Opportunity cost and production possibilities
Shen is a talented artist who sells hand-crafted goods on his website. Shen currently crafts and sells both crochet hats and baskets. He spends 8 hours
a day working on crafts. The following table gives different daily output scenarios depending on how much of his time is spent on each good.

Answers

Answer 1

Answer:

I'm not understanding can you say it in a similar way?

Answer 2

Answer:

Step-by-step explanation:

Opportunity cost and production possibilities

Shen is a talented artist who sells hand-crafted goods on his website. Shen currently crafts and sells both crochet hats and baskets. He spends 8 hours

a day working on crafts. The following table gives different daily output scenarios depending on how much of his time is spent on each good


Related Questions

Jada invested $200 in an account that earns compound interest annually.
Which equations could be used to model the amount of money that Jada would have in the account after x years?
Part A
Select the two that apply.
a: y=200-(1-0.03)
b: y=200-(1+0. 03)²
c: y = 0.03-200³
d: y=200-1.03²
e: y = (1 + 0.03) - 200³
D

Part B
(1 point)
Use your equation from Part A to determine how much money Jada would have in her account after 36 months?
Enter your answer and your work or explanation in the space provided.

Answers

The equation used to model the amount of money that Jada would have in the account after x years is [tex]y= 200(1 + {0.03})^{x}[/tex].

Jada would have in her account $218 after 36 months. The solution has been obtained by using the concept of compound interest.

What is compound interest?

When interest is calculated, it is done so using both the principal and the interest that has accumulated over the preceding period. Unlike simple interest, which does not take the principal into account when computing the interest for the following month, compound interest takes the principal into account. Compound interest is commonly represented by the letter C.I. in mathematics.

We know that formula for compound interest is

[tex]A= P(1 + \frac{r}{n} )^{nt}[/tex]

So, here A= y, P = $200 , n=1 and t=x and r = 0.03

Thus, we get

[tex]y= 200(1 + \frac{0.03}{1} )^{x}[/tex]

[tex]y= 200(1 + {0.03})^{x}[/tex]

So, the second equation is the correct one.

The amount of money Jada would have after 36 months means the amount after 3 years.

So, x=3

Putting this in the equation, we get

[tex]y= 200(1 + {0.03})^{3}[/tex]

y = 200 (1.09)

y = $218

Hence, the equation used to model the amount of money that Jada would have in the account after x years is [tex]y= 200(1 + {0.03})^{x}[/tex] and Jada would have in her account $218 after 36 months.

Learn more about compound interest from the given link

https://brainly.com/question/24274034

#SPJ1

A spherical balloon is expanding at the rate of 60 pie in^3/sec. How fast is the surface area of the balloon expanding when the radius of the balloon is 4 inches?

Answers

30 is the fast surface area of the balloon expanding when the radius of the balloon is 4 inches

Now, According to the question:

A spherical balloon is expanding at the rate of 60 pie cubic inches /sec.

The radius of the balloon is 4 inches.

Now, Solving the problem:

By using formula:

The formula for the volume of a sphere is V = 4/3 π r³,

where V = volume and r = radius.

Volume = [tex]\frac{4}{3}\pi r^3[/tex]

We have that:

Differentiate the formula:

[tex]\frac{dV}{dt}=4\pi r^2.\frac{dr}{dt}= 60[/tex]

=> [tex]\frac{dr}{dt}=\frac{60}{4\pi r^2}[/tex]

We know that [tex]A=4\pi r^2,[/tex] and so we also have

[tex]\frac{dA}{dt}=8\pi r.\frac{dr}{dt}[/tex]

Plug in what we found for dr/dt and plug in r=4 to get:

[tex]\frac{dA}{dt}=8\pi r.\frac{60}{4\pi r^2}[/tex]

[tex]\frac{dA}{dt}=\frac{120}{r}=\frac{120}{4}[/tex]

[tex]\frac{dA}{dt}=30[/tex]

Learn more about Volume of sphere at:

https://brainly.com/question/9994313

#SPJ4

Explain why [tex]\sqrt{7^3}[/tex] must be equal to [tex]7^\frac{3}{2}[/tex] if the Power of a Power Property is true for all rational exponents.

