Guest #5595975

2 months ago

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

**hope this helps you**

Guest #5595976

2 months ago

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

**hope this helps you**

Question

7. El área de un terreno de forma rectangular es 4332 m?. Si de ancho mide la tercera parte de su medida de largo, ¿Cuáles son las dimensiones del rectángulo?

Solution 1

Sea x la medida de largo del terreno. Entonces, el ancho del terreno es x/3. Como el área del terreno es 4332 m², podemos escribir la ecuación:

x(x/3) = 4332

Resolviendo para x, obtenemos:

x²/3 = 4332

Multiplicando ambos lados por 3, obtenemos:

x² = 12996

Tomando la raíz cuadrada de ambos lados, obtenemos:

x = 114

Por lo tanto, las dimensiones del rectángulo son 114 m de largo y 38 m de ancho.

x(x/3) = 4332

Resolviendo para x, obtenemos:

x²/3 = 4332

Multiplicando ambos lados por 3, obtenemos:

x² = 12996

Tomando la raíz cuadrada de ambos lados, obtenemos:

x = 114

Por lo tanto, las dimensiones del rectángulo son 114 m de largo y 38 m de ancho.

Question

Need help will give brainliest and 5 stars!

For this graph, for each vertical asymptote, write down the two limits that describe the graph of the function near the asymptote.

Solution 1

The limits on the vertical **asymptotes **of the function are given as follows:

lim x→6- f(x) = ∞

lim x→6+ f(x) = - ∞

lim x→2- f(x) = ∞

lim x→2+ f(x) = - ∞

lim x→6- f(x) = - ∞

lim x→6+ f(x) = ∞

The values of x that are outside of the **domain**—in a fraction, the zeroes in the **denominator**—are the vertical asymptotes.

When a graph reaches its vertical asymptotes, it just approaches the point rather than crossing it.

The limits on the vertical asymptotes of the function are given as follows:

lim x→6- f(x) = ∞

lim x→6+ f(x) = - ∞

lim x→2- f(x) = ∞

lim x→2+ f(x) = - ∞

lim x→6- f(x) = - ∞

lim x→6+ f(x) = ∞

The vertical asymptotes are then provided as x = -6, x = -2, and x = 2.

Each asymptote has limits to the left (shown by the minus sign) and the right (shown by the plus sign).

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Question

URGENT!! ILL GIVE

BRAINLIEST! AND 100 POINTS

Solution 1

**Answer:**

The y-intercept represents Adam's base salary

**Step-by-step explanation:**

Since it's y = 0.28x + 38,000, when x is 0, the salary is 38,000 without commission.

*Be sure to mark this as brainliest! :)*

Question

Based on the work shown on the right, check all of the possible solutions of the equation.

-8

-2

0

2

8

Diagram not drawn to scale

Solution 1

**Answer:**

8

**Step-by-step explanation:**

sqrt(2x) - x = - 4

sqrt(2x) = x - 4

2x = (x - 4) ^ 2

2x = x ^ 2 - 8x + 16

o = x ^ 2 - 10x + 16

matrix 0&=& (x - 2)(x - 8) matrix )

Details : Based on the work shown on the right, check all of the possible solutions

Question

Construct an Argument | Batter is being poured into the right rectangular prism-shaped pan so that the pan is full. What is the volume of the batter in the pan? 9 in. 3 In. 5 in.

Solution 1

**Answer:**

Valid

**Step-by-step explanation:**

The volume of the batter in the pan can be found by multiplying the length, width, and height of the right rectangular prism-shaped pan. In this case, the length is 9 inches, the width is 5 inches, and the height is 3 inches.

Using the formula for the volume of a rectangular prism, V = lwh, we can substitute the given values to find:

V = (9 in.)(5 in.)(3 in.)

V = 135 cubic inches

Therefore, the volume of the batter in the pan is 135 cubic inches. This argument is valid because it follows the basic formula for calculating the volume of a rectangular prism and uses the specific measurements provided for the length, width, and height of the pan.

