You like to watch movies at the local cinema. You have two payment options. Option a is to buy a discount card which will cost you $160, and then $20 per movie. Option b is to pay $40 per movie. After how many movies will the total costs of the two options be the same? Write a system of equations in order to solve the problem.
Answers
Let us consider the case : a discount card which will cost you $160, and then $20 per movie.
For x number of movies, Your cost is,
\(160+20x\)Taking the second case: $40 per movie. Foe x number of movies, your cost is,
\(40x\)So, when the total cost is same,
\(\begin{gathered} 160+20x=40x \\ 160=40x-20x=20x \\ \frac{160}{20}=x \\ x=8 \end{gathered}\)So after 8 movies, the total costs of the two options will be the same.
Related Questions
find the rule as an equation.
for example, y= x+m
Answers
Answer:
y= 4x
Step-by-step explanation:
2*4=8
3*4=12
4*4=16
5*4=20
6*4=24
7*4=28
Create a Venn diagram to illustrate each of the following: 26. (D ⋃ E) c ⋂ F
Answers
The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.
To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.
We shade the area where the circles for D and E overlap because the equation (D ⋃ E) denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.
The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.
The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.
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6. Journalise the following transactions
1. Bricks for Rs 60,000 and timber for Rs 35,000 purchased for
the construction of building. The payment was made by cheque.
2. Placed in fixed deposit account at bank by transfer from current
account Rs 13,000.
3. Appointed Mr. S.N. Rao as Accountant at Rs 300 p.m. and
Received Rs 1000 as security Deposit at 5% p.a. interest.
4. Sold goods to shruti for Rs 80,000 at 15% trade discount and
4% cash discount. Received 75% amount immediately through a
cheque.
5. Purchased goods from Richa for Rs 60,000 at 10% trade
discount and 5% cash discount. 60% amount paid by cheque
immediately.
6.
On 18th jan,Sold goods to shilpa at the list price of Rs 50,000
20% trade discount and 4% cash discount if the payment is made
within 7 days. 75% payment is received by cheque on Jan 23rd.
7. On 25th jan, sold goods to garima for Rs 1,00,000 allowed her
20% trade discount and 5% cash discount if the payment is made
within 15 days. She paid 1/4th of the amount by cheque on Feb 5th
and 60% of the remainder on 15th in cash.
8. Purchased land for Rs 2,00,000 and paid 1% as brokerage and
Rs 15,000 as registration charges on it. Entire payment is made by
cheque.
9. Goods worth Rs 25,000 and cash Rs 40,000 were taken away
by the proprietor for his personal use.
10. Sold goods costing Rs 1,20,000 to charu at a profit of 33% 3 %
on cost less 15% trade discount.
9
11. Paid rent of building Rs 60,000 by cheque. Half the building is
used by the proprietor for residential purpose.
12. Sold goods costing Rs 20,000 to sunil at a profit of 20% on
sales less 20% trade discount .
13. Purchased goods for Rs 1000 from nanda and supplied it to
helen for Rs 1300. Helen returned goods worth Rs 390, which in
turn were returned to nanda.
14. Received invoice at 10% trade discount from rohit and sons
and supplied these goods to madan, listed at Rs 3000.
