A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at 23 m/s . The third piece has twice the mass as the other two.

Answer:

C 5/7

Step-by-step explanation:

you have to split the 5 oranges between the 7 brothers, so you would do 5/7

5 split between 7 is the same as 5/7

Answer:5/7

Step-by-step explanation:

If you take each orange and cut them into 7 pieces then you could pass out one piece of each 1/7 of the oranges to each brother. You would do this 5 times until each brother had 5/7 and all the oranges would be passed out to the brothers.

Answer:

heres your answers

Step-by-step explanation:

George Washington  was defeated  when he went to fight the French in the Ohio River Valley.

The British then sent a trained army to attack the French Fort Duquesne.

The British suffered a defeat in the first battle of the French Indian War.

Answer:

Mathematical modeling

Step-by-step explanation:

Mathematical modeling is defined as translating the problems from an application area using the mathematical formulas.

The numerical analysis and theoretical analysis gives an insight and answers or guidance which is useful for the originating application.

It provides with the precision and direction for the solution of the problem.

Answer:

The answer to your question is a) y = x - 1  b) the point is not on the line

Step-by-step explanation:

Data

A ( -1, -2)

B (4, 3)

C ( 3, 1)

Process

1.- Find the slope of the line (m)

Formula

 m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Substitution

m = [tex]\frac{3 + 2}{4 + 1} = \frac{5}{5} = 1[/tex]

2.- Find the equation of the line

Formula

    y - y1 = m(x - x1)

Substitution

    y + 2 = 1(x + 1)

Solve for y

   y = x + 1 - 2

   y = x - 1

- Prove that the point (3, 1) is on the line

  1 = 3 - 1

  1 = 2

The point is not on the line because  1 ≠ 2

Answer:$78

Step-by-step explanation:

The two events,i.e request for full fare and the request for discounted fare ar mutually exclusive ,i.e if one happens the other cannot and vice versa .

The representation via set diagram will show a disjointed subset while P(AnB)^° is 1- (P(A)+P(B))=0.1.

Where A is the probability of full fare request while B is the probability of discounted request.

Probability (AUB)=P(A)+ P(B)=0.5×100+0.4×70=78.

Answer:

4.41 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a man flies a kite at a height of 16 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. We are asked to find how fast must he let out the string when the kite is flying on 34 ft. of string.

We will use Pythagoras theorem to solve for the length of side x as:

[tex]x^2+16^2=34^2[/tex]

[tex]x^2=34^2-16^2[/tex]

[tex]x^2=900\\\\x=30[/tex]

Now, we will use Pythagorean theorem to relate x and y because we know that the vertical side (16) is always constant.

[tex]x^2+16^2=y^2[/tex]

Let us find derivative of our equation with respect to time (t) using power rule and chain rule as:

[tex]2x\cdot \frac{dx}{dt}+0=2y\cdot \frac{dy}{dt}[/tex]

We have been given that [tex]\frac{dx}{dt}=5[/tex] , [tex]y=34[/tex] and [tex]x=30[/tex].

[tex]2(30)\cdot 5=2(34)\cdot \frac{dy}{dt}[/tex]

[tex]300=68\cdot \frac{dy}{dt}[/tex]

[tex]\frac{dy}{dt}=\frac{300}{68}[/tex]

[tex]\frac{dy}{dt}=4.4117647058823529[/tex]

[tex]\frac{dy}{dt}\approx 4.41[/tex]

Therefore, the man must let out the string at a rate of 4.41 feet per second.

Answer:

a) 0.54

Step-by-step explanation:

The correlation coefficient can be found by taking square root of R-squared value and the sign of correlation coefficient can be assessed by considering the sign of slope value. So,

r²=28.8%=28.8/100=0.288

r=[tex]\sqrt{r^{2} }[/tex]=[tex]\sqrt{0.288}[/tex]=0.5367

By rounding to two decimal places the correlation coefficient

r=0.54

We can see that slope=0.4845 has positive sign so, the correlation coefficient contains the positive sign.