Answers

 (√7)^3  is equal to 7^(3/2)

The Power of a Power Property

The Power of a Power Property states that when you have a base raised to an exponent, and that base is also raised to an exponent, you can simplify the expression by multiplying the exponents.

For example, (a^x)^y = a^(xy)

In the case of square root of 7^3, the expression (√7)^3 can be written in the form of base and exponent, where the base is √7 and the exponent is 3.

Now, we can use the Power of a Power Property to simplify the expression, by multiplying the exponents.

So, (√7)^3 = (7^(1/2))^3 = 7^(1/2 * 3) = 7^(3/2)

This means that the square root of 7^3 is equal to 7^(3/2) because the Power of a Power Property allows us to simplify the expression by multiplying the exponents.

It's worth noting that the square root of 7^3 is the same as taking the cube root of 7^3, which is 7^(3/3) = 7^1 = 7.

Learn more on  Power of a Power Property

https://brainly.com/question/26480839

#SPJ1

On the plot shown, assume the horizontal axis represents x and the vertical axis represents y. At what value of x does the function y(x) have a value of zero and a positive derivative?

Answers

At x =6 the function has a positive slope.

A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable. At x = 2 and x = 6, the function y(x) is zero, and it has a value of 1 for all other values of x. the dependent variable. Functions are essential for building physical relationships in both math and science.

A function, which generates one output from a single input, is an illustration of a rule. origin of the image. An illustration of this is Y=X2.

But

At x = 2, the function starts to decline and has a negative slope. negative derivative

while

At x = 6, the function increases with a positive slope, producing a positive derivative.

To learn more about Function :

https://brainly.com/question/29120892

#SPJ4

Use synthetic division to show that x=-3 is a root of the polynomial function f(x)=x^3-4x+15

Answers

Answer:

Step-by-step explanation:

ans = x^2 - 3x + 5

Aaliyah and Yohance are having a competition to see who can read
more pages over the coming weekend. Aaliyah has bet Ms. Solomon that
she'll read 50 more pages than Yohance. Both scholars read at an
average rate of 40 pages per hour. Yohance says that he's going to read
for 7.5 hours this weekend. How many hours will Aaliyah need to read in
order to fulfill her promise of reading 50 more pages than Yohance?
50= 40

Answers

Mathematically, Aaliyah needs to read 8.75 hours (or 8 hours, 45 minutes) to fulfill her promise of reading 50 more pages than Yohance.

What are the mathematical operations?

The mathematical operations used to determine the hours that Aaliyah needs to read this weekend to meet her target include multiplication, addition, and division.

In the first instance, we must determine the total pages read by Yohance this weekend using multiplication as follows: 300 (7.5 x 40).

Secondly, the additional pages Aaliyah will read are added to Yohance's to show the total pages read by Aaliyah.

Lastly, the total pages are divided by Aaliyah's reading speed or rate to determine the hours she requires.

                                           Aaliyah    Yohance

Average pages per hour       40             40

Additional page                     50

Yohance weekend reading time = 7.5 hours

Total pages read by Yohance this weekend = 300 (7.5 x 40)

The total pages to be read by Aaliyah this weekend = 350 (300 + 50)

Aaliyah's total weekend reading time 8.75 hours (350/40)

Thus, for Aaliyah to read 50 more pages than Yohance, she needs 8.75 hours to fulfill her promise.

Learn more about mathematical operations at https://brainly.com/question/4721701

#SPJ1

During the month of September the animal shelter saved 80 animals. In the month of October, the animal shelter saw an increase of 15% of animals being saved from the previous month. How many animals were saved in the month of October?

Answers

Answer:  In the month of October, the animal shelter saved 92 animals.

