Answer:
96 and 1160
Step-by-step explanation:
1st row → 20
2nd row → 24
3rd row → 28
the number of seats increases by 4 each row.
This indicates an arithmetic progression with common difference d = 4
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 20 and d = 4 , then
a₂₀ = 20 + (19 × 4) = 20 + 76 = 96
there are 96 seats in the last row
the sum to n terms of an arithmetic sequence where the first and last terms are known is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (first term + last term)
here a₁ = 20 and a₂₀ = 96 , then
S₂₀ = [tex]\frac{20}{2}[/tex] (20 + 96) = 10 × 116 = 1160
there are 1160 seats in the auditorium
Answer:
96 seats in the last row.
1160 seats in the auditorium.
Step-by-step explanation:
The given scenario can be modeled as an arithmetic sequence where the number of seats in each row of the auditorium is the corresponding term in the sequence:
20, 24, 28, ...General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
where:
[tex]a_n[/tex] is the nth term.a is the first term.d is the common difference between terms.For the given sequence 20, 24, 28, ...
a = 20d = 24 - 20 = 4Therefore, the equation for the number of seats in the nth row is:
[tex]\boxed{a_n=20+(n-1)4}[/tex]
To find the number of seats in the 20th row, substitute n = 20 into the found formula:
[tex]\begin{aligned}\implies a_{20}&=20+(20-1)4\\& = 20+(19)4\\& = 20+76\\& = 96\end{aligned}[/tex]
Therefore, there are 96 seats in the last row.
Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac{n}{2}(a+a_n)}[/tex]
To find the total number of seats in the auditorium, substitute n = 20, a = 20 and a₂₀ = 96 into the formula:
[tex]\begin{aligned}\implies S_{20} & = \dfrac{20}{2}(20+96)\\& = 10(116)\\& = 1160\end{aligned}[/tex]
Therefore, there are a total of 1160 seats in the auditorium.
f(x) = [tex]\frac{x-9}{6x+6}[/tex]
Find an equation for the tangent line to the graph of f at x= 11.
Tangent line: y = ??
The equation of the line tangent to the curve at x = 11 is y = (5 / 432) · x - 43 / 432.
What is the equation of the line tangent to a given curve?
Herein we have a rational function, of which we must derive the equation of the line tangent to the curve at a given point. First, find the first derivative of the function by derivative rules:
f'(x) = [(6 · x + 6) - 6 · (x - 9)] / (6 · x + 6)²
f'(x) = 60 / (6 · x + 6)²
Second, evaluate the first derivative of the function:
f'(11) = 60 / (6 · 11 + 6)²
f'(11) = 5 / 432
This value represents the slope of the tangent line.
Third, calculate the y-value of the curve:
f(11) = (11 - 9) / (6 · 11 + 6)
f(11) = 1 / 36
Fourth, determine the intercept of the tangent line:
b = 1 / 36 - (5 / 432) · (11)
b = - 43 / 432
The equation of the line tangent to the curve at x = 11 is y = (5 / 432) · x - 43 / 432.
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1. Find the domain and range of the function shown in the table.
X
y
-2
-1
5.5
0
4
3.5
0
4
-1
5.5
-1
8
-3.5
Domain of the function: {-2, -1, 0, 3.5, 4, 5.5, 8}
Range of the function: {-3.5, -1, 0, 4, 5.5, 6}
What is the Domain of a Function?In a relation which represents a function, all the x-values of the relation make up the domain of the function. That means the the elements of the domain of the function consists of all set of x-values.
What is the Range of a Function?On the other hand, all the corresponding y-values of the relation make up the range of the function. This implies that, the elements of the range of the function consists of all set of y-values.
The domain of the function is therefore: {-2, -1, 0, 3.5, 4, 5.5, 8}
The range of the function is therefore: {-3.5, -1, 0, 4, 5.5, 6}
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After spending0.6 of her money,Andina had RS 60 left . How much money had she first ?
Answer:
Step-by-step explanation:
If you use pre-tax dollars, then it lowers your taxable income now and most likely when you retire, your income will be lower, so you'll pay a lower tax rate then.
Answer: D
The total bill at a restaurant was $42.50. If you want to tip the waitress 15%, how much tip should you leave? A. $6.38
B. $6.37
C. $63.75
D. $637.50
Can anyone help me with #65?
Answer:
X = 73.448
Step-by-step explanation:
First you have to multiply 1.645 by 2.4 to get rid of 2.4 on the right side of the equation. Then you should have 3.948 = x - 69.5. After that all you have to do is add 69.5 to 3.948 then you have x.
