Answers
By using arithmetic progression, it can be calculated that
The common difference is 12
Third option is correct
What is arithmetic progression?A series of numbers is called an arithmetic progression if the difference between each term in the sequence is the same.
If there is always the same difference between any two consecutive terms in a series of integers, then progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series. A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...
This is a problem on arithmetic progression
[tex]a _1 = 5[/tex]
[tex]a_n = a_{n-1} + 12[/tex]
[tex]a_2 = a_1 + 12[/tex]
[tex]a_2 = 5 + 12 = 17[/tex]
[tex]a_3 = a_2 + 12 = 17 + 12 = 29[/tex]
[tex]a_4 = a_3 + 12 = 29 + 12 = 41[/tex]
[tex]a_2 -a_1 = 17 - 5 = 12\\a_3 - a_2 = 29 - 17 =12\\a_4 - a_3 = 41 - 29 =12[/tex]
So the common difference is 12
Third option is correct
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By using arithmetic progression, it can be calculated that, the common difference is 12.
Third option is correct
What is arithmetic progression?If the common difference between each term in the sequence is the same, a group of numbers is referred to as an arithmetic progression.
A progression is referred to as an arithmetic progression if there is consistently the common difference between any two successive terms in a series of integers. To put it simply, it indicates that the series' next number is produced by adding the previous one.
An arithmetic progression or arithmetic sequence, also known as AP, is a set of numbers where the terms are always different from one another. The numbers 5, 7, 9, 11, 13, and 15 make up one mathematical progression with a common difference of 2.
We know that the arithmetic progression, this is based on the same
[tex]\begin{aligned}& a_1=5 \\& a_n=a_{n-1}+12 \\& a_2=a_1+12 \\& a_2=5+12=17 \\& a_3=a_2+12=17+12=29 \\& a_4=a_3+12=29+12=41 \\& a_2-a_1=17-5=12 \\& a_3-a_2=29-17=12 \\& a_4-a_3=41-29=12\end{aligned}[/tex]
So the common difference is 12
Third option is correct
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Related Questions
Which operations involving complex numbers have solutions represented by (-6, 7)? 2(1 − 2i) − (4 + 3i), 2(1 + 2i) + (-4 − 3i), 2(-1 + 2i) − (4 − 3i), (-2 + 4i) + (-4 + 3i) , (-2 − 4i) + (4 − 3i)
Answers
Option 3 and 4 are the operations involving complex numbers have solutions represented by (-6, 7).
What is a complex number ?Every complex number can be expressed in the form displaystyle a+bia + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation displaystyle i2=-1. René Descartes referred to me as an imaginary number since no actual number can satisfy the aforementioned equation. The real component of the complex number displaystyle a+bia+bi is referred to as a, and the imaginary part is referred to as b. The symbols C or displaystyle "mathbb "C" are used to represent the set of complex numbers.Complex numbers are crucial to many parts of the scientific explanation of the natural world, despite the historical appellation "imaginary," and are recognized in the mathematical sciences as just as "real" as real numbers.Find the attachment answer
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Moussa sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
81 visitors purchased no costume.
6 visitors purchased exactly one costume.
3 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase more than one costume as a decimal to the nearest hundredth.
Answers
The required probability for purchasing more than one costume is 0.03.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The given problem can be solved as follows,
The number of visitors purchasing no costume, exactly one and more than one costumes are given as 81, 6 and 3 respectively.
Then, the total number is 81 + 6 + 3 = 90
Now, the probability of purchasing more than one costume is given as,
P(More than one costume) = 3/90
= 1/30
= 0.03
Hence, probability that the next person will purchase more than one costume is 0.03.
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If a figure is translated 3 units left and 3 units up, which translation moves the image back to the original position?
A.3 units right and 3 units down
B.3 units left and 3 units up
C. 3 units up
D. 3 units left
Answers
Answer:
I believe it is A
Step-by-step explanation:
Just go backwards. translations on a graph are pretty simple once you understand left vs right and up vs down.
The required translation to move the image back to the original position is 3 units right and 3 units down. Option A is correct.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
What is translation?The translation processes in geometry enable the shift of figures from one location to other.
