Answer: -7x should be written as -15x+8x or 8x-15x
===============================================
Explanation:
Multiply the first coefficient 6 and the last term -20 to get -120
We need to find factors of -120 that add to the middle coefficient -7
Through trial and error you should find that
-15 + 8 = -7
-15 * 8 = -120
Therefore, we break the -7x into -15x+8x
----------------------------
Extra info: if you want to fully factor by grouping, then follow these steps
6x^2 - 7x - 20
6x^2 - 15x + 8x - 20 ... break up -7x
(6x^2 - 15x) + (8x - 20) .... group into pairs
3x(2x - 5) + 4(2x - 5) .... factor each group
(3x + 4)(2x - 5) ..... pull out the overall GCF 2x-5
So 6x^2-7x-20 fully factors to (3x+4)(2x-5)
We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.
2) -On - 2n = 16
How do I solve this
Answer:
n = -8
Step-by-step explanation:
-0n - 2n = 16
- 2n = 16
n = 16/-2
n = -8
PLEASE HELP ME ASAP The average of 16 consecutive odd numbers is 122. Find the smallest odd number. FIRST TO ANSWER GETS BRAINLIEST
Answer:
107
Step-by-step explanation:
Hello, Let's note n the odd number that we are looking for.
If n is odd, n+1 is even but n+2 is odd again and so on and so forth.
So, the 16 consecutive odd numbers are
n, n+2, n+4, ... n+2k, ,,,, ,n+30
It means that the average is:
[tex]\displaystyle \dfrac{1}{16}(n+(n+2)+...+(n+2k)+...+(n+2*15))\\\\=\dfrac{1}{16}\sum_{k=0}^{k=15} {(n+2k)}\\\\=\dfrac{1}{16}\left(n * 16 + 2 \sum_{k=1}^{k=15} {k} \right)\\\\=\dfrac{1}{16}\left(n * 16 + 2 (\dfrac{15*16}{2}) \right)\\[/tex]
And it must be equal to 122, so we can write.
[tex]\dfrac{1}{16}\left(n * 16 + 2 (\dfrac{15*16}{2}) \right)=122\\\\n+15=122\\\\n = 122-15=107[/tex]
Thank you.
How many acres are contained in a parcel described as follows: The NE ¼ of the NW ¼; the N ½ of the NW ¼, NE ¼, of Section 10?
Answer:
1.25 acres
Step-by-step explanation:
If we assume that both the semicolon (;) and the comma (,) mean "of the", then this will be ...
(1/4)(1/4)(1/2)(1/4)(1/4) of 640 acres = 1.25 acres
Identify the y intercept of the following equation
y=-3x + 5
Answer:
5
Step-by-step explanation:
y=mx+b
B is always the y intercept.
In 1961, it was discovered that the drug thalidomide, given to pregnant mothers for morning sickness, caused birth defects. Fifty years later, the manufacturer of the drug issued a but those affected by the drug felt that the company's statement wasn't enough.
A. Mea Culpa
B. Non Sequitur
C. Tabula Rasa
D. Mano a Mano
Answer:
A) mea culpa
Step-by-step explanation:
Need to find the volume of these composite figures. Thank You!
Answer:
3. V = 1,498.24. V = 2,813.445. V = 96.293Step-by-step explanation:
3. Formula of a Cylinder + Formula of a Cone = Total
V=πr^2h + V=πr^2h
/3 = total
V = 3.14 * 36 * 10 + V = 3.14 * 36 * 10/3
V = 1,130.4 + V = 376.8 = Total
V = 1,498.24. Formula of Cone + Formula of Cone = Total
V=πr^2h
/3 + V=πr^2h
/3 = Total
V = 3.14 * 36 * 8/3 + V = 3.14 * 100 * 8 = Total
V = 301.44 + 2,512 = Total
V = 2,813.445. Formula of a cylinder + formula of a sphere = Total
V=πr^2h + V=4
/3πr^3 = Total
V = 3.14 * 4 * 5 + V = 4/3 * 3.14 * 8
V = 62.8 + V = 33.493 = Total
V = 96.293DEFINITELY hope this helped,
Kavitha
Give a recursive definition of
a) the set of odd positive integers.
b) the set of positive integer powers of 3.
c) the set of polynomials with integer coefficients.
