Answers
The first term a₁ of the geometric series is equal to 121.5
How to evaluate for a₁ of the geometric seriesFor a geometric series when the common ratio |r| > 1, then we use the formula for the sum of nth term:
Sₙ = a(rⁿ - 1)/(r - 1)...(1)
The nth term aₙ = arⁿ⁻¹
Thus for Sₙ = 4860 and aₙ = 3280.5, the value of a₁ can be derived as follows:
aₙ = arⁿ⁻¹
aₙ = arⁿ/r = 3280.5
rⁿ = a(r × 3280.5)/a
rⁿ = 9841.5/a
putting 9841.5/a for rⁿ in equation (1) we have;
Sₙ = a[(9841.5/a) - 1]/(r - 1)
Sₙ = (9841.5 - a)/(r - 1)
recall Sₙ = 4860 and r = 3 so;
(9841.5 - a)/2 = 4860
a = 9841.5 - 2(4860)
a = 121.5
Therefore, the first term a₁ of the geometric series is equal to 121.5
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Related Questions
The population of Greensville is increasing at a rate of 5.6% per year. If the population today is 8,000, what will it be 10 years from now?
Answers
The population of Greensville 10 years from now will be approximately 13,184.
To find the population of Greensville 10 years from now, we need to use the formula for compound interest:
A = P(1 + r)ᵗ
Where A is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.
In this case, the present value (P) is 8,000, the annual interest rate (r) is 5.6% or 0.056 as a decimal, and the time (t) is 10 years. Plugging these values into the formula, we get:
A = 8,000(1 + 0.056)¹⁰
A = 8,000(1.648)
A = 13,184
This calculation assumes that the population growth rate remains constant at 5.6% per year.
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50 Points! Multiple choice algebra question. Identify the type of regression that returns the equation y=3x^2. Photo attached. Thank you!
Answers
Answer:
C Exponential
Step-by-step explanation:
3x^2 -- its using an exponent
Help please!!!!
Whoever answers right gets brainliest!
Answers
The equation of the axis of symmetry of the given quadratic function is x = -2. So, correct option is C.
The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. For a quadratic function in the form y = ax² + bx + c, the equation of the axis of symmetry is given by x = -b/(2a).
In the given equation, y = 2x² + 8x - 3, the coefficients of x² and x are a = 2 and b = 8, respectively. Substituting these values in the equation of the axis of symmetry, we get:
x = -b/(2a)
x = -8/(2*2)
x = -8/4
x = -2
This means that the parabola is symmetric about the vertical line x = -2. So the correct answer is x=-2.
So, correct option is C.
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<
1
0.964
8.92
-0.982 increasing decreasing strong
z, hours
y.gallons
Generate a linear regression equation and a correlation coefficient for these data.
1
9.2
2
The linear regression equation is y =
This means there is a ¦
8.4
The correlation coefficient is
O
The number of of gallons is
3
7.7
4
6.1
weak -1.17 10.69
O+O
5
4.5
correlation between the gallons and hours.
as the hours are increasing.
-0.82
Please help bro. Im struggling.
Answers
1. The linear regression equation is y = -1.17x+ 10.69
2. The correlation coefficient is -0.982.
3. This means there is a strong negative correlation between the gallons and hours.
4. The number of gallons is decreasing as the hours are increasing.
How do we calculate for the linear regression equation and correlation coefficient?Step 1: find slope.
Formula for slope m = (n × Σ(xy) - Σx × Σy) / (n × Σ(x²) - (Σx)²)
Σx = 1 + 2 + 3 + 4 + 5 = 15
Σy = 9.2 + 8.4 + 7.7 + 6.1 + 4.5 = 35.9
Σ(xy) = (1 × 9.2) + (2 × 8.4) + (3 × 7.7) + (4 × 6.1) + (5 × 4.5) = 96
Σ(x²) = 1 + 4 + 9 + 16 + 25 = 55
n = 5
Therefore ∴
m = (5 × 96 - 15 × 35.9) / (5 × 55 - 15²) = -1.17
y-intercept b = (Σy - m × Σx) / n
b = (35.9 - (-1.17) × 15) / 5 = (53.15) / 5 = 10.63
Therefore the linear regression equation is y = -1.17x + 10.63
correlation coefficient (r): (n × Σ(xy) - Σx × Σy) / sqrt((n × Σ(x²) - (Σx)²) × (n × Σ(y²) - (Σy)²))
r = (5 × 96 - 15 × 35.9) / sqrt((5 × 55 - 15²) × (5 × 271.95 - 35.9²)) = -0.982
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The estimated population of a certain city over time is given in the table below. Answer the questions below to explain what kind of function would better model the data, linear or exponential.