[tex]3x-8\leq 4[/tex]
Step-by-step explanation:
[tex]{ \tt{3x - 8 \leq 4}} \\ \\ { \tt{3x \leq4 + 8}} \\ \\ { \tt{3x \leq12}} \\ \\ { \tt{x \leq4}}[/tex]
x-y=0
6x + 5y = -22
The lines intersect at
A. (2.-2)
B. (-2,-2)
C. (2.2)
Answer:
B
Step-by-step explanation:
x - y = 0 ( add y to both sides )
x = y → (1)
6x + 5y = - 22 → (2)
substitute x = y into (2)
6y + 5y = - 22
11y = - 22 ( divide both sides by 11 (
y = - 2
since x = y then x = - 2
the lines intersect at (- 2, - 2 )
1. How many whole numbers between 1 and 20 is divisible by 2? by4? by 6?
2. How many whole numbers between 1 and 100that are not divisible by 3? or by 11?
3. Fill the empty boxes to show the largest possible value of _ 8 9 4 9 _
4. which of the following numbers in the set is is divisible by 12? {256, 519, 822}
5. which of the following numbers in the set is divisinle by? {4256, 5225, 6336, 8119}
6. write down any 3-digit number, Repeat the 3 digits to make 6-digit number.
Divide the 6-digit number by 13 , divide again by 11. Lastly,divide the quotient from the second divisiion by 7. What did you get? Explain.
7.Find the value represent by _ in the 6 digit number, 458,___ Such that this number is the smallest divisible 3, 4, and 5.
Answer:
divisible by 2
2,4,6,
8,10,12,14,16,18,20
divisible by4
4,8,13,16,20
divisible by 6
6,12,
Solve (v +8) ^4/5= 2
Answer:
(7/8 - 4/5)^2 = 9/
1600
= 0.005625
Bank A charges a monthly service fee of $5.00 and a per-check fee of $0.15,
B while Bank B charges a monthly service fee of $2.50 and a per-check fee of
$0.35. Which of these numbers of monthly checks will cause Bank A to
charge less in fees than Bank B?
for 5 monthly checks, both banks charge the same amount.
for x < 5, Bank B charges less.
for x > 5, Bank A charges less.
For what numbers of monthly checks will Bank A charge less than Bank B?Bank A charges a fixed fee of $5.00 plus $0.15 per-check fee.
So, if you do x monthly checks, Bank A will charge you:
A(x) = $5.00 + $0.15*x
Bank B charges a service fee (fixed) of $2.50 plus $0.35 per check, then for x monthly checks they charge:
B(x) = $2.50 + $0.35*x
Both banks will charge the same amount when:
A(x)= B(x)
So we need to solve the linear equation:
$5.00 + $0.15*x = $2.50 + $0.35*x
$5.00 - $2.50 = $0.35*x + $0.15*x
$2.50 = $0.50*x
$2.50/$0.50 = x = 5
So, for 5 monthly checks, both banks charge the same amount.
for x < 5, Bank B charges less.
for x > 5, Bank A charges less.
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Answer: 19
Step-by-step explanation:
write the answer in order from top to bottom
Answer:
6% of 400 = 2 400
Step-by-step explanation:
6% of 200 is
Write the equation of the line in point-slope form that passes through the points
(
−
8
,
2
)
and
(
6
,
8
)
.
Answer:
y -2 = 3/7(x +8)
Step-by-step explanation:
You want a point-slope equation of the line through points (-8, 2) and (6, 8).
SlopeThe slope of the line is given by the formula ...
m = (y2 -y1)/(x2 -x1) . . . . . . where (x1, y1) and (x2, y2) are points on the line
Using the given points, we find the slope to be ...
m = (8 -2)/(6 -(-8)) = 6/14 = 3/7
Point-slope equationThe equation of a line with slope m through point (h, k) is written in point-slope form as ...
y -k = m(x -h)
Here, we have m=3/7, and (h, k) = (-8, 2). This means the equation of the line is ...
y -2 = 3/7(x +8)
Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:
DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600
CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260
DEBIT: Cash Dividends: 1,000
CREDITS: Fees Earned: 75,000
DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.
Total Debits = 135,260; Total Credits = 135,260
You have prepared the financial statements for December 20XX. Now, it is time to make the closing entries.
We will close the expense accounts second: what dollar amount will I enter for the Income Summary account? Specify as a whole number.
The dollar amount for the Income Summary account for expenses in making the closing entries is $60,360.
What are closing entries?Closing entries are the end-of-the-period journal entries made to transfer the temporary accounts to the Income Summary.