Here,
The given translation is ,
a figure is translated 3 units left and 3 units up,
(x' , y') ⇒ (x - 3 , y + 3 )
To shift back the image,
x' = x - 3 ⇒ x = x' + 3
y' = y + 3 ⇒ y = y' -3
Thus, the required translation to move the image back to the original position is 3 units right and 3 units down. Option A is correct.
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5. Which value is closest to (7.5 x 10³)+(5.2 x 105) ?
A.
B.
C.
D.
11.7 x 105
11.7 x 104
5.275 x 105
5.275 x 104
Answers
(5.2 * 10^5) = 520000
Adding
7500 + 520000 = 527500.
Verify,
5.275 * 10^5 = 527500. So option c is correct.
Write the fractional values under each note. Verify that the sum of the fractions is 1 for each measure.
Answers
Answer:
1/8, 1/8, 1/4, 1/4, 1/16, 1/16, 1/16, 1/16 = 1
1/2, 1/2 = 1
Step-by-step explanation:
from left to right
is this music class or math class lol?
50pts help. Please look at attached pic
Answers
Answer:
there is no attached picture...
Step-by-step explanation:
help please thankssss
Answers
if the total profit per month of a company is Rs 200,000 and its revenue per month can be obtained by adding Rs. 20,000 to the twice the cost per month, find the revenue and cost per month. ..?
Answers
Answer:
okey baik dan sangat bagus
PLEASE HELP!!!!
Which graph is linear?
Answers
Answer:
the second
Step-by-step explanation:
the second is a linear graph
Answer:
The second Graph
Step-by-step explanation:
The question is asking what graph is linear.
The first graph is of an absolute value function which is not linear.
The second is of a line. This is linear.
The third looks to be either an exponential or a logarithmic function. Both of which are not linear.
An insurance company wants to measure the safety of drivers. Which quantity provides the best measure of the safety of drivers?
Answers
The quantity that provides the best measure of the safety of drivers is A. the number of accidents per year.
What exactly is insurance?Insurance is a risk management tool. When you purchase insurance, you are purchasing protection against unforeseen financial losses. If something bad happens to you, the insurance company will pay you or someone you choose. If you do not have insurance and an accident occurs, you may be held liable for all associated costs.
Insurance is a risk management tool. When you purchase insurance, you are purchasing protection against unforeseen financial losses. If something bad happens to you, the insurance company will pay you or someone you choose. If you do not have insurance and an accident occurs, you may be held liable for all associated costs.
In this case, the number of accidents will be a factor to illustrate the safety.
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Chloe needs a 1.25-meter piece of wood for a desk that she is building. How many centimeters need to be cut off a 2-meter piece of wood in order to use it for her desk.
Answers
Chloe needs to cut 75 centimetres after the unit conversion piece of wood in order to use it for her desk.
What is unit conversion?
Unit conversion is a multi-step process that includes rounding, selecting the appropriate number of significant digits, and multiplying or dividing by a numerical factor.
Given, Chloe needs a 1.25-meter piece of wood
Total available 2-meter piece of wood
So, the extra piece of wood = 2-1.25 = 0.75 meter
Convert meter to centimetres
Then, 1 meter = 100 centimetres
0.75 meter = 0.75*100 centimetres = 75 centimetres
Hence, she needs to cut 75 centimetres piece of wood.
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What is the vertex of the graph f(z)= 2z² +82 +37
Answers
The vertex of the function is located at coordinates (119, 0).
Step-by-step explanation:1. Write the function and simplify it.[tex]f(z)= 2z^{2}+82+37\\ \\f(z)= 2z^{2}+119[/tex]
2. Find the derivative with respect to z.Check the attached image.
[tex]\frac{d}{dz} (2z^{2}+119)\\ \\f'(z)=2*2z^{2-1}\\ \\f'(z)=4z[/tex]
3. Find the roots of the resulting function.[tex]f'(z)=4z\\ \\4z=0\\ \\z=0[/tex]
4. Evaluate the calculated value in the original function.[tex]f(0)= 2(0)^{2}+119\\ \\f(0)=119[/tex]
5. Conclude.The vertex of the function is located at coordinates (0, 119).
A toy company recently added some made-to-scale models of racecars to their product line. The length of a certain racecar is 17ft. Its width is 5ft . The width of the die-cast replica is 1,25 in.
