the water park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips
there. The senior class at High School A rented and filled 10 vans and 8 buses with 472 students. High School B rented and filled 9 vans and 8 buses
with 456 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Sort the steps in order to solve this system of equations.
Answers
Answer:
The sorted steps are;
1) Write the equations: 10·x + 8·y = 472 and 9·x + 8·y = 456
2) Multiply to get one variable to eliminate: -90·x - 72·y = -4248 and 90·x + 80·y = 4560
3) Eliminate x's: 8·y = 312
4) Solve for y: y = 39 (39 buses)
5)Plug back in to find x: 10·x + 8·(39) = 472
6) Solve for x: x = 16 (16 vans)
Step-by-step explanation:
Let x = The number of students in each van and y = The number of students in each bus
We have;
For High School A;
10·x + 8·y = 472...(1)
For High School B;
9·x + 8·y = 456...(2)
Multiply equation (1) by (-9) and equation (2) by 10 to get
(10·x + 8·y) × (-9) = 472 × (-9)
-90·x -72·y = -4,248...(3)
9·x + 8·y × (10)= 456 × (10)
90·x + 80·y = 4,560...(4)
Add equation (3) to (4) gives;
-90·x -72·y + 90·x + 80·y = -4,248 + 4,560
90·x - 90·x -72·y + 80·y = -4,248 + 4,560
8·y = 312
y = 312/8 = 39
y = 39
Substituting the value of y in equation (1), gives;
10·x + 8·y = 10·x + 8 × 39 = 472
10·x + 312 = 472
10·x = 472 - 312 = 160
10·x = 160
x = 160/10 = 16
x = 16
The number of students in each van = x = 16 students
The number of students in each bus = y = 39 students.
Related Questions
Scientific notation
Express this number in scientific notation.
245,600,000,000
Answers
Answer: 2.456 x 10 to the power 11
Step-by-step explanation: Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
2.456 x 10 to the power 11
Step-by-step explanation:
7+7 please help me i need help quick right away
Answers
Answer:
very funny and 14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
7 plus 7? how old are you?
The distribution of annual profit at a chain of stores was approximately normal with mean \mu = \$66{,}000μ=$66,000mu, equals, dollar sign, 66, comma, 000 and standard deviation \sigma = \$21{,}000σ=$21,000sigma, equals, dollar sign, 21, comma, 000. The executives conducted an audit of the stores with the lowest 20\%20%20, percent of profits. What is closest to the maximum annual profit at a store where the executives conducted an audit?
Answers
Answer:
The closest to the maximum profit is [tex]x = \$ 83682[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$66,000[/tex]
The standard deviation is [tex]\sigma = \$ 21000[/tex]
The percentage of profit is 20%
Generally the closest to the maximum annual profit at a store where the executives conducted an audit is mathematically evaluated as follows
[tex]P(X > x ) = 0.20[/tex]
=> [tex]P(X > x ) = P(\frac{X -x}{\sigma } > \frac{x -66000}{21000} ) = 0.20[/tex]
From the z-table the z-score for 0.20 is
[tex]z-score = 0.842[/tex]
So
[tex]\frac{x -66000}{21000} = 0.842[/tex]
=> [tex]x = \$ 83682[/tex]
Answer:
48,000
Step-by-step explanation:
given the function f(x)=(x-2)(x+3)(2x+3), which set includes all of the zeros for the polynomial?
Answers
Answer:
{2, -3, -3/2}
Step-by-step explanation:
hi! we can set each of the binomials equal to 0 to find the zeros of this polynomial.
x-2=0
x=2
x+3=0
x=-3
2x+3=0
2x=-3
x=-3/2
The set includes all of the zeros for the polynomial would be; {2, -3, -3/2}.
What is a polynomial?They are mathematical expressions involving variables raised with nonnegative integers and coefficients(constants that are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.
We have been given the function f(x)=(x-2)(x+3)(2x+3)
Each of the binomials is equal to 0 to determine the zeros of this polynomial.
1. x-2=0
x=2
2. x+3=0
x=-3
3. 2x+3=0
2x=-3
x=-3/2
Hence, the set includes all of the zeros for the polynomial would be; {2, -3, -3/2}.
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At New years you decide to join a gym to lose all those calories gained during winter break and youre comparing two different gyms. The first gym, gym A has a 12$ initiation fee and then costs 10$ per month. The second gym , gym B has a 20$ initiation fee and then costs 6$ per month. Create an equation that aims to find when these two gyms will cost the same amount of money
Answers
Given:
For gym A, initiation fee = $12 and cost = $10 per month.
