Answers
Answer:
The explicit formula is [tex]a_{n}[/tex] = - 13 - 7n
Step-by-step explanation:
Let us at first find the type of the sequence
∵ The terms are - 20, - 27, - 34, - 41, ............
→ Find the difference between each to consecutive terms
∵ - 27 - (- 20) = - 27 + 20 = - 7
∵ - 34 - (- 27) = - 34 + 27 = - 7
∵ - 41 - (- 34) = - 41 + 34 = - 7
→ There is a constant difference between each two consecutive terms
∴ The sequence is Arithmetic
→ The explicit formula of the nth term of the arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex], wherea is the first termd is the constant differencen is the position of the number∵ a = - 20
∵ d = -7
∴ [tex]a_{n}=-20+(n-1)(-7)[/tex]
→ Simplify it
∴ [tex]a_{n}[/tex] = - 20 + (-7)(n) - (-7)(1)
∴ [tex]a_{n}[/tex] = - 20 + (-7n) - (-7)
∴ [tex]a_{n}[/tex] = - 20 - 7n + 7
→ Add the like terms
∴ [tex]a_{n}[/tex] = (- 20 + 7) - 7n
∴ [tex]a_{n}[/tex] = - 13 - 7n
The explicit formula is [tex]a_{n}[/tex] = - 13 - 7n
Related Questions
What is the domain of this function y =1|
/x
Answers
Answer:
x≠0
Step-by-step explanation:
The domain of a variable is basically what a variable can be. It's usually All Real Numbers. But this is a special case. x is a denominator. Since division by 0 is undefined, and any other number can work, the answer is x≠0. Hope this helped :)
thanks for the help in advance.
Answers
Hope this helps ya :)
Answer:
6x÷7
Step-by-step explanation:
quotient means division
6x/7
6x÷7
Jonah earns $12.50 per hour as a marketing intern. If he works for 4.5 hours, how many dollars does he earn?
Answers
Answer:
$56.25
Step-by-step explanation:
We have to multiply 12.50 x 4.5
$56.25 TRUST ME
(NEED DONE QUICK) Two angles are supplementary. One of the angles measures 4(2x+9) and the other angle measures 2(4x-8) what is the value of x?
Answers
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
Supplementary angles are angles equal to 180°.
Therefore:
[tex]4(2x+9)+2(4x-8)=180[/tex]
Now that we have our equation, let's distribute the [tex]4[/tex] and the [tex]2[/tex] into the parentheses they are next to:
[tex]8x+36+8x-16=180[/tex]
Combine like terms:
[tex]16x+20=180[/tex]
Subtract [tex]20[/tex] from both sides of the equation:
[tex]16x=160[/tex]
Divide by the coefficient of [tex]x[/tex], which is [tex]16[/tex]:
[tex]x=10[/tex]
~
Check your work by substituting [tex]10[/tex] into one of the equations above:
[tex]8(10)+36+8(10)-16=180[/tex]
[tex]80+36+80-16=180[/tex]
[tex]180=180[/tex]
It's correct!
C an you simplify 5^-8 x 5^4
Answers
Answer:
1/625
Step-by-step explanation:
Exponent Rule: [tex](b^m)(b^n) = b^{m+n}[/tex]
Exponent Rule: [tex]b^{-m}=\frac{1}{b^m}[/tex]
5⁻⁸ · 5⁴ = -8 + 4 = -4
5⁻⁴
1/5⁴
1/625
population has a mean of 200 and a standard deviation of 70 . Suppose a sample of size 125 is selected and
x
ˉ
is used to estimate μ. Use z-table. What is the probability that the sample mean will be within +1−7 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to z ) decimal places.) b. What is the probablity that the sample mean will be within +/−17 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 ) decimal places.)
Answers
a. The probability corresponding to a z-score of -9.7143 is also approximately 0.0000.
b. The probability that the sample mean will be within +/−17 of the population mean is 0.0000.
To find the probability that the sample mean will be within a certain range of the population mean, we need to calculate the z-scores for the given range and then use the z-table to find the corresponding probabilities.
For the first question, we want to find the probability that the sample mean will be within +1−7 of the population mean. To calculate this, we need to convert the range into z-scores. The range +1−7 can be rewritten as -7 to +1.