Find the length of the model.
Answers
The model's length 1.4.To do this, I'm going to put up a proportion. This time period is excessively long when compared to how long it takes to whip.
Calculate the model's length?There is a race vehicle in this question, and it's length is 21 feet. Its width is 1.4 feet. We want to know if the replica is to scale, and if so, what is the length of the replica. To do this, I'm going to put up a proportion. This time period is excessively long when compared to how long it takes to whip.As a result, since the width was also measured in inches, I'm going to refer to the length that I'm looking for as X and this time, X will be one inch. Thus, length is to wit. With regard to the race car, 21 is 2 7 as long as X is to 1.4, thus I must now cross multiply to find X. Before I do that, though, I should realize that 21/7 can be boiled down to just three numbers.In order to retrieve X alone and reverse this division by 1.4, I will multiply by 1.4, which equals x when multiplied by three. Therefore, 21 7 is three, which is equal to two x over 1.4. "4.2, 4.2 is equal to three times 1.4.To learn more about Model's length refer to:
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Given: AD ≅ BC and AD ║ BC.
Prove: ΔABC ≅ ΔCDA.
Answers
From the 2 column proof below, we have been able to prove the congruent triangles that ΔABC ≅ ΔCDA.
How to prove congruent triangles?We will use a two column proof to prove that ΔABC ≅ ΔCDA.
Statement 1; AD ≅ BC
Reason 1; Given
Statement 2; AD ║ BC
Reason 2; Given
Statement 3; AC ≅ AC
Reason 3; Reflexive Property of congruence
Statement 4; ∠DAC ≅ ∠ACB
Reason 4; If 2 parallel lines are cut by a transversal, the alternate interior angles are congruent.
Statement 5; ΔABC ≅ ΔCDA
Reason 5; Side Angle Side(SAS) Congruence Postulate
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"Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years."
Answers
After 11.61 years the given principal amount of $ 900 will be double.
What is Compound interest?
Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.
The formula for the Amount when compound interest is calculated is given by
Amount, A = P(1+r/n)^nt
P = Principal amount
r = Rate of interest
n = Number of compounds
t = Time period in years
Given:
Principal amount = $ 900
Rate of interest = 6% = 6/100 = 0.06
Number of compounds = 12 [ ∵ compounded monthly]
We need to find the time period
Assume that after 't' years the amount will be doubled
From the given data and formula,
Amount, A = 900(1+0.06/12)^12t
= 900(1+0.06/12)^12t
= 900(1 + 0.005)^12t
= 900 (1.005)^12t
As we assumed after 't' years the amount is double
=> 900 (1.005)^12t = 2 × 900
=> (1.005)^12t = 2
Applying log on both sides
=> log (1.005)^12t = log 2
=> 12t log(1.005) = log 2
=> 12t = log 2/log(1.005)
=> 12t = 0.30108/ 0.00216
=> 12t = 139.888
=> t = 11.61
Hence, after 11.61 years the given principal amount of $900 will be double.
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It keeps saying I’m wrong
Answers
Answer:
translation of 2 squares left and 1 square down
Step-by-step explanation:
consider the top vertex of both figures
S → T
then shape T is a translation of shape S
by moving 2 squares to the left and 1 square down
The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.
Answers
We want to study the population formula of a given US state according to exponential equation.
a) 23.1 millions.
b) in 2013 - 2014
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main body:
The population state is:
A = 23.1*e^(0.0153*t)
In millions.
Where t represents the number of years after 2000.
a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).
A(0) = 23.1*e^(0.0153*0) = 23.1
The population at year 2000 was 23.1 millions.
b) Now we want to solve:
A(t) = 28.3 = 23.1*e^(0.0153*t)
28.3/23.1 = e^(0.0153*t)
1.23 = e^(0.0153*t)
Now we can apply the natural logarithm to both sides:
ln(1.23) = ln( e^(0.0153*t) )
ln(1.23) = 0.0153*t
ln(1.23)/0.0153 = t = 13.5
Hence, 13.5 years after 2000 the population will be 28.3 million.