Answers
1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)
2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)
3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)
4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)
5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)
6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)
7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)
8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)
9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)
10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)
11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)
12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)
13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)
14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)
Here are the journal entries for the given transactions:
1. Bricks and timber purchased for construction:
Debit: Bricks (Asset) - Rs 60,000
Debit: Timber (Asset) - Rs 35,000
Credit: Bank (Liability) - Rs 95,000
2. Transfer to fixed deposit account:
Debit: Fixed Deposit (Asset) - Rs 13,000
Credit: Current Account (Asset) - Rs 13,000
3. Appointment of Mr. S.N. Rao as Accountant:
Debit: Salary Expense (Expense) - Rs 300
Debit: Security Deposit (Asset) - Rs 1,000
Credit: Accountant (Liability) - Rs 300
4. Goods sold to Shruti:
Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000
Credit: Sales (Income) - Rs 80,000
5. Goods purchased from Richa:
Debit: Purchases (Expense) - Rs 60,000
Credit: Accounts Payable - Richa (Liability) - Rs 60,000
6. Goods sold to Shilpa:
Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000
Credit: Sales (Income) - Rs 50,000
7. Goods sold to Garima:
Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000
Credit: Sales (Income) - Rs 1,00,000
8.Purchase of land:
Debit: Land (Asset) - Rs 2,00,000
Debit: Brokerage Expense (Expense) - Rs 2,000
Debit: Registration Charges (Expense) - Rs 15,000
Credit: Bank (Liability) - Rs 2,17,000
9. Goods and cash taken away by proprietor:
Debit: Proprietor's Drawings (Equity) - Rs 65,000
Credit: Goods (Asset) - Rs 25,000
Credit: Cash (Asset) - Rs 40,000
10. Goods sold to Charu:
Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000
Credit: Sales (Income) - Rs 1,20,000
Credit: Cost of Goods Sold (Expense) - Rs 80,000
Credit: Profit on Sales (Income) - Rs 40,000
11. Rent paid for the building:
Debit: Rent Expense (Expense) - Rs 60,000
Credit: Bank (Liability) - Rs 60,000
12. Goods sold to Sunil:
Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000
Credit: Sales (Income) - Rs 24,000
Credit: Cost of Goods Sold (Expense) - Rs 20,000
Credit: Profit on Sales (Income) - Rs 4,000
13. Goods purchased from Nanda and supplied to Helen:
Debit: Purchases (Expense) - Rs 1,000
Debit: Accounts Payable - Nanda (Liability) - Rs 1,000
Credit: Accounts Receivable - Helen (Asset) - Rs 1,300
Credit: Sales (Income) - Rs 1,300
14. Goods received from Rohit and Sons and supplied to Madan:
Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)
Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700
Debit: Accounts Receivable - Madan (Asset) - Rs 3,000
Credit: Sales (Income) - Rs 3,000
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Factor the expression 36a-16 to write an equivalent expression in which all coefficients and constants are integer values.
Answers
The expression 36a - 16 to write an equivalent expression in which all coefficients and constants are integer values is; 4(9a - 4)
How to factor Algebraic expressions?We are given the expression as; 36a - 16
Now, we want to write an equivalent expression of 36a - 16.
However, according to question, 36 and 16 are both divisible by 4. Thus, we will divide both sides by 4 to get;
36/4 = 9 and 16/4 = 4
Now, factorize the given expression 36a - 16.
Taking 4 as a common factor, we get,
36a - 16 = 4(9a - 4)
Therefore, 4(9a - 4) is the factor to write an equivalent expression 36a - 16.
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pls pls pls pls helpppppp
Answers
Answer:
33 please brainliest
Step-by-step explanation:
Answer:
They receive 33 calls in 11 hours.
Step-by-step explanation:
If they recieve 18 calls in 6 hours that means that each out they get...
18 / 6 = 3 calls
If the get 3 calls each our, that means that in 11 hours they will get...
3 x 11 = 33 calls
Jim has 1/3 of a pizza to split between four people. How much of the pizza does each person get?
Answers
Each person gets 1/12 of the pizza.
Explanation:
Jim needs to split 1/3 of a pizza to four people, or in other words, divide the 1/3 of a pizza into 4 for those people to eat.
(1/3)/4
When you divide with a fraction, it’s the same as multiplying with the reciprocal of the second number (the divisor). The reciprocal is the flip of a fraction.
(1/3)/4
=(1/3)*(1/4)
The reciprocal of 4 would be 1/4 because 4 can also be written as 4/1, which is 1/4 when flipped.
And now we multiply:
(1/3)*(1/4)
=1/12
Therefore, each person gets 1/12 of the pizza.
I hope this helps! Please comment if you have any questions.