Step-by-step explanation: In the month of October, the animal shelter saw an increase of 15% of animals being saved from the previous month. To calculate this increase, we can use the formula:

increase = (original number) x (percent increase)

In this case, the original number is 80 (the number of animals saved in September) and the percent increase is 15%. So:

increase = 80 x 0.15 = 12

This means that in October, the animal shelter saved an additional 12 animals beyond the 80 animals that were saved in September. To find the total number of animals saved in October, we add this increase to the original number:

animals saved in October = 80 + 12 = 92

So, in the month of October, the animal shelter saved 92 animals.

use ratio test to determine if the series converges

Answers

The series for this problem is absolutely convergent, as the limit assumes a value lower than 1.

What is the ratio test?

The infinite series for this problem is defined as follows:

[tex]\sum_{i = 1}^{\infty} \frac{1}{n!}[/tex]

Hence the general term is given as follows:

[tex]a_n = \frac{1}{n!}[/tex]

The limit is given as follows:

[tex]L = \lim_{n \rightarrow \infty} \left|\frac{a_{n + 1}}{a_n}\right|[/tex]

The (n + 1)th term is given as follows:

[tex]a_{n + 1} = \frac{1}{(n + 1)!}[/tex]

The factorial can be simplified as follows:

(n + 1)! = (n + 1) x n!.

Hence the limit will be calculated of:

1/[(n + 1) x n!] x n! = 1/(n + 1).

The result of the limit is given as follows:

[tex]L = \lim_{n \rightarrow \infty} \frac{1}{n + 1} = 0[/tex]

As the limit assumes a value of zero, the series is absolutely convergent.

More can be learned about the ratio test of convergence at https://brainly.com/question/14938047

#SPJ1

graphically solve x+y=3 and 3x-y=1​

Answers

I really don’t know and care

TEXT ANSWER
A dog weighs 45 pounds 12 ounces. How much does the dog weigh in kilograms?
If needed, round your answer to the nearest hundredth.
Conversion ratios:
1 lb = 16 oz
.

.
• 1 kg = 2.2 lb
Use the equation editor to show your work.

Answers

Answer:

20.80 kg

Step-by-step explanation:

45 lb + 12 oz = 45 lb + 12/16 lb = 45.75 lb

45.75 lb × (1 kg)/(2.2 lb) = 20.80 kg

Would you rather…
Five Seconds of Summer’s tutoring service charges a base charge of $5 and $5 per hour.
Fall Out Boy’s tutoring service charges a base fee of $9 and $3 per hour. Whose service
would you rather use?
Can you graph it and explain it on a table and the substitution method

Answers

Answer: Fall Out Boy's service is cheaper than Five Seconds of Summer's service.

Step-by-step explanation: The cost of Five Seconds of Summer's tutoring service can be represented by the equation:

C = 5 + 5h

where C is the total cost and h is the number of hours.

The cost of Fall Out Boy's tutoring service can be represented by the equation:

C = 9 + 3h

To compare the cost of the two services, we can use the substitution method. We can set the number of hours (h) equal to a variable and substitute that variable into the equation for both services.

For example, if we set h = 4 (4 hours of tutoring), we get:

C(Five Seconds of Summer) = 5 + 5(4) = 25

C(Fall Out Boy) = 9 + 3(4) = 21

The cost of Fall Out Boy's service is $21 and the cost of Five Seconds of Summer's service is $25. Therefore, Fall Out Boy's service is cheaper for 4 hours of tutoring.

We can also graph the cost of the two services on a coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x

Service | Equation

Five Seconds of Summer y = 5 + 5x

Fall Out Boy |                        y = 9 + 3x

Exercise 1: ABC is a triangle such that AB=5cm. A=50°and AC=5cm 1) Construct the triangle ABC. 2) What is the nature of the triangle ABC? Justity. 3) Calculate ABC and ACB. 4) Draw the height [AH) issued from A to [BC]. 5) a. Calculate BAH and CAH. b. What does [AH] represents for BAC? Justify.​

Answers

Answer:

2) Acute triangle, isosceles

3) Both are 65 degrees

4) (diagram)

5) a) both 25 degrees

b) midpoint

Step-by-step explanation:

2) If you're struggling search up "draw a triangle" and you'll find a website that will draw it for you. It will help you get an idea of it looks like and its nature.