For example: 5x 3 − 2x 2 + 3 or 7x 4 − 8x 3 + x
Answer:
a. for positive odd integers starting 1 and increaments by 2:
( first odd number ) + 2 ∈ S
b. for positive integer powers of 3 :
3( integer ) ∈ S
c. for integer coefficient of the given polynomial :
s. t ∈ S , s - t ∈ S and s + t ∈ S
Step-by-step explanation:
the odd number starts with 1 and increases by two, and the set of that would range from 1 to infinity.
A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°
Answer: Option B -- 72°
Step-by-step explanation:
If a town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Using Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. The measure of the angle between Elm Street and Pine Avenue is 72°
Answer:
b
Step-by-step explanation:
Find the value of x.
Answer:
x = 4
Step-by-step explanation:
Since, DE || AC... (GIVEN)
Therefore, by Basic Proportionality Theorem, we have:
BD/AD = BE/CE
(10-x) / x = 3/2
2(10 - x) = 3x
20 - 2x = 3x
20 = 2x + 3x
20 = 5x
x = 20/5
x = 4
A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°
Answer:
72°
Step-by-step explanation:
From the information given:
A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.
We are also told that there is a Trapezoid EFGH with EH as the Pine avenue and EF as the Elm street.
However, side FG and EH are parallel.
∠G = 108°
From the property of parallel lines :
since FG || EH
Then ∠G = ∠H = 108° (i.e corresponding angle will also be equal)
The required angle between Elm Street and Pine Avenue would be interior angles + 180° given that alternate angles are also equal.
The required angle between Elm Street and Pine Avenue = 180° - 108°
The required angle between Elm Street and Pine Avenue = 72°
Answer:
B. 72
Step-by-step explanation:
Find the lengths of the sides of the triangle PQR. P(6, 6, 1), Q(4, 4, 2), R(4, 10, 5)|PQ| = |QR| = |RP| = $$
Answer: |PQ| =3 units , |QR| = 3√5 units, |RP| = 6 units.
Step-by-step explanation:
Distance between two points (a,b,c) and (x,y,z) is given by :-
[tex]D=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}[/tex]
Given: P(6, 6, 1), Q(4, 4, 2), R(4, 10, 5)
Then,
[tex]|PQ|=\sqrt{(6-4)^2+(6-4)^2+(1-2)^2}=\sqrt{2^2+2^2+(-1)^2}\\\\=\sqrt{4+4+1}=\sqrt{9}=3[/tex]
[tex]|QR|=\sqrt{(4-4)^2+(10-4)^2+(5-2)^2}=\sqrt{0+6^2+3^2}\\\\=\sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex]
[tex]|RP|=\sqrt{(6-4)^2+(6-10)^2+(1-5)^2}=\sqrt{2^2+(-4)^2+(-4)^2}\\\\=\sqrt{4+16+16}=\sqrt{36}=6[/tex]
So, |PQ| =3 units , |QR| = 3√5 units, |RP| = 6 units.
What is the surface area of the square pyramid? 6 square meters 16 square meters 28 square meters 49 square meters
Answer:
It's 16, i did the unit test already.
Step-by-step explanation:
Alejandra works at corys coffee shop after school somedays. A customer orders comes to 4.70. The customer hands alejandra a $5 dollar bill, so she gives the customer 30 cents in change. Because alejandra loves math , she begins to think about different ways in which she could have given the customer 30 cents in change. Using only quaters, dime, nickels how many ways
Answer:
5
Step-by-step explanation:
6 nickles,3 dimes ,1 quarter +1 nickel, 2 dimes 2 nickles, 1 dime 4 nickles,
The letter b represents a nonzero constant. Solve 2bx-bx= -8 for x?
Answer:
x = -8/b
Step-by-step explanation:
2bx-bx= -8
bx = -8
Divide by b since b is nonzero
x = -8/b
15x 18 + 12+ 3+ 9
Pemdas
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{294}}}}}[/tex]
Step-by-step explanation:
PEMDAS is a acronym which helps you to remember the order of operations.
PEMDAS stands for :
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Let's solve
[tex] \sf{15 \times 18 + 12 + 3 + 9}[/tex]
Multiply the numbers : 15 × 18 = 270
⇒[tex] \sf{270 + 12 + 3 + 9}[/tex]
Add the numbers : 270 + 12 + 3 + 9
⇒[tex] \sf{294}[/tex]
Hope I helped!