Number of Years Since Last Census, x
1
2
3
4
Estimated Population, f(x)
66,118
77,212
88,340
99,535
function would better model the data because as x increases, the y values change
. The
of this function is approximately
.
Answers
The linear function is the more appropriate function that has to be used here.
How to use the linear functionTo determine which type of function better models the data, we can analyze the difference in the y values (Estimated Population) as x increases.
Differences between consecutive y values:
77,212 - 66,118 = 11,094
88,340 - 77,212 = 11,128
99,535 - 88,340 = 11,195
The differences between consecutive y values are relatively constant as x increases.
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The value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m2 – 3,500m + 18,000, where m is the approximate number of months since the start of 2020.
Over what period was the value of the card declining?
< m
Answers
If the value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m² – 3,500m + 18,000, the value of the card was declining over the period 0 < m < 7.
To determine when the value of the collectible card was declining, we need to look for when the first derivative of the function is negative. If the first derivative of the function is negative over a certain period, then the function is decreasing over that period. The first derivative of the function V(m) is:
V'(m) = 500m - 3,500
To find when the value of the card was declining, we need to solve the inequality V'(m) < 0. Solving for m, we get:
500m - 3,500 < 0
500m < 3,500
m < 7
Therefore, the value of the card was declining over the period 0 < m < 7. This corresponds to the months from January 2020 to July 2020. During this period, the first derivative of the function V(m) is negative, which means the value of the card was decreasing.
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Make x the subject of m= n+ 1 + x/p
Answers
Answer:
Step-by-step explanation:
m = n + 1 + x/p
First, we can start by subtracting (n+1) from both sides:
m - (n+1) = x/p
Then, we can multiply both sides by p to isolate x:
p(m - (n+1)) = x
So the final answer is:
x = p(m - (n+1))
Help pleaseee
Expand the logarithm as much as possible
logy^10
Answers
The expanded form of log y^10 is either 10 log y or 10 ln y
Expanding the logarithmAssuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:
log y^10 = log (y^10) / log (base)
Since the base is not specified, we can use any base we like. For example, we can use base 10 or base e (natural logarithm).
Using base 10:
log y^10 = log (y^10) / log 10
= 10 log y / 1
= 10 log y
Using natural logarithm:
log y^10 = log (y^10) / log e
= 10 log y / 1
= 10 ln y
Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.
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Please help me with this math problem
1. Josiah is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 12 in and the height of the pyramid is 14in. To get the wax for the candle, Josiah melts cubes of wax that are each 6 in by 6 in by 6 in. How many of the wax cubes will Josiah need in order to make the candle? Show your work.
Answers
Answer:
10 wax cubes
Step-by-step explanation:
the volume of the square pyramid can be found by using the following formula:
[tex]V = \frac{1}{3} * B * h[/tex]
where b is the base of the pyramid and h is the height of the pyramid
The area of the base of the pyramid is given as 12 in * 12 in = 144 in^2
So, the volume of the pyramid is:
V = (1/3) * 144 in^2 * 14 in = 2,016 in^3
Each wax cube has a volume of 6 in * 6 in * 6 in = 216 in^3.
To find the number of wax cubes needed, we can divide the volume of the pyramid by the volume of each wax cube:
Number of wax cubes = Volume of pyramid / Volume of each wax cube
Number of wax cubes = 2,016 in^3 / 216 in^3
Number of wax cubes = 9.33 (rounded to two decimal places)
Since we can't have a fraction of a wax cube, Josiah will need to use 10 wax cubes to make the candle.
Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 29 ties, 15 of which he feels go well with the sport coat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sport coat.
Answers
The probability is P = 0.51, and the odds are 15 to 14.
How to determine the probability and the odds?If all the ties have the same probability of being randomly choosen, then the probability of randomly selecting a tie that goes well with the sports coat is equal to the quotient between the number of ties that goes well with the sports coat (15) and the total number of ties.
The probability will be:
P = 15/29 = 0.51
And the odds are the number of good ties to the number of the other ones, there are 15 good ones and 14 bad ones, so the odds are 15 to 14.
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Game dice for a particular child’s game are numbered 1-10 what is the likehood of rolling a single one and ending up with an even number
Answers
Dice game for a particular child’s game are numbered 1-10. Then, the likelihood of rolling a single one and ending up with an even number is 1/20.
The probability of rolling a single one is 1/10, since there is only one die face with the number one out of ten possible outcomes.
The probability of rolling an even number is 5/10, since half of the die faces are even numbers (2, 4, 6, 8, 10) out of ten possible outcomes.
To find the likelihood of both events happening together, we need to multiply their individual probabilities;
P(rolling a single one and ending up with an even number) = P(rolling a single one) x P(ending up with an even number)
= (1/10) x (5/10)
= 1/20
Therefore, the likelihood of rolling a single one and ending up with an even number is 1/20.
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In AABC, AB=32, AC= 22, and BC= 20. What is mZA?
m
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
The value of measure of ∠A would be,
⇒ ∠ A = 38.68 degree
We have to given that;
In triangle ABC,
AB=32, AC= 22, and BC= 20
Hence, We can formulate;
⇒ sin A = BC / AB
⇒ sin A = 20 / 32
⇒ sin A = 0.625
⇒ A = 38.68 degree
Thus, The value of measure of ∠A would be,
⇒ ∠ A = 38.68 degree
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8 = -4 + v
v = what does v equal
Answers
Answer is v = 12
Below is the explanation.
Choose one of the topics below for your paragraph.
1. Write a paragraph about a trend that interests you and why it is popular. Give sentences
(Paragraph)
● For example, consider a trend in cars, food, or technology. Give sentences (Paragraph)
2. Write a paragraph about a popular TV program. Give sentences (Paragraph)
Who usually watches the program? Give sentences (Paragraph)
Why is it popular? Give sentences (Paragraph)
●
Answers
Answer:
1. A trend that gives me interest is the 1, 2 buckle my shoes 3, 4 buckle some more- The reason is why does it even exist and why did it get so popular is such a fast amount of time, and the way people get distracted on technology which we are using all over the world and it takes us away from the real world and makes us stay there.
2. Cocaine Bear it looks good and funny, I watched it with all my friends and they all enjoyed it with me.
Step-by-step explanation:
what is the quotient?
Answers
Answer:
a quotient is the result obtained by dividing one quantity by another.
A worker completes a job in a certain number of hours. The standard time allowed for the job is 10 hours, and the hourly rate of wages is Re. 1. The worker earns at the 50% rate a bonus of Rs. 2 under Halsey Plan. Ascertain his total wages under the Rowan Premium Plan.
Answers
Let's assume that the worker completes the job in 'x' hours. So, the Rowan Premium Plan formula to calculate wages is:
Total wages = (time taken / standard time) * standard wages + (time taken - standard time) * hourly rate * premium percentage
Here, the premium percentage is the percentage of time saved, which is given by:
Premium percentage = (standard time - time taken) / standard time * 100
Substituting the given values, we get:
Premium percentage = (10 - x) / 10 * 100
Premium percentage = (100 - 10x) %
Now, substituting this value in the Rowan Premium Plan formula, we get:
Total wages = (x / 10) * 4 + (x - 10) * 1 * (100 - 10x) / 100
Simplifying this expression, we get:
Total wages = (2x + 8 - x^2) / 5
So, the total wages earned by the worker under the Rowan Premium Plan is (2x + 8 - x^2) / 5.
The circle below is centered at the point (-3, 4) and has a radius of length 3.
What is its equation?
