10th term of the geometric sequence = 2560
The explicit formula for the geometric sequence is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
Where
r = common ratio
a = first number of the series
n = number of terms in the series
Common ratio (r) = 10/5 = 20/10 = 2
Here we have to find the 10th term of the series
[tex]a_{10}[/tex] = 5× [tex]2^{10-1}[/tex]
= 5×[tex]2^{9}[/tex]
= 5 × 512
= 2560
So the 10the term geometric series is 2560.
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Suppose you are stacking boxes in levels that form squares. The numbers of boxes in successive levels form a sequence. The figure at the right shows the top four levels as viewed from above.
c. Suppose you are stacking a total of 285 boxes. How many levels will you have?
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?
How do you find the square root of the following WITHOUT a calculator:
1. Square root of 2 890 000
2. Square root of 0.000004
Answer:
1. you can think that 289000= 17×17(=289)x100x100, so the result is √289x√100x√100=17 x 10x10=1700
2. 0.000004= 4x10^-6, so the Square root Is √4 x√10^-6= 2x 10^-3
Use the given statement to find the measure of numbered angle.
∠1 and ∠ form a linear pair and m ∠2=67 .
The answer is ∠1 = 113°
Linear Pair :
When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.
Now as per the question the given angle is
∠2 = 67°
It is also given that ∠1 and ∠2 form a linear pair. Therefore it means that the sum of both the angles will be 180°
∠1 + 67° = 180°
Now subtracting 67 from both sides we will get :
∠1 = 180 - 67 = 113°
Therefore, ∠1 = 113°
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A pizza maker sells either whole pizzas or pizza by the slice. A slice of pizza is 1/8 of a pizza. How many whole pizzas would 113 slices of pizza make? Express your answer as a mixed number. Explain your answer.
Answer:
Here is your answer
Step-by-step explanation:
113/8= 14 and 1/8th
Ifs= unit and A = 12s², what is the value of A, in square units?
square unit(s). (Input whole number only.)
The value of A is 3 square unit
A square number is a number multiplied by itself. This can also be called 'a number squared'. The symbol for squared is ².
Formula: s²= s x s
given that, the question is testing the concept of substitution.
A=12s^2
If s=1/2,
Substituting s with 1/2 we get;
A=12(1/2)^2
=12×1/4
=3
The answer is 3 unit squared. There is no fraction in the answer.
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Answer:
A has a value of 3 square units.
Step-by-step explanation:
Any number multiplied by itself is a square number. This is also referred to as "a number squared." 2 represents the squared sign.
Equation: s2=s x s
As a result, the question is putting the idea of substitution to the test.
A=12s^2
If s=1/2,
Substituting s with 1/2 we get;
A=12(1/2)^2
=12×1/4
=3
The answer is 3 unit squared. There is no fraction in the answer.
Simplify by combining like terms. -(2x + y) -2(-x-y)
The Simplified expression for -(2x + y) -2(-x-y) is y.
Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .
Algebraic Operation is only possible with Like terms .
For Example ; 3x , 9x are like terms .
According to the given Algebraic expression
= -(2x + y) -2(-x-y)
= -2x-y+2x+2y
Combining like terms together
We get ,
= (-2x+2x)+(2y-y)
= 0+y
=y
Therefore , the Simplified expression for -(2x + y) -2(-x-y) is y.
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At a little-known vacation spot, taxi fares are a bargain. A36 -mile taxi ride takes 42 minutes and costs $25.20. You want to find the cost of a 47 - taxi ride. What unit price do you need?
Answer:
it will cost $32.9 for a 47 mile taxi ride
Step-by-step explanation:
Since 36 miles takes 42 minutes and Costa $25.20 then 47 miles taxi rides will take
42/36 = per minute = 1.17
1.17 × 47 = 54.83
In order to find cost per minute = $25.2/42 = 0.6
then 54.83 × 0.6 = $32.898
∴it will cost $32.9 for a 47 mile taxi ride
Find the value of x.
