In a random sample of 200 students who were asked their favorite color, it
was found that twenty more students liked blue than purple and eight fewer
liked green than blue.

a. Write equations that represent this information.

Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

Learn more about rays from the given link

https://brainly.com/question/13144568

#SPJ11

Answer:

31. (25 - 8) x 3 = 51

32.  9 + 4 x (5 - 3) = 17

Step-by-step explanation:

grouping symbols

31.) 25 - 8 x 3 = 51

(25 - 8) x 3 = 51

Do the parentheses first

17 * 3 = 51

51=51

32.) 9 + 4 x 5 - 3 = 17

9 + 4 x (5 - 3) = 17

Parentheses first

9 + 4 * 2 = 17

Multiply

9+8 = 17

Add

17=17

Answer:

5

Step-by-step explanation:

7c³d²

This term has tow variables, c and d

Power of c is 3

Power of d is 2

Degree of this monomial is = 3+2 = 5

Answer:

2/9 + 5/36 = 17/36

So the probability of getting 2 marbles of the same color is 17/36 or 0.472.

Answer:

17/36

Step-by-step explanation:

In Step 1, he started with the given function f(x). Then, in Step 2, he changed f(x) to y. In Step 3, he switched x and y. In Step 4, he added something to each side. In Step 5, he multiplied each side by something. Finally, in Step 6, he replaced y with f⁽⁻¹⁾(x).

Let's go through each step in detail to explain Max's process of finding the inverse of function f:

Given

In this step, Max is given the original function f(x). This function could be any mathematical expression or equation.

Change to y

Max changes the notation of the function from f(x) to y. This is a common step when working with functions to make it easier to manipulate and find the inverse.

Switch x and y

Max swaps the variables x and y. This step is crucial in finding the inverse because it allows us to express the equation in terms of y, which represents the dependent variable, as opposed to x, which represents the independent variable.

Add to each side

In this step, Max adds something to each side of the equation. The exact value or expression added is not specified in your prompt, so it could be any constant or term. Adding the same value to both sides maintains the equality of the equation.

Multiply each side by

Here, Max multiplies each side of the equation by something. Similar to Step 4, the specific value or expression is not given, so it could be any constant or term. Multiplying both sides by the same value helps to simplify the equation further.

Replace y with f⁽⁻¹⁾(x)

In the final step, Max replaces the y variable with f⁽⁻¹⁾(x). This notation represents the inverse function of f, which is what Max is trying to find. By substituting y with f⁽⁻¹⁾(x), Max has successfully expressed the inverse function in terms of the original variable x.

To complete the statement using this information:

Max used these steps to find the inverse of function f. In Step 1, he started with the given function f(x). Then, in Step 2, he changed f(x) to y. In Step 3, he switched x and y. In Step 4, he added something to each side. In Step 5, he multiplied each side by something. Finally, in Step 6, he replaced y with f⁽⁻¹⁾(x).

Learn more about inverse of function here:

https://brainly.com/question/30350743

#SPJ11

The given probability of having six girls in a six-child family is 0.015625. To determine the method used to compute this probability, we need to analyze the information provided.

The Classical method is based on theoretical assumptions and probabilities calculated using mathematical principles. It assumes equally likely outcomes and relies on counting favorable outcomes over the total number of possible outcomes.

The Empirical method involves gathering data from observations or experiments to estimate probabilities. It relies on observed frequencies and relative frequencies to compute probabilities. However, the given probability does not suggest a sample or data collection, making it unlikely that the Empirical method was used.

The Subjective method involves assigning probabilities based on personal judgment or opinions. Individuals subjectively evaluate the likelihood of an event based on their own beliefs or knowledge.

To learn more about probability : brainly.com/question/31828911

#SPJ11

Answer:

Step-by-step explanation:

volume = πr²h = π·3²h = 63π

h = 7 cm

The height of the given cylinder is 7 cm. Therefore, option D is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the volume of a cylinder is 63π cm³ and the radius is 3 cm.