Best regards!!
Answer:
This would equal 294
Step-by-step explanation:
i added them up
how do i solve this absolute value equation
2|5x|= 10?
Answer:
x=1 x = -1
Step-by-step explanation:
2|5x|= 10
Divide each side by 2
2/2|5x|= 10/2
|5x|= 5
Absolute values have 2 solutions, one positive and one negative
5x = 5 5x = -5
Divide each side by 5
5x/5 = 5/5 5x/5 = -5/5
x = 1 x = -1
Answer:
Step-by-step explanation:
● 2|5x| = 10
● 2 × |5| ×x = 10
5 is positive so |5| = 5
● 2×5× |x| = 10
● 10×|x| = 10
● |x| = 10
● x = 1 or x = -1
Enter the number that belongs in the green box
Answer:
1
Step-by-step explanation:
Hi!
First we need to translate 2 units down. That means we need to subtract 2 from the y value. So now we have (-1,1).
For a 270 degree counterclockwise rotation the rule is to go from (x,y) to (y,-x)
So now we have (1,1). Since they're only asking for the x value, the answer is 1.
Answer:
[1, 1]
Step-by-step explanation:
Translation → [-1, 3] moves down to [-1, 1]
Now, a 90°-clockwise rotation is the exact same as a 270°-counterclockwise rotation, and according to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, bring it over to your new x-coordinate, and take the OPPOSITE of the x-coordinate and set it as your new y-coordinate:
Extended Rotation Rules
270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)
270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)
180°-rotation >> (x, y) → (-x, -y)
Then, you perform your rotation:
270°-counterclockwise rotation [90°-clockwise rotation] → [-1, 1] moves to [1, 1]
( not my answer cr BasketballEinstein on brainly, i just saw that the same question like this one was already answered FULLY somewhere else )
How many four-character passwords can be formed using the characters A, B, C, 1, 2 if the characters can be repeated
Work Shown:
The set {A,B,C,1,2} has five items. There are four slots to fill.
So we have 5^4 = 5*5*5*5 = 625 different possible passwords where the characters can be repeated.
625 four-character passwords can be formed.
----------------------------
Each character of the password is independent of previous characters, which means that the fundamental counting principle is used to solve this question.
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
----------------------------
4 independent characters.Each with 5 outcomes(A, B, C, 1 or 2).Thus, the number of passwords is:
[tex]5 \times 5 \times 5 \times 5 = 5^4 = 625[/tex]
625 four-character passwords can be formed.
A similar question is given at https://brainly.com/question/23855405
find the value of
(-3)^5/(-3)^6
Answer:
[tex] \boxed{ \bold{ \frac{1}{3} }}[/tex]Step-by-step explanation:
[tex] \mathsf{ \frac{ { - 3}^{5} }{ { - 3}^{6} } }[/tex]
To divide two terms with the same base , the power of divisor is subtracted from the power of the dividend and the same base is taken
⇒[tex] \mathsf{ { - 3}^{5 - 6} }[/tex]
⇒[tex] \mathsf{ { - 3}^{ - 1} }[/tex]
Applying law of negative index
⇒[tex] \frac{1}{3} [/tex]
Hope I helped!
Best regards!!
The functions f(x) and g(x) are graphed. Which represents where f(x) = g(x)? f(2) = g(2) and f(0) = g(0) f(2) = g(0) and f(0) = g(4) f(2) = g(0) and f(4) = g(2) f(2) = g(4) and f(1) = g(1)
Answer:
The given graph shows the relationship between the f(x) and g(x).
Since the problem is to find the points where f(x) becomes equal to g(x) then we will be focusing only to the x-axis and ignore the points of y-axis.
Out of the four choices, the correct answer for the given functions of x will be f(2) = g(2) and f(0) = g(0), f(0) and g(0) is located at the origin. So the points where the curve and line are intersecting is at f(2) and g(2) and the other point is at f(0) and g(0), neglecting the y-axis.
Step-by-step explanation:
Use a power series to approximate the definite integral, I, to six decimal places. 0.1 x arctan(5x) dx 0.