Question

What meaning of the statement this?

Solution 1

The meaning of the given **statement** is concept of a **cyclic subgroup** in group theory.

**What is cyclic group?**

In group theory, a **cyclic group **is a group that can be generated by a **single element**. That is, it is a group that is generated by a single element a, where any element of the group can be expressed as a power of a.

The order of a cyclic group is equal to the order of its **generator**. If the generator has order n, then the cyclic group has n elements. The **group operation** in a cyclic group can be either additive or multiplicative, depending on the notation used.

The statement defines a cyclic subgroup is a subgroup of a group that is generated by a single element. The element used to generate the subgroup is called the generator of the cyclic subgroup. The set of all powers of the generator, including the inverse powers and the identity element, forms the cyclic subgroup.

In other words, the cyclic subgroup generated by an element a of a group is the smallest subgroup that contains a. It consists of all possible combinations of a and its inverse under the group operation.

A group or subgroup is called cyclic when it can be generated by a single element. In other words, if every element of the group can be expressed as a power of a single element, then the group is cyclic.

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Question

In circle O, chords AB and CD intersect at E, AE = 3 inches, BE = 8 inches, and CE is 2 inches longer than DE. What is the length of DE, expressed in inches?

Solution 1

Okay, let's break this down step-by-step:

* Circle O has chords AB and CD that intersect at E

* AE = 3 inches

* BE = 8 inches

* CE is 2 inches longer than DE

So we know:

AE = 3 inches

BE = 8 inches

CE = DE + 2 inches

To find DE, we can use the Pythagorean theorem for any right triangle:

a^2 + b^2 = c^2

In this case:

3^2 + 8^2 = c^2

9 + 64 = 73

c = 8 inches

So the hypotenuse AE forms a right triangle with leg BE of length 8 inches.

Now we have the length of one leg (BE = 8 inches) and the hypotenuse (AE = 8 inches).

We can use the relation between leg, hypotenuse and sine to calculate the other leg (DE):

sin(A) = DE / 8

DE = 8 * sin(A)

Without knowing the angle A, we can make an estimate:

sin(A) ≈ A (for small A)

So DE ≈ 8A inches

Now we know:

CE = DE + 2 inches

And DE ≈ 8A inches

So: 8A + 2 = DE

=> DE = 10A

And since A is small, we can say: DE ≈ 10 * A inches

To summary, if AE = 3 inches and BE = 8 inches,

then DE ≈ 10 * A inches

DE is approximately 10 times some small angle A.

Does this make sense? Let me know if you have any other questions!

Question

Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man who is 66.7 inches tall. (to 4 decimal places)

Solution 1

**Answer:**

!

**Step-by-step explanation:**

Details : Adult men have heights with a mean of 69.0 inches and a standard

Question

help with calculus. determine wheter each labeled point is an absolute maximum or minumum OR a relative maximum or minimum or neither

Solution 1

The **relative maximum **and **minimum** **point** as well as the absolute maximum and minimum points based on labeled points on the **graph** are;

Points 1, 3, and 5 are relative maximum points

Points 2 and 4 are relative minimum points

Point 5 is an absolute maximum point

Point 2 is an absolute minimum point

A **relative maximum **is a point in which the maximum with regards to the immediate **surrounding** points.

Therefore, the relative maximum points are;

The points 1, 3, and 5

The** relative minimum points **are points that are the minimum points, when compared with the surrounding points

The relative minimum are the points 2 and 4

The absolute maximum is the point which is at the highest point on the graph

The absolute maximum on the graph is therefore, the [oint 5

The absolute minimum on the graph is the point which is the minimum point compared to all other points

Therefore, the absolute minimum point is the point 2

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Question

Jordan, Jessica, Eloise, and James travel to Europe. They see many famous places.

\

The friends hiked on a trail in the Austrian Alps. They hiked 1.08 kilometers on Monday and 0.94 kilometer on Tuesday.