For gym B, initiation fee = $20 and cost = $6 per month.
To find:
The equation that aims to find when these two gyms will cost the same amount of money,
Solution:
Let the number of months be x.
Cost function = Initiation fee + (cost)(x)
Cost function for gym A is
[tex]f(x)=12+10x[/tex]
Cost function for gym B is
[tex]g(x)=20+6x[/tex]
Cost of these two gyms are equal if f(x)=g(x).
[tex]12+10x=20+6x[/tex]
Therefore, the required equation is [tex]12+10x=20+6x[/tex].
On solving this equation, we get
[tex]10x-6x=20-12[/tex]
[tex]4x=8[/tex]
[tex]x=2[/tex]
Hence, after 2 months the cost of these two gyms are same.
A man can type 21 words per minutes. how long will it take him to type 3780 words
Answers
3780 divided by 21=180
if 2^6=y^3 what is y?
Answers
Answer:
y=4
Step-by-step explanation:
simplify 2^6 --> 64
find the cube root of 64,
y=4
What is y +3 = 7(2 – 2) written in standard form?
Choose 1 answer: :
А)
-7x +y = -5
B
y=73 – 5
С
y = 7x – 17
– 7x + y = -17
Answers
Answer:
C)
Step-by-step explanation:
y+3=7x+7•−2
Multiply 7 by −2.
y+3=7x−14
Rewrite the equation with the sides flipped.
7
x
−
14
=
y
+
3
All shirts are the same price. Which deal is cheaper per shirt?
A) Buy 2 shirts and get 25% off.
B) Buy 3 shirts and save 30%.
Answers
Answer:
The answer of this question is option A
If I buy 2 shirts for $20 and get 25% off, I will have spent $15. This would come out to $7.50 per shirt.
If I buy 3 shirts for $30 and get 30% off, i will have spent $21. Which is $7 per shirt.
The answer is option B
A rhombus has 4 equal sides.
What is the order of rotational symmetry for a rhombus?
1
2
3
4
Answers
Answer:
B. 2
Step-by-step explanation:
Got Correct On MyPath.
The order of rotational symmetry for a rhombus is 2.
What is Polygon?A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end
A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral.
In a rhombus, opposite sides are parallel and the opposite angles are equal.
All the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles
Rotational Symmetry of a Rhombus has four equal sides but of varying angles.
A rhombus has two lines of symmetry (vertical and horizontal), an order of two, and the angle of rotation of 180 degrees
Hence, the order of rotational symmetry for a rhombus is 2.
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HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!
Answers
I got 2 : 3. You didn’t give answer choices but after you commented the answer choices I was able to determine that 2:3 is the answer.
2 + 29m - 9m - 5 =
HELP
Answers
Answer:
20m-3
Step-by-step explanation: hope that helps :)
2+29m−9m−5
=2+29m+−9m+−5
Combine Like Terms:
=2+29m+−9m+−5
=(29m+−9m)+(2+−5)
=20m+−3
Why is the base of the parallelogram 1/2 the circumference of the circle?
Answers
Consistent System of Equations
In other words.:Counterclockwise of negative x positive + the absolute value of 18 - 45 will equal 1/2
Someone pls help me.
Answers
identity property in multiplication goes to the second option
commutative property goes to the first option
identity property in addition goes to the last option
associative property goes to the fourth option
distributive property goes to the third option
I may have gotten some wrong , if I did I am very sorry,if i didnt get any wrong, then I hoped this helped!
2(7y−1)= 40 what is y?
Answers
Step-by-step explanation:
[tex]14y - 2 = 40 > > 14y = 42 > > y = 3[/tex]
Answer:
y=3
Step-by-step explanation:
Remember PEMDAS
Find a counterexample to show that the given conjecture is false:
The sum of two positive even integers is always an odd integer.
Answers
Answer:
20 + 16 = 36
Step-by-step explanation:
The conjecture: "The sum of two positive even integers is always an odd integer" can be easily be proven false with a counterexample.
Pick A=20 and B=16, both are positive even integers.
The sum of both A + B = 36 is an even integer. This is a counterexample because being even is the contrary of being odd.
Counterexample: 20 + 16 = 36
In fact, the conjecture is always false, since there cannot be found any pair of positive integers whose sum is odd.
Other possible counterexamples are:
10 + 8, 700 + 40, 12 + 14, etc.
PLZ ANSWER THIS QUICK! THANK U!!