Answer to 11+(-7) please
Answers
Answer:
4
Hope this helps! Add 11 and -7
A limo weighs 3 tons, 1,000 pounds. How many pounds does the limo weigh?
Note: 1 ton = 2,000 pounds
Answers
Answer:
2000 times 3 = 6000 + 1000 = 7000 pounds
Identify the number of solutions of the system of linear equations.
x=y+3z=6
x-2y = 5
2x - 2y + 5z = 9
no solution
exactly one solution
infinitely many solutions
Solve the system. If there are infinitely many solutions, write the ordered triple in terms of z. If there is no solution, lea
The solution is (x, y, z)
-1.2
3
Answers
The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.
Let's solve the system of linear equations correctly.
The given system of linear equations is:
x = y + 3z = 6
x - 2y = 5
2x - 2y + 5z = 9
To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:
From equation 1, we have:
x = y + 3z
Substituting this value of x in equation 2:
(y + 3z) - 2y = 5
y + 3z - 2y = 5
-z + 3z = 5 - y
2z = 5 - y
Now, let's substitute the value of x in equation 3:
2(y + 3z) - 2y + 5z = 9
2y + 6z - 2y + 5z = 9
11z = 9
Simplifying the equation, we find:
z = 9/11
Now, substituting this value of z back into the equation 2z = 5 - y, we get:
2(9/11) = 5 - y
18/11 = 5 - y
18/11 - 5 = -y
18/11 - 55/11 = -y
-37/11 = -y
y = 37/11
Finally, we can substitute the values of y and z into equation 1 to find the value of x:
x = y + 3z
x = 37/11 + 3(9/11)
x = 37/11 + 27/11
x = 64/11
Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).
The system has exactly one solution.
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Question: 18 of 19
Lesson 18
Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle 0 = 50°
Choice 'A' OV
Choice 'B'O V
Choice 'C'OV
Choice 'D' OV
(38.3, 32.1)
(33.8, 31.2)
(32.1, 38.3)
(31.2, 33.8)
4
Answers
The component form of the following vectors is Option A. V = (38.3, 32.1).
To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.
The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.
In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.
The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).
Let's calculate the components:
x = 50 * cos(50°) ≈ 38.3
y = 50 * sin(50°) ≈ 32.1
Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).
Therefore, the correct answer is A. V = (38.3, 32.1).
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The question is incomplete. Find the full content below:
Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle θ = 50°
A. V = (38.3, 32.1)
B. V = (33.8, 31.2)
C. V = (32.1, 38.3)
D. V = (31.2, 33.8)
are the ratios 2:1 and 20:10 equivalent
Answers
Yes, there is an analogous ratio between 2:1 and 20:10.
What ratio is similar to 2 to 1?We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.
By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.
As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.
The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:
20 ÷ 10 : 10 ÷ 10
= 2 : 1
As a result, both ratios have the same reduced form, 2:1, making them equal.
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Write polynomial function from graph
Answers
Answer:
6i
Step-by-step explanation:
because I did this assignment
Answer:
12s67v6₹+tygzgxhfucxh
El cateto más largo de un triángulo rectángulo es 4m más largo que el cateto más corto. La hipotenusa es 8m más larga que el cateto más corto. Hallar las longitudes de los lados del triángulo.
Answers
The lengths of the sides of the triangle are as follows;
Short leg = 12 cm.
Longer leg = 16 cm.
Hypotenuse = 20 cm.
What is Pythagorean theorem?In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
c represents the hypotenuse of a right-angled triangle.a represents the adjacent side (shorter leg) of a right-angled triangle.b represents the opposite side (longer leg) of a right-angled triangle.Note: Let the variable x represent the smaller leg.
The hypotenuse is 8 cm longer than the longer leg: x + 8 = x + 8.
Substituting the given parameters into the Pythagorean's theorem formula, we have the following;
c² = a² + b²
(x + 8)² = x² + (x + 4)²
x² + 16x + 64 = x² + x² + 8x + 16
x² - 8x - 128 = 0
Adjacent leg, x = 12.