Hence the correlation coefficient r=0.54.

The dimension of pen is 42 feet by 36 feet

Solution:

Let "x" be the width of pen

Let "y" be the length

Farmer wants each side of the pen to be at least 20 feet long

[tex]x\geq 20[/tex]

The farmer has 120 feet of fence to enclose an area of 1512 square feet

The amount of fencing is equal to the perimeter of fence which is 2 times the width plus only one length since the other side (length) is along the barn

2x + y = 120

Therefore,

y = 120 - 2x

The area of barn is given as 1512 square feet

The area of rectangle is given as:

[tex]Area = length \times width[/tex]

[tex]1512 = x \times y\\\\1512 = x \times (120-2x)\\\\1512 = 120x - 2x^2\\\\2x^2-120x + 1512 = 0[/tex]

Divide the entire equation by 2

[tex]x^2-60x + 756 = 0[/tex]

Factor the left side of equation

[tex]x^2-60x+756 = 0\\\\(x-18)(x-42) = 0[/tex]

Therefore, we get two values of "x"

x = 18 or x = 42

Since, [tex]x\geq 20[/tex]

Therefore, x = 42 is the solution

Thus, width = x = 42 feet

Length = y = 120 - 2x

y = 120 - 2(42)

y = 120 - 84

y = 36

Thus the dimension of pen is 42 feet by 36 feet

The area of a shape is the amount of space it occupies.

The dimension of the pen is 42 by 36 feet.

The perimeter is given as:

[tex]\mathbf{P = 120}[/tex]

Because one of the sides does not need fencing, the perimeter would be:

[tex]\mathbf{P = 2x + y}[/tex]

Make y the subject

[tex]\mathbf{y = P - 2x}[/tex]

Substitute 160 for P

[tex]\mathbf{y = 120 - 2x}[/tex]

The area of a pen is:

[tex]\mathbf{A = xy}[/tex]

Substitute [tex]\mathbf{y = 120 - 2x}[/tex]

[tex]\mathbf{A = x(120 -2x)}[/tex]

Substitute 1512 for Area

[tex]\mathbf{x(120 -2x) = 1512}[/tex]

Open brackets

[tex]\mathbf{120x -2x^2 = 1512}[/tex]

Rewrite as:

[tex]\mathbf{2x^2 -120x + 1512 = 0}[/tex]

Divide through by 2

[tex]\mathbf{x^2 -60x + 756 = 0}[/tex]

Expand

[tex]\mathbf{x^2 -18x - 42x + 756 = 0}[/tex]

Factorize

[tex]\mathbf{(x -18)(x - 42) = 0}[/tex]

Solve for x

[tex]\mathbf{x =18 \ or\ x = 42}[/tex]

The dimension must be at least 20.

So, we have:

[tex]\mathbf{x = 42}[/tex]

Recall that:

[tex]\mathbf{y = 120 - 2x}[/tex]

This gives:

[tex]\mathbf{y = 120 - 2 \times 42}[/tex]

[tex]\mathbf{y = 36}[/tex]

Hence, the dimension of the pen is 42 by 36 feet.

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Answer:

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one student ticket.

On the first day of ticket sales the school sold 24 adult tickets and 3 student tickets for a total of $223.00. This means that

24x + 3y = 223 - - - - - - - - - - - -1

The school took in $152 on the second day by selling 7 adult tickets and 6 student tickets. This means that

7x + 6y = 152 - - - - - - - - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 3, it becomes

144x + 18y = 1338

21x + 18y = 456

Subtracting, it becomes

123x = 882

x = 882/123

x = 7.17

Substituting x = 7.17 into equation 2, it becomes

7 × 7.17 + 6y = 152

50.19 + 6y = 152

6y = 152 - 50.19 = 101.81

y = 101.81/6 = 16.97

Question: John drove to a distant city in 5 hours.

When he returned, there was less traffic and the trip took only 3 hours.