How many kilometers did they hike in all? Describe how to use the grids to solve the problem. Then use the grids to find the solution.

Solution 1

The total number of **kilometers **that the friends **hiked **in all would be 2. 02 km.

The total **distance **that Jordan, Jessica, Eloise, and James **hiked **in the **Austrian Alps, **can be found to be :

= Distance on Monday + Distance on Tuesday

= 1. 08 + 0. 94

= 2. 02 km

Using **grids**, you can represent a single box as 0. 1 km so that for 1. 08 km you will have a grid of 108 cubes. Do the same for Tuesday to get 94 cubes.

Add them up and you will get 202 cubes which would be 2.02 km.

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Question

. The perimeter of a rectangle is twice its area. If the perimeter is 32L and the breadth is the square of its length, L, find a. length b. Breadth c. Perimeter d. Area of the rectangle.

Solution 1

The **rectangle** have length = 4, breath = 16, **perimeter** = 40, and **area** = 64.

The **perimeter** of a **rectangle** is the sum of length of its four sides or the sum of its length and breadth, multiplied by two. While the **area** is the length multiplied by the breadth.

**Perimeter** = 2(L + B)

**Area** = L × B

From the question;

2(L + B) = 2LB

32L = 2L(L²)...(1) {since B = L²}

from equation (1), L = 4 by solving for L

so;

B = 4² = 16

**perimeter** of the rectangle = 2(4 + 16) = 40

**area** of the rectangle = 4 × 16 = 64

Therefore, the **rectangle** have length = 4, breath = 16, **perimeter** = 40, and **area** = 64.

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Question

In a game of cards you win $1 if you draw a heart (except the ace), $5 if you draw an ace (including the ace of hearts), $10 if you draw the king of spades and $0 for any other card. Let W be the amount you win playing this game, what the probability distribution of W?

Solution 1

There are four possible outcomes in this game: winning $1, winning $5, winning $10, or winning $0.

The probability of winning $1is the probability of drawing one of the 11 hearts that are not the ace of hearts. There are 52 cards in the deck, so the probability of drawing any one of them is 1/52. However, there are 11 hearts that win $1, so the probability of winning $1 is:

P(W = $1 ) = 11/52

The probability of winning $5 is the probability of drawing the ace of hearts, which is 1/52.

P(W = $5) = 1/52

The probability of winning $10 is the probability of drawing the king of spades, which is also 1/52.

P(W = $10) = 1/52

The probability of winning $0 is the probability of drawing any other card, which is 39/52.

P(W = $0) = 39/52

Details : In a game of cards you win $1 if you draw a heart (except the ace),

Question

At Downtown Pizza, 4 of the last 6 pizzas sold had pepperoni. What is the experimental probability that the next pizza sold will have pepperoni?

Solution 1

The answer of the given question based on the **experimental probability **is the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.

Experimental probability is ratio of number of times event occurs to the total number of trials or observations conducted in experiment or real-life situation. It is based on actual observations or data and is also known as **empirical probability.**

Experimental probability is used when it is not possible or feasible to determine the theoretical probability of an **event**, or when the theoretical probability does not match the actual outcomes observed in a given situation. In such cases, experimental probability provides an estimate of the likelihood of an event occurring based on real-life data.

The experimental probability that the next pizza sold will have pepperoni is the ratio of the number of pepperoni pizzas sold to the total number of pizzas sold in the recent past.

According to the problem, 4 of the last 6 pizzas sold had pepperoni. So, the experimental probability of the next pizza sold having pepperoni is:

experimental probability = number of pepperoni pizzas sold / total number of pizzas sold

experimental probability = 4 / 6

experimental probability = 2 / 3

Therefore, the experimental probability that the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.

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Question

(42) Using a waste factor of 6 percent, determine the number of cubic yards of concrete needed to pour the foundation walls shown in Figure 11.4. The footing is 12 foot wide and 1 foot thick.

