Answers
The description and definition and values of the sequence are;
a. Each term of sequence A is produced from the previous term by multiplying the previous term by 2
b. Each term of sequence B is produced from the previous term by adding 10 to the previous term
c. [tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]
d. B(n) = 2 + (n-1) × 10
e. B(9) > A(9)
What is a sequence of numbers?A sequence is series of objects that follow each other in a particular order.
a. The terms of sequence A are;
1/4, 1/2, 1, 2, 4
Therefore, each term is produced from the previous term by multiplying the previous term by 2 as follows;
1/4 × 2 = 1/2,
1/2 × 2 = 1
1 × 2 = 2
2 × 2 = 4
b. The values in sequence B are;
2, 12, 22, 32, and 42
Therefore, each term is produced from the previous term by adding 10 to the previous term as follows;
2 + 10 = 1212 + 10 = 2222 + 10 = 3232 + 10 = 42c. The definition of the nth term of sequence A is found using the formula for a geometric progression as follows;
nth term of a GP is; A(n) = a•r^(n-1)
Where;
a = The first term = 1/4
r = The common ratio = 1/2/(1/4) = 2
The nth term of sequence A is therefore;
[tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]d. The definition of the nth term of sequence B is found using the formula for a arithmetic progression as follows;
nth term of a AP is; B(n) = a + (n-1)•d
Where;
a = The first term = 2
d = The common difference = 12 - 2 = 10
The nth term is therefore
B(n) = 2 + (n-1) × 10
e. The value of A(9) is therefore;
[tex] A(9) = \frac{1}{2} \times 2^{(9-1)} = 64 [/tex]
Which gives; A(9) = 64
The value of B(9) = 2 + (9-1) × 10 = 82
B(9) = 82
Which gives;
B(9) = 82 > A(9) = 64
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Related Questions
At a local recreation center, there were 36 people working out, 18 people swimming, and 27 were playing basketball. What percentage of people were there to swim? Round your answer to the nearest tenth.
Answers
Answer:
22.2%
Step-by-step explanation:
Total number of people at the recreation center=81
Number of people swimming=18
=18/81 x 100
=22.22222
Round of to the nearest tenth
=22.2%
Simplify the the following
Answers
Answer:
Answer is in the picture attached
2. Is 4x-3=19 true, false, or open? (1 point)
true
false
Open
Answers
In the metric system, how many milligrams are needed to make a gram?
Answers
Answer:
In one gram, there are 1000 milligrams.
To convert g to mg, multiply the gram value by 1000.
f(x)= 3x - 2 and g(x) = 2x+1
Answers
Answer:
What do I solve for with these functions?
Step-by-step explanation:
identify whether the statement describes inferential statistics or descriptive statistics. the average age of the students in a statistics class is 20 years.
Answers
The statement ''The average age of the students in a statistics class is 20 years'' describes descriptive statistics.
As they're used to represent a particular records set, metrics like average, median, mode, standard deviation, and variety are categorized underneath descriptive information.however, when a speculation check is carried out to make inferences about a population from sample records, it's miles known as inferential data.As right here we're given the average age of all 20 students in the magnificence right here, and we are not seeking to prediction from the sample records, and we're directly getting it as a population parameter. therefore descriptive statistics is the correct solution here.via creating summaries of records samples, descriptive statistics can be used to describe the characteristics of a facts set.To learn more about descriptive statistics visit:
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it takes $24$ minutes for jana to walk one mile. at that rate, how far in miles will she walk in $10$ minutes? express your answer as a decimal to the nearest tenth.
Answers
This shows that she covered 0.4 miles in 10mins
Rate of changeSpeed is defined as the rate of change of distance.