Answer:
definite integral I = 0.001591 to six decimal places
Step-by-step explanation:
The definite integral is given as:
[tex]\int ^{0.1}_{0} \ x \ arctan (5x) \ dx[/tex]
For arctanx , the power series is in the order [tex]x - \dfrac{x^3}{3}+ \dfrac{x^5}{5}-\dfrac{x^7}{7}+...[/tex]
[tex]arc tan \ x = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ x ^{2n+1}}{2n +1}[/tex]
The next step is to substitute the value of 5x for x in the above equation;
So,
[tex]arc tan \ (5x) = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ (5x) ^{2n+1}}{2n +1}[/tex]
To multiply both sides by (x); we have
[tex]x\ arc tan \ (5x) = x \ \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5 ^{2n+1} \times x^{2n+1}}{2n +1}[/tex]
[tex]x\ arc tan \ (5x) = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5 ^{2n+1} \times x^{2n+2}}{2n +1}[/tex]
Taking the integral on both sides with respect to x;
[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5^{2n +1}}{2n+1} \ \int ^{0.1}_0 x^{2n+2} \ dx[/tex]
[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5^{2n +1}}{2n+1} \ [(0.1)^{2n+3}][/tex]
[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5^{2n +1} \times (0.1)^{2n+3} }{(2n+1)(2n+3)}[/tex]
[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = [\dfrac{5 \times (0.1)^3}{1.3}-\dfrac{5^3(0.1)^3}{3.5}+\dfrac{5^5(0.1)^7}{5.7}-\dfrac{5^7(0.1)^9}{7.9}+ ...][/tex]
[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = [\dfrac{1}{600}-\dfrac{1}{1200}+\dfrac{1}{112000}-\dfrac{1}{806400}+ ...][/tex]
[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx =1.591 \times 10^{-3}[/tex]
[tex]\mathbf{\int^{0.1}_{0} \ x \ arctan (5x) \ dx =0.001591}[/tex] to six decimal places
Temperatures in Kelvin of various sites on the moon are an example of which type of data?
Answer: Continuous Data
Quantitative data
TemperatureTemperature is a measure of how hot or cold something is; more specifically, temperature is a measure of the average kinetic energy of the particles in an object, which is a sort of energy related with motion.Quantitative data is described as data in the form of counts or numbers, with each data-set having a unique numerical value.Temperatures in Kelvin of various sites on the moon are an example of quantitative data.Find out more information about the temperature here:
https://brainly.com/question/15267055?referrer=searchResults
Hello! Stay safe and Please answer In a hurry Thanks!
Answer:
4
Step-by-step explanation:
An equilateral triangle has 3 equal sides.
So
4(x-1) = x +8
4x-4=x+8
3x=12
x=4
Same result obtained when comparing the other pairs of equations.
The following sample observations were randomly selected. (Round intermediate calculations and final answers to 2 decimal places.)
x 4 5 2 6 9
y 4 6 2 7 7
The regression equation is y (with a hat) = ______ + _______
When X is 7 this gives y (with a hat) = _________
Answer:
yhat=1.36+0.74x
when x=7 then yhat=6.54
Step-by-step explanation:
Th regression equation is
yhat=a+bx
where slope b is
[tex]b=\frac{nsumxy-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }[/tex]
and intercept a is
a=ybar-bxbar
x 4 5 2 6 9
y 4 6 2 7 7
xy 16 30 4 42 63
x² 16 25 4 36 81
n=5.
sumx=26.
sumy=26.
sumx²=162.
sumxy=155.
[tex]b=\frac{5*155-(26)(26)}{5*162-(26)^{2} }[/tex]
[tex]b=\frac{99}{134 }[/tex]
b=0.7388
b=0.74 (rounded to 2 decimal places)
xbar=sumx/n=26/5=5.2
ybar=sumy/n=26/5=5.2
a=ybar-b*xbar
a=5.2-0.7388*5.2
a=5.2-3.8418
a=1.3582
a=1.36 (rounded to 2 decimal places)
Thus, the required regression equation is
yhat=1.36+0.74x
When x is 7 this gives yhat
yhat=1.36+0.74*7
yhat=1.36+5.18
yhat=6.54
A person filing his federal income tax return with the Single filing status had a
taxable income of $31,850. According to the table below, how much of that
income will he have left over after paying his federal income tax?
