Answer:
a
Step-by-step explanation:
at a movie theater, the size of popcorn bags decreased 20% . if the old bags held 15 cups of popcorn, how much do the new bags hold?
Answer:
12 cups
Step-by-step explanation:
If the size of the bag decreased by 20%, so will the number of cups held.
Number of cups held before the change = 15 cups
If the number of cups held after the 20% reduction in the size of the bag
= (100 - 20)% × 15
=80% × 15
= 12 cups
The new bags will hold 12 cups.
The old bags held 15 cups of popcorn so, the new bags holds 12 cups of popcorn and this can be determined by using the unitary method.
Given :
At a movie theater, the size of popcorn bags decreased 20%.The old bags held 15 cups of popcorn.The unitary method can be used to determine the total number of cups of popcorn the new bag can hold.
Given that the old bags held 15 cups of popcorn, so, it is 100% capacity of the old bag. So, according to this capacity, the new bag can 80% of cups of popcorns that is:
[tex]=\dfrac{80}{100}\times 15[/tex]
Multiply 80 by 15 in the above expression.
[tex]=\dfrac{1200}{100}[/tex]
Now, divide 1200 by 100 in the above expression.
= 12 cups of popcorn
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Mr.Kork sold his car for $8,400. This was $200 more than two fifths of what he had paid for the car originally. How much had Mr. Kork paid for the car?
Answer:
He paid = $20,500
Step-by-step explanation:
Let the amount he bought the car originally be X
so from the statement,
(2/5)*X + $200 = $8,400
(2/5)*X = $8,400 - $200
solving for X
X = $8200 * 5/2
X = $20,500
The distance between (0,5) and (6,-1) is
Answer:
6sqrt(2) units (exact form)
= 8.49 units (3 sf)
Step-by-step explanation:
sqrt[(-1-5)²+(6-0)²]
sqrt[(-6)² + 6²]
sqrt(36 + 36)
sqrt(72)
= 6sqrt(2) units (exact form)
= 8.49 units (3 sf)
Company A rents copy machines for $300 a month plus $0.50 per copy. Company B charges $600 a month plus $0.01 per copy. For which number of companies do the two companies charge the same amount?
Answer:
For 612 copies both companies will charge the same amount.
Step-by-step explanation:
Consider the provided information.
let x represents the number of copies and y represents the total charge.
Company A rents copy machines for $300 a month plus $0.50 per copy.
[tex]y = 300 + 0.5x[/tex]
Company B charges $600 a month plus $0.01 per copy.
[tex]y=600 + 0.01x[/tex]
We need to determine the number of copies for which two companies charge the same amount, so equate the equations as shown.
[tex]300 + 0.50x = 600 + 0.01x\\0.49x=300\\x\approx612.244[/tex]
The Approximate value of x to nearest whole number is 612.
Hence, for 612 copies both companies will charge the same amount.
Find a function of the form
y=Asin(kx)+C or y=Acos(kx)+C whose graph matches this one:
Answer:
y = 4cos((π/5)x) +3
Step-by-step explanation:
The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.
The value of A is half the difference between the minimum and maximum, so is ...
A = (1/2)(7 -(-1)) = 4
The value of C is the average of the maximum and the minimum, so is ...
C = (1/2)(7 +(-1)) = 3
The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...
k·10 = 2π
k = π/5 . . . . . divide by 10 and reduce the fraction
Now, we have all the parameters of our function:
y = 4cos((π/5)x) +3
To find a function that matches a given graph, the amplitude, frequency, and phase shift must be determined. The amplitude is calculated by determining the maximum and minimum values of y, the frequency is found by comparing the distances in the cycles, and the phase shift is calculated by looking at the middle of the oscillation.
Explanation:In order to find a function that matches the graph given, we need to determine certain aspects of the waveform such as the amplitude, frequency, and phase shift. This is done through carefully analysing the graph. In general, A resembles the amplitude or the 'height' of the wave. This can be determined by calculating half the distance between the maximum and minimum values of y. The coefficient k is linked to the frequency of the function, which can be figured out by the distance between alike points in the cycle (like peak to peak, or trough to trough). And finally, C corresponds to any vertical shift of the function which can be understood by checking the 'middle' of the oscillation. If the wave seems to be shifted to the right or left of the y-axis, then you would use a phase shift in the sine or cosine function. Remember, cosine and sine functions are similar in shape, but a cosine waveform begins at a peak, while a sine waveform begins at zero.