If it takes 24 minutes for jana to walk one mile, the rate of Jana is expressed as;
Rate= 24/1 mile
Rate = 24min/mile
In order to determine the distance she walk in 10 minutes, we will have;
Distance in 10min = 10/24
Distance in 10 min = 0.4 miles
This shows that she covered 0.4 miles in 10mins
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Evaluate rs + 14s when r = 6 and s = 1/4
Answers
Answer:
5
Step-by-step explanation:
rs + 14s
(6)(1/4) + 14(1/4)
[tex]\frac{6}{4}[/tex] + [tex]\frac{14}{4}[/tex] = [tex]\frac{20}{4}[/tex] = 5
Answer:
5
Step-by-step explanation:
rs + 14s
r = 6
s = 1/4
= 6*1/4 + 14*1/4
= 6/4 + 14/4
= (6+14) / 4
= 20/4
= 5
the area of the rectangle is 14yd squared and the length of the rectangle is 3yds leass than twice the width
Answers
The dimensions of the rectangle are:
Length = 7/2 ydWidth = 4 ydTotal area = 14 yd²What is the area?The quantity area expresses the extent of a region on a plane or curved surface. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.To find the dimensions of the rectangle:
Let,
Area = A = 14Width = wLength = 2w-3A = lwA = (2w-3)wExtend the area equation as follows:
A = 2w2-3wRearrange:
2w2 - 3w - A = 0Substitute known information for A:
2w2 - 3w - 14 = 0To solve quickly, factor the left side (or use the quadratic formula):
(w+2)(w - 7/2) = 0The factorial solutions for w are -2 and 7/2.
Assuming this is a genuine rectangle, the width must be positive.
As a result, the length is:
2(7/2) - 3That is,
7 - 3 = 4Therefore, the dimensions of the rectangle are:
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The complete question is given below:
The area of a rectangle is 14 yd², and the length of the rectangle is 3 yd less than double the width. find the dimensions of the rectangle.
WILL CHOOSE BRAINLIEST!!!
Answers
Answer: 51.96m
Step-by-step explanation:
We can solve this using cosine, remember SOHCAHTOA, so cos is adjacent over hypotenuse.
hyp = 60
adj = ?
[tex]cos = \frac{adj}{hyp}\\cos 30 = \frac{x}{60} \\\\cos30 *60=x\\x=51.96m[/tex]
phytoremediation is the use of plant growth to purify pollutants from soil, water, or air. suppose that a crop of brake ferns can remove 15 milligrams (mg) per square meter of a particular pollutant from the soil in 20 weeks. after 20 weeks, the ferns are harvested and a new crop is planted. if c represents the number of crops of brake ferns needed to phytoremediate soil contaminated with 170mg per square meter of the pollutant down to healthy levels of 5mg per square meter, which equation best models the situation?
Answers
Equation that best models the situation is where c = 11
What is phytoremediation?
Living plants are used in phytoremediation technologies to purify contaminated soil, air, and water. According to the definition, it involves "the use of green plants, associated microbes, suitable soil amendments, and agronomic techniques to either contain, remove, or render dangerous environmental toxins harmless." The word is a combination of the Greek words phyto (plant) and remedium (remedy) (restoring balance). Despite being appealing due to its low cost, phytoremediation hasn't been shown to significantly address any environmental issues, at least not to the point where contaminated space has been returned. A cost-effective plant-based method of environmental cleanup called phytoremediation is being proposed. It makes use of plants' capacity to concentrate elements and chemicals from the environment and to detoxify different contaminants. The ability of certain plants, known as hyperaccumulators, to bioaccumulate substances is what causes the concentrating effect. The impact of cleanup is very different. Organic contaminants, which can be destroyed, are typically the main targets for phytoremediation while toxic heavy metals cannot. Several field tests supported the viability of employing plants to clean up the environment.
Let the number of crops needed to remove pollution = c
Since one crop can remove 15 mg of pollution per square meter.
Then, "c" number of crops may remove "15 C" mg of pollutant per square meter.
Now, the total amount of pollution per sq. meter Equals 170 mg
Additionally, it is necessary to reduce pollution to 5 mg per square meter.
Consequently, the equation for the scenario is given by,
Pollutants 'c' crops can remove from the total amount of pollution equal the amount of pollution required, or 170-15c=5.