If John averaged 26 mph faster on the return trip, how fast did he drive each way

Answer:

For the first trip he drove at a speed of 39 mph

For the second trip he drove at a speed of 65 mph

Step-by-step explanation:

Let the distance for both journey be Z because they are equal.

Let the speed for the first journey be X

Let the speed of the second journey be Y

Formula for speed = distance ÷ time

For the first journey the speed X = Z ÷ 5

For the second journey the speed Y = Z ÷ 3

Since John averaged 26 mph faster in the second trip than the first trip due to traffic, it means that the difference in speed between the first & second trip is 26 mph

Difference in speed = (Z÷3) - (Z÷5) = 26

subtracting both results to  (5Z-3Z) ÷ 15 = 26

Upon cross multiplication

2Z = 390

Z = 390÷2 = 195 miles

Therefore speed for first journey = 195 ÷ 5 = 39 mph

Speed for second journey = 195 ÷ 3 = 65 mph

To verify, 65 - 39 = 26 mph

Answer:

Russia gets 267 baseball cards in a year.

Step-by-step explanation:

Given:

Number of packs given per month = 2

Number of cards in each pack = 11

Number of cards given on his birthday = 3

Now, we know that, there are 12 months in a year.

Using unitary method, the total number of packs given in year and total cards can be calculated. So,

Packs given in 1 month = 2

∴ Packs given in 12 months = 2 × 12 = 24

Number of cards in 1 pack = 11

∴ Number of cards in 24 packs = 11 × 24 = 264

Now, his birthday will come once in a year. So, additional cards received by him will be 3 only. So,

Total number of cards = Number of cards in 24 packs + Additional cards

Total number of cards = 264 + 3 = 267

Therefore, Russia gets 267 baseball cards in a year.

The discount amount of exercise machine is $ 102

The sales price of machine is $ 748

Solution:

Given that,

Original price of machine is $ 850

Discount rate = 12 %

To find: discount amount and sales price of machine

Given that discount rate is 12 % , which means 12 % of original price of machine

Discount amount = 12 % of original price of machine

Discount amount = 12 % of 850

[tex]Discount\ Amount = 12 \% \times 850\\\\Discount\ Amount = \frac{12}{100} \times 850\\\\Discount\ Amount = 0.12 \times 850 = 102[/tex]

Thus the discount amount is $ 102

Sales price = Original price - Discount amount

[tex]Sales\ Price = 850 - 102\\\\Sales\ Price = 748[/tex]

Thus the sales price of machine is $ 748

Answer:

Option A) Whether or not a subject graduates high school      

Step-by-step explanation:

We are given the following experiment in the question:

Experiment:  if preschool attendance is associated with high school graduation for low-income students.

Independent variable: preschool attendance

The children were divided into two groups, one group will attend preschool program, the second group will not attend preschool.

The response variable is another term for dependent variable.

Here,

Dependent variable: whether or not children will graduate from high school.

Because this is dependent on the variable whether the child attends the preschool or not.

Option A) Whether or not a subject graduates high school

Final answer:

The response variable in the study is A) Whether or not a subject graduates high school. This measures the outcome of the treatment, which is preschool attendance for low-income children.

Explanation:

In this study, the response variable is the outcome that the researcher is trying to measure as a result of manipulating the experimental conditions. The experimental condition in this case is whether the child attends preschool or not. Hence, the response variable would be A) Whether or not a subject graduates high school. The preschool attendance (C) is the independent variable or treatment variable, as it is what the researcher manipulates and controls. The variables of the length of time it takes to graduate (B), and the income status of the children (D) are not the focus of the measurement for the direct effect of preschool attendance.

Low-income children have been observed to have various educational disadvantages compared to their wealthier peers, such as lower standardized test scores, lower graduation rates, and higher dropout rates. The study aims to investigate if attending preschool can help bridge the educational achievement gap that starts before children even enter formal schooling. By assigning low-income children randomly to either attend preschool or not, the researcher can control for other variables and focus on the impact of preschool attendance on high school graduation.