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HELP THANK YOU SO MUCH!!
Find the length of the diagonals. Find WY.
W: (-4,5)
Y: (3,-6)
See image Below:
Answers
Length of diagonal WY is 13.03 units
What is Distance Formula?
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).
This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
According to the given question:
WXYZ is a rectangle and diagonals of a rectangle are equal in length
Coordinates of W = (-4,5) and Y = (3,-6)
To find the length of diagonal WY, we need to find distance between points W and Y.
Using distance formula to find WY
= √((3 – (-4))² + (-6 – 5)²)
= √170
= 13.03 units
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Question 9 of 25 Choose the equation that represents this situation. Use p to represent the price of a phone and to represent the total cost. An online business adds a $6 shipping fee to the price of each phone it sells. O A. t = 6p OB. t=p+6 O C. p=t+ 6 O D. t + p = 6
Answers
Choose the equation that represents this situation.
Use p to represent the price of a phone and t to represent the total cost. An online business adds a $6 shipping fee to the price of each phone it sells.
A. t = 6p
B. t = p + 6
C. p = t + 6
D. t + p = 6
Suppose that $11,353 is invested at an interest rate of 5.7% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answers
Answer:
Step-by-step explanation:
1)11357*(105.7/100)^t
2)1 year 12000.121 2 year 12684 5 year 14979.1 10 years 19763.3
3)11357*(105.7/100)^t=22714 so t+12.5
If the functions are combined using addition, which statements describe the resulting graph h(x)? Check two options. domain: x ≥ –2 domain: x ≥ 2 The point (2, 2) is on h(x). The point (–2, 0) is on h(x). The point (0, –3) is on h(x).
Answers
Answer:
(25,-5)
Step-by-step explanation:
I need help with my home work
Answers
Answer:
Below
Step-by-step explanation:
If congruent then
x = y+5 and
x+3 = 3y <======sub in the first equation for 'x'
y+5 +3 = 3y
8 = 2y then y = 4 x = y+5 = 9
If we used the formula f(x)= 10x to get the values for f(x) in the range from x =1 to x(limits are inclusive) We would end up with which lists?
Answers
The range for the given function, with x=1 is 10.
The given function is f(x)=10x.
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Here, put x=1 in the function y=10x, we get
y=10(1)
y=10
So, the range for the given x=1 is y=10.
Therefore, the range for the given function, with x=1 is 10.
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Question 1 One solution. 2x - 1 =_________x - 1
Answers
Answer:
2
Step-by-step explanation:
2x-1 = __x-1
Make both sides match to make the statement true.
2x-1 = 2x-1
2 M 1 0 2 B 4 5 6 Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A'B'C'. What are the coordinates of triangle A'B'C'? OA) A'(0, 4), B'(4, 0), C´(8, 8) B) A'(4, 0), B'(0, 4), C'(8,8) C) A'(0, -4), B'(-4, 0), C'(-8, -8) OD) A'(0, 4), B'(4, 0), C'(16, 16) Mange a N not a fan o
Answers
The coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).
What are coordinates?
A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Here, we have
Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A'B'C'.
A = ( 0,2)
B = (2, 0)
C = (4,4)
After applying dilated by a factor of 2, we get
A' = (0,4)
B' = (4,0)
C' =(8,8)
Hence, the coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).
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Three sides of a triangle have lengths 4, 5, and 6. The angle between the two sides 5 and 6 is nearest: a. 83° b. 56°C. 41° d. 32°
Answers
In the given triangle, the angle between the two sides 5 and 6 is nearest 41°.
The term triangle means the polygon which has three sides and three angles and three vertices,
Here we have given that three sides of a triangle have lengths 4, 5, and 6.
And here we need to find the angle between the two sides 5 and 6
According to the given values, let us consider a = 4, b = 5 and c = 6
So, the angle between 5 and 6 can be written as ∠b
And it can be calculated as the following is one way to perform the calculation and it may not be the best way.