Upon solving the equation, we get, c= 11.
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[tex]\frac{-x}{3} + 4 = 20[/tex]
Answers
The solution of the linear equation:
-x/3 + 4 = 20
Is x = -48
How to solve the linear equation?Here we have the linear equation:
-x/3 + 4 = 20
And we want to solve it for x. Which means that we need to isolate x in one of the sides of the linear equation.
Remember that we can perform the same operation in both sides of the equation, so we start by subtracting 4 in both sides, then we get:
-x/3 + 4 - 4 = 20 - 4
-x/3 = 16
Now we can multiply both sides of the equation by -3, then we get:
-3*(-x/3)= -3*16
x = -48
The solution of the linear equation is x = -48
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Simplify the following. (Do NOT evaluate!) √80y^3
Answers
After simplifying the expression √80y³, we get the answer as 4 y √5 y.
We are given that:
√80y³
We have to simplify it.
We will first make the factors of it.
Factors of 80:
80 = 2 × 2 × 2 × 2 × 5
Factors of y³:
y³ = y × y × y.
Now the expression can be re- written as:
√2 × 2 × 2 × 2 × 5 × y × y × y.
Simplifying it:
2 × 2 × y √5 y
4 y √5 y
Therefore, after simplifying the expression √80y³, we get the answer as 4 y √5 y.
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choose the first set in the list of natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number.
Answers
The given number is a real number.
What are real numbers?A real number is a value of a continuous quantity that can be used to indicate a distance along a line in mathematics.
We are given the following in the question:
{natural numbers, whole numbers, integers, rational numbers, real numbers}
π / 108
We have to tell the type of number that describes the given fraction.
Evaluating the value, we have,
0.0290888208666...........
This is not a natural number or a whole number. This is not a rational number.
Since is an irrational number, thus quotient of an irrational number and a rational number is an irrational number.
Thus, it is a real number.
The complete question is given below:-
Choose the first set in the list of natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. StartFraction pi Over 108 EndFraction.
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How many solutions (m, n) exist for the equation n = √(100 - m²) where both m and
n are integers?
(A) 4
(C) 7
(D) 8
(B) 6
(E) 10
Answers
Answer:
A) 4
Step-by-step explanation:
First note that m cannot exceed 10 otherwise 100-m² will be negative and √(100-m²) will not be a real number much less an integer
Enumerate all values of m from 0 through 10, find the square, subtract from 100 and see if the result is a perfect square.- we take the square root and see if it is an integer value. The table below details everything. m and n are integers on in 4 cases m = 0, 6, 8 or 10.
Hence the answer is 4 solutions
m m² 100-m² √(100-m²)
0 0 100 10
1 1 99
2 4 96 9.797958971
3 9 91 9.539392014
4 16 84 9.16515139
5 25 75 8.660254038
6 36 64 8
7 49 51 7.141428429
8 64 36 6
9 81 19 4.358898944
10 100 0 0
Evaluate.
4-6 |3-5| /3
Answers
Answer:
0
Step-by-step explanation:
I really need help on 16 and 18 I'm super confused problem because I'm tired but I really need help
Answers
Answer:
Hello,
Step-by-step explanation:
16)
Area of the square= 5²=25 (unit of square)
17)
Volume of the cube =3^3 =27 (unit of volume)
18)
side of the cube =5 (unit of lenght)
Volume of the cube = (5 (unit of lenght)) ^3
=125 * (unit of lenght)^3 =125 (unit of volume)
midpoint of line segment with endpoints (3.2,2.5) and (1.6,-4.5)
Answers
The midpoint of the line segment with the endpoints is (2.4, -1)
How to determine the midpoint of the line segment with the endpoints?The endpoints are given as:
(3.2,2.5) and (1.6,-4.5)
The midpoint of the line segment with the endpoints is calculated as
Midpoint = 0.5 * (x1 + x2, y1 + y2)
So, we have:
Midpoint = 0.5 * (3.2 + 1.6, 2.5 - 4.5)
Evaluate the sum
So, we have:
Midpoint = 0.5 * (4.8, -2)
Evaluate the products
So, we have:
Midpoint = (2.4, -1)
Hence, the midpoint of the line segment with the endpoints is (2.4, -1)
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value of x in the equation −3(3x−4)=15−8x?