For the hypotenuse, we have:
Hypotenuse, c = x + 8
Hypotenuse, c = 12 + 8
Hypotenuse, c = 20 cm.
For opposite side, we have:
opposite side, b = 12 + 4
opposite side, b = 16 cm.
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Complete Question:
The shorter leg of a right triangle is 4 cm shorter than the longer leg. The hypotenuse is 8 cm longer than the longer leg. Find the lengths of the sides of the triangle.
How do you solve -2 1/2+3/4÷3/8
Answers
Step-by-step explanation:
1. use PEMDAS (Parentheses, Exponent, Multiplication & Division, Addition & Subtraction). you would do 3/4 divided by 3/8 first.
3/4 / 3/8 = 2
2. add 2 to -2 1/2 (or if it's easier to understand, do 2 minus 2 1/2)
-2 1/2 + 2 = -1/2 OR 2- 2 1/2 = -1/2
answer is -1/2
HELPPP ASPA 60 POINT!!!!!Show to draw a line segment that measures 92 millimeters. i need it to be in words not a photo please
Answers
A line segment that measures 92 millimeters in length can be drawn using scale.
Given that,
A line segment has to be drawn which has a measure of length 92 millimeters.
We know that,
10 millimeters = 1 centimeter
1 millimeter = 1/10 centimeters
92 millimeters = 92/10 = 9.2 centimeters
So it is enough to draw a line segment of length 9.2 centimeters.
In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.
In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.
So draw a line segment starting from 0 to 9.2.
Hence the line segment is drawn with scale.
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what is tthe most cheapest thing you can buy
Answers
Wheat. Actually, the entire agriculture complex, including corn, beef, pork and beans could fit this description. But for now we will focus on wheat.
Well, if it is a trick question, then I would say that the answer is the air we breathe. We don't need to buy it.
Answer:
Air
Hope you could understand.
If you have any query , feel free to ask
In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student is a
female given that they have an A?
Answers
The probability that a student is a female given that they have an A is; 2/7
How to find the probability?From the given table, we see that;
Number of males that got A = 4
Number of males that did not get A = 8
Number of females that got A = 6
Number of females that did not get A = 3
The probability that a student is a female given that they have an A is;
P(Female|A) = 6/(4 + 8 + 6 + 3)
P(Female|A) = 6/21 = 2/7
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can you help me please
Answers
Hence the correct option is to translate down 2 unit
Transformations can be non-rigid (when the preimage's size or shape is unaltered) or stiff (where the size is changed but the shape remains the same). These are the fundamental guidelines that this concept abides by. It is a straightforward approach to alter 2D forms.
Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets.
We have the parent function f(X)= x
and transformed function is g(x)= -3f(x+5)-2
the parent function f(x) is translated dawn 2 units and stretched by 5 .
Hence the correct option is to translate down 2 unit
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A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per
hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per
week. His goal is to make at least $300 per week.
1. Create a system of equations or inequalities that models the situation. Define the variable you use
Answers
Answer:
15x20/300
Step-by-step explanation:
you multiply 15 and 20 then didvide that answer to 300
These are the points (20,0), (0,20), (20,5) are a few points which represent the number of hours a student can work each job to meet his goal.
Let ;
The hour spent in mow lawns is represent by x,
And represent the hour spent for gardening by y.
According to the question;
He charges $15 per hour to work mow lawns .
And $20 per hour to gardening .
Total no. of hours allowed to work = 20 hours per week
Then the inequality to represent the cost constraint will be,
15x+20y ≥ 300
Since,
He cannot work for more than 15 hours per week, the inequality to represent the time constraint will be,
x + y ≤ 20
On solving the inequalities,
15(20-y) + 20y = 300
300 - 15y + 20y = 300
5y= 0
y = 0
For value of x put y = 0
x + 0 = 20
It states if he work only in mows law for 20 hours he can earn $15 =(15)(20) =$300
All pairs of positive numbers whose sum is less than 20, are solutions to the given system of inequalities.