Answer:
1 15 degrees
Step-by-step explanation:
Exterior angle is equal to sum of opposite interior angles
Lisa has $375 left after paying her total expenses for the month. She wants to buy an exercise machine for$660. How much would she have to save for three months to have enough to buy this new exercise machine? For four months? For six months?
Answer:
Step-by-step explanation:
285 dollars. the left money = 660 - 375 =285
solve for x.
also write the equation needed please
Answer:
x = 12
Equation: 6x + 8 = 80
Step-by-step explanation:
A triangle's angles add up to 180 degrees. Knowing this, the angle represented by the "6x + 8" must equal 80 degrees since the other two angles add to 100 degrees.
Tamara is creating a model of a rectangle. She has 26 inches of yellow ribbon to use for the border of the rectangle. She wants the length, l, to be 3 inches greater than the width, w. Which system of equations could Tamara use to find the dimensions of a rectangle that uses all of the ribbon?
A system of equations. 2 l plus 2 w equals 26. 3 l equals w.
A system of equations. 2 l plus 2 w = 26. l equals 3 w.
A system of equations. 2 l plus 2 w equals 26. l equals w plus 3.
A system of equations. 2 l plus 2 w equals 26. l plus 3 equals w.
The systems of equations which Tamara can use to find the dimensions of a rectangle that uses all the ribbons is;
2l + 2w = 26l = w +3System of equationsIf follows from the task content that the systems of equations which best models the situation and can be used to find the dimensions is required.
Hence, since the perimeter of a rectangle is; P = 2l +2w.
2l + 2w = 26Also, the length of the rectangle is 3 inches greater than its width, we have;
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Which quantity decreases as the sample size increases?
a. the standard deviation
b. the standard error
c. the population mean
d. the mean of all the sample means
The standard deviation decreases as the sample size increases.
What is standard deviation?The degree of data dispersion from the mean is measured by the standard deviation. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
A region containing 68 percent of the total number of data points would be defined by one standard deviation, or one sigma, shown above or below the average value on that normal distribution curve. Ninety-five percent of the data would be covered by two sigmas above or below, whereas three sigmas would cover 99.7 percent.
The standard deviation is significant because it reveals the degree of dispersion of the values in a particular dataset. Every time we examine a dataset, we look for the following metrics: the dataset's geographic center.
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Kristen goes hiking every 3 days and swimming every 2 days. She did both kinds of exercise today. How many days from now will she next go both hiking and swimming again?
Kristen will do both the exercises together, 6 days from now.
We are told that Kristen goes hiking every 3 days and swimming every 2 days.
The day she will do both the exercises together will be the day which is a multiple of the LCM of 2 and 3.
Now, since 2 and 3 are both prime numbers, their LCM (lowest common multiple) will simply be their product, which comes out to be-
LCM (2, 3) = 2 * 3
= 6
Thus, Kristen will do both the exercises on every 6th day.
Thus, if she went for both swimming and hiking today, she will do both the exercises together again 6 days from now.
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Write the equation of each line in standard form.
slope =-1 ;(-3,3)
The standard equation for the given slope is x + y = 0.
These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b using the m given in the problem and the b you just solved. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.
y = 3 and x = -3 and m = - 1
To find b, we will plug in the known parameters listed above.
3 = −1(-3) +b
To solve for b, move 3 to the other side of the equation.
3=3+b
b=0
Standard form equation:
y = -x + 0
x + y = 0
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Q is in the interior of right PRS. if m PRQ is 4 times larger as m QRS,what is m PRQ
help
I will be using your answer in the question so follow the prompt carefully.
Answer:
1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.
Therefore, they are all equal.
Step-by-step explanation:
1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.
Therefore, they are all equal.
The dance committee consisted of 10 students. The committee will select three officers at random. What is the probability that Alice, David, and Carlene are selected?
The probability that Alice, David, and Carlene are selected is 1/120.
What is meant by probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
3 people can be chosen from 10 people in 10C3 ways and Alice, David, and Carlene can be chosen in only one way.
10C3 = 10! / (10 - 3)! 3!
= (10 [tex]*[/tex] 9 [tex]*[/tex] 8 [tex]*[/tex] 7!) / (7! [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1)
= 120
So, the number of possible outcomes is 120 and the number of favorable outcomes is 1. Therefore, the probability is 1/120.
The probability that Alice, David, and Carlene are selected is 1/120.
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If the radius of a circle is 5, what is the diameter?
Answer:
d=10
d=2r=2·5=10
Write a recursive definition for each sequence. 2,-4,8,-16, . . . .
A recursive definition of the given Geometric progression is: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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.
Now,
Given: 2, -4, 8, -16, ...
Here, [tex]r = \frac{-4}{2} = -2[/tex] and a₁ = 2.
Thus, a recursive formula for this geometric progression can be: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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Which expressions are equivalent to (d^1/8)^5
Using exponent properties we can get two equivalent expressions:
⁸√d^5
d^(5/8)
Which expressions are equivalent to (d^1/8)^5?Here we need to use two properties, these are:
ⁿ√x = x^(1/n)
(x^n)^m = x^(n*m)
Now, if we use the first property, we can rewrite the expression as:
(d^1/8)^5 = ⁸√d^5
Which is an equivalent expression.
If we use the other property we can get:
(d^1/8)^5 = d^( (1/8)*5) = d^(5/8)
Which is another equivalent expression.
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Determine whether each statement is always, sometimes, or never true. (Lesson 1-5 )
If two angles are supplementary, then one of the angles is obtuse.
If two angles are supplementary, then one of the angles is obtuse: Never TRUE
What do we mean by obtuse angles?An obtuse angle is one that is less than 180 degrees but greater than 90 degrees. Obtuse angle degrees include 110°, 135°, 150°, 179°, 91°, and others. As a result, all angles ranging from 90° to 180° are obtuse. The hypothesis that if two angles are supplementary, one is obtuse and the other acute is false. This is due to a situation in which two angles are supplementary but neither is acute or obtuse. When we have two right angles, we get this. A supplementary angle cannot be formed by two obtuse angles. Obtuse angles are defined as angles that are greater than 90° in length. The sum of two obtuse angles will be larger than 180°. When we add obtuse angles, the property of supplementary angles is violated.Therefore, the statement "if two angles are supplementary, then one of the angles is obtuse" is never TRUE.
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Quanto e {2×-3y=34×-y=11
Answer: x=4
Step-by-step explanation:
Find four solutions of the equation. Write the solutions as ordered pairs. 3x-y=-6
Solving the Question
We're given:
3x-y=-6Find 4 solutionsWe can start by isolating one of the variables, like y:
[tex]3x-y=-6\\-y=-3x-6\\y=3x+6[/tex]
Now we can find four solutions by plugging in any number for x:
[tex]y=3x+6\\y=3(1)+6\\y=3+6\\y=9[/tex]
First solution: (1,9)
[tex]y=3x+6\\y=3(2)+6\\y=6+6\\y=12[/tex]
Second solution: (2,12)
[tex]y=3x+6\\y=3(3)+6\\y=9+6\\y=15[/tex]
Third solution: (3,15)
[tex]y=3x+6\\y=3(4)+6\\y=12+6\\y=18[/tex]
Fourth solution: (4,18)
Possible AnswersFirst solution: (1,9)
Second solution: (2,12)
Third solution: (3,15)
Fourth solution: (4,18)
What is 38 plus negative 17 in integers?
Answer:
Step-by-step explanation:
38 + (-17) = 21
Answer:
The answer would be 55
Step-by-step explanation:
38-(-17)
38+ +17
55
Refer to ®N . If EN = 13 feet, what is the diameter of the circle?