We know that, the formula to find the volume of a cylinder is πr²h.

Now, πr²h=63π

π×3²×h=63π

h= 7 cm

Therefore, option D is the correct answer.

To learn more about the volume visit:

https://brainly.com/question/13338592.

#SPJ5

The maximum area that the farmer can enclose for the rectangular garden is 488 sq ft and the dimensions of the rectangular garden are 24ft and 12 ft respectively.

It is given that a farmer decided to enclose a rectangular garden with one side using the barn of a tree and other 3 sides with 48 ft of fencing.

Let the length of the rectangle be y and the breadth of the rectangle be u.

So perimeter of the fencing needed = y + 2u (as one side is barn)

∴ y + 2u = 48

⇒ y = 48 - 2u (equation 1)

Area = yu (equation 2)

Putting the value of variable y from equation 1 in equation 2 we have,

Area = (48-2u)u

∴ Area = 48u - 2\(u^{2}\)

⇒ Area = -2\(u^{2}\) + 48u

⇒ Area = -2(\(u^{2}\) - 24u)

⇒ Area = -2(\(u^{2}\) - 24u + 144) + 288   (using completing the square method)

⇒ Area = -2\((u-12)^{2}\) + 288

So the maximum area is 288 sq units as for any value of u the area value will decrease as seen from the above equation.

So if Area = 288

Then yu = 288

⇒ u = 288/y equation 3

Putting this value in Perimeter equation 1 we have,

y = 48 - 2u

⇒ y = 48 - 2 x \(\frac{288}{y}\)

⇒ \(y^{2} = 48y - 576\)

⇒ \(y^{2} - 48y + 576 = 0\)

⇒ \((y-24)^{2}\) = 0

Solving we get y = 24 ft

Hence the value of u is calculated as follows:

⇒ u = 288 / y

⇒ u = 288/ 24 = 12 ft

The maximum area that the farmer can enclose is 488 sq ft and the dimensions of the rectangle are 24ft and 12 ft respectively.

To learn more about perimeter click here:

https://brainly.com/question/2142493

#SPJ4

Answer:

t=-28

Step-by-step explanation:

Answer:

17.2 feet

Step-by-step explanation:

The length of the ladder is 20.4 feet.

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Given that, the angle of elevation of the ladder is 73° when the bottom of the ladder is 15 feet from the side of the house.

Let the height of side of a house be x.

Now, tan73°=x/15

x/15=0.9192

x=0.9192×15

x=13.8 feet

Let the length of the ladder be y.

y²=15²+13.8²

y²=415.44

y=√415.44

y=20.4 feet

Therefore, the length of the ladder is 20.4 feet.

To learn more about the heights and distance visit:

brainly.com/question/24271007.

#SPJ5

Answer:

C=3.1

Step-by-step explanation:

9×7×3.1=195.3 cm cubed

Answer:

no it does not belong to the graph

Step-by-step explanation:

plug in the x-coordinate and see if it gives you the y-coordinate (1). if 1 is what comes out, then it is not a point on the graph.

y = -2(1/2)

y = -1

y = -1  when x = 1/2, which is not 1 so it does not belong to the graph

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

Visit to know more about Probability:-

brainly.com/question/13604758

#SPJ11

Answer:

The area will decrease by 9%.

Step-by-step explanation:

The area of a rectange is given by the formula below.

\(\boxed{\text{Area of rectangle}= \text{length}×\text{width}}\)

Let the original length and width of the rectangle be L and W respectively.

Start by finding the original area:

Original dimensions

Length= L= 100%L

Width= W= 100%W

Original area= LW

Let's find the dimensions of the new rectangle in terms of L and W.

New dimensions

Length= (100% +30%)L= 130%L

Width= (100%-30%)W= 70%W

New area

\( = \frac{130}{100} L \times \frac{70}{100} W\)

\( = \frac{91}{100} LW\)

= 91% LW

Comparing the new area with the original area:

100% LW- 91% LW= 9% LW

∴ The area will decrease by 9%.