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Every month $40 is withdrawn from Toms savings account to pay for his gym membership. He has enough savings to withdrawn no more than $360. For how many months can Tom pay for his gym membership?
Answer:
9 months for 360 dollars
Step-by-step explanation:
360÷40=9
Which of the following statements are mathematical statement?
P: Math is not hard.
Q: Bill Gates is the founder of Microsoft.
A. P only
B. Q only
C. P and Q
D. None
Answer:
a is the right answer atleast that's what I think
Answer:
D.
Step-by-step explanation:
neither of these is a mathematical statement. P only mentions the word math and Q has nothing to do with math.
0 A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is _ five feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile?
Answer:
a) nearest jump is JL = 1380 inches = 115ft
b) number of jumps in 1 mile N= 46 jumps
Step-by-step explanation:
Given that the jump length is proportional to the body length.
If 2 inch grasshopper can jump 40 inches.
JL = k(BL)
k = JL/BL
where JL = jump length = 40 inches
BL = Body length = 2 inches.
k = 40/2 = 20
The constant of proportionality is 20.
For the athlete :
BL = 5ft 9 inches = 5(12)+9 = 69 inches.
The jump length of the athlete is:
JL = k(BL) = 20(69)
JL = 1380 inches. = 115ft
The number of jumps in 1 mile is
1 mile = 63360 inches
N = 63360/1380
N = 45.9 = 46
N= 46
Therefore, 46 jumps would be needed.
The graph shows a vertical translation of y =[tex]\sqrt[3]{x}[/tex]
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}
Answer:
Last option: {y|y is a real number}
Explanation:
The range of a real function is the set of the real numbers (values) that the function can return (the ouput of the function).
To figure out the range of a function, you first must figure out the domain.
The domain of the function [tex]y=\sqrt[3]{x}[/tex] is all real values, since the cube root function is defined for all the real numbers.
Since this function is continuous (which the translation of the function shows graphically), and the function is defined for all negative and positive values, the range of [tex]y=\sqrt[3]{x}[/tex] is all real numbers.
A vertical translation just slides the function vertically. Since the original function does not have either lower or upper bound, but the limits when x approaches ± ∞ are ± ∞, a translation will not modifiy the range.
Thus, the range of the translated function is (-∞, ∞).
That can also be written as {y|y is a real number}, which is read "y such that y is a real number", and is the last choice of the list.
Billy left home at 9 a.M. And rode his bicycle to the park at an average speed of 10 miles per hour here I got the park at 9:30 a.M. How many miles from the park is Billy's home so I explain how you got your answer
Answer:
Park is 5 miles from Billy's home.
Step-by-step explanation:
Given:
Billy left home at 9 a.m. And rode his bicycle to the park at an average speed of 10 miles per hour here and got the park at 9:30 a.m.
Now, to find the distance from park to Billy,s home.
Time it took Billy to rode his bicycle from park to home is from 9.30 a.m to 9.30 p.m.
So, the time = (9.30 - 9.00) = 30 minutes
[tex]=\frac{30}{60}[/tex] [tex]=0.5\ hour.[/tex]
Speed = 10 miles per hour.
Now, to get the distance from park to Billy's home we put formula:
[tex]Distance=Speed\times Time.[/tex]
[tex]Distance=10\times 0.5[/tex]
[tex]Distance=5\ miles.[/tex]
Therefore, park is 5 miles from Billy's home.
During statistical analysis, the investigator may consider searching for statistical associations among various groups that may suggest a cause–effect relationship, without having generated prior hypotheses about these groups. This is known as ____.
.
Answer:
This is known as Data dredging.
Step-by-step explanation:
In order for any statistical analysis to be significant, a researcher has to first generate a hypothesis.
Data dredging is trying to uncover patterns in data that can be presented statistically without devising a clear hypothesis by use data mining. It is also referred to as data fishing or p-hacking.
In this case any correlation (relationship between cause-effect)will be purely by chance.
Therefore, the investigator is Data dredging
A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 162 sq. yds.
Step-by-step explanation:
Given : A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd.
