The required sample sizes are given as follows:
a) Previous estimate of 0.52: n = 1839.
b) No previous estimate: n = 1842.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of 0.995, so the critical value is z = 2.575.
The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
For an estimate of 0.52, the parameters are given as follows:
[tex]M = 0.03, \pi = 0.52[/tex]
Hence the sample size is obtained as follows:
[tex]0.03 = 2.575\sqrt{\frac{0.52(0.48)}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.575\sqrt{0.52 \times 0.48}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.52 \times 0.48}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\right)^2[/tex]
n = 1839.
Without a previous estimate, the sample size is given as follows:
[tex]0.03 = 2.575\sqrt{\frac{0.5(0.4)}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.575\sqrt{0.5 \times 0.5}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.5 \times 0.5}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.5}}{0.03}\right)^2[/tex]
n = 1842.
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A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 2425 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week? (100 points!)
Answer:
Step-by-step explanation:
Let's assume that the first car used x gallons of gas during the week, then the second car used (75 - x) gallons of gas because the total gas consumption by both cars is 75 gallons.
The first car's fuel efficiency is 30 miles per gallon, so it traveled (30x) miles during the week.
The second car's fuel efficiency is 35 miles per gallon, so it traveled (35(75 - x)) miles during the week.
The total distance traveled by both cars is given as 2425 miles, so we can set up the equation:
30x + 35(75 - x) = 2425
Expanding the equation:
30x + 2625 - 35x = 2425
Simplifying:
-5x = -200
x = 40
Therefore, the first car used 40 gallons of gas during the week, and the second car used (75 - 40) = 35 gallons of gas during the week.
Answer: Car 1 used 40 gallons and car 2 used 35 gallons.
Step-by-step explanation: In this problem, we will use a system of equations to reach our answer. We can let x be the gallons consumed by the first car, and y be the gallons consumed by the second car(these are both for one particular week only). We know the total consumption of gas is 75 gallons so the gallons consumed by car 1 and car 2 have to add up to 75. We can then create the equation x+y=75. We know that car 1 has an efficiency of 30 miles per gallon and 35 miles per gallon for car 2. The miles produced by x gallons in car 1 can be represented by 30x=# of miles. we can use 35y = # of miles for car 2. We know the combined total of miles from both cars is 2425 so we can make the equation 30x+35y=2425 miles. Now that we have our equations, we can simply solve them to find our answers.
x+y=75
x=75-y Isolating a variable
30x+35y=2425
30(75-y)+35y=2425 Substituting the variable we isolated
2250-30y+35y=2425
2250+5y=2425
5y=175
y=35
x+(35)=75
x=40
y=35 and x=40
Car 1 used 40 gallons and car 2 used 35 gallons.
Hope this helps!
30-year mortgage with an annual interest rate of 4.9%
made a $55,000 down payment on the house.
monthly payment : $1,035
house price : $250,000
total cost after all payments been made: $427,600
question:
Property taxes vary from State to State and City to City, but 1% of the property's appraised value is a good estimate of how much the annual property taxes will be for the property. Assuming Marisa purchased the house for the same price as its appraised value, how much can she expect to pay each year on property taxes?
Answer:
If the house price is $250,000, then 1% of the appraised value is:
0.01 x $250,000 = $2,500
So Marisa can expect to pay $2,500 in annual property taxes.
Step-by-step explanation:
I have the 650 students at Westmoreland junior high 80% will attend the field trip how many students will attend the field trip
Answer:
520
Step-by-step explanation:
So you multiply 650 by 0.8 and you get 520. 0.8 is 80% but in a decimal form.
If the quarterly interest at 10.5% is $3,150, the principal amount of a loan is
The principal amount of the loan is $1,200,000.
What is simple interest?
Simple interest is the amount of borrowing-related interest that is computed using only the initial principal and a constant interest rate.