Answers
Answer:x=−19
Step-by-step explanation: work in your head ppl
Answer: -3
Step-by-step explanation:
trust me
Write an absolute value equation that has the solutions x= -10 and x= -5.
Answers
The absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.
According to the question.
We have solutions of a absolute value equation.
As we knoaw that, the non-negative value of a real number x without regard to its sign is known as its absolute value or modulus equation in mathematics and is indicated by the symbol |x|.
To find the absolute value equation whose solution are x = -10 and x = -5 we need to add some previous steps, which make the equation an absolute value equation.
|(x+10)(x+5)|=0,
x=-10 and x=-5
Hence, the absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.
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Solve the equations and check the results a. 4x+5=17-2x
Answers
6x=12
X=12:6
X=2
Pls solve this question step by step
Answers
Answer:
Step-by-step explanation:
Which graph does not represent a function?
Answers
Answer:
Choice 3
Step-by-step explanation:
The graph fails the vertical line test.
Suppose Aji and sunshine have to pay $11 in royalties for each Beatles song and $7 for each Donovan song. How many of each type should they put on their CD to minimize their royalty costs?
Answers
To minimize their royal costs to $200, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.
What are ratios?Ratios are numerical relationships between variables that show how much each variable is contained in another.
Ratios are stated in fractions, percentages, or decimals.
Data and Calculations:Total songs to include in the song = 20
The ratio of Donovan and Beatles = 5:1.5
The number of Donovan songs to include = 15 (20/6.5 x 5)
The number of Beatles songs to include = 5 (20/6.5 x 1.5)
Royalty cost per Donovan song = $11
Royalty cost per Beatles song = $7
Total royalty costs for Donovan and Beatles song = $200 ($11 x 15 + $7 x 5)
Thus, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.
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Question Completion:Aji and Sunshine want to make a CD of songs from the 1960s to donate to their school library to be broadcast during school picnics. Sunshine's parents were big fans of the 60s singer Donovan, and they named her after his song "Sunshine Superman." Aji's folks were devotees of the Beatles. Aji and Sunshine want their CD to consist entirely of songs by Donovan and the Beatles. Because Sunshine is named after a Donovan song, she wants to include at least as many Donovan songs as Beatles songs. Aji agrees. In return, Sunshine agrees to include at least five Beatles songs. 5 1.5 To provide enough variety to make the mix interesting, they decide to include at least 20 songs altogether.
Underground Floors charges $8 per square foot of wood flooring plus $150 for installation. Woody's Hardwood Flooring charges $6 per square foot plus $200 for installation. At how many square feet of flooring would the two companies charge the same amount for flooring? If you were going to put flooring on your kitchen floor that had an area of 120 square feet, which company would you choose?
Answers
AT 25 SQUARE FEET OF FLOORING
CHOOSE WOODY'S HARDWOOD FLOORING
HOW TO COMPARE RATE OF FLOORING OF TWO COMPANY ?Typically, the price of engineered hardwood flooring is $6 to $10 per square foot, plus $1.75 to $2.20 per square foot for installation. High-quality hardwood flooring typically costs between $6 and $13 per square foot from customers. Your home renovation project could be very stressful. Expectations, timeframes, budgets, and the cost of flooring contractors all need to be harmonized.
There will always be a time when you want to give up on the renovation project. For some reason, finding someone to install your flooring is usually the first step.
CALCULATION1 - 8s + 150 = 6s + 200
2s = 50
s= 25 sq.feet
2 - 120 * 8 + 150 = 1110
120 * 6 + 200 = 920
1110 > 920
so choose woody's hardwood flooring.