Answers
Marge's plan costs .14 cents per minute plus a monthly fee of $24. Dan's plan costs .12 cents per minute plus a monthly fee of $28. How many minutes (m) are required for both plans to cost the same for the month?
Answers
Answer:
6 min for Marge's and 7 for Dan's plan
Step-by-step explanation:
0.14x6=0.84
0.12x7=0.84
Solve:
7 - 3(-9x + 3) = 11
Answers
explaination: hope this helped
Whoever can help me 1st I will mark the brain liest
Answers
A is 163 and C is 143
Can someone answer this?
Answers
Answer:
y = 1500 + 800x
Step-by-step explanation:
This is the answer because Elisa charges 1500 dollars no matter what. That value is not dependant on anything. Every hour she is with the client is 800 dollars. That is why it is represented as 800x. X being the amount of hours. You add the two together to find how much Elisa's services cost.
4. During a 12- hour period, the temperature dropped 48°. How many degrees did the temperature drop each hour.
Is the answer negative or positive? Please help..
Answers
Answer:
-4
Step-by-step explanation:
A car rental company charges a daily rate of $ 27 plus $ 0.1 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $ 45.5. How many miles did you drive? Give your answer to the nearest whole mile. miles
Answers
Answer:
185 miles.
Step-by-step explanation:
According to the given situation, the calculation of mile is shown below:-
Assume drive = x miles
Total bill incurred = ($27 + 0.1 x) = $45.5
Now we will solve the above equation:
0.10x = $45.5 - $27
0.10x= 18.5
x = 18.5 ÷ 0.10
x = 185 miles.
So, the correct answer is 185 miles.
The same is to be considered
Cassie has a rectangular window that is 40 Inches long and 25 inches wide. She wants to put a metal frame around the edges of her window. How many inches of metal frame will she need? Please help me
Answers
Answer:
she will need 130 inches lf metal
Step-by-step explanation:
One side lf the window is 40 and the other side lf the window is 25 ,so just multiply those by 2.That will give you 50 and 80 just add those together and you get 130
An artist sells paintings for $100 each. For each painting, the cost of the canvas
is $10 and the cost of the paints is $8.
How much profit (a positive amount of money earned after paying for
the costs) would the artist earn if she were to sell 10 paintings?
Answers
Answer:
820 in profit
Step-by-step explanation:
The artist makes $82 in profit on each painting. 82 x 10 is 820
help i need help with pre-algebra
Answers
Write 3.01 repeating as a mixed number.
Answers
Answer:
3 1/100
Step-by-step explanation:
Place the decimal number over a power of ten.
4x - 1 = 2(2x + 2)
what is the answer?
Answers
Answer:
x = undefined
Step-by-step explanation:
Expand brackets
4x - 1 = 4x + 4
Rearrange and make like terms next to each other
4x - 4x = 4 + 1
0x = 5
x = 5/0
when 0 is the denominator the answer is undefined
Answer: from what i calculated there is no solution
Step-by-step explanation:
The temperature at 8 p.m. was 6 degrees. at 2 p.m. the temperature decreased 13 degrees. What was the temperature at 2 a.m.?
Answers
Step-by-step explanation:
Given parameters:
Temperature at 8pm = 6°C
Temperature at 2am = decreased by 13°C
Unknown:
Temperature at 2am
Solution:
Since this is a temperature decrease problem, the temperature at 2am should be lesser.
Temperature at 2am = Temperature at 8pm - Temperature decrease
= 6°C - 13°C
= -7°C
A country is dealing with a serious macroeconomic problem. Businesses
around the country have been shutting down, leaving millions of people out of
work. Even citizens with a high level of education and technical skills are
struggling to find jobs.
Which problem is this country dealing with?
A. A high unemployment rate
B. A high level of inflation
C. A low per capita GDP
D. A rapid growth in GDP
Answers
Answer:
A: A high unemployment rate
Step-by-step explanation:
A high unemployment rate is the problem which is dealing by the country
What is Business?Business is the practice of making one's living or making money by producing or buying and selling products.
Given that a country is dealing with a serious macroeconomic problem. Businesses around the country have been shutting down, leaving millions of people out of work.
Even citizens with a high level of education and technical skills are
struggling to find jobs.
This problem is dealing with high unemployment rate.
Unemployment is a measure of the percentage of the labor force that is without work but actively seeking employment.
By given data it suggests that many businesses have shut down, leading to a significant increase in the number of people who are out of work. This situation is often referred to as a high unemployment rate.
Hence, a high unemployment rate is the problem which is dealing by the country.
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