To find the principal amount of a loan, we need to use the formula for simple interest:
I = Prt
Where I is the interest, P is the principal, r is the interest rate as a decimal, and t is the time in years.
In this case, we know that the interest is $3,150 and the interest rate is 10.5%. We also know that the interest is earned quarterly, so the time period is 1/4 of a year, or 0.25 years.
Substituting these values into the formula, we get:
3150 = P * 0.105 * 0.25
Solving for P, we get:
P = 3150 / (0.105 * 0.25) = $1,200,000
Therefore, the principal amount of the loan is $1,200,000.
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theodore goes to a baseball game and buys 3 water that cost x dollars each and a bag of popcorn for $4.50 write an expression in simplest form that reprsent the total amount if money therdore spent
What is the error 3x+4.50x
7.50 x
the experssion to find the total amount of money theodore is spent 7.50x
The answer to this question is as follows It's vital to keep in mind that equation while this is the same phrase you used, the x only applies to the cost of the water and not the cost of the popcorn.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The formula to calculate Theodore's overall spending is:
3x + 4.50
This is due to the fact that he purchased three waters at a cost of x each, for a total cost of x, and a bag of popcorn at a cost of $4.50. The entire amount of money he spent may be calculated by adding these two expenses.
By condensing the formula 3x + 4.50, we obtain:
7.50x
It's vital to keep in mind that while this is the same phrase you used, the x only applies to the cost of the water and not the cost of the popcorn.
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Can anyone help me out with this?
The solution to the system of equations is given below.
What is function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given is the system of equations as shown in the image.
{ 1 } -
x - 2y = - 7
2x + 5y = 8
We can write -
x = 2y - 7
Now -
2(2y - 7) + 5y = 8
4y - 14 + 5y = 8
9y = 22
{y} = 22/9
x = 44/9 - 7
x = 44/9 - 63/9
{x} = - 19/9
{ 2 } -
5x - 3y = 16
3x + 6y = 18
We can write -
5x - 3y = 16
x + 2y = 9
So -
x = 9 - 2y
5(9 - 2y) - 3y = 16
45 - 10y - 3y = 16
45 - 13y = 16
45 - 16 = 13y
13y = 29
y = 29/13
x = 9 - 58/13
x = 117/13 - 58/13
x = 59/13
Similarly, we can solve the other two system of equations.
Therefore, the solution to the system of equations is given above.
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Find the area of the figure.
What are all possible values of x that satisfy the inequality x3−8≥1?
Answer:
x is greater than or equal to 3
Step-by-step explanation:
I'm gonna assume you meant 3x-8
Treat it as an equation
3x-8 =1, 3x=9, x=3
If its x^3 -8
x^3 -8 =1, x^3=9, x is greater than or equal to the cubed root of 9
d) Como se observa, al igualar las expresiones y resolver la ecuación que resulta, se
obtiene el mismo valor para x indicado en la tabla. ¿Qué pueden decir de este
valor con respecto a la gráfica?
Answer:
El valor obtenido para x es una solución a la ecuación y, por lo tanto, es un punto en la gráfica de la función. Esto significa que el punto (x,y) en la gráfica se encuentra en la recta que representa la ecuación
Step-by-step explanation:
The mean age of a family of seven is 23 years. The median is 16 years, the modes are 12, years and 45 years, and the range is 35 years. Find the ages of the seven family members
Let's use the given information to set up equations to solve for the ages of the family members.
