5-121. For parts (a) and (b), rewrite the expression without parentheses. For (c) and (d), solve each equation.
a. 2x(x + 3)
b. (3x + 2)(x-3)
c. 4y -2(6-y) = 6
d. x(2x-4)= (2x + 1)(x-2)

Answer:

Area = 4

Step-by-step explanation:

The degree of a vertex represents the number of other actors or actresses that an actor or actress has worked with in movies.

The neighborhood of a vertex represents the set of actors or actresses that an actor or actress has worked with in movies.

Isolated vertices represent actors or actresses who have not worked with any other actors or actresses in any movie, while pendant vertices represent actors or actresses who have only appeared in one movie with another actor or actress in the Hollywood graph.

The Hollywood graph is an undirected graph because the relationship between actors and actresses is mutual.

Each vertex in this graph represents an actor or actress, and the degree of a vertex represents the number of other actors or actresses that they have worked with in movies. In other words, the degree of a vertex represents the number of edges that are connected to that vertex.

The neighborhood of a vertex in a graph refers to the set of all vertices that are adjacent to it. In the context of the Hollywood graph, the neighborhood of a vertex represents the set of actors or actresses that a particular actor or actress has worked with in movies.

An isolated vertex in a graph is a vertex that has no edges connected to it. In the context of the Hollywood graph, an isolated vertex represents an actor or actress who has not worked with any other actors or actresses in any movie.

A pendant vertex in a graph is a vertex that has only one edge connected to it. In the context of the Hollywood graph, a pendant vertex represents an actor or actress who has only appeared in one movie with another actor or actress in the Hollywood graph.

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Answer:

C

Step-by-step explanation:

The number of minutes spent on drawing and writing a comic book will be 50 minutes and 25 minutes, respectively.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Let 'x' and 'y' be the number of minutes spent on drawing and writing a comic book, respectively. Then the equations are given as,

x + y = 75          ....1

x = y + 25         ....2

From equations 1 and 2, then we have

y + 25 + y = 75

2y = 50

y = 25 minutes

Then the value of 'x' is given as,

x = 25 + 25

x = 50 minutes

The number of minutes spent on drawing and writing a comic book will be 50 minutes and 25 minutes, respectively.

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The proportion i/k = 12 can be used to find the length of sides i and k if the perimeter is 12 units. To solve for the length of each side, the equation i + k = 12 is used, and then the two sides are divided by each other to get the proportion i/k = 12.

The proportion i/k = 12 can be used to find the length of sides i and k of a shape if the perimeter is 12 units. In order to solve for the length of each side, the equation i + k = 12 is used to determine the sum of the sides. The two sides are then divided by each other, resulting in the proportion i/k = 12. This proportion can then be used to find the length of sides i and k. For example, if the length of side i is 8, then the length of side k is 4. This can be determined by dividing 8 by 4, which results in the proportion i/k = 2. If the perimeter is 12 units, then the equation i + k = 12 can be used to determine that the length of side i is 6 and the length of side k is 6, since 6 + 6 = 12. The proportion i/k = 12 can then be used to confirm that the length of side i is 6 and the length of side k is 6.

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The complete question is

Which proportion can be used to find the length of sides ik if the perimeter is 12 units?

The program to cost of each container and the total cost of producing all the containers is given below.

The program based on the information will be:

#include <iostream>

using namespace std;

int main() {

int r,h,c,n;

cout<<"Enter the base radius : ";

cin>>r;

cout<<"\nEnter the height : ";

cin>>h;

cout<<"\nEnter the cost per square cm : ";

cin>>c;

cout<<"\nEnter the number of containers : ";

cin>>n;

int s_area = (3.14*r*2)+(2*3.14*r*h);

int cost = c*s_area;

int t_cost = n*cost;

cout<<"\nCost of each container : "<<cost<<endl;

cout<<"Total cost : "<<t_cost<<endl;

}

Based on the above, we've created a program to take the radius of the base, the height of the container, the cost per square centimeter of the material cost.

