There is need of total of 9 levels to stack 285 boxes.
What is a sequence ?A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.
Some examples for sequence are :
2,4,6,8,10,12
3,9,27,81,243
What is recursive sequence ?The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.
In a sequence , first term always known as initial term.
and difference between two terms are known as common difference. It is denoted by d.
General form of sequence is :
[tex]a_1,a_2,a_3,----,a_n[/tex]
where , [tex]a_n[/tex] = last term in sequence.
According to question,
Also, number of boxes at level recursively n =[tex]a_{n-1} + n^2[/tex]
The formula to find number of level for 285 boxes is :
[tex]a_n > =285[/tex]
now, find each level
[tex]a_1 = 1 , a_2 = 1 + 2^2 = 5 , a_3 = 5+3^2 = 14,\\a_4 = 14 + 4^2 = 30\\a_5 = 30 + 5^2 = 55\\a_6 = 55 + 6^2 = 91\\a_7 = 91 + 7^2 = 140\\a_8 = 140 + 8^2 = 204\\a_9 = 204 +9^2 = 285[/tex]
thus, to stack 285 boxes total numbers of level are 9.
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The complete question is :
Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.
a. How many boxes of same size would need for next lower level?
b. How many boxes of same size would need to add the 3 levels?
c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?
An item sold for $500. three years later it was only worth $10. how much is the annual depreciation rate
The annual depreciation rate is $163.33.
Depreciation rate is calculated using the formula
Annual Depreciation Rate =(Total Depreciable Cost)/(time) ..where time is in years.
In the given Question
The original cost of item = $500
Cost of item after 3 years = $10
Total Depreciable Cost = (original cost of item) -(Cost of item after 3 years)
=500-10
=$490
So,
Annual Depreciation Amount = (Total Depreciable Cost)/(time)
Annual Depreciation Amount =490/3=163.33
Hence, the item cost would depreciate $163.33 per year.
which means every year the amount will depreciate by $163.33
Therefore, the annual depreciation rate is $163.33 .
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Match each expression with its translation.
1. 4 d
2. y-4
3. 4+x
4. 4÷n
NEXT ESTION
udentAssignment/index?eh-1005519587#
ASK FOR HELP
four divided by a number
four added to a number
the product of a number and four
the difference between a number
and four
Answer:
Step-by-step explanation:
division is ÷
addition is +
product is the word for the answer of multiplying numbers together
difference is the word for the answer of subtracting numbers
in this problem, any variable is called a number.
4 d : this is the product. you can write 4 x d, but a shortcut is to exclude the multiplication
y - 4 : this is subtraction, so the difference
4 + x : this is addition
4 ÷ n : this is division
ALGEBRA Which equation is equivalent to 7 x-3(2-5 x)=8 x ?
F 2 x-6=8
G 22 x-6=8 x
H -8 x-6=8 x
J 22 x+6=8 x
According to this the given equation the correct option is G. 22x - 6 = 8x
What precisely is algebra?Algebra is a field of mathematics that aids in the depiction of issues or situations using mathematical expressions. To construct a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division.
What is the primary goal of algebra?Algebra is a generalized version of arithmetic in which variables stand in for nonspecific numbers. Its objective seems to be to solve algebraic equations including equation systems.
According to given data:The equation is = 7x-3(2-5x)=8x
Now simplifying the equation:
7x-3(2-5x)=8x
7x - 6 + 15x = 8x
22x - 6 = 8x
According to this the correct option is G. 22x - 6 = 8x
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-9(-4)-6 find the value of expression
Answer:
30
Step-by-step explanation:
-9 × -4 = 36 (the two negatives cancel each other out)
36 - 6 = 30
Use your results from Exercises 1-6 to determine whether the given measures define 0 , 1,2, or infinitely many acute triangles. Justify your answers.
a=10, b=10, m
An unlimited number of acute triangles can be formed from two sides without an angle measurement, such as a = 10 m and b = 10 m.
As an illustration -
If our side lengths are 10m and 10m, and our angle value goes from 0 to 90 degrees, how many different acute triangles can we create?
Construct a triangle with sides of 10 and 10 metres, an angle of 45 degrees, and a third side that can be extended to the desired length. You have built a triangle.
By changing the third side's length and angle, we can make a whole different triangle that is identical to this one.
Never forget to choose the side lengths and angles. There is a suggestion that you might decide to take a different step. The same angles can be used to make an unlimited number of different triangles.
As a result, with a single angle and a single side length, we can create an endless number of triangles.