We know that the mean age of the family is 23 years, so we can write:
(sum of ages) / 7 = 23
sum of ages = 161
We also know that the median age is 16 years, which means that the ages of the family members can be arranged in order from smallest to largest, and the middle age (or the average of the two middle ages, if there are an even number of ages) is 16. We can use this information to set up an equation:
(3rd smallest age + 4th smallest age) / 2 = 16
3rd smallest age + 4th smallest age = 32
Next, we know that the range of the ages is 35 years, which means that the difference between the largest age and the smallest age is 35. We can use this information to set up another equation:
largest age - smallest age = 35
Finally, we know that the modes (the most common ages) are 12 years and 45 years. This means that there are two family members whose ages are 12 years and two family members whose ages are 45 years. We can use this information to set up two more equations:
number of 12-year-olds + number of 45-year-olds = 4
12 x number of 12-year-olds + 45 x number of 45-year-olds = sum of ages
We now have five equations and five unknowns (the ages of the seven family members). We can solve for these unknowns using algebra. One possible set of ages that satisfies all of the equations is:
2, 2, 12, 16, 20, 45, 64
(Note that the ages do not have to be integers, but this particular set of ages happens to be integers and satisfies all of the given conditions.)
An 18-inch-wide by 3-foot-deep trench is dug in the ground and a water line with a 3.5 inch outside diameter is placed in the trench. The water line is placed on 6 inches of bedding, and bedding surrounds the pipe to a height of 2.5 inches above the water line. The length of the trench is 500 feet. Determine the volume of excavation needed for the water line.
Answer: Here you go.
Step-by-step explanation:
To calculate the volume of excavation needed for the water line, we first need to calculate the cross-sectional area of the trench.
The trench has a width of 18 inches and a depth of 3 feet, or 36 inches. So the cross-sectional area of the trench is:
18 inches x 36 inches = 648 square inches
Next, we need to subtract the cross-sectional area of the water line from the cross-sectional area of the trench to get the area of the excavation. The water line has a 3.5 inch outside diameter, so the radius is 1.75 inches. The cross-sectional area of the water line is:
π x (1.75 inches)^2 = 9.62 square inches
The area of the excavation is therefore:
648 square inches - 9.62 square inches = 638.38 square inches
To convert square inches to cubic feet, we need to multiply by the length of the trench in feet. The length of the trench is 500 feet. So the volume of excavation needed for the water line is:
638.38 square inches x 500 feet = 1,909,140 cubic inches
To convert cubic inches to cubic feet, we divide by 12^3 (12 inches per foot, cubed):
1,909,140 cubic inches ÷ (12 x 12 x 12) = 11.04 cubic feet
Therefore, the volume of excavation needed for the water line is approximately 11.04 cubic feet.
Can someone explain/help me with this problem?
1. The finance charge on the loan is $9,920.
2. The total deferred payment price of the airplane is $39,120.
What is the finance charge on the loan?To find the finance charge on the loan, we need to first determine the amount financed. George Bell made a 15% down payment on the airplane, so the amount financed is:
= $29,200 - (0.15)($29,200)
= $29,200 - $4,380
= $24,820
The total amount of payments made over the life of the loan is:
= $579/month x 60 months
= $34,740
The finance charge on the loan is:
= $34,740 - $24,820
= $9,920.
What is the total deferred payment price of the airplane?The total deferred payment price of the airplane is the sum of the down payment and the total amount of payments made over the life of the loan. The down payment is 15% of the purchase price which is:
= 0.15 * $29,200
= $4,380
The total amount of payments made over the life of the loan is:
= $579/month * 60 months
= $34,740
The total deferred payment price of the airplane is:
= $4,380 + $34,740
= $39,120.
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how to solve 10-[p+3] when p=7
Answer:
0
Step-by-step explanation:
plug in 7 for "P"
so 10 - [7+3]
solve the inside first, which is 10, therefore 10-[10] leaving you with no solution or 0 as answer
Wickers Restoration Services had the following transactions on May.
Received $48,000 from sale of common stock.
Paid rent on office for the month, $880.
Purchased supplies on account, $1,750.
Earned fees, receiving cash, $12,600.
Paid creditor on account, $1,000.
Paid automobile expenses for month, $375, and miscellaneous expenses, $250.
Paid office salaries for the month, $3,900.
Earned fees that the customer will pay next month, $2,400.
Determined that the cost of supplies used was $280.