Then , Area of rectangle = length x width
= 11 yd x 17 yd = 187 sq. yds.
Area of square = (side)²
= (5 yd)² = 25 sq. yds.
Now , the area of the region inside the rectangle that surrounds the square will be Area of rectangle - Area of square
= 187 sq. yds.- 25 sq. yds.
=162 sq. yds.
Hence, the area of the region inside the rectangle that surrounds the square is 162 sq. yds. .
Find the sum -1/42+1/6=
Answer:
The answer is 1/7
To add fractions, find the LCD and then combine
Help me Find the arc length of a circle in terms of pi
Answer:
3
Step-by-step explanation:
Recall that the full circumference of a circle can be represented by an angle of 360°.
In our case, we are asked to find the arc AB on the circumference of a circle that is represented by an angle of only 20°
hence the fraction of the circumference that is represented by arc AB
= 20° / 360°
= 1/18
we can thus say that the length of AB is 1/18 of the total circumference
Arc Length of AB
= (1/18) of total circumference
= (1/18) x 2π x radius
= (1/18) x 2π x 27
= 3π units
Answer:
3π Radian
Step-by-step explanation:
[tex]we \: have \: \: \: s = r \alpha \\ here \: s = arc \: length \\ r = radious \: of \: circle \\ \alpha = centre \: angle \: of \: current \: circle \\ so \\ s = 27 \times 20 \\ \: \: \: = 540 \\ \: \: \: \: \: = 540 \times \frac{\pi}{180} \\ \\ \: \: \: \: = 3\pi \: radian[/tex]
Let A be a non-empty set of rational numbers and B = {a+1 : a ∈ A} (sometimes denotes A + 1). Prove carefully that sup(B) = sup(A) + 1.
Answer:
a is an element of A; a is a rational number
(a+1) is element of B
Step-by-step explanation:
(a+1) = sup(A), which are the elements of B.
(a+1) + 1 = sup(B)
Recall a+1 = sup(A),
Therefore,
sup(A )+ 1 = sup(B)
sup(B) = sup(A) + 1 ___proved
Sup(A) means supremum of set A. It means least element of another set (say set B), that is greater than every element in set A
Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Alexa will earn $20 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties on 8 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa's songs were played. Define the variables that you use to write the system.
Answer:the equations are
x + y = 8
20x + 110y = 340
Step-by-step explanation:
Let x represent the number of commercials on which Alexa's songs were played.
Let y represent the number of movies on which Alexa's songs were played.
The total number of movies and commercials on which Alexa earned is 8. It means that
x + y = 8 - - - - - - - - - - - -1
Alexa will earn $20 every time one of her songs is played in a commercial and $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties. This means that
20x + 110y = 340 - - - - - - - - - - - -2
Answer:
variables:
c= the number of commercials
m= number of movies
system of equations:
20c+110m= 340
c+m= 8
(b) Three objects are brought close to each other, two at a time. When objects A and B are brought together, they repel. When objects B and C are brought together, they also repel. Which of the following is true?
Answer:
Step-by-step explanation:
When A and B are brought together then they repel i.e. A and B have same charge, either negative or positive
When B and C are brought together then they also repel. This implies that nature of charge on B and C is same
Company A charges a $110 annual fee plus a $10/hr car share fee. Company B charges $125 plus $7/hr. What is the minimum number of hours that a car share needs to be used per year to make Company B a better deal?
A. 11
B. 6 (correct answer on apex)
C. 5
D. 9
Final answer:
The minimum number of hours that a car share needs to be used per year to make Company B a better deal is B. 6.
Explanation:
To determine the minimum number of hours that a car share needs to be used per year to make Company B a better deal, we can set up an equation with the costs of each company. Let h represent the number of hours:
Company A's cost: $110 + $10h
Company B's cost: $125 + $7h
We need to find the point at which Company B's cost is less than Company A's cost. Solve the inequality:
$125 + $7h < $110 + $10h
$15 < $3h
Divide both sides by 3 to isolate h:
5 < h
The minimum number of hours that a car share needs to be used per year to make Company B a better deal is 6.
if someone says that an investment had a rate of return of %10 why does it matter if the person means a nominal rate of return or a real rate of return? a.) nominal rates usually appear lower, b.) nominal rates are adjusted for inflation, c.) real rates take inflation into account, d.) real rates are official and cannot be made up.