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Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
15,20,24
The following set of numbers 15, 20, and 24 can be the measures of the sides of an acute triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 15, b = 20, and c = 24
a + b > c 15 + 20 > 24 35 > 24 True
a + c > b 15 + 24 > 20 39 > 20 True
b + c > a 20 + 24 > 15 44 > 15 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
15^2 + 20^2 = 625
2. Compare it to the square of the largest side.
24^2 = 576
625 > 576
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 15, 20, and 24 can be the measure of the sides of an acute triangle.
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Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. -5,10,-20,40, . . . . . . .
It is a geometric sequence since it has a common ratio. The next two terms are -80, 160
Let a sequence be:
a(1), a(2), a(3), a(4), a(5), ...
To determine whether the sequence is an arithmetic sequence, or a geometric sequence, or neither, we need to check how its consecutive terms relate to each other.
They have a common difference.The given sequence is:
-5,10,-20,40, . . .
Let us check whether they have a common difference:a(2) - a(1) = 10 - (-5) = 15
a(4) - a(3) = 40 - (-20) = 60
So they don't have a common difference.
Let us check whether they have a common ratioa(4)/a(3) = 40/(-20) = -2
a(3)/a(2) = -20/(10) = -2
a(2)/a(1) = 10/(-5) = -2
So they have a common ratio, i.e. r = -2.
Therefore, we can conclude that -5,10,-20,40, . . is a geometric sequence.
In a geometric sequence, the next term is equal to the previous term times the ratio.
We already have: -5,10,-20,40, ...
Hence:
Next term after 40 = 40 . (-2) = -80
Next term after -80 = -80 . (-2) = 160
Thus, the next two terms are -80, 160
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Another one please anyone available to help?!
The prime factors of 80 are 2, 2, 2, 2, and 5, then its decomposition is:
80 = 2*2*2*2*5 = 2⁴*5
How to express a number as a product of its prime factors?
To do this, we start with our number, which in this case is 80, and we start dividing it by prime numbers.
The first prime number is 2, taking the quotient:
80/2 = 40
So 2 is a factor.
Now we try to divide again by 2:
40/2 = 20
Now we can divide by 2 again:
20/2 = 10
And again:
10/2 = 5
And 5 is another prime number, so now we only can divide by 5:
5/5 = 1
So, we divided by 2 four times and by 5 one time, then the decomposition in prime factors is:
80 = 2*2*2*2*5 = 2⁴*5
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What type of errors do you think scientist make with measurements?
Ready?
Answer:
The errors that may occur in the measurement of a physical quantity can be classified into six types: constant error, systematic error, random error, absolute error, relative error and percentage error.
Step-by-step explanation:
Hope this will be helpful for you.
Determine the solutions of the equation: absolute value of the quantity one fourth times x plus 7 end quantity minus 3 equals 24. x = −136 and x = 136 x = −136 and x = 80 x = −112 and x = 80 x = −80 and x = 80
The solutions are x = 80 and x = -136
Given equation is [tex]|\frac{x}{4}+7|-3=24[/tex].
We need to solve for x.
Absolute value function is given by, [tex]|x| = \left \{ {{x\ if\ x\geq 0} \atop {-x\ if\ x < 0}} \right.[/tex]
So the equation may have two solutions.
We use the property of absolute value to solve [tex]|\frac{x}{4}+7|-3=24[/tex]
⇒ [tex](\frac{x}{4}+7)-3=24[/tex] and [tex]-(\frac{x}{4}+7)-3=24[/tex]
⇒ [tex](\frac{x}{4}+7)=27[/tex] and [tex](\frac{x}{4}+7)=-27[/tex]
⇒ [tex]\frac{x}{4}=20[/tex] and [tex]\frac{x}{4}=-34[/tex]
⇒ x = 80 and x = -136
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Answer:
The solutions are x = 80 and x = -136
Step-by-step explanation:
6
The endpoints of AB are -16 and -4. Find the coordinate of the point P that partitions the segment in
the ratio 2 : 1.
The coordinate of point P is
The coordinate of point P is -8.
We are given that the endpoints of AB are -16 and -4.
This means that A is at -16 and B is at -4
Therefore, the total length of the line AB will be-
-16 - (-4) = -12 units
But since length cannot be negative, we take only the absolute value, the length of AB comes out to be 12 units.
Now, point P divides AB in the ratio 2:1
The length of these two parts will be
12 × 2/3 and 12 x 1/3
= 8 units and 4 units
This means that AP = 8 units and PB = 4 units
Hence the coordinate of P will be (-16 + 8) or (-4 - 4)
Thus, the coordinate of point P is -8.
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Find the length of a segment ab but a= -7 and b=9
The length of a segment ab is 16 units.
Given that, a= -7 and b=9.
We need to find the length of a segment ab.
What is a line segment?In geometry, a line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.