A) 27,490.00
B) 28,325.00
C) 3525.00
D) 4360.00
The solution is Option A.
The amount of income left over after paying the federal income tax is given by the equation A = $ 24,490.00
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of income left over be represented as A
Now , the equation will be
The amount of taxable income is $31,850.00
And , the taxable income is in the range $ 8,350 - $ 33,950
So , the fixed tax for the amount is $ 835.00
The percentage of tax is 15 % of the amount over
So , the amount over = $ 8,350
Substituting the values in the equation , we get
The amount over = $31,850.00 - $ 8,350.00
The amount over = $ 23,500.00
Now , 15 % of amount over = 23,500 x ( 15/100 )
15 % of amount over = $ 3,525.00
And , Total tax = 15 % of amount over + fixed tax for the amount
Total tax = $ 3,525.00 + $ 835.00
Total tax = $ 4,360.00
Now , the amount of income left over A = amount of taxable income - Total tax
Amount of income left over A = $31,850.00 - $ 4,360.00
Amount of income left over A = $ 27,490.00
Therefore , the value of A is $ 27,490.00
Hence , the amount left over is $ 27,490.00
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
7.142857143
How is this rounded to two decimal places?
Answer:
you look at the third decimal place which will affect the second decimal place.
in this case: 2 affects 4 -- leaves it as 4
so the number rounded to two decimal places is 7.14
4(4+2x)=7(x-4)
A: The solution set is (_) Simplified
B: There is no solution
Pick one and if A then simplify the answer
Answer:
x=-44
Step-by-step explanation:
4(4+2x)=7(x-4)
[expanding the brackets]
16+8x=7x-28
[grouping like terms]
8x-7x= -28-16
x= - 44
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed{x = -44}[/tex]
[tex]4(4+2x)=7(x-4)[/tex]
Solution :
[tex]4(4+2x)=7(x-4)[/tex]
[tex]( 2x + 4 ) = 7 ( x - 4 )[/tex]
[tex]4 . 2x + 4 . 4 = 7x - 7 . 4[/tex]
[tex]8x + 16 = 7x - 28[/tex]
[tex]( 8x + 16) + ( -16 - 7x ) = ( 7x - 28 ) + ( -16 - 7x )[/tex]
[tex]( 8x + 16 ) + ( -7x - 16) = (7x - 28 ) + ( -7x - 16)[/tex]
[tex]8x + 16 - 7x - 16 = 7x - 28 - 7x - 16[/tex]
[tex]8x - 7x + 16 - 16 = 7x - 7x - 28 - 16[/tex]
[tex]x = -44[/tex]
( A: The solution set is (_) Simplified )
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
3. Why can the numerator and denominator of a rational expression be divided by their common factors? What conditions must be placed on the value of the variables when a rational expression is simplified?
Answer:
Step-by-step explanation:
Hello, do you agree that for any real number a (different from 0)
[tex]\dfrac{a}{a}=1[/tex]
?
5/5 = 1 for instance.
So, when you have the same common factor at the numerator and at the denominator you can eliminate it. For instance.
[tex]\dfrac{10}{4}=\dfrac{5*2}{2*2}=\dfrac{5}{2}\cdot \dfrac{2}{2}=\dfrac{5}{2}[/tex]
You just need to be careful with 0, as dividing by 0 is not allowed.
Hope this helps
Thank you.
Write an equation of the line below.
Answer: y=2x+2
Step-by-step explanation:
slope-intercept form: y=ax+b
----------------------------------------
#1 Find the slope
- Use rise/run to find the slope: 8/4=2
- Use slope formula: (2-(-6))/(0-(-4))=8/4=2
#2 Find the y-intercept
- Given the point (2, 0) it is already the y-intercept which is 2
----------------------------------------
a=2
b=2
y=2x+2
snailpace coach company is running a trip to "the anoraks" concert. they have seven 52-seater coaches and eight 12-seater minibuses. the coach company forks out £23 for each ticket. it also costs them £150 to run each coach and £80 per minibus. how much will the company have to pay in total to run the trip
Total seats: 52 x 7 + 8 x 12 = 364 + 96 = 460
Total cost for total seats = 460 x 23 = 10,580
Cost for buses: 150 x 7 + 80 x 8 = 1050 + 640 = 1690
Total cost = 10,580 + 1,690 = $12,270