-10
-5
5
Answers
Answer:
C. (x + 3)² + (y - 4)² = 9
Step-by-step explanation:
The equation for a circle is r² = (x - a)² + (y - b)² where "r" is the radius and (a, b) is the center.
We are given that (-3, 4) is the center and the radius is 3, so that means a = -3, b = 4, and r = 3. Insert the values to their respective places in the equation:
3² = (x - (-3))² + (y - 4)²
9 = (x + 3)² + (y - 4)²
Answer:
equation of a circle: (x-a)²+(y-b)²=r²
(x-(-3))²+(y-4)²=3²
(x+3)²+(y-4)²= 9
(x+6x+9)+(y-8y+16) =9
x+6x+9+y-8y+16=9
x+y+6x-8y+9+16-9=0
x+y+6x-8y+16 =0
The weights of four similar packs of tomatoes are listed below.
Pack A: 2.456 pounds
Pack B: 2.457 pounds
Pack C: 2.454 pounds
Pack D: 2.459 pounds
Malcolm rounds the weights to the nearest hundredth pound. Which weight does
not round to 2.46 pounds?
A 2.456 pounds
B 2.457 pounds
C 2.454 pounds
D 2.459 pounds
Answers
Answer:
The weight that does not round to 2.46 pounds is C 2.454 pounds.
Step-by-step explanation:
Based on the given information, the weights of the four similar packs of tomatoes are as follows:
Pack A: 2.456 poundsPack B: 2.457 poundsPack C: 2.454 poundsPack D: 2.459 poundsMalcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:
Pack A: 2.46 poundsPack B: 2.46 poundsPack C: 2.45 poundsPack D: 2.46 poundsFrom the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.
Solution to augmented matrix? Never seen a problem like this one. How do I solve it?
Answers
The row of zeros at the bottom immediately lets us conclude "infinitely many solutions". This system is consistent and dependent. This is because we have 0x+0y+0z = 0 aka 0 = 0 which is always true for any choice of x, y, and z.
The second row of values lead to the equation 0x+0y+1z = 6, aka z = 6
The first row says: 1x+6y+0z = 1 which is the same as x+6y = 1
Let's say we isolate x
x+6y = 1
x+6y-6y = 1-6y
x = 1-6y
Then we have these three values or expressions
x = 1-6yy = any real numberz = 6All of the infinitely many solutions are of the form (x,y,z) = (1-6y, y, 6)
A lot of textbooks will use a parameter such as t, so we could write it as (1-6t, t, 6).
The choice of the letter for the parameter does not matter. I think t is most popular because it represents time. Each (x,y,z) point could represent a particle's location at any given time.
If t = 0, then we have (1, 0, 6)If t = 1, then we have (-5, 1, 6)If t = 2, then we have (-11, 2, 6)If t = 3, then we have (-17, 3, 6)and so on.
=============================
Conclusion:
There are infinitely many solutions of the form (x,y,z) = (1-6t, t, 6) where t is any real number.
This system is consistent and dependent.
Is AB perpendicular to CD? Explain? pls yall fwm on the answer
Answers
Answer: No
Step-by-step explanation: They are not perpendicular due to the slopes. Perpendicular will have the same slopes value wise, but one is negative and one positive.
MO is parallel to PR. Angle RQN=115. What is MNQ?
Answers
Since MO is parallel to PR, then angle MNQ and angle RQN are alternate interior angles and are congruent. Therefore, angle MNQ = angle RQN = 115 degrees.
What are alternate interior anglesWhen a line that intersects two parallel lines, also known as a transversal, creates an intersection with a pair of other lines, it forms what is referred to as alternate interior angles.
From the diagram we can see that RQN and MQN are similar angles from the diagram
Hence we have that RQN=115 = MNQ
Therefore MNQ = 115 degrees
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Help me with this question please
Answers
Answer:
A line that is perpendicular to another is one that has a slope that is the multiplicative reciprocal of the original funtion's slope and it also has the opposite sign in front. Considering a slope with a value of [tex]\dfrac{1}{7}[/tex], the reciprocal multiplicative is 7, because is a number that equals 1 if multiplied by the original value. Then, we change the sign for it, making it -7.