3) We know that sides AB and AC are 5cm. So this triangle is an isosceles which makes the 2 remaining angles equal (if you draw a diagram it will be clear)

So:

180-50/2 = 65

ABC and ACB = 65 degrees each

4) Construct the line AH down the middle like in the diagram I drew.

5) a) Since AH is a straight line, we know that the angle AHB will be 90 degrees. After question 3 we also know that angle ABH is 65 degrees.

BAH = 180-90-65

BAH = 25 degrees

CAH = 50 - 25

CAH = 25 degrees

b) AH is the midpoint for BAC because the 2 segments formed are both 25 degrees.

specify the number of significant figures in each of the following numbers and determine the result of the following calculation to the correct number of significant figures. 3.115 0.2281 712.5 45

Answers

The result of the calculation is 680.

The number 3.115 has four significant figures, the number 0.2281 has four significant figures, the number 712.5 has three significant figures and the number 45 has two significant figures. This means that when performing calculations with these numbers, the answer must be rounded to the least number of significant figures, which is two.

The calculation is 3.115 + 0.2281 + 712.5 - 45. Using the rules of significant figures, we can calculate this as 3.1 + 0.2 + 713 - 45.

The result of the calculation is 675.3 and this must be rounded to the least number of significant figures, which is two. Therefore, the result of the calculation is 680.

Learn more about  significant figures here:

https://brainly.com/question/29153641

#SPJ4

Cual pesa menos marca con una x la casilla correspondiente ?

Answers

Las pesas de menor masa son listadas como sigue:

32 hectogramos 80 decigramos 9500 decigramos 90 gramos 5 kilogramos 8500 hectogramos

¿Cuál es la pesa de menor masa?

En esta pregunta tenemos seis casos de tres pesas, entre las cuales debemos determinar cuál tiene la menor masa. Esto implica el uso de la conversión entre unidades de masa a una única unica, tal que la pesa de menor capacidad será la de menor cantidad. El procedimiento se resume a continuación:

Convertir las masas a una única unidad.Elegir la masa de menor numeración.

Caso 1

32 hectogramos - 3200 gramos

4 kilogramos - 4000 gramos

500 decagramos - 5000 gramos

La pesa de 32 hectogramos reporta la menor masa.

Caso 2

35 gramos

4500 miligramos - 4.5 gramos

80 decigramos - 8 gramos

La pesa de 80 decigramos reporta la menor masa.

Caso 3

9500 decigramos - 950 gramos

6 kilogramos - 6000 gramos

70 hectogramos - 7000 gramos

La pesa de 9500 decigramos reporta la menor masa.

Caso 4

365 decigramos - 3650 gramos

90 gramos

30 decagramos - 300 gramos

La pesa de 90 gramos reporta la menor masa.

Case 5

75 hectogramos - 7500 gramos

5 kilogramos - 5000 gramos

6200 gramos

La pesa de 5 kilogramos reporta la menor masa.

Case 6

8500 hectogramos - 850000 gramos

30 kilogramos - 30000 gramos

900 decagramos - 9000 gramos

La pesa de 8500 hectogramos reporta la menor masa.

Para aprender más sobre unidades de masa: https://brainly.com/question/22075428

#SPJ1

Calculate the following, then convert your result to degrees, then give the quadrant of the terminal side.

Answers

The angles converted to degrees are: 615°, 165°, 112.5° with their respective quadrants of their terminal side as: 3rd, 2nd, and 2nd.