The closing entries are:
Revenue to income summaryExpenses to income summaryIncome summary (net income or loss) to retained earningsDividends to retained earnings.How will the closing entry be for expenses?The closing entry for expenses will be as follows:
Debit Income Summary $60,360
Credit:
Salaries Expense: 32,800
Rent Expense: 16,800
Depreciation expense - office equipment: 3,960
Advertising expense: 4,000
Office supplies expense: 2,800
To close the expenses to the Income Summary account.Data and Calculations:Salaries Expense: 32,800
Rent Expense: 16,800
Depreciation expense - office equipment: 3,960
Advertising expense: 4,000
Office supplies expense: 2,800
Total expenses = $60,360
Thus, the dollar amount for the Income Summary account for expenses in making the closing entries is $60,360.
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Triangle DHS has the coordinates D(-5, 1), H(-4, 5) and S(-1, 2). What are the coordinates of D'H'S' if DHS is translated 2 units right and 1 unit down?
The new coordinates after translating 2 units right and 1 unit down are D'(-3,0), H'(-2,4) and S'(1,1) respectively.
Given, triangle DHS has the coordinates D(-5, 1), H(-4, 5) and S(-1, 2). Now, we have to find the coordinates of D'H'S' if DHS is translated 2 units right and 1 unit down.
A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.
To translate the point P(x,y), 'a' units right and 'b' units down, use P′(x+a,y-b).
Now, let's proceed to solve the question according to above listed points accordingly.
D(-5, 1), H(-4, 5) and S(-1, 2), these coordinates are translated 2 units right and 1 unit down. So, we will simply add 2 to the x-coordinate of the points and will subtract 1 from the y-coordinate.
Let's translate D, H and S accordingly into D', H' and S'.
D(-5,1)⇒ D(-5+2, 1-1)⇒ D'(-3,0)
H(-4,5)⇒ H(-4+2, 5-1)⇒ H'(-2,4)
S(-1,2)⇒ S(-1+2, 2-1)⇒ S'(1,1)
Therefore, the new coordinates after translation are D'(-3,0), H'(-2,4) and S'(1,1) respectively.
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Stanley analyzes the table of values for a polynomial function. He has determined through applying Descartes’ rule of sign that there is 1 negative real zero, and either 1 or 3 positive real zeros. He has also determined that the upper bound of the function is 3.
a) The degree of the polynomial function is 4
b) The positive real zeros does the function have are 3
a. The degree of the polynomial is equal to the sum of the real and complex zeros. There are four total zeros in the sum (1 negative real) + 3 positive real/complex). The polynomial has a degree of 4.
The solution to part b and the end-behavior, which tends to - for |x|, both support the even degree.
b. The intermediate value theorem informs you that, given the numbers in the table, there will be zeros in the intervals (0, 1), (1, 2), and (2, 3). Within certain time periods, the function's sign changes. Thus, there are three genuine positive zeros.
By examining the table of function values, Stanley is unable to infer anything about Descartes' rule of signs.
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Complete question -Stanley analyzes the table of values for a polynomial function. He has determined through applying Descartes’ rule of sign that there is 1 negative real zero, and either 1 or 3 positive real zeros. He has also determined that the upper bound of the function is 3.
X , f(x)
-2, -105
-1, 0
0, 5
1, -2
2, 3
3, -20
4, -175
a. What is the degree of the polynomial function? How can you tell?
b. How many positive real zeros does the function have? How can you tell?
Find the volume of a sphere with a diameter of 6 centimeters.
A. 12 cubic centimeters
B. 288 cubic centimeters
C. 9 cubic centimeters
D. 36 cubic centimeters
(Please pick one of the answers above)
Step-by-step explanation:
A 12 cubic centimeters I think
Solve the equation. 5-2x/3 +1 -3x-2/5=-x
Answer: x = 21/10
............................................................................................................................
How can i solve this 47kg (5m/s^2)
Answer:
Is this the complete problem?
Step-by-step explanation:
the curve with equation y=ax^2+bx+c passes through (0,-1) and has a stationary point of (2,-9). find the values of a, b and c
Answer:
Step-by-step explanation:
[tex]F(x)=ax^{2} +bx+c[/tex]when we derivate the original general equationwe get[tex]F'(x)=2ax+x[/tex]For a stationary point we know that the gradient m which in this point is expressed by F'(x) is equal to 0 in the given x coordinate of the stationary point mathematically ⇒F'(2)=0When we plug in the x coordinate in our derived equation we have[tex]2a(2)+2=0\\4a+2=0\\4a=2\\\frac{4a}{4} =\frac{2}{4} \\a=\frac{1}{2}[/tex]Therefore we can plug in the value of a we have got in the original equation.[tex]F(x)=\frac{1}{2} x^{2} +bx+c\\[/tex]We have two unknowns in the equation with two points in the function we can use to get the unknowns b and cIn the F(0)=-1[tex]-1=\frac{1}{2} (0)^{2} +b(0)+c\\c=0[/tex]But if we are to check carefully we know that c is the y-intercept wherein x=0 and we already had the point so there was no point of calculating it.