*Note that percentage is equivalent to dividing a number by 100.

Answer:

  1414 kL

Step-by-step explanation:

The volume of the donut-shaped moat is the product of its surface area and depth. The area is the product of its centerline length and its width.

The diameter of the centerline of the moat is (50 m -5 m) = 45 m. The length of that centerline is ...

  C = πd = π(45 m) = 45π m

The area is this length times the width of the moat:

  moat area = (45π m)(5 m) = 225π m²

The volume is the product of the area and the depth of the moat:

  V = Ah = (225π m²)(2 m) = 450π m³ ≈ 1413.72 m³

1 cubic meter is 1000 liters, 1 kiloliter.

The volume of the moat is about 1414 kL.

Using the properties of parallelograms and the given information, we proved that BAEC is equal to FABC. We utilized angle-angle similarity and the proportional relationships of corresponding sides in similar triangles to establish the equality.

To prove that BAEC = FABC, we will use the properties of parallelograms and the given information.

Given:

ABCD is a parallelogram.

BE is parallel to CD.

BF is parallel to AD.

To prove:

BAEC = FABC

Proof:

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Let's denote the length of AB as a, BC as b, AD as c, and CD as d.

Since BE is parallel to CD and AD is parallel to BF, we have angle ABE = angle CDF and angle ADB = angle BFD.

By alternate interior angles, angle CDF = angle FAB.

Now, we have two pairs of congruent angles: angle ABE = angle CDF and angle ADB = angle BFD.

Using angle-angle similarity, we can conclude that triangle ABE is similar to triangle CDF and triangle ADB is similar to triangle BFD.

As the corresponding sides of similar triangles are proportional, we have the following ratios:

AB/CD = AE/CF (from triangle ABE and triangle CDF similarity)

AD/BC = BD/CF (from triangle ADB and triangle BFD similarity)

Cross-multiplying the ratios, we get:

AB * CF = CD * AE (equation 1)

AD * CF = BC * BD (equation 2)

Adding equation 1 and equation 2, we have:

AB * CF + AD * CF = CD * AE + BC * BD

Factoring out CF, we get:

CF * (AB + AD) = CD * AE + BC * BD

Since AB + AD = CD (opposite sides of a parallelogram are equal), we have:

CF * CD = CD * AE + BC * BD

Simplifying, we get:

CF = AE + BC

Therefore, we have shown that BAEC = FABC.

For more such question on parallelograms. visit :

https://brainly.com/question/970600

#SPJ8

Answer:

x = 1 and y = 4

Step-by-step explanation:

5x+2y+2x+6y = 39

7x+8y = 39

Trial and error method:

the answer that satisfies the equation are: x = 1 and y = 4

Hope this helps.

Good Luck

Answer:

(1, 4 )

Step-by-step explanation:

Given the 2 equations

5x + 2y = 13 → (1)

2x + 6y = 26 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate the term in y

- 15x - 6y = - 39 → (3)

Add (2) and (3) term by term to eliminate y

- 13x = - 13 ( divide both sides by - 13 )

x = 1

Substitute x = 1 into either of the 2 equations and evaluate for y

Substituting into (1)

5(1) + 2y = 13

5 + 2y = 13 ( subtract 5 from both sides )

2y = 8 ( divide both sides by 2 )

y = 4

Solution is (1, 4 )

D(t)= 6sin (pi/5t) + 10

General form:

y = A sin (Bx +C) +D

Where:

A = amplitude

D= vertical shift

C = phase shift B= period

For the given function:

Amplitude = 6

Phase shift = 10

The bottom graphs are Cosine functions, so they are not.

Among the top ones, The first one has an amplitude of 6 and the second one has an amplitude of 3 .