Solution 1

The 7.34 cubic yards of concrete needed to pour the foundation walls, which is calculate the **volume** of the walls and then add the waste factor of 6%.

To find the volume of the concrete needed to pour the foundation walls, we first need to find the total area of the **walls**. We can do this by breaking it down into three sections

The two 26 ft x 1 ft walls

Area = 2 x (26 ft x 1 ft) = 52 sq ft

The two 42 ft x 1 ft walls

Area = 2 x (42 ft x 1 ft) = 84 sq ft

The 12 in x 15 in x 12 ft wall

First, we need to **convert **the dimensions to feet:

Length = 12 in ÷ 12 = 1 ft

Breadth = 15 in ÷ 12 = 1.25 ft

Height = 12 ft

Area = (1 ft + 1.25 ft) x 2 x 12 ft = 51 ft²

Total area of the walls = 52 sq ft + 84 sq ft + 51 sq ft = 187 sq ft

Now, we need to add the **waste factor** of 6% to this to account for any material that may be lost or wasted during the pouring process

Total area with waste factor = 187 sq ft + 6% of 187 sq ft = 198.22 sq ft

Finally, we need to calculate the volume of concrete needed, assuming a thickness of 1 ft

Volume = area x thickness = 198.22 sq ft x 1 ft = 198.22 cubic ft

Since 1 cubic yard is equal to 27 cubic feet, we can convert the volume to **cubic yards**

Volume in cubic yards = 198.22 cubic ft ÷ 27 = 7.34 cubic yards

Therefore, we need 7.34 cubic yards of concrete to pour the foundation walls with a 6% waste factor.

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Question

what is the leading coefficient of a third-degree function that has the output of -110 x=3 and has zeros of 14, I, -I

Solution 1

The **leading coefficient** of a third-degree function that has the output of -110 x=3 and has zeros of 14, I, -I is 10

If a third-degree **function** has zeros 14, I, and -I, it can be factored as: f(x) = a(x - 14)(x - I)(x + I)

'a' denotes the leading **coefficient**.

We may use the knowledge that the function's output is -110 when x = 3 to calculate the value of 'a'.

Substituting x = 3 into the function's factored form yields:

f(3) = a(3 - 14)(3 - I)(3 + I) = -110

When we **simplify** this equation, we get:

a(-11)(3 - I)(3 + I) = -110

a(-11)(9 - I^2) = -110

a(-11)(9 + 1) = -110 (since I2 = -1)

a(-11)(10) = -110

-110a = -1100

a = 10

Hence , the third-degree **function's** leading coefficient is 10.

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Question

Michael has an average daily balance on his credit card of $327.50. His credit card charges 11.99% annual interest. What will his monthly finance charge be?

Solution 1

**Answer:**

**First, we need to calculate Michael's daily interest rate:**

**0.1199 / 365 = 0.0003282**

**Then, we can calculate his daily finance charge:**

**327.50 x 0.0003282 = 0.1075**

**To find his monthly finance charge, we multiply his daily finance charge by the number of days in a month:**

**0.1075 x 30 = 3.225**

**So Michael's monthly finance charge will be $3.23 (rounded to the nearest cent).**

Details : Michael has an average daily balance on his credit card of $327.50.

Question

TOPIC 1 ANGLES AND TRIANGLES

SKILLS PRACTICE continued

PROBLEM SET 2: Classifying Angles

> Identify each pair of angles as complementary, supplementary, or vertical angles.

Solution 1

Each pair of **angles** has been identified as adjacent, complementary, **supplementary**, or vertical angles as shown in the image attached below.

In Mathematics and Geometry, a **complementary angle** can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°);

55 + 35 = 90°

In Mathematics and Geometry, **adjacent angles** can be defined as two (2) angles that share a common vertex and a common side. This ultimately implies that, both **angles** 1 and 2, 5 and 6, 9 and 10 are pair of **adjacent angles**.