Paid dividends, $2,400.
Question Content Area
a. Prepare the journal entries for the above transactions on May. If an amount box does not require an entry, leave it blank.
The journal entries for the aforementioned transactions in May are as follows:
1. a $48,000 profit from the selling of ordinary stock:
Cash 48,000
Stock 48,000
2. Paid $880 in rent for the office for the month:
Rent Expense 880
Cash 880
3. $1,750 worth of supplies were bought on credit:
Supplies 1,750
Accounts Payable 1,750
4. Paid fees, cash received, $12,600:
Cash 12,600
Fees Earned 12,600
5. $1,000 creditor account payment:
Accounts Payable 1,000
Cash 1,000
6. Spent $375 in transportation expenses for the month as well as $250 in other expenses:
Automobile Expense 375
Miscellaneous Expense 250
Cash 625
7. $3,900 in office salaries were paid for the month:
Salaries Expense 3,900
Cash 3,900
8. $2,400 in earned fees that the client will pay the next month:
Accounts Receivable 2,400
Fees Earned 2,400
9. determined that the $280 cost of the supplies used:
Supplies Expense 280
Supplies 280
10. Dividends paid, $2,400:
Retained Earnings 2,400
Cash 2,400
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A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000.
the ticket price needs to be lowered by approximately $8.33 in order to fill all seats in the stadium.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000.
Let's assume that if the ticket price is lowered by $x, the corresponding increase in attendance is 3000x.
Then, if the ticket price is lowered by $x, the new attendance will be:
33,000 + 3000x
We want to find the ticket price that will result in full capacity, which is 58,000 spectators.
So, we can set the new attendance equal to 58,000 and solve for x:
33,000 + 3000x = 58,000
3000x = 25,000
x = 25,000/3000
x ≈ 8.33
Therefore, the ticket price needs to be lowered by $8.33 to $1.67 in order to fill all seats in the stadium.
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Complete question:
A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. how much ticket price to be lowered so that all seats will be full?
Class A: 87, 93, 96, 88, 92, 90, 100, 93, 91, 96
Class B: 72, 69, 54, 66, 63, 74, 59, 64, 70, 68
1. Find the mean, median, and mode for class A
Mean
Median
Mode
2. Find the mean, median, and mode for class B
Mean
Median
Mode
Answer:
Class A: 87, 93, 96, 88, 92, 90, 100, 93, 91, 96
Mean: 92.6
Median: 92.5
Mode: 93 and 96
Class B: 72, 69, 54, 66, 63, 74, 59, 64, 70, 68
Mean: 65.9
Median: 67
Mode: No mode or 0
Step-by-step explanation:
You're welcome.
QUESTION 7
Consider the following argument: If Russia invades the Ukraine, America will impose trade sanctions upon Russia. Russia
invades the Ukraine. So American will impose trade sanctions upon Russia. What is the logical form of this argument?
O a. Modus Tollens
O b. Disjunctive Syllogism
O c. Hypothetical Syllogism
O d. Affirming the consequent
O e. Modus Ponens
The logical form of this argument in " If Russia invades the Ukraine, America will impose trade sanctions upon Russia" is c. Hypothetical Syllogism.
What is Hypothetical Syllogism?A hypothetical syllogism is a logical argument that uses two conditional statements, or "if-then" statements, to draw a conclusion. The general form of a hypothetical syllogism is:
If A is true, then B is true.
If B is true, then C is true.
Therefore, if A is true, then C is true.
Here's an example of a hypothetical syllogism:
If it rains, then the ground is wet.
If the ground is wet, then the grass is slippery.
Therefore, if it rains, then the grass is slippery.
Therefore, option C is correct.
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How much larger is a great white shark than a horn shark how many bamboo sharks would that equal
Answer: A great white shark can grow up to 20 feet in length, while a horn shark can grow up to 3 feet in length. Therefore, a great white shark is 17 feet larger than a horn shark.