The formula for calculating the z-score is:
z = (x - μ) / (σ / √n)
In this case, the population mean (μ) is 200, the standard deviation (σ) is 70, and the sample size (n) is 125.
For -7:
z = (-7 - 200) / (70 / √125) = -7.2857
For +1:
z = (1 - 200) / (70 / √125) = -9.7143
Next, we look up the corresponding probabilities in the z-table. From the z-table, the probability corresponding to a z-score of -7.2857 is approximately 0.0000, and the probability corresponding to a z-score of -9.7143 is also approximately 0.0000.
Therefore, the probability that the sample mean will be within +1−7 of the population mean is 0.0000.
For the second question, we want to find the probability that the sample mean will be within +/−17 of the population mean. Using the same approach, we calculate the z-scores:
For -17:
z = (-17 - 200) / (70 / √125) = -17.8571
For +17:
z = (17 - 200) / (70 / √125) = -20.2857
Looking up the probabilities in the z-table, we find that the probability corresponding to a z-score of -17.8571 is approximately 0.0000, and the probability corresponding to a z-score of -20.2857 is also approximately 0.0000.
Therefore, the probability that the sample mean will be within +/−17 of the population mean is 0.0000.
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Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.
How many miles did Priya run last week
Elena writes the equation 1/9(x﹣7) = 4 to describe the situation. She solves the equation by multiplying each side by 9 and then adding 7 to each side. How does her solution compare to the way you found Priya’s miles?
Answers
Answer:
1) The number of miles Priya ran last week was 43 miles
2) The way Elena found Priya's miles is faster compared to the way it was found here
Step-by-step explanation:
1) The number of miles Priya ran this week = The number of miles Priya ran last week - 7
The number of miles Priya ran this week = 9 × The number of miles Elena ran this week
The number of miles Elena ran this week = 4 miles
Therefore;
Let the number of miles Priya ran last week = x miles
The number of miles Priya ran this week = (x - 7) miles
Therefore, we have
(x - 7) = 9 × The number of miles Elena ran this week = 9 × 4 miles = 36 miles
x = (36 + 7) miles = 43 miles
The number of miles Priya ran last week = x miles = 43 miles
The number of miles Priya ran last week = 43 miles
2) From (x - 7) = 9 × The number of miles Elena ran this week = 9 × 4 miles = 36 miles, we have;
(x - 7) = 9 × 4
1/9(x - 7) = 4
Therefore, multiplying by 9, we have;
9 × 1/9(x - 7) = 9 × 4
(x - 7) = 9 × 4 = 36
x - 7 + 7 = 36 + 7
x = 43 miles
Therefore, the way Elena found Priya's miles is faster compared to the way it is found here
Q. 3) (20 p.) Consider the integral ∫ 1/z-a dz where C is any closed contour that goes around the point z = a once in the positive direction. Evaluate the integral on the contour with starting point at z = a + eᶦ ⁰.
Answers
To evaluate the integral ∫ 1/(z-a) dz along a closed contour C that goes around the point z=a once in the positive direction, we can apply Cauchy's Integral Formula. The integral is equal to 2πi times the residue, which is 2πi * 1 = 2πi.
The value of the integral depends on the properties of the function inside the contour, specifically whether the function has a singularity at z=a.
The given integral is of form ∫ 1/(z-a) dz, where z-a represents the denominator. If contour C encloses the point z=a and the function 1/(z-a) has a singularity at z=a, we can apply Cauchy's Integral Formula. According to the formula, the integral evaluates to 2πi times the value of the function at the singularity.
In this case, the function 1/(z-a) has a simple pole at z=a. When integrating around a simple pole, the value of the integral is 2πi times the residue of the function at the pole. The residue of 1/(z-a) at z=a is simply 1.
Therefore, evaluating the integral ∫ 1/(z-a) dz along the given contour C with a starting point at z=a + e^i0, we find that the integral is equal to 2πi times the residue, which is 2πi * 1 = 2πi.
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Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.
Answers
Answer:
1,3,5
Step-by-step explanation:
Answer:
A.B. E.
Hope this helps!
Step-by-step explanation:
5+9-4+5= what? What is the answer?