A pair of negative numbers will also solve both constraints, but is not applicable in this situation because a student, cannot work for negative hours, or for a negative amount of money.
So, (20,0), (0,20), (20,5) are a few points which represent the number of hours a student can work each job to meet his goal.
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The square root of the variance is called the: standard deviation beta covariance coefficient of variation
Answers
Answer:
standard deviation
Step-by-step explanation:
how did cotton production affect the Texas economy? We have to write it in our own words. You don't have to write the whole answer just give some ideas.
Answers
Answer:
it made Texas thrive because they were one of the leading cotton producers and made a lot of money off of it
The basic rate pay is K8.20. If the overtime is paid at time-and-a-quarter, what is the overtime rate of pay?
Answers
The overtime rate of pay is K10.25.
The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.
To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.
By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.
Therefore, the overtime rate of pay is K10.25.
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An $800 bond earns 4% simple annual interest how much will the bond earn in the interest after 6 years?
Answers
As a result of answering the given question, we may state that As a result, after 6 years, the bond will earn $192 in interest.
what is interest ?Divide the principal by the interest rate, period, and other factors to get simple interest. The formula in marketing is simple: return = principal + interest + hours. This method makes it easiest to calculate interest. Interest is frequently expressed as a percentage of the main balance. He will only pay half of the entire interest if he borrows $100 from a friend and agrees to repay it with 5% interest. $100 (0.05) = $5. You must pay interest when you borrow money, and you must charge interest when you lend it. Interest is often calculated as an annual percentage of the loan balance. This proportion is known as the loan's interest.
To compute simple interest, use the following formula:
The interest rate = (Principal x Rate x Time)
where:
The principal is the bond's initial amount, which is $800 in this example.
The annual interest rate is 4%, or 0.04 in decimal form.
Time is the number of years, which in this case is six.
When we enter these values into the formula, we get:
(800 x 0.04 x 6) = $192 in interest
As a result, after 6 years, the bond will earn $192 in interest.
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Which of the following lines has a slope of -1?
Answers
Answer:
I do not see any lines
Step-by-step explanation:
GIVING OUT BRAINLIST QUICK! NUMBER 6
Answers
Answer:
40
Step-by-step explanation:
AREA=LW
L₁W₁=40
L₂W₂=160
x(L₁W₁)=L₂W₂
x(L₁W₁)=L₂W₂
x(40)=160
x=40
11. The coordinate grid shows points P, Q, R, and S. All the coordinates for these points
are integers.
What is the value of the x-coordinate of point P?
Answers
Answer:
-6
Step-by-step explanation:
Answer: -6
Step-by-step explanation:
A caterpillar moves across the grass at a rate of 423 feet every 7 minutes. How fast does the caterpillar move in feet per minute?
Answers
A 20-ounce soda cost $1.20. How much does the soda cost per ounce?
Answers
Answer:
Your answer is 0.06, hun!
Step-by-step explanation:
1.20 divided by 20 = 0.06
Stay happy-Livia
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
hay 1230 personas, entre hombres y mujeres. Si se sabe que el número de mujeres, supera en 150 al número de hombres. ¿Cuántos hombres están habitando la mini ciudad?
Answers
There are 540 men living in the mini city.
x + (x + 150) = 1230
Simplifying this equation, we get:
2x + 150 = 1230
Subtracting 150 from both sides, we get:
2x = 1080
Dividing both sides by 2, we get:
x = 540
Therefore, there are 540 men living in the mini city.
To check our answer, we can substitute x = 540 into our original equation:
540 + (540 + 150) = 1230
690 = 1230
This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.
We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:
x + (x + 150) = 1230
Simplifying this equation, we get:
2x + 150 = 1230
Subtracting 150 from both sides, we get:
2x = 1080
Dividing both sides by 2, we get:
x = 540
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