Bamboo sharks can grow up to 5 feet in length. Therefore, to equal the length of a great white shark, you would need 4 bamboo sharks (since 4 x 5 = 20).
Step-by-step explanation:
-3
21V
0
-1 1 3
-2
zoom in
X
*REQUIRED 1
4. Vocabulary: Identify the vertex of the
parabola.
O (2,0)
) r = 0
Oy=3x-2
Oy=0
O(-2,0)
(0,-4)
The vertex of the parabola is ( 0, -4). The correct option is F.
What is a vertex of parabola?A vertex of a parabola is the point at which the parabola changes direction. It is the point on the parabola where the curve reaches its minimum or maximum value, depending on whether the parabola opens upward or downward.
A parabola is a type of conic section, a geometric shape formed by the intersection of a plane and a cone. In particular, a parabola is formed when a plane intersects a right circular cone parallel to one of its generating lines.
From the given graph the vertex of the parabola is,
Vertex = ( 0, -4 )
Therefore, the vertex is (0,-4).
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What is the slope of a line parallel to the y-axis?
Answer:
The slope of a line parallel to Y-axis is zero.
What is the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labeled 1-10?
The probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.
What is meant by probability?An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur.
In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.
It is said that there are 10 balls in a bag, labelled 1-10.
Now,
The number of ways the ball labelled 1 is picked is 1
The number of ways the ball labelled 2 is picked is 2
So the number of ways a ball labelled certain number is picked is 1.
Now there is no replacement.
So the total number of balls decreases by 1 when 1 ball is taken.
Then,
The probability of choosing the ball numbered 1 = 1/10
The probability of choosing 2 = 1/9
The probability of choosing 3 = 1/8
.
.
.
the probability of choosing 10 = 1
Total probability of choosing the balls in consecutive order = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.
Therefore the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.
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A boy walks 3km at a speed of km/h. If the journey takes 35 min, find the value of v.
The value of the speed(v) is 5.14 km/hr
What is speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector. Speed is measured in m/s and km/hr
speed = distance / time
distance = 3km
converting the time in seconds to hour,
time = 35 mins = 35/60 = 7/12 hr
speed = 3 ÷ 7/12
= 3× 12/7
= 36/7
= 5.14 km/hr
therefore the speed of the boy is 5.14 km/hr
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P=$4000; r=9%;t=2 years; A=?
Answer:
First, if it's a simple interest problem, convert R percent to r a decimal, r = R/100 = 9%/100 = 0.09 per year, then, solving our equation
I = 4000 × 0.09 × 2
I = 4000 × 0.18
I = $720.00
The simple interest accumulated on a principle of $4,000.00 at a rate of 9% per year for 2 years is $720.00.
Hope this helps. (Compound interest will be added if the equation needs it)
Use Tools The tape measure shows inches. Label the
number of inches equivalent to 2½, 3, 3½, and 4 feet.
The equivalent number of inches is given as follows:
2 and 1/2 feet: 30 inches.3 feet: 36 inches.3 and 1/2 feet: 42 inches.4 feet: 48 inches.How to obtain the equivalent number of inches?The equivalent number of inches is obtained applying the proportions in the context of the problem.
A proportion is applied as the unit conversion rate from feet to inches is given as follows:
1 feet = 12 inches.
Hence the measures are converted from feet to inches multiplying the amounts by 12, as follows:
2 and 1/2 feet: 2.5 x 12 = 30 inches.3 feet: 3 x 12 = 36 inches.3 and 1/2 feet: 3.5 x 12 = 42 inches.4 feet: 4 x 12 = 48 inches.More can be learned about proportions at https://brainly.com/question/24372153
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i can’t get this question
Answer:
19
y = 6x - 11 it says the input is 5 so you input 5 as x
y = 6(5) - 11
y = 30 - 11
y = 19
A football player is running straight down the sideline towards the goal line at 8m/s. As he cross the 50-yard line, a defensive player 13.7m inside is running to catch him. At what velocity must the defensive player run in Order to catch the man with the ball before he scores
oh my God cr7 ans messi are running
look at the triangles below. Choose true or false for each of the statements about them. A value of x = 16 results in congruent triangles. A value of x = 27 results in congruent triangles. A value of x = 31 does not result in congruent triangles.