In conclusion, the linear pair theorem is sometimes referred to as linear pair postulate (**supplementary** angle) and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.

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Question

Write the equation of the line that passes through the points (5,4) and (5,-8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Solution 1

**Answer: x=5**

**Step-by-step explanation:**

Not much calculations needed, but since we have two points where x=5, a vertical line that is equal to x=5 will hit both points. I attached it visually below!

Question

n

2. The point (-1,5) is the solution

to a set of linear equations. One

of the following CANNOT be the

other equation?

A. y = -2x

B. y = -5x

C. y = -x +4

1

Dy=-x+²/

2

9

2

Solution 1

Therefore, the **equation **that **cannot **be the **other **equation is A. y = -2x.

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

Here,

To check which equation cannot be the other equation, we can substitute the coordinates of (-1,5) into each of the equations and see if they hold true.

A. y = -2x

When x = -1, then y = -2(-1) = 2, so (-1,5) does not satisfy this equation. Therefore, this cannot be the other equation.

B. y = -5x

When x = -1, then y = -5(-1) = 5, so (-1,5) does satisfy this equation.

C. y = -x + 4

When x = -1, then y = -(-1) + 4 = 5, so (-1,5) does satisfy this equation.

D. y = -x²/2 + 9/2

When x = -1, then y = -(-1)²/2 + 9/2 = 5, so (-1,5) does satisfy this equation.

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Question

Calculus Riemann sum challenge problem.

Solution 1

The **limit **of the given sum as n approaches infinity is **0.**

We have the limit as n approaches **infinity **of the sum from i = 1 to n of 1/(n+i). We can rewrite this sum using the hint provided as:

[tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex](1/ n + i) = [tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex] (1/n) * (1 + i/n)

To find the limit, we need to take the limit of the Riemann sum as n approaches infinity. This is equivalent to taking the limit of the area of n rectangles under the curve y=1/x as n approaches infinity.

As n becomes very large, the width of each rectangle becomes very small, and the height of each **rectangle **approaches 1/n. Therefore, the area of each rectangle approaches zero.

We can then express the limit as an **integral**:

[tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex](1/ n + i) =[tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex] (1/n) * (1 + i/n) =[tex]\lim_{n \to \infty} \int ^1 _{1+1/n}[/tex] 1/x dx

Evaluating this integral gives:

[tex]\lim_{n \to \infty} \int ^1 _{1+1/n}[/tex] 1/x dx = [tex]\lim_{n \to \infty}[/tex] ln(1+1/n) = ln(1+0) = 0

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Details : Calculus Riemann sum challenge problem.

Question

Find the value of x in each triangle

Solution 1

**Answer:b 40**

**A60**

**Step-by-step explanation:**

Solution 2

**Answer:**

**Step-by-step explanation:**

**so for figure a:**

*we can find x by using sin which is sin = opposite/hypotenuse so *

*- sin30= x/10cm(sin30 is equivalent to 1/2 or 0.5)*

*- 0.5= x/10cm or 1/2=x/10cm (i'm gonna use the 2nd option)*

*- 10cm * 1/2=x*

*-x=5cm*

* and for figure b*:

*here we also use sin*

*- sin 50= x/8cm (sin 50 is equivalent to 0.7660 )*

*- 0.7660= x/ 8cm*

*-0.7660 * 8cm=x*

*- x= 6.128cm and when estimated x= 6cm*

Question

NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #2

Solution 1

Changing the base from 5/7 to 7, the **end behavior** of the function would be given as follows:

- As x -> -∞, f(x) -> 0.

- As x -> ∞, f(x) -> ∞.

The **end behavior **of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The **function **for this problem is given as follows:

f(x) = 4(5/7)^x.

**Changing the base** to 7, it would have an absolute value greater than 1, hence the function would be **increasing **with the end behavior given as follows:

- Approaches the horizontal asymptote y = 0 at the left of the graph -> As x -> -∞, f(x) -> 0.