Answers
Answer: 5
Step-by-step explanation:
Answer:
The answer of 5+9-4+5 is 15
write the sentence as inequality. one-half is at least 3 times a number p
Answers
Answer: 1/2 > 3p
Step-by-step explanation:
Write EQUAL if the regular expression is Equal, else with UNEQUAL. a. (ab)*a = a(ba)* b. (bataa)* = (b+a)*a c. (a+b)*ab(a+b)* = b*ab(a+b)* d. (aa+bb)*=(aa)*(bb)* e. (a+b)*aat=(a+b)* f. (a+b)*(a+b)=(a+b)' g. (a*b*)* = (b*a*)* h. (aatab)*=a(a+b)* i. (ab)*a(ba)* = (ab)*a j. a*+ b* = (a+b)*
Answers
a. UNEQUAL
b. EQUAL
c. EQUAL
d. EQUAL
e. UNEQUAL
f. EQUAL
g. EQUAL
h. UNEQUAL
i. EQUAL
j. EQUAL
a. UNEQUAL: The regular expression (ab)a does not match the language described by a(ba). The former represents strings that start and end with 'a', with any number of 'ab' pairs in between, while the latter represents strings that start with 'b' or 'a' and end with 'a'.
b. EQUAL: The regular expression (bataa)* is equal to (b+a)*a. Both expressions represent strings that start with 'b' or 'a' and end with 'a', with any number of 'bat' or 'a' sequences in between.
c. EQUAL: The regular expression (a+b)ab(a+b) is equal to bab(a+b). Both expressions represent strings that contain the substring 'ab', with any number of 'a' or 'b' characters before, between, or after.
d. EQUAL: The regular expression (aa+bb)* is equal to (aa)(bb). Both expressions represent strings that consist of any number of repetitions of either 'aa' or 'bb'.
e. UNEQUAL: The regular expression (a+b)aat does not match the language described by (a+b). The former represents strings that end with 'aat', while the latter represents strings that can contain any combination of 'a' and 'b' characters.
f. EQUAL: The regular expression (a+b)*(a+b) is equal to (a+b)'. Both expressions represent any combination of 'a' and 'b' characters.
g. EQUAL: The regular expression (ab)* is equal to (ba)*. Both expressions represent any combination of 'a' and 'b' characters, with any number of 'a' and 'b' pairs in between.
h. UNEQUAL: The regular expression (aatab)* does not match the language described by a(a+b)*. The former represents strings that contain the substring 'aatab', while the latter represents strings that start with 'a' and can contain any combination of 'a' and 'b' characters.
i. EQUAL: The regular expression (ab)a(ba) is equal to (ab)*a. Both expressions represent strings that start and end with 'a', with any number of 'ab' pairs in between.
j. EQUAL: The regular expression a*+b* is equal to (a+b)*. Both expressions represent strings that can contain any number of 'a' or 'b' characters.
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PLEASE HELP ME WITH THIS ITS 10 POINTS!!! Im begging you
Answers
Answer:
x = 5 weeks
Step-by-step explanation:
MX + B
Jacob: 7x + 40
Savannah: 5x + 50
Equality:
7x + 40 = 5x + 50
subtract 5x from both sides of equation
2x + 40 = 50
subtract 40 from both sides of equation
2x = 10
divide by 2
x = 5 weeks
Answer:
j = 7x +40; s = 5x +50x = 5Step-by-step explanation:
Jacob is saving $7 per week, so after x weeks, he has saved 7x in addition to the $40 he started with:
j = 7x +40
Similarly, Savannah is saving $5 per week in addition to the $50 she started with, so her savings will be ...
s = 5x +50
Jacob and Savannah will have the same amount of money when ...
j = s
7x +40 = 5x +50 . . . . substitute for j and s
2x +40 = 50 . . . . . . . . subtract 5x from both sides
2x = 10 . . . . . . . . . . . . subtract 40 from both sides
x = 5 . . . . . . . . . . . . . . divide both sides by 2
_____
Comment on the equations
I used j and s for the amounts that Jacob and Savannah accumulated, because I like to use variable names that remind me what they stand for. You may be expected to write these as y = equations, where y stands for the amount each person has saved.
What is 1 5/8 plus 3 3/4?