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A manufacturer wishes to determine the cost of producing an open-top cylindrical container. The surface area of the container is the sum of the area of the circular base plus the area of the outside (the circumference of the base times the height of the container). Create C program to take the radius of the base, the height of the container, the cost per square centimeter of the material (cost), and the number of containers to be produced (quantity). Calculate the cost of each container and the total cost of producing all the containers.

The probability of seeing exactly 5 hearts out of 10 cards is[tex](13/52)^5 × (39/52)^5.[/tex]

The probability of seeing exactly 5 hearts out of 10 cards can be calculated as follows: The total number of cards in a deck is 52. The number of hearts in a deck is 13. Since no card has been removed from the deck, the probability of seeing a heart is 13/52. The probability of seeing a non-heart is 39/52. Since we are looking at 10 cards, the probability of seeing exactly 5 hearts,

p(h)= 13/52

p(nh) = 39/52

hence, [tex](13/52)^5 × (39/52)^5[/tex]

This means that the probability of seeing exactly 5 hearts out of 10 cards is [tex](13/52)^5 × (39/52)^5.[/tex]

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The required, 68.2 divided by 0.4 is equal to quotient 170.5, as per the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
68.2 divided by 0.4 is given as,

To divide a decimal value by another decimal value, you can use the same process as dividing whole numbers, but you need to make sure that the decimal points are lined up correctly.

= 68.2 / 0.4

= 682/4
= 170.5

Therefore, 68.2 divided by 0.4 is equal to 170.5.

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Answer: D. 6 cm

Step-by-step explanation:

V = 4/3πr^3

r = (3 V/4π)^1/3 = (3* 900/4*π)^1/3 = 5.98942

Answer: A

Step-by-step explanation: This is how to solve: 3239 / (36 *365)

That's 0.246499239 kills per day, so none died

I hope this helped!

Answer:

a = 6 ft.

------------------------------

Given is an isosceles right triangle.

As per property of a such triangle, its hypotenuse is √2 times its leg.

That is:

Answer:

a = 6 ft

Step-by-step explanation:

We have to find,

→ The value of a in the diagram.

Formula we use,

=> Using Pythagoras theorem.

→ (Hyp)² = (Opp)² + (Base)²

Forming the equation,

→ (6√2)² = (a)² + (a)²

Now the value of a will be,

→ (6√2)² = (a)² + (a)²

→ (a)² + (a)² = (6√2)²

→ 2a² = 36 × 2

→ 2a² = 72

→ a² = 72 ÷ 2

→ a² = 36

→ a = √(36)

→ [ a = 6 ft ]

Hence, the value of a is 6 ft.

a. Brand U will be $1,051.92 cheaper than Brand V. Option A is the correct answer to the given question.

To calculate the lifetime cost of each oven, we need to consider the initial purchase price, daily electricity costs, and lifespan. For Brand U, the lifetime cost would be:

Lifetime cost = Price + (Avg. Cost/Day × 365 days × Lifespan)

= $2,250 + ($0.16 × 365 × 24)

= $4,013.60.

For Brand V, assuming two repurchases to equalize the lifespan, the lifetime cost would be: Lifetime cost = Price + (Avg. Cost/Day × 365 days × Lifespan × 3)

= $725 × 3 + ($0.28 × 365 × 8 × 3)

= $3,961.68.

Therefore, Brand U will have a lower lifetime cost than Brand V by $1,051.92 (option a).

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Complete Question

Pam has just moved into a new home and wants to purchase an oven. She expects to live in this house for the foreseeable

future. She has narrowed her choices down to two options. Consider the following table, which describes the prices, daily

electricity costs, and lifespans of the two ovens she is considering: T Brand Price Avg. $2,250  Cost/Day $0.16 Lifespan Brand U 24 years Brand V $725 $0.28 8 years

Which brand will have the lower lifetime cost, and how much lower will it be?

Hints: If the product's expected lifespans differ, assume that repurchase(s) at the same price is possible to equalize the

lifespans. Remember that six of the twenty-four years will be leap years, and round all dollar values to the nearest cent.

a. Brand U will be $1,051.92 cheaper than Brand V.

b. Brand U will be $976.92 cheaper than Brand V.

C. Brand V will be $75 cheaper than Brand U.

Answer:

Its actually B, (Brand U will be $976.92 cheaper than Brand V).