- Increases as the input increases, that is, as x -> ∞, f(x) -> ∞.

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Question

A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 20400 dollars?

Solution 1

To the nearest tenth of a year, the person must leave the money in the **bank **for 15.5 years.

We can use the formula for compound interest:

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

where A is the final amount, P is the **principal **(initial investment), r is the annual **interest **rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

We know P = 8000, r = 0.0475, and we want A = 20400. We also know that the interest is compounded daily, so n = 365.

Let's solve for t:

20400 = 8000[tex](1 + 0.0475/365)^{(365t)}[/tex]

2.55 = [tex](1.00013)^{(365t)}[/tex]

Taking the natural **logarithm **of both sides, we get:

after solving

Using a calculator, we find:

t ≈ 15.5

So, to the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.

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Question

Students are painting a mural. So far the mural is painted one fourth blue two 8 red and three 12 green

Solution 1

To find out what fraction of the mural has been painted, we need to add the fractions that represent the amount of blue, red, and green paint used.

One fourth blue can be written as 1/4, two 8 red is equivalent to 1/4 (since 2/8 reduces to 1/4), and three 12 green is equivalent to 1/4 (since 3/12 reduces to 1/4).

Therefore, the fraction of the mural that has been painted is:

1/4 + 1/4 + 1/4 = 3/4

So, the students have painted 3/4 of the mural so far.

One fourth blue can be written as 1/4, two 8 red is equivalent to 1/4 (since 2/8 reduces to 1/4), and three 12 green is equivalent to 1/4 (since 3/12 reduces to 1/4).

Therefore, the fraction of the mural that has been painted is:

1/4 + 1/4 + 1/4 = 3/4

So, the students have painted 3/4 of the mural so far.

Details : Students are painting a mural. So far the mural is painted one fourth

Question

Eulerize this graph in the most efficient way possible, considering the weights of the edges.

Solution 1

We can** eulerize this graph** in the most efficient way possible by making these **vertices **have even degree through adding an edge between them.

We can **Eulerize a graph** by ensuring to add edges to the graph in a way that preserves its connectivity while ensuring that all **vertices** have **even degree.**

A good method to do this is by adding edges between pairs of **vertices **that have **odd degree** until all vertices have **even degree**.

In the scenario above, all the vertices have **odd degree** except for the first and last vertices. To make these vertices have **even degree**, we go ahead and add an edge between them.

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Question

Which is the Which is the completely factored form of 4x2 + 28x + 49?

(x + 7)(4x + 7)

4(x + 7)(x + 7)

(2x + 7)(2x + 7)

2(x + 7)(x + 7)

completely factored form of 4x2 + 28x + 49?

Solution 1

(2x+7)(2x+7) = 4x^2 + 28x + 49

Question

42 SING A chef makes batches of dumpling wrappers for shrimp dumplings. She uses 2 cups of flour for each batch and a total of an additional § cup of flour to keep the dough from sticking. She uses 21 cups of flour to make n batches of dumpling wrappers. How many batches of dumpling wrappers does the chef make?

Solution 1

The **chef** makes 11 batches of **dumpling wrappers**.

**What is dumpling wrapper?**

**Dumpling wrappers** are thin **pieces** of **dough** that are used to **wrap** around fillings to make dumplings. They are a **staple** in many **Asian cuisines**, including Chinese, Japanese, Korean, and Thai. The dough is typically made with flour, water, and salt, and is rolled out into thin circles or squares. The size and thickness of the wrappers can vary depending on the type of dumpling being made and the regional cuisine. Dumpling wrappers can be used to make a variety of dumplings, such as pork and cabbage dumplings, shrimp dumplings, potstickers, and gyoza.

Let's assume that the chef makes "n" batches of dumpling wrappers.

For each batch of dumpling wrappers, the chef uses 2 cups of flour.

So, the total amount of flour used for making "n" batches of dumpling wrappers is 2n cups of flour.