Answers
Answer:
5 5/8
Step-by-step explanation:
I just know
a.
What is the actual net income for the month? What, if any, changes could have been made to the actual amounts this
month to keep the actual net income at a positive value?
The actual net income for the month is -$85. Less money could have been spent on food,
recreation and clothes.
b. The actual net income for the month is $85. No changes necessary.
C. The actual net income for the month is -$85. No changes necessary.
d. The actual net income for the month is $85. Less money could have been spent on food,
recreation and clothes.
Answers
Answer:
D.
Step-by-step explanation:
Answer:d
Step-by-step explanation:
Which ordered pair is a solution to the set of linear inequalities below?
Answers
I am not 100% sure but I believe its D
Which equation represents the graph below?
Answers
Answer:y=-4+3x
Step-by-step explanation:the slope would be 3 and the y-intercept is -4
which two things are workers in the arts av technology and communication cluster most focused on? check all that apply
Answers
Answer:
Communicating and performing
Step-by-step explanation:
I just did that question and got it correct
Answer:
3 and 5
Step-by-step explanation:
Find the area of a circle with radius, r = 14cm.
Give your answer rounded to 3 SF.
Answers
Answer:
616 cm^2
Step-by-step explanation:
using π r ^ 2
22/7 × 14^2
616 cm^2
acqueline reads 25 pages every night. Which graph correctly displays y, the total number of pages that Jacqueline has read after x days?
On a coordinate plane, a graph titled Total Pages Jacqueline Has Read has days on the x-axis and Pages on the y-axis. A horizontal line is at y = 25.
On a coordinate plane, an exponential curve graph titled Total Pages Jacqueline Has Read has days on the x-axis and Pages on the y-axis.
On a coordinate plane, a graph titled Total Pages Jacqueline Has Read has days on the x-axis and Pages on the y-axis. A line goes through points (0, 25) and (13, 40).
On a coordinate plane, a graph titled Total Pages Jacqueline Has Read has days on the x-axis and Pages on the y-axis. A line goes through points (1, 25) and (2, 50).
Answers
Answer:
On a coordinate plane, a graph titled Total Pages Jacqueline Has Read has days on the x-axis and Pages on the y-axis. A line goes through points (1, 25) and (2, 50).
Step-by-step explanation:
Answer:
D- (1,25) (2,50)
Step-by-step explanation:
edge 2020
Use the function g(x)=5x−2
to complete the table.
x
g(x)
-4
-7
0
23
38
Answers
Answer:
komi chunga lilo mas te ordo
Step-by-step explanation:
Does anyone know the answer 2=10-4y;2
Answers
Answer:
y = 2
Step-by-step explanation:
2 = 10 - 4y
Subtract 10 from both sides;
-8 = -4y
Divide both sides by -4
y = 2
What is the range of this function?
A {-4, 1, 7, 15,}
B {-4, -1, 15, 18}
C {-4, -1, 1, 4, 7, 8, 15, 18,}
D {-1, 4, 8, 18,}
Answers
An annuity-immediate has 32 payments of $500 per period. The effective rate of interest per period is 8% for the first 12 periods and 4% for the following 20 period: (A) Find the accumulated value of the annuity. Round your answer to 2 decimal places. x (B) Find the present value of the annuity. Round your answer to 2 decimal places. x
Answers
a. The Total Accumulated value of the annuity is $17205.50
b. The Total Present value of the annuity is $6357.31
(A) To find the accumulated value of the annuity, we need to calculate the future value of each payment and sum them up. The annuity has 32 payments of $500 per period.
For the first 12 periods, the effective rate of interest is 8%. Using the formula for the future value of an ordinary annuity, which is FV = P X ((1 + r) ^ n - 1) / r, where FV is the future value, P is the payment, r is the interest rate per period, and n is the number of periods, we can calculate the accumulated value for these 12 periods:
FV1 = $500 X ((1 + 0.08) ^ 12 - 1) / 0.08= 14572.5
For the following 20 periods, the effective rate of interest is 4%. Using the same formula, we can calculate the accumulated value for these periods:
FV2 = $500 X ((1 + 0.04) ^ 20 - 1) / 0.04=2633.00
To find the total accumulated value of the annuity, we sum up the two values:
Accumulated Value = FV1 + FV2=$17205.50
(B) To find the present value of the annuity, we need to discount each payment to the present using the appropriate discount rate for each period. Since the annuity has different interest rates for the first 12 periods and the following 20 periods, we need to discount each payment separately.