∠B = arc cos(a² + c² - b²)/2ac
When we apply the values one the formula, then we get
=> 0.72273 rad
The approximate degree is written as
=> 41.41°
When we round off it then we get the resulting value,
=> 41°
Therefore, option (c) is correct.
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Which letter represents the mesosphere?
A
B
C
D
Answers
Answer:
A represents the mesosphere
If Corey scored higher than the mean on his SAT, but Jerry scored lower than the mean on his SAT, how will both Z scores differ? Jerry's Z score will be positive, while Corey's Zscore will be negative Jerry's Z score will be negative, while Corey's Z score will be positive Both Jerry and Corey's Z scores will be positive Both Jerry and Corey's Z scores will be negative
Answers
Based on the provided information, Jerry's Z score will be negative, while Corey's Z score will be positive.
A Z-score refers to a numerical measurement that defines the raw value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it means that the data point's score is identical to the mean score. A negative z-score indicates that the data point is below average or mean and a positive z-score indicates that the data point is above average or mean. Consider the formula for z score which is given by:
z = (x - µ)/σ where x is the given data value, µ is the mean, and σ is the standard deviation.
Hence, if the x < µ, the z score will be negative while if x > µ, the z score will be positive. As Corey scored higher than the mean on his SAT, his z score will be positive, and Jerry scored lower than the mean on his SAT, his z score will be negative.
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Find how long it takes $2500 to double if it is invested at 6% interest compounded semiannually. Use the formula A=P(1+r/n) to solve the compound interest problem.
It will take approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
In 11.71 years the amount will double to the principal amount
What is Compound interest:The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal amount and Compounded interest. This is the major distinction between compound and simple interest is this.
The formula used for
Amount, A = P(1+r/n)^ntwhere P = Principal amount
r = Rate of interest in decimal
n = Number of compounds per year
t = Time period
Here from the given data,
Principal amount, p = $ 2500
Rate of interest, r = 6% = 6/100 = 0.06
Number of compounds, n = 2 [ ∵ 12/6 = 2 ]
Here we need to find the time period
Let's assume that after 'n' years the amount will be doubled i.e $ 5000
From the given problem,
Amount, A = 2500(1+0.06/2)²ⁿ
= 2500(1+0.06/2)²ⁿ
= 2500(1 + 0.03)²ⁿ
= 2500 (1.03)²ⁿ
As we assumed after 'n' years the amount is $ 5000
=> 2500 (1.03)²ⁿ = 5000
=> (1.03)²ⁿ = 2
Apply to log on both sides
=> log (1.3)²ⁿ = log 2
=> 2t log (1.3) = log 2
=> 2t = log 2/ log(1.03)
=> 2t = 0.301029996/(0.0128372247)
[ use calculator for log (1.03) and log 2]
=> 2t = 23.4497722
=> t = 11.7248861
=> t = 11.71 ≅ 11 years
Therefore,
In 11.71 years the amount will double to the principal amount
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Jenny and Julie each drank a cup of hot chocolate after playing in the snow. Jenny put 6 more marshmallows in her cup than Julie. Together Jenny and Julie had a total of 6 marshmallows. How many marshmallows did Jenny (x) and Julie (y) each have in their hot chocolate?
Answers
Jenny has 6 marshmallows in her hot chocolate and Julie has 0 marshmallows in her hot chocolate
System of equations: Determining the number of marshmallows in hot chocolateFrom the question, we are to determine the number of marshmallows Jenny and Julie each have in their hot chocolate
From the given information,
"Jenny put 6 more marshmallows in her cup than Julie"
Then, we can write that
x - y = 6 ---------- (1)
Also,
"Together Jenny and Julie had a total of 6 marshmallows"
That is,
x + y = 6 ---------- (2)
Add equations (1) and (2) together
x - y = 6
+ [x + y = 6
--------------------
2x = 12
x = 12/2
x = 6
Substitute the value of x into equation (2)
x + y = 6
6 + y = 6
y = 6 - 6
y = 0
Hence, Jenny has 6 and Julie has 0
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