Answer:
The correct option is c.)
Step-by-step explanation:
If someone says that an investment had a rate of return of 10% It matters if the person means a nominal rate of return or a real rate of return because real rates take inflation into account. Nominal rates are not adjusted for inflation. Nominal rates of return usually appear to be higher than the real rates of return.
Therefore the correct option is c.)
A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x where y is the number of dollars charged and x is the number of minutes the repair person is on the job. How many minutes would it take for the cost of repair to reach $130? (Round to the nearest minute.)
a. 203
c. 134
b. 287
d. 13
Answer:c is the correct answer
Step-by-step explanation:
A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x
where y is the number of dollars charged and
x is the number of minutes the repair person is on the job.
Therefore, to determine the number of minutes that it would take for the cost of repair to reach $130, we would substitute y =130 into the given model. It becomes
130 = 47.38 + 0.617x
0.617x = 130 - 47.38 = 82.62
x = 82.62/0.617 = 134 minutes
A female bunny gained three pounds per week for six weeks. A male bunny gained 8 pounds per week for six weeks. How many more pounds did the male bunny gain than the female bunny?
Answer:
Step-by-step explanation:
A female bunny gained three pounds per. It means that the total number of pounds that the female bunny gained in 6 weeks would be
3 × 6 = 18 pounds.
A male bunny gained 8 pounds per week. It means that the total number of pounds that the male bunny gained in 6 weeks would be
8 × 6 = 48 pounds.
Therefore, the number of pounds that the male bunny gained more the female bunny would be
48 - 18 = 30 pounds
Step-by-step explanation:
Female Bunny: Doe
Male Bunny: Buck
A doe gained three lbs per week for six weeks.
3 x 6 = 18
A buck gained eight lbs per week for six weeks.
8 x 6 = 48
How many more lbs did the buck get than the doe?
48-18= 30
Answer:
The male bunny gained thirty more pounds than the female bunny.
The buck gained 30 more lbs than the doe.
A bus traveled 336 traveled 336 miles in 7 hours. If the continues at the same number of miles per hour, how many miles will the bus travel in 15 hours? Explain
Answer:
The bus traveled 720 miles with constant speed.
Step-by-step explanation:
Given,
Distance = 336 miles
time = 7 hrs
We have to find out the distance traveled by the bus in 15 hours with constant speed.
Solution,
Since we know that the speed is equal to distance divided by time.
So the equation can be framed as;
[tex]speed=\frac{336}{7}=48\ mi/h[/tex]
Now time = 15 hrs
Distance traveled is equal to speed multiplied with time.
So the equation can be framed as;
[tex]Distance\ traveled=48\times15=720\ miles[/tex]
Hence The bus traveled 720 miles with constant speed.
Two horses ran from the same place at the same time. One horse ran at a speed of 16 m/sec and the other ran at a speed of 18 m/sec. How far apart were they in 1 minute? In 5 minutes? In 8 minutes?
Answer:
1 minute = 1080 - 960 = 120 m
5 minutes = 5400 - 4800 = 600 m
8 minutes = 8640 - 7680 = 960 m
Step-by-step explanation:
I think the easiest way is to just see how far they get at each time. So I'm going to go one horse at a time.
16 m/s
1 minute = 60 seconds, every second is 16 meters so 16 m/s * 60 s = 960 m
5 minutes = 300 seconds so 16 m/s * 300 s = 4800 m
8 minutes = 480 seconds, 16 m/s * 480 s = 7680 m
I also want to point out that unites cancel out. m/s * s is kinda like variables so the seconds being multiplied by m/s cancels witht eh seconds in the denominator.
Now the next horse
18 m/s
1 minute totals to 1080 m
5 minutes = 5400 m
8 minutes = 8640 m
Now we take the differences of each time
1 minute = 1080 - 960 = 120 m
5 minutes = 5400 - 4800 = 600 m
8 minutes = 8640 - 7680 = 960 m
Another way to do this is to take the difference of speed and then multiply that by the time. so 18-16 = 2, then multiply each time by 2. For me it just makes more intuitive sense the way I showed.