For the first 12 periods, the discount rate is 8%. Using the formula for the present value of an ordinary annuity, which is PV = P * (1 - (1 + r) ^ -n) / r, where PV is the present value, P is the payment, r is the interest rate per period, and n is the number of periods, we can calculate the present value for these 12 periods:
PV1 = $500 X (1 - (1 + 0.08) ^ -12) / 0.08=$2328.31.
For the following 20 periods, the discount rate is 4%. Using the same formula, we can calculate the present value for these periods:
PV2 = $500 X (1 - (1 + 0.04) ^ -20) / 0.04=$4092.
To find the total present value of the annuity, we sum up the two values:
Present Value = PV1 + PV2=$6357.31
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The function f has a domain of { 2, 4, 6, 8} and a range of {1, 3, 5}. Could f be represented by {(2,1), (4,3), (6, 5), (8,1)}? Explain your answer.
Answers
Answer:
yes
Step-by-step explanation:
The coordinates don't have more than 1 of the same input and the x values are in the domain and the y values are in the range.
Hope this helps
Tyra buys 14 gallons of gas for $35. How could she figure out how much 1 gallon of gas cost her?
Answers
Answer:
$2.50
Step-by-step explanation: 35 divided by 14 is 2.5
Answer:
Divide $35 by 14 gallons to figure out the cost of 1 Gallon ---> 35 ÷ 14 = 2.5 ----> $2.50 per gallon
Which expression is not equivalent to mn + 5
Answers
En una empresa de mensajería, el costo por enviar un paquete es de $6.000 por una distancia de un kilometro o fracción del mismo, y $ 1.100 adicionales por cada kilometro o fracción de este.
a) ¿Cuánto cuesta enviar un paquete de 1,2 km? ¿5,9 km? ¿7 km? ¿10,5 km? Explica tu respuesta.
b) Halla la expresión algebraica que representa el costo del envío de un paquete en función de la distancia. Explica tu respuesta.
Answers
Hey can someone help me out here? I have 3 questions i will give brainliest and it's worth 100 points no cap.
1.) For the following conditional statement, write the a.)
inverse and b.) converse.
If it is Saturday, then there is no school.
2.) Write the following statement in if-then form.
All freshman are required to attend orientation.
3.) Fill in the blank for the following two-column proof.
Given: 3x+1=-14 Prove: x=-5
Statements Reasons
1. 3x+1=-14 Given
2. 3x=-15 ________________________
3. X=-5 Division Property
Answers
Answer:
see below
Step-by-step explanation:
1. The inverse means take the not of both sides
If it is Saturday, then there is no school.
Inverse If it is not Saturday, then there is school.
The converse flips the then and the if
If there is no school, then it is Saturday.
2.) The first given part is the if, what will happen is the then part
If you are a freshman, then you are required to attend orientation.
3.)
Given: 3x+1=-14 Prove: x=-5
Statements Reasons
1. 3x+1=-14 Given
2. 3x=-15 Subtraction Property of equality ( since we subtract 1 from each side)
3. X=-5 Division Property ( since we divide each side by 3)
Jordan has a garden that is enclosed by a rectangular fence. The perimeter of the garden is 84 feet. The length of one side of fencing is 8 yards. What is the area of Jordan’s garden
Answers
Answer:
432 square feet
Step-by-step explanation:
We know perimeter of rectangle is 2(length + width)
we already know that length is 8 yards
and perimeter is 84 feet
we need to find width first
then
we find area of garden by using formula
area of rectangle = length * width
first we need to convert yards into feet as perimeter is in yards
1 yard = 3 feet
8 yards = 3*8 feet = 24 feet
now we plug value of length and perimeter in formula
perimeter = 2(length + width)
84 = 2(24 + width)
84/2 = 24 + width
=> 42 = 24 + width
=> width = 42 - 24 = 18
Thus, width of garden is 18 feet
now
area of Jordan's garden = length * width = 24* 18 feet square
area of Jordan's garden = 432 square feet