How to convert the angles from radian to degree

We simplify each angles of the angle in the radian to a single fraction and then convert them to degree by multiplying by 180°/π as follows:

11π/4 + 2π/3 = (33π + 8π)/12 {12 is the LCM of the denominators}

11π/4 + 2π/3 = 41π/12

11π/4 + 2π/3 = 41π/12 × 180°/π

11π/4 + 2π/3 = 615°

The terminal side of 615° is in the 3rd quadrant

π/6 - 5π/4 = (2π - 15π)/12 {12 is the LCM of the denominators}

π/6 - 5π/4 = -13π/12

π/6 - 5π/4 = -13π/12 × 180°/π

π/6 - 5π/4 = -195°

π/6 - 5π/4 = 165° {changing -195° to positive angle by adding 360°}

The terminal side of 165° is in the 2nd quadrant.

9π/8 - π/2 = (9π - 4π)/8 {8 is the LCM of the denominators}

9π/8 - π/2 = 5π/8

9π/8 - π/2 = 5π/8 × 180°/π

9π/8 - π/2 = 225°/2

9π/8 - π/2 = 112.5°

The terminal side of 112.5° is in the 2nd quadrant.

Therefore, the angles converted to degrees are: 615°, 165°, 112.5° with their respective quadrants of their terminal side as: 3rd, 2nd, and 2nd.

Know more about angles here:https://brainly.com/question/15866976

#SPJ1

6. A parabola has focus (-1, 6) and directrix y = 4. Determine whether each point on
the list is on this parabola. Explain your reasoning.
a. (-1,5)
b. (1,7)
c. (3,9)

Answers

Answer:a

Step-by-step explanation:

Sunny works at the library for three weeks longer than three over four of the school year a school year is 36 weeks long as son is college how many weeks in the school year did Sonny work at a library

Answers

Answer:

A school year is 36 weeks long, so 3/4 of the school year is 36 * (3/4) = 27 weeks.

If Sunny works at the library for three weeks longer than three over four of the school year, he works for 27 + 3 = 30 weeks.

So, Sunny works at the library for 30 weeks in the school year.

The number of weeks in the school year that Sonny worked at the library is; 30 weeks

How to solve Algebra Word problems?

We are told that Sunny works at the library for three weeks longer than three over four of the school year a school year is 36 weeks long.

Now, since he works three weeks longer than three over four of the school year, then the expression is;

³/₄(36) + 3

= 27 + 3

= 30 weeks

That figure represents the number of weeks in the school year that Sonny worked at the library.

Read more about Algebra word problems at; https://brainly.com/question/13818690

#SPJ1

when publishing their results, the researcher feels that it would be unethical not to include the raw data which they have used to support their findings. so the researcher publishes the findings of the study, including all the supporting data on all the study participants, in a well known journal.

Answers

The most clearly violated principle of ethical research in this scenario is individual information should be kept private, only summary results should be made public.

Ethical research requires that the privacy and confidentiality of study participants be protected. This is because the information collected from participants is often sensitive and personal, and the participants may have trusted the researcher to keep their information private.

In this scenario, the researcher has published the raw data, including personal information such as each participant's name, residence, and medical history, which could potentially compromise the privacy of the participants.

This is a clear violation of the principle of confidentiality, as the participants may not have agreed to have their personal information made publicly available.

It is important for researchers to be transparent and honest in their reporting of results, but they also have a responsibility to protect the privacy of their participants.

The publication of raw data, including personal information, should only be done with the explicit consent of the participants or under special circumstances where it is necessary for scientific advancement or the public good.

In conclusion, while the researcher's intention of being transparent in their reporting of results is commendable, the publication of the raw data, including personal information, is a clear violation of the principle of ethical research and could have serious consequences for the privacy and confidentiality of the study participants.

Hence, the correct answer is D.

To know more about Ethical research, here

https://brainly.com/question/5104690

#SPJ4

--The given question is incomplete; the complete question is

"A researcher collects various pieces of information from volunteers for a study into the health effects of drinking and smoking. The information collected includes each volunteer's name, residence, age, height, weight, medical history and their history of smoking cigarettes and drinking alcohol. All participants agreed to provide their information after the researcher explained how it would be used.

When publishing their results, the researcher feels that it would be unethical not to include the raw data which they have used to support their findings. So the researcher publishes the findings of the study, including all the supporting data on all the study participants, in a well-known journal.