Thus, correct answer is a. -7.
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Can you help me with this
Answers
Answer: 6/1
Step-by-step explanation: 2/1 x 3/1 = 6/1
A red marble is drawn from a bag containing 3 red and 3 blue marbles. If the red marble is not replaced, find the probability of drawing a second marble that is blue.
Answers
The probability of drawing a second marble that is blue is 3/5
Finding the probability of drawing a second marble that is blue.From the question, we have the following parameters that can be used in our computation:
A red marble is drawn from a bag containing 3 red and 3 blue marbles.
If the marbles were not replaced, then we have
P(Red) = 3/6
Now there are
3 blue marbles and 2 red marbles left
So, we have
The probability of choosing a blue marble, after a red marble is
P(Blue) = 3/5
Evaluate
P(Blue) = 3/5
Hence, the probability of choosing a blue marble, after a red marble is 3/5
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Review the proof.
Step
1
2
3
5
6
7
8
Statement
cos(2x)= 1-2sin²(x)
Let 2x = 0.
Then x =
cos() = 1-2sin²()
-1 + cos() = -2sin²)
1 + cos(e) = 2sin²)
1-cos(0) = sin²)
sin() = ±
1-cos(0)
2
Which step contains an error?
O step 2
O step 4
step 6
O step 8
Answers
The error is in step 2 based on the given statement.
How to solveThe given statement is[tex]cos(2x) = 1-2sin^2(x),[/tex] and it is not appropriate to simply let 2x = 0.
By doing this, you are only considering a specific case where x = 0, rather than proving the statement for all values of x.
To properly prove the given statement, you should consider using trigonometric identities or double-angle formulas to establish the equivalence between cos(2x) and 1-2sin²(x) for all x.
Thus, the error is in Step 2
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cost function definition
Answers
Find f(-1).
Provide your answer below:
f(t)=-3t²-2t+1
Answers
Answer:
f(-1)=0
Step-by-step explanation:
To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :
[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]
[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0
5. Find x and y of a , b and c
Answers
The value of x and y will be
a) x= 48 y= 72
b) x= 10 y= 3
c) x= 18 y= 3
What is triangle proportionality theorem ?
Triangle Proportionality Theorem Statement
If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.
DA/BD = EC/BE
How we can calculate the value of x and y from the figure ?
The value of x and y can be calculated as
a ) x/4 + 5 =x/2-7 y/3-6=66-2/3y
x/4- x/2 = -7-5 y/3+ 2y/3= 66 + 6
x-2x/4=-12 3y/3= 72
x= 48 y=72
b) x/5 +3 = 4x-35 2y + 1 = 5y-8
x/5 - 4x = -35-3 2y-5y= -8-1
x-20x/5 = -38 -3y=-9
-1 9x/5 = -38 y=3
x= 10
c) x/3 + 2= 2x/3-4 5y=7y/3+8
x/3-2x/3= -4-2 5y-7y/3=8
-x/3 = -6 15y-7y=8x3
x= 18 y=3
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Evaluate the determinant
1
03
03
0)2
w2
1 , where w is a cube root
co
2 1 o
of unity.
Answers
In this case, the cube root is = 0
Why is this so?We can use the rule Sarrus to evaluate the determinant
1 w w²
w w² 1
w² 1 w
Starting with the first column, we can wrte out the terms for the diagonal products and
then sum the terms for the products of the diagonal elements that wrap around
(1 x w² x w) +(w x 1 x w²) + (w² x w x w) - (w ² x w x 1) - (w x w² x w) - (1 x w x w ²)
Simplifying each term:
w³ + w³ + w³ - w³ -w³ - w³
We can see that all the terms cancel out, leaving us with a determinant of 0. So it is clear that
|1 w w²|
|w w² 1 |
|w² 1 w | = 0
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Evaluate the determinant 1 w w2 , w w2 1, w2 1 w. where w is a cube root of unity.
What is the area of this figure? 11 mm 3 mm 2 mm 2 mm 4 mm 2 mm 5 mm 3 mm Write your answer using decimals. Use 3.14 for л.
Answers
Answer: 116.985 mm2
Step-by-step explanation: