Given the formula, find the first five terms and the 10th term of each
sequence.
a n = -4 × 2 n-1
Can you teach me this?
Then I will try the next?
Answers
Given formula: \(\sf A_n= -4(2)^{n-1}\)
simplify substitute the number of term by replacing n
Find first five terms:
\(\sf A_1= -4(2)^{1-1}\) ⇒ \(\sf A_1= -4\)
\(\sf A_2= -4(2)^{2-1}\) ⇒ \(\sf A_2= -8\)
\(\sf A_3= -4(2)^{3-1}\) ⇒ \(\sf A_3= -16\)
\(\sf A_4= -4(2)^{4-1}\)⇒ \(\sf A_4= -32\)
\(\sf A_5= -4(2)^{5-1}\)⇒ \(\sf A_5= -64\)
Tenth term:
\(\sf A_{10}= -4(2)^{10-1}\) ⇒ \(\sf A_{10}= -2048\)
Answer:
\(\sf a_1=-4\\a_2=-12\\a_3=-20\\a_4=-28\\a_5=-36\\a_{10}=-76\)
Step-by-step explanation:
\(\textsf{Given sequence}: \sf a_n=-4(2n-1)\)
This formula is for the nth term of the sequence.
Therefore, to find any term of the sequence, substitute the position of the term you wish to find as n.
For example, to find the 10th term, substitute n = 10 into the formula:
\(\begin{aligned}\sf a_{10} & =-4[2(10)-1)]\\ & = -4(20-1)\\ & = -4(19)\\ & = -76\end{aligned}\)
To find the first 5 terms, substitute n = 1 through n = 5 into the formula:
\(\sf a_1=-4[2(1)-1]=-4(2-1)=-4(1)=-4\)
\(\sf a_2=-4[2(2)-1]=-4(4-1)=-4(3)=-12\)
\(\sf a_3=-4[2(3)-1]=-4(6-1)=-4(5)=-20\)
\(\sf a_4=-4[2(4)-1]=-4(8-1)=-4(7)=-28\)
\(\sf a_5=-4[2(5)-1]=-4(10-1)=-4(9)=-36\)
Related Questions
Central Park in New York City is shaped like a rectangle. On a map of the park
in the coordinate plane, three of the vertices are located at (-1.25, -0.25),
(-1.25, 0.25), and (1.25, 0.25). Distances on the map are in miles. What is the
perimeter of Central Park? Show your work,
Answers
Answer:
6
Step-by-step explanation:
Given that the coordinate plane, three of the vertices of the rectangle are located at (-1.25, -0.25),
(-1.25, 0.25), and (1.25, 0.25)
The length L of the shape will be:
L = 0.25 - ( - 0.25 )
L = 0.25 + 0.25
L = 0.5
The width of the shape will be:
W = 1.25 - ( - 1.25)
W = 1.25 + 1.25
W = 2.5
Perimeter P = 2L + 2W
Substitute the Length and the width into the formula
P = 2(0.5) + 2(2.5)
P = 1 + 5
P = 6 metres
Therefore, the perimeter of the shape is 6 metres
Please help I will mark brainliest!
Answers
Answer:
It is the 4th one because all are greater than -2
Step-by-step explanation:
1 point) find a basis of the subspace of r3 r3 defined by the equation −3x1−3x2−8x3=0−3x1−3x2−8x3=0. basis: {{ ⎡⎣⎢⎢⎢⎢⎢⎢[ ⎤⎦⎥⎥⎥⎥⎥⎥], ⎡⎣⎢⎢⎢⎢⎢⎢[ ⎤⎦⎥⎥⎥⎥⎥⎥] }.
Answers
A basis for the subspace is {{1,0,-3/8}, {0,1,-3/8}}. This can be answered by the concept from Sets.
To find a basis of the subspace of R3 defined by the equation −3x1−3x2−8x3=0, we can first rearrange the equation as x3 = (-3/8)x1 - (3/8)x2.
Then we can rewrite the subspace as Span{{1,0,-3/8}, {0,1,-3/8}} since these two vectors span the subspace of solutions to the equation.
Therefore, a basis for the subspace is {{1,0,-3/8}, {0,1,-3/8}}.
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an ir signal has a percent transmittance of 45%. what does this mean with respect to how the sample interacted with the ir light source? group of answer choices
Answers
If an IR signal has a percent transmittance of 45%, then the sample absorbed 55% of the IR light
The percent transmittance of an IR signal = 45%
The equation of percent transmittance is
Percent transmittance = ( I / Io ) × 100
Where Io is the intensity of the IR signal entering the sample
I is the intensity of the IR signal leaving the sample
If the Io = I, then the percent transmittance is 100% that means the sample did not absorb any light and if Io= 0 then the the percent transmittance is 0% then sample absorbed all the light
Here, the percent transmittance is 45%, that mean the 55% of light absorbed by the sample
Therefore, the sample absorbed 55% of the IR light
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y - 7.3 = 2(x - 8.8) slope =
Answers
Answer:
Step-by-step explanation:
mitchels room measures 10 inches by 6 inches on a scale drawing. what are the actual measermets of his room (in feet) of he uses a scale of 1 to 24?
width height
Answers
Answer:
20 ft by 12 ft
Step-by-step explanation:
(10 in x 24) / 12 ft = (240 in / 12 ft) = 20 ft
(6 in x 24) / 12 ft = (144 in / 12 ft) = 12 ft
the top says for the first box : Part A Explain how Mrs. Soto could apply the
following theorem to the problem of restoring
the gate to its original rectangular shape.
Answers
Answer:
The given theorem proves that the door is not a rectangle right now since, the door came out of shape, it can be proved by the Pythagorean theorem. If the length is set to a certain shape, and the width is set to a certain shape, and drawn to diagonals. If solved by the Pythagorean Theorem, if the length of two diagonals are similar then and only then the door would be a rectangle.
Hope this helps!
I will give you 30 points
Answers
1. Three examples of situations where consistency is important:
HealthcareFinancial transactionsSports RulesHow do these portray consistency?Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.
Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.
Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.
2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.
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What percent of 75 is 27?
Answers
Answer:
37.5%
Step-by-step explanation:
To find what percent of 75 is 27, you must put 27 over 75
\(\frac{27}{75}\)
When simplified, this is equal to 3/8 or 0.375
When turned into a percent, this is equal to 37.5%.
#YourWelcome.
Answer:
36%
Step-by-step explanation:
percentages can be found by the equations of parts/whole * 100
so 27/75 is .36
.36*100 is 36
so it's 36%
Follow the steps to find the product of and 0.55.
Estimate the product of and 0.55.
1/4-
Convert the decimal 0.55 to a fraction.
V55/100
What is the product of the two numbers?
X 110/150 or 11/15
110/300 or 11/30
77/103
Answers
1) Estimate value of the product of 2/3 and 0.55 is, 2/3.
2) The fraction part is, 55 / 100
3) The product of the two numbers is, 11/30
We have to given that,
Estimate the product of 2/3 and 0.55.
And, Convert the decimal 0.55 to a fraction.
And, The product of the two numbers.
Now,
Estimate the product of 2/3 and 0.55,
So, we can round 0.55 to the nearest whole number, which is 1.
Then, multiply 2/3 by 1 to get an estimate of the product.
so, The correct answer is 2/3.
Now, we can convert the decimal 0.55 to a fraction,
= 0.55
= 55/100
= 11/20
Thus, The correct answer is, 55/100.
And, the product of 2/3 and 0.55,
= 2/3 x 55/100
= 110/300
= 11/30.
Hence, The correct answer is, 110/300 or 11/30
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Simplify (1+1/3)^2-2/9
Answers
The simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
What is the simplified form of the given expression?Given the expression in the question;
( 1 + 1/3 )² - 2/9
Add the two terms inside the parenthesis
( (3+1)/3 )² - 2/9
( 4/3 )² - 2/9
Apply product rule to 4/3
4²/3² - 2/9
Raise 4 and 3 to the power of 2
16/9 - 2/9
Combine the numerators over common denominator
( 16 - 2 ) / 9
14/9
Therefore, the simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
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Is this statement true or false explain why 6,203 > 6,320
Answers
Answer:
false
Step-by-step explanation:
The ph measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0. 3. What is approximately, the probability that the pH measurements of a randomly selected water specimen is value between 7. 5 and 8. 2
Answers
The probability that a randomly selected water specimen has a pH value between 7.5 and 8.2 is approximately 0.6287. We can calculate it in the following manner.
We are given that pH measurements of water specimens from various locations along a river basin are normally distributed with a mean of 8 and a standard deviation of 0.3. We want to find the probability that a randomly selected water specimen has a pH value between 7.5 and 8.2.
To solve this problem, we can standardize the pH values using the standard normal distribution, which has a mean of 0 and a standard deviation of 1.
First, we find the z-scores for pH values of 7.5 and 8.2 as follows:
z1 = (7.5 - 8) / 0.3 = -1.67
z2 = (8.2 - 8) / 0.3 = 0.67
Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores:
P(-1.67 < Z < 0.67)
Using a standard normal distribution table or calculator, we find that the area under the curve between -1.67 and 0.67 is approximately 0.6287.
Therefore, the probability that a randomly selected water specimen has a pH value between 7.5 and 8.2 is approximately 0.6287.
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How many rebounds should your team expect to have in 15 missed shots?
Answers
It is unlikely that the projected rebounds in 15 shots will actually happen.
Explain about the term probability?A probability is a scaled version of the likelihood or chance that a specific event will take place. Both percentages with values ranging from zero to one and percentages extending from 0% to 100% can be used to describe probabilities.Total shots fired equals 10.
To find that there were 15 shots total.
Consider S to be the likelihood that your team will rebound and miss a shot.
P(S) = Number of rebounds / Total Number of outcomes
P(S) = 7/15
P(S) = 0.46
Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.
Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.
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The complete question is-
During a basketball game, you record the number of rebounds from missed shots for each team. How many rebounds should your team expect to have in 15 missed shots?
Picture for question is attached.
What is negative times a negative?
Answers
Answer:
positive
Negative x negative = positive.
Here is an example:
-2 x -4 = 8.
Hope it helps!
positive
Negative x negative = positive.
Here is an example:
-6 x -2 = 12
Hope it helps!
Each unit of a product can be made on either machine A or machine B. The nature of the machines makes their cost functions differ, x² 6 Machine A Machine B C(x) = 60+ C(y) = 160+ y³ 9 Total cost is given by C(x,y)= C(x) + C(y). How many units should be made on each machine in order to minimize total costs if x+y=14,520 units are required? The minimum total cost is achieved when units are produced on machine A and units are produced on machine B. (Simplify your answer.)
Answers
To minimize total costs while producing 14,520 units, approximately x = 6280 units should be made on machine A and approximately y = 9240 units should be made on machine B.
Let's represent the number of units produced on machine A as x and the number of units produced on machine B as y. We are given that x + y = 14,520 units.
The total cost function is given by C(x, y) = C(x) + C(y) = 60x + 160 + y^3.
To find the minimum total cost, we can minimize the total cost function C(x, y) with respect to x or y.
First, let's express one variable in terms of the other using the equation x + y = 14,520:
x = 14,520 - y
Substituting this expression for x in the total cost function
C(y) = 60(14,520 - y) + 160 + y^3
Expanding and simplifying
C(y) = 60y - 60y^2 + y^3 + 160
To find the minimum, we need to take the derivative of C(y) with respect to y, set it equal to zero, and solve for y:
C'(y) = 60 - 120y + 3y^2 = 0
Simplifying further, we get:
3y^2 - 120y + 60 = 0
Dividing through by 3, we have:
y^2 - 40y + 20 = 0
Using the quadratic formula, we can solve for y:
y = (40 ± √(40^2 - 4*1*20)) / 2
Simplifying
y = (40 ± √(1600 - 80)) / 2
y = (40 ± √1520) / 2
Since we are dealing with a physical quantity of units, we can discard the negative solution and consider the positive solution:
y = (40 + √1520) / 2
Now, we can substitute this value of y back into the equation x + y = 14,520 to find x:
x + (40 + √1520) / 2 = 14,520
x = 14,520 - (40 + √1520) / 2
Therefore, to minimize total costs while producing 14,520 units, approximately x = 6280 units should be made on machine A and approximately y = 9240 units should be made on machine B.