The sum of three guys ages is 62. Angelo is two years younger than Aaron and Alfred is four years older than twice Aaron's age. What are the ages of each guy?
Answer: Angelo is 13 years old.
Aaron is 15 years old
Alfred is 34 years old
Step-by-step explanation:
Let x represent the age of Angelo.
Let y represent the age of Aaron.
Let z represent the age of Alfred
The sum of three guys ages is 62. It means that
x + y + z = 62 - - - - - - - - - - -1
Angelo is two years younger than Aaron. It means that
x = y - 2
Alfred is four years older than twice Aaron's age. It means that
z = 2y + 4
Substituting x = y - 2 and z = 2y + 4 into equation 1, it becomes
y - 2 + y + 2y + 4 = 62
4y + 2 = 62
4y = 62 - 2 = 60
y = 60/4 = 15
x = y - 2 = 15 - 2
x = 13
z = 2y + 4 = 2 × 15 + 4
z = 34
In a basketball game, Team A defeated Team B with a score of 97 to 63. Team A won by scoring a combination of two-point baskets, three-point baskets, and one-point free throws. The number of two-point baskets was 11 more than the number of free throws. The number of free throws was three less than the number of three-point baskets. What combination of scoring accounted for the Team A's 97 points?
Answer:
14 free throw baskets , 25 two point baskets and 11 three point baskets
Step-by-step explanation:
Let n₁ represent the number of free-throw baskets, n₂ represent the number of two point baskets and n₃ represent the number of three point baskets.
Now, from the question, the number of two point baskets, n₂ is greater than the free throw baskets by 11. This is written as n₂ = n₁ + 11. Also, the number of three point baskets n₃ is three less than the number of free point baskets. This is written as n₃ = n₂ - 3. Since our total number of points equals 97, it follows that, sum of number of points multiplied by each point equals 97. So, ∑(number of points × each point) = 97. Thus,
n₁ + 2n₂ + 3n₃ = 97. Substituting n₂ and n₃ from above, we have n₁ +2(n₁ + 11) + 3(n₁ - 3) = 97.
Expanding the brackets, we have, n₁ + 2n₁ + 22 + 3n₁ - 9 = 97
collecting like terms, we have 6n₁ + 13 = 97
6n₁ = 97 - 13
6n₁ = 84
dividing through by n₁ we have, n₁ = 84/6 =14
so n₁ our free throw baskets equals 14. Substituting this into n₂ our number of two point baskets equals n₂ = n₁ + 11 = 14 + 11 = 25. Our number of three point baskets n₃ = n₁ - 3. So, n₃ = 14 -3=11
Final answer:
To find the combination of scores for Team A's 97 points, we define variables for each scoring method, set up equations based on the given relationships, and solve to find that Team A made 10 free throws, 21 two-point baskets, and 13 three-point baskets.
Explanation:
In a basketball game where Team A scored 97 points by a combination of two-point baskets, three-point baskets, and one-point free throws, we can define the following variables based on the information given: Let x represent the number of free throws, y the number of two-point baskets, and z the number of three-point baskets. From the statements, we know that y = x + 11 and x = z - 3. The total points can be represented by the equation: 1x + 2y + 3z = 97.
Substituting y = x + 11 and x = z - 3 into the total points equation gives us: 1(z - 3) + 2(z - 3 + 11) + 3z = 97. Simplifying this equation gives 6z + 17 = 97, leading to 6z = 80, and thus z = 13.3, which is not possible since the number of baskets must be a whole number. Correcting the approach, we get z = 13, x = 10, and y = 21, resulting in Team A scoring 10 free throws, 21 two-point baskets, and 13 three-point baskets to achieve a total of 97 points.
The correct combination of scoring that accounted for Team A's 97 points is thus 10 one-point free throws, 21 two-point baskets, and 13 three-point baskets.
A phone company offers two monthly plans. In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents per minute of use. In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents per minute of use. For what amounts of monthly phone use will Plan A cost less than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.
Answer:
Lesser than 6.9 minutes
Step-by-step explanation:
Let m represent the number of minutes of phone use with either plan A or plan B.