Answer: Without a visual representation of the triangles, it's difficult to determine whether the statements are true or false.
However, in general, the side lengths of a triangle determine its shape and size. If two triangles have the same side lengths, then they are congruent, meaning they have the same shape and size. Therefore, if the triangles in question have different side lengths for x = 16, x = 27, and x = 31, then it's possible that the statements are either true or false, depending on the specific side lengths.
Without additional information, it's not possible to determine whether the statements are true or false.
Step-by-step explanation:
What is the area of this shape
Answer:45
Step-by-step explanation: see how if you cut off that spike and you plug it in the non-shaded part it fits. Now you’ve got yourself a rectangle so the area is 3+2= 5 x 9= 45
2.1.1 How many packets of patties should she buy? 2.1.2 Julia calculates that if she buys 42 packets of patties, there will be a leftover of 4 patties. Justify her answer by showing all the necessary calculations. 2.2.1 Julia also sells cold drinks for the school function. A 2litre bottle of orange juice costs R18,95. A 1,5 litre bottle of cola costs R14.50. Two learners John and Peter had the following argument: John says buying a 2litre bottle of orange juice is much cheaper than buying 1.5litre butte of cola. Who is correct? Verify your answer by giving all the necessary calculations (5 (5)
Therefore, John is incorrect, as buying a 2-liter bottle of orange juice is actually slightly more expensive per liter than buying a 1.5-liter bottle of cola.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.
Here,
2.1.1 To determine how many packets of patties Julia should buy, we need to know the total number of patties needed for the school function. Let's assume that each person will eat one patty.
If there are 300 people attending the function, then Julia needs to buy:
300 x 1 = 300 patties
Each packet of patties contains 12 patties, so the number of packets needed can be calculated as follows:
300 patties ÷ 12 patties/packet = 25 packets
Therefore, Julia should buy 25 packets of patties.
2.1.2 To justify Julia's calculation, we can use algebra. Let's assume that the number of packets of patties she buys is x. We know that there are 12 patties in each packet, so the total number of patties is 12x. We also know that if she buys 42 packets, there will be a leftover of 4 patties.
This can be represented as the following equation:
12x + 4 = 42 x 12
Simplifying this equation:
12x = 500 - 4 = 496
x = 496/12 = 41.33 (rounded to two decimal places)
Since we can't buy a fractional number of packets, Julia would need to buy 42 packets of patties. This would give her a total of:
12 x 42 = 504 patties
She would then have 4 leftover patties, as calculated earlier. Therefore, Julia's calculation is correct.
2.2.1 To determine whether buying a 2-liter bottle of orange juice is cheaper than buying a 1.5-liter bottle of cola, we need to compare the price per liter of each drink.
For orange juice, the price per liter is:
R18.95 ÷ 2 liters = R9.475/liter
For cola, the price per liter is:
R14.50 ÷ 1.5 liters = R9.67/liter
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solve each system using substitution
y=1/2x+4
x-y=8
We are given the following system of equations:
y = (1/2)x + 4 ---(1)
x - y = 8 ---(2)
We can solve this system of equations by substitution method.
From equation (2), we have:
x - y = 8
Solving for x, we get:
x = y + 8
Substitute this value of x in equation (1):
y = (1/2)(y+8) + 4
Simplifying and solving for y, we get:
y = 2
Now, substitute this value of y back in equation (2) to find the value of x:
x - 2 = 8
x = 10
Therefore, the solution of the given system of equations is (x, y) = (10, 2).