The principle of ethical research most clearly violated (if any) is:

A. the researcher has falsified results

B. the researcher has failed to report negative results

C. no ethical principles have been violated; there was no informed consent

D. individual information should be kept private, only summary results should be made public"--

Question Help
Mr. Kent has 264 books on 4 shelves in his house. He has the same number of books on each shelf. To find the number of
books on each shelf, he divided 264 by 4. How many tens did he regroup as ones? How many books are on each shelf?
Mr. Kent regrouped
(Type whole numbers.)
tens as
ones.
CTTS

Answers

The number of tens that he regrouped as ones is equal to 2 tens.

The number of books that are on each shelf is equal to 66 books.

What is a quotient?

In Mathematics, a quotient simply refers to a mathematical expression that is typically used for the representation of the division of a number by another number.

Based on the information provided above, the number of books on each shelf is given by this quotient:

Quotient = 264/4

Quotient = 66

For the number of tens that Mr. Kent regrouped as ones on the shelf, we have the following:

26/4 = 24/4 + 2 = 2 tens.

Read more on quotient here: https://brainly.com/question/26133947

#SPJ1

please help asap its due today

Answers

Answer:

c < 10 = The bag contains fewer than 10 carrots.

c > 10 = Catherine biked farther than 10 miles.

c < 20 = The chair is shorter than 20 inches

c > 20 = Carlos scored over 20 points

which fraction on the number line is equal to 3?

Answers

Answer: 12/4

Step-by-step explanation: 12/4 = 3/1 = 3

Evaluate the expression by finding the absolute value.

|10| – |‐5| + |‐3|

Answers

The absolute value of the given expression is 8.

What is absolute value?

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Given that an expression |10| - |‐5| + |‐3| we need to find its absolute value,

|10| - |‐5| + |‐3|

= 10 - 5 + 3

= 5 + 3

= 8

Hence, the absolute value of the given expression is 8.

Learn more about absolute values, click;

https://brainly.com/question/1301718

#SPJ1

Henry pays $540.00 for one dozen collector’s edition baseball cards?

Answers

The cost of the one baseball card will be $45

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the cost of one dozen baseball cards is $540. The cost of one baseball card will be calculated by dividing the total cost by 12.

Cost = 540 / 12

Cost = $45

Hence, the cost of one card will be $45.

To know more about an expression follow

https://brainly.com/question/5994271

#SPJ1

tanya incorrectly says that the solution of the systems of equations is (-3, -2). what is the correct solution? 6g-3h=-3 7=h-5g

Answers

The correct solution to the system of equation is (-2, -3)

How to determine the correct solution

From the question, we have the following parameters that can be used in our computation:

6g-3h=-3

7=h-5g

Divide through 6g-3h=-3  by 3

so, we have

2g-h=-1

Make h the subject

h = 2g + 1

So, we have

7 = 2g + 1 - 5g

Evaluate the equation

-3g = 6

So, we have

g = -2

This becomes

h = 2 * -2 + 1

Evaluate

h = -3

Hence, the solution is (-2, -3)

Read more about system of equation at

https://brainly.com/question/13729904

#SPJ1

What is the end behavior for f(x)=x^5

Answers

The end behavior for f(x)=x^5 is as x approaches infinity, f(x) approaches infinity and as x approaches negative infinity, f(x) approaches negative infinity

How to determine the end behavior

From the question, we have the following parameters that can be used in our computation:

f(x) = x^5

Calculate f(oo) and f(-oo) i.e the function at infinity and negative infiniyt

So , we have

f(x) = (oo)^5 = +oo

f(x) = (-oo)^5 = -oo

This means that x increases with f(x)

Read more about end behaviour at

https://brainly.com/question/19319976

#SPJ1

In which quadrants do solutions for the inequality y is greater than one fifth times x plus 3 exist?

Answers

The solutions for the inequality "y is greater than one fifth times x plus 3" lies in both quadrant I and quadrant II.