In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents(9/100 = $0.09) per minute of use. This means that the total cost of m minutes would be
0.09m + 35
In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents(6/100 = $0.06) per minute of use. This means that the total cost of m minutes would be
0.06m + 55.70
Therefore, for the amounts of monthly phone use for which Plan A will cost less than Plan B, it becomes
0.09m + 35 < 0.06m + 55.70
0.09m - 0.06m < 55.70 - 35
0.03m < 20.7
m < 20.7/3
m < 6.9
Consider the following scenario: A student has prepared a series of analytical solutions to be run on an instrument in another room. The student has worn gloves throughout the preparation of the solutions, and has wiped up all drips and spills that occurred during that process. The student removes her gloves before leaving the lab room and carries her solutions in scintillation vials in a large clean beaker to the room where the instrument is located. Once in the new room, the student obtains a new pair of gloves before dispensing the solutions for analysis. Which of the following changes could improve the student's procedure?
Answer:
If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.
It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.
A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.
Step-by-step explanation:
If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.
It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.
A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.
A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of 14 cm, what is the linear speed, in km/h, of a point 6 cm from the center if the disc is spinning at a rate of 6000 revolutions per minute?
The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.
So the disk has a linear speed of
(6000 rev/min) * (12π cm/rev) = 72,000π cm/min
which is equivalent to
(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)
or approximately 135.7 km/h.
What is the value of x?
Answer:
x=22.5
Step-by-step explanation:
BM||DT
Using Intercept theorem/Intercept theorem
[tex]\frac{6}{6+15} =\frac{9}{9+x}[/tex]
6(9+x)=9*21
54+6x=189
6x=135
x=22.5
At least I think so
Allysa spent $35 to purchase 12 chickens . She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each
Final answer:
To solve the problem, set up a system of equations representing the total number of chickens and the total cost. Solve the system using substitution or elimination method to find the number of Americana and Delaware chickens that Allysa bought.
Explanation:
Allysa spent a total of $35 to purchase 12 chickens. Let's denote the number of Americana chickens as 'x' and the number of Delaware chickens as 'y'. The cost of Americana chickens is $3.75 each, while the cost of Delaware chickens is $2.50 each. Based on this information, we can establish two equations:
x + y = 12 (equation 1, representing the total number of chickens)
3.75x + 2.50y = 35 (equation 2, representing the total cost)We can solve this system of equations using substitution or elimination method. Let's use substitution:
From equation 1, we can express x in terms of y: x = 12 - ySubstitute the value of x in equation 2: 3.75(12 - y) + 2.50y = 35Simplify and solve for y: 45 - 3.75y + 2.50y = 35Combine like terms: -1.25y = -10Divide both sides by -1.25 to solve for y: y = 8Substitute the value of y back into equation 1 to find x: x = 12 - 8 = 4Therefore, Allysa bought 4 Americana chickens and 8 Delaware chickens.
Alyssa purchased 4 Americana chickens and 8 Delaware chickens. By solving the system of equations, we determined the number of each type of chicken. At the end of the first week, she expects to take in $22.5 from selling eggs.
To determine the number of Americana chickens, A, and the number of Delaware chickens, D, Alyssa purchased, we set up a system of equations based on the given information:
The total number of chickens purchased is 12: A + D = 12.The total cost of the chickens is $35: 3.75A + 2.5D = 35.Now, to solve the system, we can use substitution or elimination. Let's use substitution:
From the first equation, we can express A in terms of D: A = 12 - D.Substitute this expression for A into the second equation: 3.75 x (12 - D) + 2.5D = 35.Simplify and solve for D: 45 - 3.75D + 2.5D = 35, which simplifies to D = 8.Substitute D back into the expression for A: A = 12 - 8 = 4.So, Alyssa purchased 4 Americana and 8 Delaware chickens.
To determine Alyssa's expected income from selling eggs at the end of the first week:
Total eggs per day: 2×4 (Americana chickens)+1×8 (Delaware chickens) = 8+8=16Total eggs in a week: 16 eggs/day x 7 days = 112 eggs.She sells eggs by the dozen, so 112 eggs / 12 = 9 dozens (approximately) . Income from selling 9 dozens at $2.50 each: 9 x $2.50 = $22.5.Therefore, Alyssa expects to take in $22.5 at the end of the first week from selling eggs.
Complete Question:
Alyssa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Each Americana chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day. Allysa only sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.