Correct answer:

Answer:

95 times

Step-by-step explanation:

Probability of rolling a 5 =1/6

So no. of times 5 is expected when the number cube is rolled out 570 times = 570*1/6 = 95 times

1)First determine the probability of rolling a 5

2)Since you can only roll a 5 once in a 6-sided cube the probability is ⅙ or about 0.1667

3)Multiply the probability and the total number of rolls

.1667 * 570= 95

Answer : 95 times

According to the given information, the two equations that are true for  x=-2  and  x=2  are  4x²-16=0  and  2(x-2)²=0.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

The values of  x=-2  and  x=2  satisfy the equation  4x²=16, so  4x²-16=0  is true for both  x=-2  and  x=2.

The equation  x²=-4  has no real solutions, so it is not true for either  x=-2  or  x=2.

The equation  3x²+12=0  is not true for either  x=-2  or  x=2 , because  3x²+12  is always positive for any real value of  x .

The equation  2(x-2)²=0  is only true for  x=2 , because plugging in  x=-2  gives  2(-4)² =32 ≠0.

Therefore, the two equations that are true for  x=-2  and  x=2  are  4x²-16=0  and  2(x-2)²=0 .

To know more about equations visit:

brainly.com/question/17499155

#SPJ1

Answer:

guns, steel, and quinine (c)

Step-by-step explanation:

did the assignment on edge 2021 trust :))))

Answer:

23

4* 4  = 16

cir = 2\(\pi\)r = 2\(\pi\)(1.2) = 2.4\(\pi\)

16 + 2.4\(\pi\) = 23.53

Step-by-step explanation:

The correct option regarding whether each inequality symbol has to be flipped is:

The inequality symbol needs to be flipped when these two following conditions happen:

There is only one option in which the symbol has to be flipped, which is:

-3x < 15.

As:

The other inequality with the negative multiplier is:

-8 > 9.3 - x

However, x can be flipped to the left side, as follows:

x > 9.3 + 8.

Which means that the symbol does not need to be flipped.

More can be learned about inequalities at https://brainly.com/question/25275758

#SPJ1

Answer:

The mean is lower than the median which is lower than the mode.

Step-by-step explanation:

Answer:

Step-by-step explanation:

24 boys to 18 girls, total students:

Ratio of boys to the total number of students:

Correct choice is B

Answer:

Solution given;

girl's=18

boys=24

total no of students=24+18=42

now

the ratio of boys to the total number of students in the class=\( \frac{24}{42} \)

=24:42is the required ratio.

The expression to find the perimeter of a square with a side length of 3x units is: 4(3x) = 12x.

This means that the perimeter of the square can be found by multiplying the length of one side (3x) by 4, since a square has four equal sides.

To understand why this expression is correct, it's helpful to recall that the perimeter of any polygon is the sum of the lengths of its sides. For a square, all four sides are equal, so we can simply add the length of one side to itself three times to find the total perimeter.

In this case, the length of one side is 3x, so the perimeter is:

3x + 3x + 3x + 3x = 12x

Therefore, the expression 4(3x) = 12x correctly represents the perimeter of a square with a side length of 3x units.

To know more about length click here

brainly.com/question/30625256

#SPJ11

From the Pythagorean theorem, we can relate the values:

We can rewrite the expression as it follows:

If we name this expression as: A: (x + 6) and B: (x - 8)

We now have:

The only way for this expression to be zero is if A of B, or both equal zero. From this, we have:

The first answer, x = - 6, has no real meaning because there no sense someone waked a negative amount of kilometers. From this, we know that Michelle walked 8 km.

The answer, as explained, is C: 8km.

The x-intercept is 5 and the y-intercept is 2.

The standard form of the line is 2x + 5y = 10.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

Hence, the x-intercept is 5 and the y-intercept is 2.

Let's find the equation in standard form.

Ax + By = C

where

Using slope intercept form,

y = mx + b

where

Hence, using (5, 0) and (0, 2)

m = 2 - 0 / 0 - 5

m = - 2 / 5

Therefore.

y = - 2 / 5x + 2

Hence, let's multiply through by 5 to eliminate the fraction

5y = -2x + 10

Therefore, the standard form is as follows:

2x + 5y = 10

learn more x and y-intercepts here: https://brainly.com/question/14180189

#SPJ1

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.