Answer:

Step-by-step explanation:

So 8 times more than 2/3

The total ascension of the swimmer can be calculated by multiplying the distance ascended each time by the number of ascents, resulting in 5 and 1/3 meters.

The total ascension of the swimmer can be calculated by multiplying the distance ascended each time by the number of ascents. In this case, the swimmer ascended 2/3 meters 8 times.

Total ascension = 2/3 meters * 8 ascents = 16/3 meters = 5 and 1/3 meters.

Therefore, the distance representing the swimmer's total ascension is 5 and 1/3 meters.

Answer:

a) Number of calories burned in [tex]x[/tex] hours of cycling [tex]600x[/tex] and Number of calories burned in [tex]y[/tex] hours of Swimming is [tex]400y[/tex].

b)The equation in general form that relates number of hours of cycling and swimming carols needs to perform to loose 5 pounds is [tex]6x+4y=160[/tex].

Step-by-step explanation:

Given:

5 pounds of body fat = 16000 calories

Number of calories burn in 1 hour of cycling = 600

Number of calories burn in 1 hour of swimming = 400

Part a:

We need to find number of calories will Carol burn in [tex]x[/tex] hours of cycling and number of calories will Carol burn in [tex]y[/tex] hours of swimming.

Solution:

Now we know that;

1 hr of cycling = 600 calories burned

[tex]x[/tex] hr of cycling = Number of calories burned in [tex]x[/tex] hours of cycling.

By using Unitary method we get;

Number of calories burned in [tex]x[/tex] hours of cycling = [tex]600x[/tex]

Also we know that;

1 hr of swimming= 400 calories burned

[tex]y[/tex] hr of swimming = Number of calories burned in [tex]y[/tex] hours of swimming.

By using Unitary method we get;

Number of calories burned in [tex]y[/tex] hours of Swimming = [tex]400y[/tex]

Hence Number of calories burned in [tex]x[/tex] hours of cycling [tex]600x[/tex] and Number of calories burned in [tex]y[/tex] hours of Swimming is [tex]400y[/tex]

Part b:

We need to write equation in general form that relates number of hours of cycling and swimming carols needs to perform to loose 5 pounds.

Solution:

Now given;

5 pounds = 16000 calories.

So we can say that;

Total number of calories to be burn is equal to sum of Number of calories burned in [tex]x[/tex] hours of cycling  and Number of calories burned in [tex]y[/tex] hours of Swimming.

framing in equation form we get;

[tex]600x+400y=16000[/tex]

Now dividing both side by 100 we get;

[tex]\frac{600x}{100}+\frac{400y}{100}=\frac{16000}{100}\\\\6x+4y=160[/tex]

Hence the equation in general form that relates number of hours of cycling and swimming carols needs to perform to loose 5 pounds is [tex]6x+4y=160[/tex].

Answer:

hi

Step-by-step explanation:

12 a 2 in box # 1

4-6a for box # 2

2a*2+8a box # 3

12a*2- 8 a box # 4

have a good day hope this helps

Answer:

The answer to your question is  below

Step-by-step explanation:

Remember that the greatest common factor of a set of numbers is the greatest factor common to all the numbers.

              Greatest common factor        Factor           Expression

                           2a²  + 8a                  2a(a + 4)                2a

                          12a² - 8a                 4a(3a - 2)                4a

                            4a + 8                     4(a + 2)                    4

                            4 - 6a                      2(2 - 3a)                  2

Answer:

275 people more attended the play on Saturday then on Friday.

Step-by-step explanation:

Given:

number of people attended play on Friday = 537

Number of people attended play on Saturday = 812.

We need to find how many people more attended the play Saturday then on Friday.