What is a quadrant?

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate and y-coordinate of a cartesian coordinate.

Generally speaking, there are four (4) major quadrants in any graph and these include the following:

Quadrant IQuadrant IIQuadrant IIIQuadrant IV

y is greater than one fifth times x plus 3 ⇒ y > x/5 + 3.

Next, we would use an online graphing calculator to plot the given inequality. Therefore, the required solution is the shaded area above the dash line as shown in the graph attached below.

Read more on quadrant here: brainly.com/question/2551599

#SPJ1

How to solve
Er∆\54+7(54*6/7/∆)

Answers

Answer:

e

Step-by-step explanation:

e

Using the same situation you described in #3, now interpret what the part-to-part ratio 2:1 means in the situation. Use complete sentences in your answer.

#3 situation
A classroom has 50 people.
The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So, how many boys and girls are there?

The answer would be :
2x+3x=50
5x=50
x=
x=10
2x= 2×10=20
3x =3*10=30

20 girls and 30 boys.

Answers

There are 30 boys and 20 girls in the classroom.

How to determine the number of boys and girls?

Let the variable p represent the number of people. Next, we would translate the given word problem into an algebraic equation by using a ratio as follows;

Number of girls + Number of boys = Total number of people

2p + 3p = 50

5p = 50

Dividing both sides of the equation by 5, we have the following:

p = 50/5

p = 10 people.

For the number of girls, we have:

2g = 2(10)

2g = 20 girls.

For the number of boys, we have:

3g = 3(10)

3g = 30 boys.

Read more on ratio here: brainly.com/question/27817533

#SPJ1

Please help with writing linear functions

Answers

The function would be [tex]f(x)=\frac{1}{2}x + 1 \ and\ f(x)=\frac{1}{2}x - \frac{1}{2}[/tex]

What is linear function?

A linear function is one with one or two variables that does not have exponents. It is a function that has a straight line graph.

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. To find the equation of the linear function given the values of x and f(x), we can use two points and use the slope-intercept form of the equation.

A way to find the equation of the linear function is to use the point-slope form: f(x) = m(x-x1) + f(x1), where (x1,f(x1)) is a point on the line.

If we use the points (-4,-2) and (0,0) we can find the slope:

m = (0 - (-2)) / (0 - (-4)) = 2/4 = 1/2

then using point-slope form:

f(x) = 1/2(x - (-4)) + (-2)

f(x) = 1/2x + 1

so the equation of the linear function is f(x) = 1/2x + 1

Alternatively, we can use the two points (-2,-1) and (0,0) we can find the slope:

m = (0 - (-1)) / (0 - (-2)) = 1/2

then using point-slope form:

f(x) = 1/2(x - (-2)) + (-1)

f(x) = 1/2x - 1/2

so the equation of the linear function is f(x) = 1/2x - 1/2.

Therefore, equation f(x) = 1/2x+1 and f(x) = 1/2x - 1/2 represents the given values of x and f(x)

To know more about linear functions visit,

https://brainly.com/question/2248255

#SPJ1

PLS HELP answer these 5 questions! I need explanations and work! If you help me, you will get 50 points!! PLS HELP ASAP due TMR!!!

Answers

18) The expression with greater value are a and b. = 256  (19) the density of the object is X⁶ (20) The mass of the object is Y¹⁴  (21) The simplified expression is (3x)²  (22) Tobe uses the multiplication law for the exponent

How to solve the problems?