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Please help will mark brainliest
Answers
Answer:
-4
Step-by-step explanation:
Answer:
y = 1/3x - 3
Step-by-step explanation:
When conducting a scientific investigation, how many variables should be tested?.
Answers
An experiment usually has three kinds of variables: independent, dependent, and controlled. The independent variable is the one that is changed by the scientist.
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
The variable you alter, regulate, or change in an experimental study to examine its effects is known as an independent variable. It is named "independent" because it is unaffected by any other study variables.
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Out of 1,200 students that attend Norman Rockwell Middle School, how many would most likely sign up for after school tutoring, if 48 out of 80 students randomly surveyed said they would like to have extra help after school?
Answers
Answer:
720
Step-by-step explanation:
Out of 80 students the no. of students who sign up=48
So, out of 1200 students 48×1200÷80=720 students sign up.
a party has a ratio of men to women as 8:13.Two more men join, 5 women leave. The new ratio then becomes 7:10..find the original number of people in the party both men and women?
Answers
Answer:
revenge time
Step-by-step explanation:
Write an integer that represents 5 inches of snow melting. *
Answers
Answer:
-5
Step-by-step explanation:
There was five inches of snow, correct? Now, the five inches are melting. It's kinda like subtraction.
5 - 5
What does x = ?
5/2 • x =1
Answers
Answer:
2/5
Step-by-step explanation:
5/2x = 1
2/5 x 5/2x = 1 x 2/5
x = 2/5
Answer:
x = 2/5
Explanation:
Step 1: Multiply both sides by 2/5.
(2/5) * (5/2x) = (2/5) * (1)
x = 2/5
Find the value of x so that the function has the given value.
f(x)=8x+2;f(x)=8
Answers
what is the solution for 15= -x +10
Answers
Answer:
-5
Step-by-step explanation:
15=-x+10
x-10=-15
x=-15+10
x=-5
Four times the sum of 5 and some number is 20. What is the number?
Answers
This is the answer to your problem
6-5(2x-3)=4x+7
Solve for x
Answers
Answer:
1
Step-by-step explanation:
6 - 5(2x-3) = 4x + 7
-5(2x-3) = 4x + 1
-10x + 15 = 4x + 1
-14x = -14
14x = 14
x = 1
Find the volume of the rectangular prism.
Answers
Answer:
8 x 8 x 8 = 512
Step-by-step explanation:
Hope this helps! Have a great day :)
Answer:
512
Step-by-step explanation:
LxWxH
8x8x8=512
"5 to the second power", what does the exponent 2 tell us to do with the
base 5?
Answers
Answer:
The exponent 2 tells us that we must multiply 2 five's together.
So we have: 5^2 = 5 x 5
Let me know if this helps!
Answer:
The exponent 2 tells us to multiply the base 5 by itself
Step-by-step explanation:
An exponent tells us to multiply the base by itself the amount of times of the exponent
In this case, the base is 5 and the exponent is 2
The exponent is telling us to multiply our base: 5 by itself
5x5
Which table represents a linear function?
Answers
Step-by-step explanation:
the second table
......................
Use substitution to determine if (0,2) is an element of the solution set for the system of equations. x+3y=6 -x+4y=8 (0,2) is a solution of the system. (0,2) is not a solution of the system.
Answers
The correct statement is: "(0,2) is a solution of the system."
To determine if (0, 2) is an element of the solution set for the system of equations:
Equation 1: x + 3y = 6
Equation 2: -x + 4y = 8
We can substitute the values x = 0 and y = 2 into both equations and check if they hold true.
For Equation 1:
0 + 3(2) = 6
6 = 6
The equation is true.
For Equation 2:
-(0) + 4(2) = 8
8 = 8
The equation is also true.
Since both equations hold true when x = 0 and y = 2, (0, 2) is indeed a solution of the system.
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