Solution:

Now we can say that;

To find Number of people more attended the play on Saturday then on Friday can be calculated by subtracting the number of people attended play on Friday from Number of people attended play on Saturday.

framing in equation form we get;

Number of people more attended = [tex]812-537 = 275[/tex]

Hence 275 people more attended the play on Saturday then on Friday.

t = 9 + s is the expression for number of pages in terry's essay

Solution:

Given that, Terry's essay has 9 more pages than stacey's essay

Let "s" be the number of pages in Stacey essay

Let "t" be the number of pages in terry essay

To find: Expression for the number of pages in terry's essay

From given statement,

Terry's essay has 9 more pages than stacey's essay

Which means, number of pages in terry essay is 9 more than number of pages in Stacey essay

Therefore,

Number of pages in terry essay = 9 + number of pages in Stacey essay

[tex]t = 9 + s[/tex]

Thus the expression for number of pages in terry's essay is found

Answer:

Step-by-step explanation:

A nickel is worth 5 cents. Converting to dollars, it becomes

5/100 = $0.05

A dime is worth 10 cents. Converting to dollars, it becomes

10/100 = $0.1

Let x represent the number if nickels.

Let y represent the number of dimes.

He has no more than 19 coins. This means that

x + y ≤ 19

He has no less than $1.30 combined. This means that

0.05x + 0.1y ≥ 1.3

If Nolan has 5 nickels, then, substituting x = 5 into x + y ≤ 19, it becomes

5 + y ≤ 19

y ≤ 19 - 5

y ≤ 14

substituting x = 5 into 0.05x + 0.1y ≥ 1.3, it becomes

0.05 × 5 + 0.1y ≥ 1.3

0.25 + 0.1y ≥ 1.3

0.1y ≥ 1.3 - 0.25

0.1y ≥ 1.05

y ≥ 1.05/0.1

y ≥ 10.5

Therefore, all possible values for the number of dimes that he could have would be

10.5 ≤ y ≤ 14

Answer:

[tex]y=4e^{-(x+1)}[/tex] will be the solutions.

Step-by-step explanation:

The given equation is [tex]y=C_{1}e^{x}+C_{2}e^{-x}[/tex]

Therefore, for x = -1

[tex]4=C_{1}e^{-1}+C_{2}e^{1}[/tex] ------(1)

Now y'(-1) = -4

y'(x) = [tex]C_{1}e^{x}-C_{2}e^{-x}[/tex] = -4

[tex]C_{1}e^{-1}-C_{2}e^{1}[/tex] = -4 -----(2)

By adding equation (1) and (2)

[tex]2C_{1}e^{-1}=0[/tex]

[tex]C_{1}=0[/tex]

From equation (1),

[tex]4=0+C_{2}e^{1}[/tex]

[tex]C_{2}=4e^{-1}[/tex]

By placing the values in the parent equation

y = [tex]4e^{-1}\times e^{-x}[/tex]

y = [tex]4e^{-(x+1)}[/tex]

Answer:

a) The probability is %55

b) The probability is %0.15

c) The probability is %9.15

d) The probability is %91.85

Step-by-step explanation:

a) We need to basically subtract probability of 0 type blood from 1:

P=1-0.45=0.55

b) The probability of one person that is having A blood type is %11. Then probability of four persons that are having A blood type will be:

(0.11)^4=0.00015

c) We need to approach to this question same as B. Probability of having not 0 type of blood is %55. Then probability of four persons that are not having 0 type of blood will be:

(0.55)^4=0.0915

d) To find the probability we can simply subtract probability of four persons that are having 0 type blood from 1:

1-0.0915=0.9185

Answer: the correct option is D

Step-by-step explanation:

Note: the chapter summary can be found in chapter 22 of the Pearson Education,Inc. (PDF format).

In the chapter, a single slit aperture diffraction and a circle aperture diffraction was discussed.

A circle aperture diffraction occurs when light pass through a tiny hole or aperture to produce a circular disc image. This disc is called Airy's disc.

To calculate the aperture diameter,d we can use the formula below;

d= m× λ/ sin θ. ------------------------------------------------------------------------------(1).

The single slit aperture diffraction is when light pass through a single slit to produce. The wavelength, λ is greater than the width of the aperture.

Answer: This relation is reflexive, antisymmetric and transitive so it is a partial order relation.

Step-by-step explanation: A relation is called a partial order relation if and only if it is reflexive, antisymmetric and transitive. We will check these three characteristics for the given relation.