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solve the problem. a basketball player makes approximately 69% of free throws. if she plays in a game in which she shoots 7 free throws, what is the probability the she will make all 7?
Answers
If she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188
For given question,
a basketball player makes approximately 69% of free throws.
So, the probability of success (p) = 0.69
the probability of failure (q) = 0.31
She plays in a game in which she shoots 7 free throws.
So, n = 7
We need to find the probability that she will make all 7.
Using Binomial probability Distribution,
For x = 7,
[tex]P(x = 7) =~ ^7C_7\times (0.67)^7\times (0.31)^{7-7}\\\\P(x=7)= 1\times 0.0606\times 0.31\\\\P(x=7)=0.0188[/tex]
Therefore, if she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188
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For the set {3, 4, 5, 8,x), the
mean, median and mode all
have the same value. What
is the value of x that would
make this true?
Your lunch costs $10.95 at a
Answers
Answer:
x = 5
Step-by-step explanation:
Mode: The most frequently occurring data value.
Median: The middle value when all data values are placed in order of size.
Mean: The sum of all data values divided by the total number of data values.
As the mode is the most frequently occurring data value, x must be 3, 4, 5 or 8.
If the mode is 3 or 4, then the data set will be {3, 3, 4, 5, 8} or {3, 4, 4, 5, 8}. Therefore, the median would be 4.
If the mode is 5 or 8, then the data set will be {3, 4, 5, 5, 8} or {3, 4, 5, 8, 8}. Therefore, the median would be 5.
Therefore, the median is 4 or 5.
[tex]\boxed{\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}}[/tex]
If x = 4, the mean would be:
[tex]\sf \implies mean=\dfrac{3+4+5+8+4}{5}=\dfrac{24}{5}=4.8[/tex]
If x = 5, the mean would be:
[tex]\sf \implies =\dfrac{3+4+5+8+5}{5}=\dfrac{25}{5}=5[/tex]
Therefore, the only value of x that allows the mean, median and mode to all have the same value is x = 5.
What is the difference between positive association and negative association as it pertains to the relationship between two variables?.
Answers
A positive association occurs when an increase in one variable is generally associated with the increase in the second variable and a negative association occurs when one variable tends to decrease as the other increases.
What is meant by an association relationship between two variables?An association is any relationship between two factors that produces them subordinate, i.e. knowing the value of one variable gives us some data around the possible values of the moment variable.
The objective of this variable is to utilize clear measurements and visualisations to investigate affiliations among different kinds of factors.
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What is the simplified form of the quantity x over 4 plus y over 3 all over the quantity x over 3 minus y over 4?
Answers
The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y).
What is an expression?An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.
For example 3x +5y
Given the phrase,
x over 4 = x/4
y over 3 = y/3
Combine x/4 + y/3
x over 3 minus y over 4 = x/3 - y/4
Therefore ;
(x/4 + y/3) ÷ (x/3 - y/4)
⇒ (3x + 4y)/12 ÷ (4x - 3y)/12
The second fraction will inverse in multiplication
⇒ (3x + 4y)/12 × 12/(4x - 3y)
⇒ (3x + 4y) / (4x - 3y).
Hence "The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y)".
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suppose that $a$ and $b$ are digits, not both nine and not both zero, and the repeating decimal $0.\overline{ab}$ is expressed as a fraction in lowest terms. how many different denominators are possible?
Answers
The possible denominators are {3, 9, 11, 33, 99}.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
We have been given that a and b are digits, not both nine and not both zero, and the repeating decimal.
⇒ 100x = ab⋅abababab
⇒ x = 0.abababab
Subtract the above equation from 100x = ab⋅abababab,
So 99x = ab
The denominator of this fraction will always be a divisor of 99 when represented in the lowest term = 3⋅3⋅11
According to this, we have the options in the set. {1, 3, 9, 11, 33, 99}.
Since a and b both are not both 9 and not both zero the denominator 1 cannot be possible.
Hence, the possible denominators are {3, 9, 11, 33, 99}.
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