Step-by-step explanation:

trust

Answer:

Yes, 26

Step-by-step explanation:

78 miles ÷ 3 gallons = 26 mpg

The full meaning of CCTV is Closed-Circuit Television. It refers to a system of video cameras and monitors that are used for surveillance and security purposes. The cameras capture live video footage, which is then transmitted to a set of monitors or a central control room for viewing. The cameras are connected to the monitors through a closed circuit, meaning that the signal is not broadcast publicly and can only be viewed by authorized individuals. CCTV systems are commonly used in homes, businesses, and public spaces to deter crime and provide a record of events.

The original polynomial, [tex]x^2 + 7x + 12[/tex], it can be seen that the two are the same, thus confirming that the polynomial was correctly factored.

To check the result after factoring a polynomial, one can use the FOIL method to ensure that the factored polynomial is equivalent to the original polynomial. The FOIL method stands for First, Outer, Inner, Last, and is used to multiply two binomials. To check the result, one would use the FOIL method to multiply the factored polynomial, and compare the result to the original polynomial. For example, let’s consider the polynomial[tex]x^2+7x+12[/tex]. After factoring, this can be written as (x+4)(x+3). To check the result, one would multiply the two binomials together, (x+4)[tex](x+3) = x^2 + 3x + 4x + 12[/tex]. Comparing this to the original polynomial, [tex]x^2 + 7x + 12[/tex], it can be seen that the two are the same, thus confirming that the polynomial was correctly factored.

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The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches is approximately 34.4 inches, found using the Pythagorean theorem.

The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches can be calculated using the Pythagorean theorem, which states that the square of the sum of the squares of the lengths of the legs determines the length of the hypotenuse.

So, if we call the length of the hypotenuse "h", we have [tex]h^{2}[/tex] = [tex]20^2 + 28^2[/tex]

Solving for h:

[tex]h^2 = 20^2 + 28^2[/tex]

[tex]h^2[/tex] = 400 + 784

[tex]h^2[/tex] = 1184

h = [tex]\sqrt{1184}[/tex]

h ≈ 34.4 in.

So, the length of the hypotenuse is approximately 34.4 inches, rounded to the nearest tenth.

The Pythagorean theorem is a fundamental mathematical relationship that states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal tothe squared lengths of the two legs added together. In this case, the two legs have lengths of 20 inches and 28 inches, and the length of the hypotenuse can be found by solving for the square root of the total of the leg squares.

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Answer:

27 children.

Step-by-step explanation:

Let's call the number of children who chose apples x. Then, the number of children who chose bananas is 0.25x. The number of children who chose watermelon is 60 - x - 0.25x = 60 - 1.25x.

Since 30% of the children chose apples, we know that:

0.30 * 60 = x

So, x = 18, which means 18 children chose apples.

And since 25% of the children chose bananas, we know that:

0.25 * 60 = 0.25x = 15

So, 15 children chose bananas.

Finally, the number of children who chose watermelon is:

60 - 18 - 15 = 27 children.

Answer:

1) Vertical angles

2) Corresponding

3) Alternate exterior

4) Same-Side Interior

Step-by-step explanation:

The functions are matched with their periods as follows:

The period of a trigonometric function is the smallest positive value of "T" for which the function repeats itself.

Note that to determine the period of a function, we need to identify how the function changes over one cycle. The period can then be obtained by dividing the length of the cycle by the number of complete cycles in the full range of the function.

1) y = - 3 ⁢ tan ⁡ 3 ⁢ x: The period of the tangent function is π/b, where b is the coefficient of x. So, the period of y = - 3 ⁢ tan ⁡ 3 ⁢ x is π/3.

2) y = 6 ⁢ sin ⁡ 3 ⁢ x: The period of the sine function is 2π/b, where b is the coefficient of x. So, the period of y = 6 ⁢ sin ⁡ 3 ⁢ x is 2π/3.

3 )y = - 4 ⁢ cot ⁡ x 4: The period of the cotangent function is π/b, where b is the coefficient of x. So, the period of y = - 4 ⁢ cot ⁡ x 4 is π.