Reflexive: We need to have that for all [tex]x\in\mathbb{N}[/tex], [tex]xRx[/tex]. This is obviously true since each prime factor of [tex]x[/tex] is certainly a factor of [tex]x[/tex].

Antisymmetric: We need to show that for all [tex]x,y\in\mathbb{N}[/tex] if both [tex]xRy[/tex] and [tex]yRx[/tex] then it must be [tex]x=y[/tex]. To show this suppose that two, otherwise arbitrary, natural numbers [tex]x[/tex] and [tex]y[/tex] are taken such that [tex]xRy[/tex] and [tex]yRx[/tex]. The first of these two says that every prime factor of [tex]x[/tex] is a factor of [tex]y[/tex]. The second one says that every prime factor of [tex]y[/tex] is a factor of [tex]x[/tex]. This means that every prime factor of [tex]x[/tex] is also the prime factor of [tex]y[/tex] and that every prime factor of [tex]y[/tex] is the prime factor of [tex]x[/tex] i.e. that [tex]x[/tex] and [tex]y[/tex] have the same prime factors meaning that they have to be equal.

Transitive: The relation is called transitive if from [tex]xRy[/tex] and [tex]yRz[/tex] then it must also be [tex]xRz[/tex]. To see that this is true of the given relation take some natural numbers [tex]x,y[/tex] and [tex]z[/tex] such that [tex]xRy[/tex] and [tex]yRz[/tex]. The first condition means that each prime factor of [tex]x[/tex] is the factor of [tex]y[/tex] i.e. that all the prime factors of [tex]x[/tex] are contained among the prime factors of [tex]y[/tex]. The second condition means that each prime factor of [tex]y[/tex] is a factor of [tex]z[/tex] i.e. that all the prime factors of [tex]y[/tex] are contained among the prime factors of [tex]z[/tex]. So we have that all of the prime factors of [tex]x[/tex] are contained among the prime factors of [tex]y[/tex] and they themselves are contained among the prime factors of [tex]z[/tex]. This means that certainly all of the prime factors of [tex]x[/tex] are contained among the prime factors of [tex]z[/tex] meaning by the given definition of [tex]R[/tex] that [tex]xRz[/tex] which is what we needed to show.

Answer:

0.0079 cm.

Step-by-step explanation:

We have been given that the last page of a book is numbered 764. The book is 3.0 cm thick, not including its covers.

We know that each page is marked on both sides, so we will find total number of pages by dividing 764 by 2 as:

[tex]\text{Total number of pages}=\frac{764}{2}[/tex]

[tex]\text{Total number of pages}=382[/tex]

To find the average thickness of each page, we will divide thickness of book by total number of pages as:

[tex]\text{Average thickness of each page}=\frac{3.0}{382}[/tex]

[tex]\text{Average thickness of each page}=0.0078534031413613[/tex]

We can see that there are 3 significant figures in 764 and 2 significant digits in 3.0.

We know that the result of a multiplication or division is rounded to the number of significant figures equal to the smallest number of significant figures among the numbers being multiplied/divided. So we need to round our answer to 2 significant digits.  

[tex]\text{Average thickness of each page}\approx 0.0079[/tex]  

Therefore, the average thickness of each page is approximately 0.0079 cm.

Answer:

34.8

Step-by-step explanation:

1. Convert percent to decimal

40.00/100=.4

2.Multiply decimal by subtotal

87*.4=34.8

Peter will save $34.80 on the coat.

Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is often denoted by the symbol "%".

If the coat is on sale for 40% off, Peter will only need to pay 60% of the original price.

60% of $87 can be calculated as follows:

= 60/100 x $87

= $52.20

Therefore, the amount that Peter will save on the coat is:

= $87 - $52.20

= $34.80

So, Peter will save $34.80 on the coat.