EN is a radius and the diameter is twice the radius. The diameter of the circle is 26 ft.
What is meant by diameter?In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.
Here, CF is a radius and the diameter is twice the radius.
Diameter of a circle = 2r
d = 2r
Where, r = 13
Diameter of a circle, d = 2r
Diameter of a circle = 2(13)
Diameter of a circle = 26
Therefore, the diameter of the circle is 26 ft.
Here, EN is a radius and the diameter is twice the radius.
Therefore, the diameter is 26 ft.
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is √196 rational or irrational
Answer:
rational
Step-by-step explanation:
the square root of 196 is 14 ( whole number) therefor it is rational
this qestion is hard hope you can it get it right and dont just geuss
The correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.
How to prove supplementary angles?
Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair are always supplementary.
Now, looking at the given image, we can see a total of 8 angles formed from the transverse lines.
Angles 1 and 4 can be classified as Linear Pairs because Linear pair of angles are formed when two lines intersect each other at a single point.
Similarly, angle 4 and angle 8 are classified as corresponding angles because Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal
Thus, the correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.
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Ms. Turner drove 100 miles in January. She drove 3 times as many miles in March as she did in January. She drove 4 times as many miles in February as she did in March. How many miles did Ms. Turner drive in February?
Step-by-step explanation:
100x4=400miles
400miles in February
OR
300x4=1200 miles
1200 miles in February
I don't know what is the correct one tho
Answer:
Step-by-step explanation:
1200 miles
In Triangle ABC, the measure of angle B is 50 degrees. Select all (there may be one or more) possible measure angles of A and C if ABC is a right triangle.
By using angle sum property, The value of ∠ A = 40° and ∠ C = 90°
A triangle's total angle is 180°.
Using angle sum property,
∠A+∠B+∠C = 180°
assuming B = 50°
replacing in the formula
∠A+50+∠C = 180°
Due to the triangle's right angle, A+90=180-50
∠A = 130° - 90
∠ A = 40°
The angles A and C must be more than 90 degrees since the ABC is a right triangle.
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Complete question -In triangle ABC, the measure of angle B is 50 degrees. Select all possible values for the measures of A and C if ABC is an right triangle. m\angle∠A= 58 degrees; m\angle∠C= 72 degrees m\angle∠A= 100 degrees; m\angle∠C= 30 degrees m\angle∠A= 80 degrees; m\angle∠C= 50 degrees m\angle∠A= 60 degrees; m\angle∠C= 70 degrees m\angle∠A= 90 degrees; m\angle∠C= 40 degrees m\angle∠A= 105 degrees; m\angle∠C= 25 degrees
Answer:
m∠A = 40°, m∠B = 75°, m∠C = 65° (A)
m∠A = 136°, m∠B = 28°, m∠C = 16° (B)
m∠A = 60°, m∠B = 60°, m∠C = 60° (E)
Step-by-step explanation:
i did the assignment and got it wrong at first then it showed me the right answers
Write an explicit and a recursive formula for each arithmetic sequence. -3,0,3,6, . . . . .
The recursive formula is a(n) = a(n-1) + 3 while the explicit formula is a(n) = 3n - 6.
In an arithmetic sequence, the following applies:
a(n) = a(n-1) + d (This is the recursive formula)
a(n) = a(1) + (n-1) . d ( This is the explicit formula)
Where:
a(n) = nth term
a(n-1) = (n-1)th term
d = common difference
a(1) = the first term
The given sequence is:
-3, 0, 3, 6, ....
The common difference (d) = 0 - (-3) = 3
Hence, the recursive formula is:
a(n) = a(n-1) + 3
Note that a(1) = -3. Hence, the explicit formula is:
a(n) = a(1) + (n-1) . d
a(n) = -3 + (n-1) . 3
a(n) = -3 + 3n - 3
a(n) = 3n - 6
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