solve the question
in a group of 65 students 40students want to be a doctor and 20 wants to be a social worker. the number of students who want to be a doctor only and the student who wants to be a social worker only are in the ratio 3:1 by drawing venn diagram find.
1)how many students want to both?
2)how many want to be both?​

When a ball is droped from 2m heights and rises by 75%, then the height of ball after forth bounce is equals to 0.632 meters.

If an object is thrown from high and has a bouncing feature, each bouncing is less than the initial height until it stops. Each bounce reduces the growth rate until it reaches zero. In order to calculate the height of each bounce, so we can estimate what percentage the object will reach after each bounce. If we get the percentage of each bounce, we can easily determine the height of each bounce. We have, a ball is droped from 2 meters and bounce up to 75%. That is height of first bounce is determined by using percentage, height is 2 m × 75% = 2 m×0.75 = 1.5 m

In second bounce, height is 1.5 m × 75%

= 1.5 m×0.75 = 1.12 m

In third bounce, 1.12 m× 75%

= 1.12 m×0.75 = 0.843 m

In forth bounce, height is 0.843× 75%

= 0.843× 0.75 = 0.632 m

The height the ball reaches on its forth bounce is 0.632 m.

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Complete question :

A ball is dropped from a height of 2 meters and rises up by 75% of its height on each bounce. How high would the forth bounce be?

Step-by-step explanation:

The velocity of the particle at a given value of θ can be found by taking the derivative of the position vector with respect to time:

v(θ) = dr/dt = dr/dθ * dθ/dt = dr/dθ * ω

where ω is the angular velocity and dr/dθ is the derivative of the position vector with respect to θ.

The position vector r = a * e^(b * θ) * i + a * b * e^(b * θ) * j

Taking the derivative with respect to θ:

dr/dθ = a * b * e^(b * θ) * i + a * b^2 * e^(b * θ) * j

So the velocity of the particle is given by:

v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * j

Answer:

Step-by-step explanation:

v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * jj

The system of equations for cost of company A and B is c = 40 + 2s and c = 40 + 4s respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The amount of videos streamed is = s

The cost of streaming each video is = c

The amount of money charged by company A as membership fee is = $40.

The amount of money charged by company A per video stream is = $2.

The equation for cost of company A will be -

c = 40 + 2s

The amount of money charged by company B as membership fee is = $40.

The amount of money charged by company B per video stream is = $4.

The equation for cost of company A will be -

c = 40 + 4s

Therefore, the equations are c = 40 + 2s and c = 40 + 4s.

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Video streaming company A charges a one-time $40 membership fee and $2 per video stream

Video streaming company B charges a one-time $20 membership fee and $4 per video stream.

Let the variable s represent the amount of videos streamed and let the variable c represent the cost

For how many video streams will the cost be the same for both companies?

Which system of equations can be used to solve this problem?

The value of x is 7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∠TUV = 9x + 1

∠TUW = 7x - 9

∠WUV = 5x - 11

Now,

∠TUV = ∠TUW + ∠WUV

Substituting the values.

9x + 1 = 7x - 9 + 5x - 11

Adding like terms.

9x + 1 = 12x - 20

1 + 20 = 12x - 9x

21 = 3x

Dividing 3 on both sides.

x = 21/3

x = 7

Thus,

x is 7.

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Answer: (−10)=2(+1)

Step-by-step explanation:

According to the mathematical calculations made, the results are as follows: the length of DF is 3.87 cm, the length of XF is 4.89 cm. The point 2cm from E is 5cm from X and the angle of D is 60°.

In this problem, we have to apply the Pythagorean theorem to find the lenght of DF line.

a² + b² = c²

7² + b² = 8²

49 + b² = 64

b² = 15

b = 3.87

In this problem, we have to apply the Pythagorean theorem to find the lenght of XF line.

a² + b² = c²

3² + 3.87² = c²

9 + 14.97 = c²

23.97 = c²

4.89 = c

According to the information of the graph we can conclude that the point 2cm from E is on the line EX, and it is located 2cm from E and 5cm from X.

We know that F has a angle less than D so we can infer that F has an angle of 30° and D has an angle of 60° which we can check with a compass.

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Answer: it's C

Step-by-step explanation:

Answer:D

Step-by-step explanation:

The answer choice that is the best measure of center for the data, and what is its value is D. The median is the best measure of center, and it equals 8.

A measure of center gives an idea of the central tendency of the data.

The median is a better choice here because it is not affected by extreme values, unlike the mean.

From the dots plotted on the line graph, it is evident that there are more data points around 8 than any other value. Hence, the median of the data would be closest to 8.

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Answer: The median is the best measure of center and it equals 8

Step-by-step explanation:have a good day!

Yes, television commercials are an effective way to promote a new product.

The survey organization conducted a telephone survey in December 2008 to gauge the effectiveness of television commercials in promoting new products among a sample of 1,009 randomly selected adults in the United States.