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416.67 pounds of food should be given all five lions each day

Solution:

Given that, three adult lions together eat 250 pounds of food a day

Thus, 3 adult lions = 250 pounds of food per day

Two more adult lions joined the group and ate food at the same rate as the original three

Now number of adult lions = 3 adult lions + 2 adult lions = 5 adult lions

Let "x" be the food ate by 5 adult lions

Thus we can say,

3 adult lions = 250 pounds of food per day

5 adult lions = "x" pounds of food per day

This forms a proportion and we can solve the sum by cross multiplying

[tex]\frac{3}{5} = \frac{250}{x}\\\\3 \times x = 250 \times 5\\\\3x = 1250\\\\x = 416.67[/tex]

Thus 416.67 pounds of food should be given all five lions each day

Answer:

Option 2) A binomial variable with 25 independent trials                  

Step-by-step explanation:

We are given the following in the question:

Sample size = n

R: the number of people from the sample who answer yes to the question whether they have read a novel in the past year.

[tex]var(R) = 6[/tex]

[tex]p =0.40[/tex]

Then, the random variable R follows a binomial distribution:

[tex]var(R) = npq\\6 = n(0.4)(1-0.4)\\\\n = \dfrac{6}{0.4\times 0.6}\\\\n = 25[/tex]

Thus, R is a binomial variable with 25 independent trials.

Answer:

A binomial variable with 25 independent trials

Answer:

Harry had $90 and Kayla had $120 at the beginning.

Step-by-step explanation:

Given:

Initial amount of Harry's money = 75% of Kayla's initial amount.

Harry earned $30 and Kayla earned 25% more.

Harry's final amount = 80% of Kayla's final amount.

Let the initial amount of Kayla be 'x'.

As per question:

Initial amount of Harry's money = 75% of Kayla's initial amount.

Initial amount of Harry's money = 75% of [tex]x[/tex]

Initial amount of Harry's money = [tex]0.75x[/tex]

Now, Harry earned $30 more. So, total amount of Harry is given as:

Final amount of Harry's money = [tex]0.75x+30[/tex]

Kayla also earned 25% more of her money. So, final amount of Kayla's money is given as:

Kayla's final amount = [tex]x+25\%\ of\ x=x+0.25x=1.25x[/tex]

Now, again as per question:

Harry's final amount = 80% of Kayla's final amount.

[tex]0.75x+30=0.80\times 1.25x[/tex]

[tex]0.75x+30=1x[/tex]

[tex]1x-0.75x=30[/tex]

[tex]0.25x=30[/tex]

[tex]x=\frac{30}{0.25}=\$120[/tex]

Therefore, initial money Kayla had = $120

Initial money Harry had = [tex]0.75x=0.75\times 120=\$90[/tex]

Hence, Harry had $90 and Kayla had $120 at the beginning.

Answer:

Italian style = 19,000 packages

French style = 13,000 packages

Oriental style = 53,000 packages

Step-by-step explanation:

let the number of packages of Italian style = x

let the number of packages of French style = y

let the number of packages of Oriental style = z

See the attached table which summarize the problem

Using the table we can get the following system of equations:

0.4x + 0 * y + 0.2z = 18,200

0.3x + 0.5y + 0.3z = 28,100

0.3x + 0.5y + 0.5z = 38,700

Solving the 3 equations together to find x , y and z

Using the calculator

x = 19,000

y = 13,000

z = 53,000

To find the point at which the total cost of rental is the same for both companies, set the cost functions C(m) and T(m) equal to each other and solve for m. In this case, the car needs to be driven approximately 273 miles.

To determine the number of miles, m, that a car needs to be driven in a day to equal the total cost at both rental companies, we need to find when C(m) is equal to T(m).

C(m) = $41 + $0.10m

T(m) = $0.25m

Setting these two equations equal to each other gives the equation $41 + $0.10m = $0.25m. Solve this equation to find the value of m.

Subtract $0.10m from both sides, leaving: $41 = $0.15m. Next, divide both sides by $0.15 to obtain the value of m, which is m = $41/$0.15 = 273.33. Therefore, the car needs to be driven approximately 273 miles for the rental cost to be the same at both companies.

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