4) y = 2 ⁢ cos ⁡ 2 ⁢ x 3: The period of the cosine function is 2π/b, where b is the coefficient of x. So, the period of y = 2 ⁢ cos ⁡ 2 ⁢ x 3 is 3π.

5 )y = - 2 3 ⁢ sec ⁡ x 5: The period of the secant function is 2π/b, where b is the coefficient of x. So, the period of y = - 2 3 ⁢ sec ⁡ x 5 is 2π/5.

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To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.

This conversion factor takes into account the difference in volume between a liter and a fluid ounce.

1 fl oz = 29.5735 mL

1 L = 1000 mL

So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:

(mg/L) * 1000 / 29.5735 = (µg/fl oz)

Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:

x (µg/fl oz) = x (mg/L) * 1000 / 29.5735

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The probability that he does not select a comedy is 12/23

If we assume that all the movies have the same probability of being randomly selected, then the probability of selecting a movie that is not a comedy is equal to the quotient between the number of movies that aren't comedies and the total number of movies.

There are:

3 action ones.

11 comiedies.

9 dramas

For a total of 23 movies, and 12 of them are not comedies, then:

P = 12/23

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Probability that exactly one doesn't grow is 0.004

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

If a seed is planted, it has a 60% chance of growing into a healthy plant.

the probability of growing is 60/100 = 0.6

the probability of not growing is 1-0.6 = 0.4

eleven seeds are planted,

and 10 should grow and exactly one doesn't grow

so probability = 0.6*0.6*0.6*0.6*0.6*0.6*0.6*0.6*0.6*0.4=0.004031

= 0.004

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Answer:

Step-by-step explanation:

5. Diagram 2 shows a cylinder and a cuboid. Diagram 2 shows a cylinder and a cuboid. Fold / Use = 271 30 cm Find the value of x and give the correct answer to the multiple of two places. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Answer / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us

If we multiply the values by 3 and then add 4 the new mean are 79 and and variance are 144.

Mean = E(x) = 25 , and variance = var(x) = 16 multiply by the value by 3 and add 4

mean = 3 x 24 + 4 = 79

Variance = 3^2 x 16 = 9 x 16 = 144

=> mean = 79 , variance = 144

Variance is a statistical measure that represents the degree of dispersion or variation in a set of data. It is the average of the squared differences between each value and the mean of the data set. The variance shows how spread out the data is and how much each value deviates from the average.

A high variance indicates that the data points are spread out over a wide range, while a low variance indicates that the data points are clustered around the mean. Variance is useful in various fields, including finance, engineering, and social sciences, where it is used to analyze data, test hypotheses, and develop predictive models. Standard deviation is a more intuitive measure of variation as it is expressed in the same units as the data, while variance is expressed in squared units.

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Complete Question: -

If we have a data set with a mean of 25 and a variance of 16, what are the new mean and variance if we multiply the values by 3 and then add 4?

A. Mean - 79, variance - 144

B. Mean - 79, variance - 48

C. Mean - 87, variance - 144

D. Mean - 87. variance - 48 ОООО

The value of x is given as follows:

x = 130º.

To obtain the value of x, we must consider the exterior angle theorem, which states that each interior angle is supplementary with it's interior angle, meaning that the sum of their measures is of 180º.

As the interior angle is of 50º, the measure of the exterior angle x is given as follows:

x = 180 - 50

x = 130º.

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The size of the key space is 256^8, or 2^64. The average key search time would be 2^64/processing power of PC, which would be a very large number.

The question is asking about the size of the key space if 8 randomly chosen 8-bit ASCII characters are used, and how long it would take to find a key on a single PC.

The size of the key space if all 8 characters are randomly chosen 8-bit ASCII characters is 256^8 = 2^64 = 18,446,744,073,709,551,616.

The average key search time with a single PC would be 18,446,744,073,709,551,616 / 2,000,000,000,000 (2 trillion) operations per second = 9,223,372,036,854,775.8 seconds, which is approximately 292,030 years.

The size of the key space for an 8-bit ASCII character is 2^64 combinations. On average, it will take a single PC 2^64 / (processing speed of PC in Hz) seconds to search through the entire key space.

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