The survey asked the respondents whether they believed that television commercials were an effective way to promote a new product at the time of the survey. The results of the survey can provide insights into the public's perception of television commercials as a tool for promoting new products, as well as how this perception may have changed over time.

The findings can also be useful for marketers and advertisers who want to understand consumer attitudes toward television commercials and use this information to guide their advertising strategies. However, it's important to note that the results of this survey are limited to the specific time and population studied and may not be generalizable to other populations or time periods.

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The value of k from the equation is k = -20

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = kx   be equation (1)

Let the first point be P ( 4 , -80 )

Substituting the values in the equation , we get

-80 = 4k

Divide by 4 on both sides of the equation , we get

k = - ( 80/4 )

On simplifying the equation , we get

k = -20

Hence , the equation is k = -20

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Answer:

12/8 = 1.5 °C per hour

Step-by-step explanation:

basically write the change over time in a formula, calculate it and find the answer, using the answer u can say that:

over the course of 8 hrs, the temperature has been reducing by a rate of 1.5°C/hr. (link it to the context as well)

The simplified form of the expression is given by 4⁹/y³

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here : The exponents (4³/y)³

Simplifying we get

(4³/y)³

When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

4³ ˣ ³ / y³

4⁹/y³

Thus the simplified form of the expression is given by 4⁹/y³

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Answer: Depends

Step-by-step explanation: When solving a system using elimination, you may have to multiply both equations by a certain value in order to use the method. However, there are a few instances where you will only need to multiply one. This normally happens when there is a higher multiply representing x or y from one equation to another.

The measure of angle Y, according to the stated statement, is 55 degrees.

An adverb used to describe something which goes together with something else and improves or completes it is complimentary (as in complementary colors)

The total of two complimentary angles is 90 degrees. As a result, we have:

m∠S + m∠Y = 90

Substituting the given equation m∠S = 5(m∠Y) − 240°, we get:

5(m∠Y) − 240° + m∠Y = 90

By merging like variables in the equation, we can reduce it to:

6(m∠Y) - 240° = 90

Adding 240 to both sides, we get:

6(m∠Y) = 330

Dividing both sides by 6, we get:

m∠Y = 55

Therefore, the measure of angle Y is 55 degrees.

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Answer: I believe its 4.16 centimeters

Step-by-step explanation:

I do not have an explanation, but I hope the answer is correct.

Answer:

c = [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

First, expand the brackets by applying the Distributive Law:

[tex]= -8c + 8 = 3[/tex]

Then bring all the like terms together and isolate c. Move '3' to the left and '8c' to the right: of the equation:

[tex]= 8 - 3 = 8c[/tex]

= [tex]5 = 8c[/tex]

= [tex]c = \frac{5}{8}[/tex]

Answer:

Total number of paintbrushes

= 53 ÷ 25%

= 53 ÷ 0.25

= 212

Answer:

If 53 paintbrushes represent 25% of the total number of paintbrushes Daniel has, we can use the following formula to find the total:

total number of paintbrushes = (number of paintbrushes / percentage) x 100

Plugging in the values we know, we get:

total number of paintbrushes = (53 / 25) x 100

Simplifying, we get:

total number of paintbrushes = 212

Therefore, Daniel has a total of 212 paintbrushes in all.

Evaluating multiple companies before making an investment decision helps to make informed decisions, diversify your portfolio, and maximize returns.

It is critical to consider multiple companies before investing because:

Diversification reduces the risk of loss because the performance of one company does not determine the overall performance of your portfolio.

Opportunity Cost: Comparing and selecting the best investment options allows you to avoid missing out on potential higher returns by evaluating multiple companies.

Due Diligence: Investing in a company necessitates extensive research and due diligence. When you look at multiple companies, you can compare financial statements, management, products, and other factors that can affect stock performance.

Finally, evaluating multiple companies prior to making an investment decision allows you to make informed decisions, diversify your portfolio, and maximize returns.

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The equivalent value of the equation is n = 0.3

Given data ,

Let the equation be represented as A

Now , the value of A is

3.6 = 12n   be equation (1)

On simplifying , we get

Divide by 12 on both sides , we get

n = 3.6 / 12

On further simplification , we get

n = 0.3

Hence , the expression is n = 0.3

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The required equation in a system of equations that has a solution (4, −1) is given as y = -1/4x.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Let's assume that the equation passing through the origin and (4, -1)

The equation is given as,

(y₂ - y₁) /  (x₂ - x₁)

y - y₁ = (y₂ - y₁) /  (x₂ - x₁) (x - x₁)
y - 0 = -1 - 0 / 4 - 0 [x - 0]
y = -1/4x

Thus, the required other equation in a system of equations has a solution (4, −1) is given as y = -1/4x.

