giving us x = 4 1/2.
Now, we can substitute x = 4 1/2 into the equation 2*x^2 - 3x + 6 - 3/x +2/x^2.
We can simplify the equation by multiplying both sides by x^2, giving us:
2*x^2 - 3x + 6 - 3/x +2 = 10*x^2 - 3x + 6.
Now, we can combine all of the terms with x:
10*x^2 - 6x + 6 = 0.
Finally, we can solve the equation using the quadratic formula:
x = 3/5 or x = 2.
Therefore, the answer to the equation is 10*(3/5)^2 - 6(3/5) + 6 = 4.8, or 10*2^2 - 6(2) + 6 = 16.
Find the circumference of the circle. Use 3.14 for the value of π, Round your answer to the nearest tenth.
Enter your answer and also show your work to demonstrate how you determined your answer.
given: circle a externally tangent to circle b. a common internal tangent is segment ab line s line r
Circle A externally tangent to circle B, a common internal tangent is line r. so, the correct answer is A).
In a configuration where Circle A is externally tangent to Circle B, a common internal tangent is a line that is tangent to both circles and lies between them. This line is commonly referred to as the "direct common tangent" or "line of centers" and is denoted by letter r.
Line r is the direct common tangent because it passes through the centers of both circles and is perpendicular to the line segment that connects their centers. It also separates the two circles into distinct regions. Therefore, line r is the correct answer.
Line s is a common external tangent because it is tangent to both circles but lies outside of them, while segment AB is not a tangent but rather a chord of Circle A. So, the correct option is A).
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___The given question is incomplete, the complete question is given below:
Given: Circle A externally tangent to Circle B.
A common internal tangent is
A. line r
B. Line s
C. Segment AB
Find the slope of the following graph and enter your result in the empty box.
Answer:
1
Step-by-step explanation:
slope = rise/run = 1/1 = 1
A rectangular paperboard measuring 33 inches long and 24 inches wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value 3.14 , and do not round your answer. Be sure to include the correct unit in your answer.
Answer: 565.92 square inches.
Step-by-step explanation:
To find the area of the paperboard that remains, we need to subtract the area of the semicircle from the area of the rectangle.
The rectangle has a length of 33 inches and a width of 24 inches, so its area is:
A_rect = length x width
A_rect = 33 in x 24 in
A_rect = 792 sq in
To find the area of the semicircle, we need to first find its radius. The diameter of the semicircle is the same as the width of the rectangle, which is 24 inches. So, the radius is:
r = 1/2 x diameter
r = 1/2 x 24 in
r = 12 in
The area of the semicircle is:
A_semicircle = 1/2 x pi x r^2
A_semicircle = 1/2 x 3.14 x 12^2
A_semicircle = 1/2 x 3.14 x 144
A_semicircle = 226.08 sq in
To find the area of the paperboard that remains, we subtract the area of the semicircle from the area of the rectangle:
A_remaining = A_rect - A_semicircle
A_remaining = 792 sq in - 226.08 sq in
A_remaining = 565.92 sq in
Therefore, the area of the paperboard that remains is 565.92 square inches.
Please help me to solve question 12 asap
The height of the pole is approximately 17.75 meters.
Describe Trigonometry?The main trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. They are used to relate the angles of a right triangle to the lengths of its sides. The sine function gives the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle. The cosine function gives the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent function gives the ratio of the length of the opposite side to the length of the adjacent side.
Let's denote the height of the pole as h, and let's denote the distance between the pole and the student's original position (due west of the pole) as x.
From the student's original position, we have a right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 40°. So, we have:
tan(40°) = h/x
From the student's new position (10 m due south of the original position), we have another right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 35°. The distance between the pole and the student's new position is (x+10) meters (the student moved 10 m south). So, we have:
tan(35°) = h/(x+10)
Now we have two equations with two unknowns (h and x). We can solve for x in terms of h from the first equation:
x = h/tan(40°)
Substitute this expression for x into the second equation:
tan(35°) = h/((h/tan(40°))+10)
Simplify and solve for h:
h = (10 tan(35°) tan(40°)) / (tan(40°) - tan(35°)) ≈ 17.75 m
Therefore, the height of the pole is approximately 17.75 meters.
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John plans to practice piano at least 2 hours this weekend.
If he practices 1 hours on Saturday and 14 hours on Sunday, will he meet his goal?
Answer:
Yes
Step-by-step explanation:
Yes because 1+14=15 hours and that is more than two
The length of a rectangle is 3 cm longer than twice the width. The area of the
rectangle is 90 sq cm. Find the length and the width of the rectangle.
PLEASEE HELP ITS DUE TONIGHT!!!
Find the area of the shaded region
Answer: 84
Step-by-step explanation:
Area of whole rectangle = lb = 11x9 = 99
Area of Inner rectangle = lb = 5x3 = 15
Area of Shaded region = Area of whole rectangle - Area of Inner rectangle
= 99 - 15
= 84
Answer:
Area of shaded region = 84 units²
Step-by-step explanation:
Area = Area of bigger - Area of smaller
[tex] { \tt{area = (11 \times 9) - (5 \times 3)}} \\ \\ { \tt{area = 99 - 15}} \\ \\ { \tt{area = 84 \: units {}^{2} }}[/tex]