The given parameters are

18) (a)   2³ · 2⁵ Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

This implies 2³⁺⁵ = 2⁸ = 256

(b) (4)⁷/(4)³

Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

4⁷⁻³ = 4⁴ = 256

(19)  Mass = X¹⁵ grams

Volume = X³ cm₁

Density = Mass/Volume

= X¹⁵/X³³

X¹⁵⁻³ = X⁶

Density = X⁶

(20) Density = Y¹⁰ grams/cm³

Volume = Y⁴ cm³

Mass = Density*volume

Mass = Y¹⁰ · Y⁴

= Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

Y¹⁰⁺⁴

= Y¹⁴

(21) [ (3x)¹/³ · (3x)²/³)] / (3x)²/³

Using both multiplication and division laws of indices

(3x)²⁻¹

This is equal to  (3x)¹

(22) 8⁷· 8³ · 8²

Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

8⁷⁺³⁺² = 8¹²

Learn more about indices on https://brainly.com/question/28093573

#SPJ1

Other Questions
Which is the mRNA molecule that would be transcribed from this DNA template: TGG-CAA-GTA-CGT latanoprost drops are prescribed for the client with glaucoma. the client returns to the health care clinic for evaluation. which finding noted in the client indicates a side effect associated with the use of these eye drops In order for a fossil to be an index fossil, it has to have all of the following characteristics: ______________________. (Select all that apply)- Easy to identify- Abundant- Found in a small geographic area- Very rare- Appearing in a very short time frame- Covers a wide geographic area 6=7/w-3 solve for w?????? an organization is responsible to many different entities. in order to meet the demands of these groups, organizations must participate in stakeholder management. stakeholder management means that group of answer choices stakeholders and managers inevitably work at cross-purposes. interests of the stockholders are not the only interests that matter. all stakeholders receive financial rewards. stakeholders are second in importance to the stockholders. The Oedipus complex, the psychosexual conflict that occurs at the phallic stage of development, is characterized by a three- to five-year-old boy whoa. represses his need for genital self-stimulation.b. loves his mother but has feelings of anger and envy toward his father.c. loves his father but has feelings of anger and envy toward his mother.d. fantasizes about tragic Greek heroes. What are your top 3 priorities at work examples? Brian invests 7900 into his bank account. He receives 2. 3% per year compound interest. How much will Brian have after 5 years? Give your answer to the nearest penny where appropriate a 3-year-old boy has developed otitis media and requires antibiotics. in order to increase the chance that the boy will take his prescribed medication, the nurse should: DETERMINE MEANING How does Jefferson use the words necessary and convenient, and how doeshe refine the meanings of these words in this text? What was the effect on China of the Boxer RebellionChinas first Five-Year Plan called for the government totake money from industry and farming.seize private land and businesses.invest money in technology and education.privatize agriculture and businesses. Magnesium ribbon reacts with an aqueous solution of copper(ll) chloride in a single-replacement reaction. Which are the products of the balanced net ionic equation for the reaction? ethnocentrism is maintained and perpetuated by , which are overgeneralizations about the appearance, behavior, or other characteristics of members of particular categories. group of answer choices mores folkways stereotypes xenocentric attitudes Taylan i elling platic and wooden frame. He old 7 total frame. The number of platic frame Taylan old wa 5 le than twice the number of wooden frame. How many of each type of frame did Taylan ell? 2. When readers are introduced to Daisy Buchanan, she is described as reclining on a couch in the middle of a room where a breeze blows in from the windows, causing the cuttains and the women's dresses to flutter freely. How might Fitzgerald's description of this room contribute to his portrait of the main ferale character, Daisy Buchanan? How do literary devices like imagery and figurative language contribute to the characterization of Daisy? Finally, does Tom's act of shutting the windows reveal anything about how Tom's personality differs from Daisy personality? Is the following an example of intrinsic or extrinsic rewards? Joshua is an ICU nurse at a major hospital. Despite struggling with low staffing and increased nurse-to-patient ratios, Joshua feels positively about his work because he has wonderful coworkers and feels he is really making a difference in his patients' lives. Why do you think the Industrial Revolution led to so many advances in technology? Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations What epic convention is displayed in the following passage?"Sing to me of the man, muse..."divine interventioninvocationin medias resepithet The authors of "Excerpt from Gadgets: Built To Not Last" and "Dont Fix Your Fridge, Just Buy a New One" give advice to consumers. What advice does each author give? Which author is the most convincing? Use one detail from both the excerpt and the article to support your response. (total 2 details; one from each text)