The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimetres (cm), millimetres (mm) or by conventional units like feet or inches.
Now, the length of a segment ab=a+b
=7+9=16
Therefore, the length of a segment ab is 16 units.
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-4(m+3)=24
SHOW YOUR WORK
Answer:
Answer: M=-9
Step-by-step explanation:
[tex]\frac{-4(m+3)}{-4} =\frac{24}{-4} M + 3 = -6 (Subtract -3 from 3 and -6) M = -9[/tex]
For each equation, find the center and radius of the circle.
(x+3)²+(y-5)²=81
The equation of the circle (x + 3)^2 + (y - 5)^2 = 81 has a radius of 9 and a center located at (3 , 5).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 3)^2 + (y - 5)^2 = 81, is in standard form, then
h = -3
k = 5
r = 9
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I need help with 43 please
Answer:
6y ≤ 10
Step-by-step explanation:
6 times a number y= 6y
less than or equal to = ≤
10 = 10
so...
6y ≤ 10
Answer:
6y = 10
Step-by-step explanation:
Identify the location of point P under translation (x+3, y+1) .
A. (0,6)
B. (0,3)
C. (2,-4)
D. (2,4)
The location of point P under the translation is (2, 4)
How to identify the location of point P under the translation?The complete question is added as an attachment
The location of point P is
P = (-1, 3)
The translation is given as:
(x+3, y+1)
So, we have
P' =(-1 + 3, 3 + 1)
Evaluate
P' = (2, 4)
Hence, the location of point P under the translation is (2, 4)
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ALGEBRA The measure of the larger acute angle in a right triangle is two degrees less than three times the measure of the smaller acute angle. Find the measure of each angle.
The measure of each angle is 23 degrees, 67 degrees, and 90 degrees.
What is Acute angle ?The acute angle can be defined as the angle less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle.
What is a Right triangle ?Right triangle is also known as right angled triangle. If a triangle has atleast one 90° angle then the triangle is said to be a right angled triangle. A right angle triangle always follows the Pythagoras theorem.
Now, According to statement given :
Let smaller acute angle = x,
and measure of larger acute angle = 3x-2
Since, it is right triangle the acute angles must be complementary
x + (3x-2) = 90
4x - 2 = 90
4x = 92
x = 23
i.e. smaller acute angle is 23
now second angle = 3x-2 = 3(23) - 2 = 67
and third angle is 90 , as this is a right angled triangle.
Thus, The measurement of each angle is 23 degrees, 67 degrees, and 90 degrees.
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Select the reason that best supports statement 7
Answer:
C because ur adding
Between 11 P.M. and 8:20 A.M., the water level in a swimming pool decreased by 4/9 in . Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
That means that each hour it drops about 0.0625 inches
Divide the decrease in water level by the length of the time interval.
decrease = 7/12 inches ≅ 0.583 inches
Time interval: From 11 pm to 8:20 am you have 9:20 hours = (9 + 20/60) hours ≅ 9.33 hours
So the water drops at a rate of about
0.583/9.33 inches/hour ≅ 0.0625 inches/hour
Therefore, each hour it drops about 0.0625 inches.
The rate constant, or the specific rate constant, is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.The rate constant is a proportionality factor in the rate law of chemical kinetics that relates the molar concentration of reactants to reaction rate. It is also known as the reaction rate constant or reaction rate coefficient and is indicated in an equation by the letter k.
Rate constant is dependent on the temperature. For zero-order reaction, rate constant's unit is mol L - 1 s - 1 . For first-order reaction, rate constant's unit is . For second-order reaction, rate constant's unit is mol - 1 L s - 1 .
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Find the distance between the pair of points. Round to the nearest tenth.
W(2,0) and X(8,6)
Distance between the pair of points W(2,0) and X(8,6) is equal to
8.5 units(nearest tenth).
As given in the question,
Given points are W(2,0) and X(8,6)
Distance between the pairs of points = [tex]\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2} }[/tex]
= [tex]\sqrt{(6-0)^{2}+(8-2)^{2} }[/tex]
= [tex]\sqrt{36 +36}[/tex]
=[tex]\sqrt{72}[/tex]
= [tex]8.5[/tex] units (nearest tenth)
Therefore, distance between the pair of points W(2,0) and X(8,6) is equal to 8.5 units (nearest tenth).
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Compare the two numbers. Use > or < .
4, √12
The value of √12 is equals to 3.46, and the number 4 is larger than the number 3.46.