To get the value of b now substitute/plug in the other point (2,-9) in the equation[tex]F(x)=\frac{1}{2} x^{2} +bx\\c=0 \\F(2)=-9\\-9=\frac{1}{2}(2)^{2} +b(2)\\ -9=2+2b\\-9-2=2b\\-11=2b\\b=\frac{-11}{2}[/tex]Please help me with this question
Step-by-step explanation:
try this option (see the attachment), if it is possible, check the yellow text.
part 1 of 2
Video games cost $20 each. The video store
is running a special of 2 games for $33.
What is the cost per game under the spe-
cial?
Answer in units of dollars/game.
part 2 of 2
How much do you save per game?
Answer in units of dollars/game.
Answer: C i took the test
" If you buy a new cell phone, your opportunity cost is the time you could spend talking on the phone."
Step-by-step explanation:
I took the test and got an A hope this helps.
х °
51 °
39°
127°
Find value of x .
Answer:
x = 143
Step-by-step explanation:
You want the fourth angle when three of the angles around a point are given.
Angle totalThe total of angles around a point is 360°. That means ...
x° +51° +39° +127° = 360°
x = 360 -217 . . . . . . . . . . . subtract 217 and simplify
x = 143
__
Additional comment
This means the figure is not drawn to scale, and the diagonal is not a straight line.
In a mathematical statement, ____ usually means “multiplication.”
• base
• is
• of
• percent
One of the planet Saturn's rings has a diameter of approximately 2.5 × 105
kilometers. What is the diameter of the ring, in kilometers, written in standard
notation?
A.
2,500
B.
25,000
C. 250,000
D. 2,500,000
Answer:
its b
Step-by-step explanation:
cause i said so
15. m 16. m 17. m 18. m 19. m 20. m
Answer:
15. 125
16. 160
17. 110
18. 150
19. 35
20. 80
Step-by-step explanation:
This should work, if not, well sorry
A student has a savings account earning 3% simple interest. She must pay $1200 for first-semester tuition by September 1 and $1200 for second-semester tuition by January 1. How
much must she earn in the summer (by September 1) to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1200 between September 1
and January 1? (Round your answer to the nearest cent.)
Using simple interest, it is found that she needs to earn $2,391.07 during the summer.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = A(0)(1 + rt)
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.For this problem, the objective is to have $1200 in 3 months = 0.25 years, hence the parameters are given as follows:
A(0.25) = 1200, t = 0.25, r = 0.03.
Hence we have to solve for A(0):
A(0)(1 + 0.03 x 0.25) = 1200
A(0) = 1200/(1 + 0.03 x 0.25)
A(0) = $1,191.07.
She also needs to earn $1,200 to pay the first-semester bill on time, hence:
1200 + 1191.07 = $2,391.07.
She needs to earn $2,391.07 during the summer.
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In triangle ABC,
m
M
M
M
Answer:
In a triangle all angles add up to make 180 degrees. If a triangle is equal like this one, Δ, then all angles equal 60 degrees.
Step-by-step explanation:
If this is incorrect, then explain what you want more precisely.
To factory plants are making TV panels, yesterday plan a produce 9000 panels. 3% of the panels from plan an and 10%.to factory plants are making TV panels, yesterday plan a produce 9000 panels. 3% of the panels from plan a and 10% of the panels from Plant be were defective how many panels dead plant be produced if overall percentage of the defective panels from two plants what’s 7%?
The number of panels from plant B that were produced if the overall percentage of the defective panels from two planet were 7% is 9000 panels.
How to Solve Algebra Word Problems?
We are given;
Number of TV panels to be produced = 9000 panels
Percentage of panels from plan A that were defective = 3%
Percentage of panels from plan B that were defective = 10%
Let n represent the number of panels from plant B.
Thus, we can write the algebraic equation as:
0.1(9000) + 0.03(n) = 0.07(9000 + n)
900 + 0.03n = 540 + 0.07n
900 - 540 = 0.07n - 0.03n
0.04n = 360
n = 360/0.04
n = 9000 panels
The number of panels from plant B that were produced if the overall percentage of the defective panels from two planet were 7% is 9000 panels.
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Find the distance between the point (-5,4) and the origin. Enter the distance as a radical or a decimal rounded to the four decimal place.
Answer:
6.4031
Step-by-step explanation:
please help if possible
Answer: (5,2)
Step-by-step explanation:
5 + 2 = 7
5 = 2 + 3