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3 3/2 hours as a decimal= 4.5

1 1/3 hours as a decimal = 1.3

Duration of the film show = 4.5 hours

Hours spent on advertisements = 1.3 hours

Actual duration of the film = 4.5 - 1.3 hours

= 3.2 hours

3.2 hours as a fraction = 3 1/5 hours.

Therefore, the actual duration of the film was 3 1/5 hours.

Movie lasted 3 hours and 10 minutes

[tex]3\frac{3}{2} - 1 \frac{1}{3} = \frac{9}{2} - \frac{4}{3} = \frac{27 - 8}{6} = \frac{19}{6} = 3 \: \frac{1}{6} [/tex]

The percent markup for the cost of shirt = 50%

Let us assume that the cost of each shirt be x dollars

A department store buys 300 shirts at a cost of $1,800.

Using unitary method the price of each shirt would be,

x = 1800/300

x = 6 dollars

A department store sells 300 shirts for $9 each.

So, Selling price of one shirt = $9

Price markup = Selling price - Cost price

                      = $9 - $6

                      = $3

The percent markup would be,

p = (Price markup / cost price) × 100

p = (3/6) × 100

p = 50%

Therefore, the percent markup = 50%

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The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equations are given below.

y = - 2x + 17           ...1

y = x - 7                 ...2

From equations 1 and 2, then we have

x - 7 = - 2x + 17

3x = 24

x = 8

Then the value of 'y' is given as,

y = 8 - 7

y = 1

The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

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Answer:

14

Step-by-step explanation:

formula

SQURED A+B=C

10+b =18

100+b=324

100-100 324-100

=224

squre root of 224

is 14

The possible values are -

(a²,b²) = p

(a²,b) = p if p|-r and (a²,b) = p² if p|r

(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r

What is gcd?

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Since (a, b) = p it can be written a = pr and b = ps where r and s are integers such that (r, s) = 1.

Then a² = p²r².

Then by Theorem 1.7, (a²,b) = (p²r²,ps) = p(pr²,s).

By Theorem 1.8, (r²,s) = 1 .

Thus, there are two cases to consider: if p|s then, (a²,b) = p², and if p|-s then (pr²,s) = 1 (Again by Theorem 1.8)  so that (a²,b) = p in that case.

Thus, there are two cases for (a²,b): namely p or p².

The same analysis shows that (a³,b) must be either p, p² or p³ depending on the power of p that divides b.

Analyze (a²,b³) as follows.

Using the notation already introduced, and

Theorem 1.7, it is obtained that (a²,b³) = (p²r²,p³s³) = p²(r²,ps³).

Since, (r, s) = 1, Theorem 1.8 shows that (r²,s³) = 1.

Therefore, there are two possibilities for (a²,b³) -

(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r.

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Answer:

Below

Step-by-step explanation:

To add or subtract fractions they must have a common denominator

  you can multiply them together to find A common denominator

   2 x 9 = 18

so now yo have to convert the fractions to 18ths

1/2 * 9/9    ( this is just multiplying by '1') = 9/18

5/9 * 2/2 = 10 / 18    

now 1/2 - 5/9  then equals  9/18 - 10/18 = (9-10)/18 = - 1/18

Answer:

Step-by-step explanation:

a. The equation of the line that describes the relationship between distance and time for Car X can be found by using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula: m = (change in y) / (change in x) = (distance traveled) / (time elapsed) = 174 miles / 3 hours = 58 miles per hour.

Since the car starts at time x = 0 and has traveled 174 miles at time x = 3, the y-intercept (b) can be found by setting x = 0 and solving for y: y = 58x + b, and y = 174 when x = 3, so b = 174 - 58(3) = -160.

Putting it all together, we get the equation: y = 58x - 160.

b. The graph that represents the relationship between distance and time for Car X is a line that passes through the point (0, -160) and has a slope of 58. This line represents the linear relationship between the distance traveled and the time elapsed for Car X.

The y-intercept of -160 represents the distance traveled when time is equal to 0. The slope of 58 represents the rate of change of the distance traveled with respect to time. This means that for every hour that passes, Car X travels 58 miles.

Answer:

4h^3 - 8h^2 + 17h + 3

Step-by-step explanation:

I put it into my calculator, let me know if that helped!

The distance across the lake is approximately 62.5 meters, rounded to the nearest hundredth of a meter.

To find the distance across the lake (BC), we can use the following formula based on triangle similarity:

BC/AD = DB/DE

Where BC is the distance across the lake, AD is the known direct measurement made by Dominic, DB is the known measurement from point B to the landmark, and DE is the known measurement from point D to the landmark.

Let's assume that AD = 100 meters, DB = 50 meters, and DE = 80 meters. Then we can calculate BC as follows:

BC = (BC/AD) * AD = (DB/DE) * AD

BC = (50/80) * 100

BC = 62.5 meters

So, the distance across the lake is approximately 62.5 meters, rounded to the nearest hundredth of a meter.

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