What does "square root" mean?The square root of a number x in mathematics is a number y whose square (the result of multiplying the number by itself, or y y), equals x.The radicand is the expression (or number) whose square root is being considered.The phrase or number in this instance that appears under the radical sign is known as the radicand, and it is 9.Square roots of negative integers can be discussed in relation to complex numbers.In any circumstance where the idea of an object's "square" is stated, square roots can be considered more generally.These include, among other things, function spaces and square matrices.The value of √12 = 3.46, and the number 4 is larger than the number 3.46.
Therefore, 4 > √12.
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Determine whether each sequence is geometric. If so, find the common ratio. 1,2,3,4, . . . . .
The given sequence is not geometric.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 1, 2, 3, 4, ....
Here, 2/1 ≠ 3/2 ≠ 4/3
Since, the none of the ratio of the consequent and the previous term is not equal, the sequence does not satisfy the required condition and hence, is not geometric.
Hence, The given sequence is not geometric.
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Plane P contains lines a and b. Line c intersects plane P at point J.
Lines a and bare parallel, lines a and care skew, and lines band care not skew.
Draw a figure based upon this description.
Step-by-step explanation:
you cant make things in brainly
Namid bought 20 raffle tickets. If a total of 500 raffle tickets were sold, what is the probability that Namid will not win the raffle?
According to the question, Namid bought [tex]20[/tex] raffle tickets. And the total number of raffles sold was [tex]500[/tex].
Now. to calculate the probability in which Namid will not win the raffle:
[tex]P(Win) = \frac{P(E)}{n(E)} = \frac{20}{500} = \frac{1}{25}[/tex]
[tex]P(No Win) = 1-P(Win) = 1 - \frac{1}{25} = \frac{24}{25} = 96%[/tex]
Therefore, the probability that Namid will not win the raffle is [tex]96[/tex] percentage.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Points F, Q, and D are coplanar.
We can find whether three points are coplanar by using vector approach.
What is Coplanar?In geometry, a of group points in space are coplanar if there exists a geometric plane that contains them all. For instance, three points are always coplanar, and if the points are distinct and non-collinear, the plane they exist is unique.
We can check whether the given point F,Q and P are coplanar by first forming vectors of the each given point. The vector form for general point (a,b,c) can be written as [tex]a\hat{i}+b\hat{j}+c\hat{k}[/tex].
The vector forms of point F,Q and P can be given as 'f', 'q' and 'p'. The scalar triple product of the vectors 'f', 'q' and 'p' can be found out by finding the scalar product of vector 'f' with the cross product of the vectors 'q' and 'p' .
For the points F,Q and P to be coplanar the triple scalar product must be zero else the points are not coplanar.
This implies f·(q×p)=0 must be satisfied for three points to lie on the same plane.
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The correct question is " How can you say points F, Q and D are coplanar?"
The box-and-whisker plot below represents some data set. What is the value of the second quartile?
The median is at 55. Therefore, the second quartile of the data set is: 55.
What is the Second Quartile of a Data?50% of any given data set lies below the second quartile. Thus, the second quartile can be described as the median of a data set.
In a box-and-whisker plot, the median is the mark at where the vertical line divides the box of the box-and-whisker plot.
In the box-and-whisker plot given, the median is at 55. Therefore, the second quartile of the data set is: 55.
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[ Brainliest ]
On a coordinate plane, the ___ is the place where the x-axis and y-axis intersect.
answer should be origin
I need help I don’t get it
Answer:
Step-by-step explanation:
Perimeter = 2(l + w)
Area = l x w
l = 6 - 3 = 3 (Difference in x cords from A to B)
w = 5 - (-1) = 6 (Difference in y cords from A to C)
Perimeter = 2(3 + 6) = 18 units
Area = 3 x 6 = 18 square units
what's the pattern? 7,11,19,35
The pattern of each number changes.. they are all factors of 4, the 4 turns into 8, than the 4 or 8 turns into 16.
7+4=11
11+8=19
19+16=35
[4×2=8, 8×2=16]
At a swim meet, the order of the divers is randomly selected. If there are 12 divers, what is the probability that Danielle, Nora, and Li will dive first, second, and third, respectively?
The probability that Danielle, Nora, and Li will dive first, second, and third, respectively is 1/1320.
Since we are provided that in the meet, the orders of the drivers are randomly selected so, the total number of drivers is: 12
let A be the event in that Danielle was the first to dive.
B be the event that Nora been the second to dive.
and C is the event that Li has been the third to dive into.
P(A), probability of Danielle to dive first = 1/12
P(B), probability of Nora to dive second = 1/11
and P(C), probability of Li to dive in third = 1/10
So, the total probability that Danielle, Nora, and Li will dive first, second, and third, respectively = P(A) x P(B) x P(C)
= 1/12 x 1/11 x 1/10
= 1/ 1320
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