In addition to the 2 cups of flour for each batch, the chef also uses an additional § cup of flour to keep the dough from sticking. So, the total amount of flour used for "n" batches is 2n + § cups of flour.

According to the problem statement, the chef uses a total of 21 cups of flour to make "n" batches of dumpling wrappers. So, we can set up the following equation 2n + § = 21

To solve for "n," we need to first convert the § cup of flour to a decimal. § is equivalent to 0.25 cups of flour.

So, the equation becomes 2n + 0.25 = 21

Subtracting 0.25 from both sides,

2n = 20.75

Dividing both sides by 2,

n = 10.375

Since we can't have a fraction of a batch, we can round up to the nearest whole number. Therefore, the chef makes 11 batches of dumpling wrappers.

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Solution 2

The **chef** makes 11 batches of **dumpling wrappers**.

**What is dumpling wrapper?**

**Dumpling wrappers** are thin **pieces** of **dough** that are used to **wrap** around fillings to make dumplings. They are a **staple** in many **Asian cuisines**, including Chinese, Japanese, Korean, and Thai. The dough is typically made with flour, water, and salt, and is rolled out into thin circles or squares. The size and thickness of the wrappers can vary depending on the type of dumpling being made and the regional cuisine. Dumpling wrappers can be used to make a variety of dumplings, such as pork and cabbage dumplings, shrimp dumplings, potstickers, and gyoza.

Let's assume that the chef makes "n" batches of dumpling wrappers.

For each batch of dumpling wrappers, the chef uses 2 cups of flour.

So, the total amount of flour used for making "n" batches of dumpling wrappers is 2n cups of flour.

In addition to the 2 cups of flour for each batch, the chef also uses an additional § cup of flour to keep the dough from sticking. So, the total amount of flour used for "n" batches is 2n + § cups of flour.

According to the problem statement, the chef uses a total of 21 cups of flour to make "n" batches of dumpling wrappers. So, we can set up the following equation 2n + § = 21

To solve for "n," we need to first convert the § cup of flour to a decimal. § is equivalent to 0.25 cups of flour.

So, the equation becomes 2n + 0.25 = 21

Subtracting 0.25 from both sides,

2n = 20.75

Dividing both sides by 2,

n = 10.375

Since we can't have a fraction of a batch, we can round up to the nearest whole number. Therefore, the chef makes 11 batches of dumpling wrappers.

Learn more **dumpling wrappers** here,

https://brainly.com/question/25421984

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Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Paul has scored 82 , 88 , and 87 on the first three. What range of scores on the fourth test will give Paul a C for the semester (an average between 70 and 79 , inclusive)? Assume that all test scores have a non-negative value.

Solution 1

Scores between **23 & 59** will give Paul a C for the semester (an **average **between 70 and 79).

The **sum** of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, **23 & 59** to get an average score of 70 & 79.

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Details : In a class in which the final course grade depends entirely on the

Question

I need help with questions 2 and 3 please.

Solution 1

**Answer:**

1.x=7 or x=-7

2.x=root of 65 or x=-root of 65

**Step-by-step explanation:**

I have put what I mean by root 65

Question

Kleen Company acquired patent rights on January 10 of Year 1 for $881,100. The patent has a useful life equal to its legal life of eight years. On January 7 of Year 4, Kleen successfully defended the patent in a lawsuit at a cost of $49,200.

Required:

a. Determine the patent amortization expense for Year 4 ended December 31.

b. Journalize the adjusting entry on December 31 of Year 4 to recognize the amortization. Refer to the Chart of Accounts for exact wording of account titles.

Solution 1

a. The patent amortization expense for Year 4 ended December 31 is $110,138.

b. The adjusting entry on December 31 of Year 4 to recognize the amortization is:

Patent amortization expense 110,138

Accumulated patent amortization 110,138

b. The adjusting entry on December 31 of Year 4 to recognize the amortization is:

Patent amortization expense 110,138

Accumulated patent amortization 110,138

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