Use an Addition or Subtraction Formula to simplify the equation. sin(3θ) cos(θ) − cos(3θ) sin(θ) = Square root 2/2 Find all solutions in the interval [0, 2π). (Enter your answers as a comma-separated list.)

Final answer:

The combined width of the three tables is 14 feet 4 inches, calculated by first converting each table's width to inches, adding them together, and then converting the total back to feet and inches.

Explanation:

To find the combined width of the three tables placed side by side, you need to add the widths together. First, convert all measurements to inches, add them, and then convert back to feet and inches.

Table 1: 2 feet 9 inches = (2 × 12) + 9 = 24 + 9 = 33 inches

Table 2: 4 feet 8 inches = (4 × 12) + 8 = 48 + 8 = 56 inches

Table 3: 6 feet 11 inches = (6 × 12) + 11 = 72 + 11 = 83 inches

Now, add the inches: 33 + 56 + 83 = 172 inches.

To convert 172 inches back to feet and inches, divide by 12 (since there are 12 inches in a foot): 172 ÷ 12 = 14 feet 4 inches (since 172 divided by 12 is 14 with a remainder of 4).

Therefore, the combined width of the tables is 14 feet 4 inches.

Answer: 400/400 which reduces to 1/1

Step-by-step explanation:

In 2006, 112.8 million households owned at least one TV set. About 5.8 million households owned 3 or more TV sets in 2006. What percentage of those owning atleast one TV set was this? Round to the nearest integer

5.8 / 112.8 = 0.051418 which is 5.1418 percent, rounds down to 5%.

Answer:

Lines e and f are parallel since their alternate exterior angles 75 ad 75 are congruent.

Step-by-step explanation:

Parallel lines mean that angle relationships exits where specific angles are congruent to each other. 75 and 75 are in the position of alternate exterior angles for lines e and f. Since they are congruent, these lines must be parallel. However, a and b have same side exterior angles which must add to 180. 75 + 115 does not equal 180. It equals 190. Therefore a and b cannot be parallel.

Answer:

E and F on edgenuidy

Step-by-step explanation:

did it rn

Orange juice contains some amount of sugar in it. There is 176 g of sugar present in a 2000 ml bottle of orange juice.

Given:

A 250 ml glass of orange juice contains 22 grams of sugar.

It is required to calculate the amount of sugar present in the 2000 ml bottle of juice.

Now, the amount of sugar present in 1 ml of juice will be,

[tex]\dfrac{22}{250}=\dfrac{11}{125}\rm \; g[/tex]

So, the amount of sugar in 2000 ml of juice will be,

[tex]\dfrac{11}{125}\times 2000=11\times 16\\=176\rm \; g[/tex]

Therefore, there is 176 g of sugar present in a 2000 ml bottle of orange juice.

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The probability of randomly selecting a heart or a spade is 1/2. The probability of randomly selecting a heart or a spade or a club is 3/4. The probability of randomly selecting a two or a diamond is 17/52.

(a) There are 13 hearts and 13 spades in a standard deck of cards. The probability of randomly selecting a heart or a spade can be calculated as:

P(Heart or Spade) = P(Heart) + P(Spade) = 13/52 + 13/52 = 26/52 = 1/2

(b) To find the probability of randomly selecting a heart or a spade or a club, we add the probability of selecting a club to the previous result:

P(Heart or Spade or Club) = P(Heart or Spade) + P(Club) = 1/2 + 13/52 = 39/52 = 3/4

(c) There are 4 twos and 13 diamonds in a standard deck of cards. The probability of randomly selecting a two or a diamond can be calculated as:

P(Two or Diamond) = P(Two) + P(Diamond) = 4/52 + 13/52 = 17/52

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The speed of the boat in still water is 4mph and the speed of the current is 2mph.

Using the distance formula expressed as:

Distance = speed * time

d = st

Let x be the ​crew's rowing rate in still water and;

let y be the rate of the current

If a crew rows with the​ current and it travels 18 miles in 3 hours, the

3(x+y)=18

If they row against the​ current, the crew rows 6 miles in 3 hours then;

3(x-y)=6  

The equations becomes

x + y = 6

x - y = 2

Add both equations

2x = 6 + 2

2x = 8

x = 4

Recall that x + y = 6

4 + y = 6

y = 2

Hence the speed of the boat in still water is 4mph and the speed of the current is 2mph.

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Answer:

The square is inscribed in a circle that means the square is drawn inside a circle such that it's vertices lie on the circle.

You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square i.e. Diagonal of the square is equal to diameter of the circle.

We could also see the image of such figure.

To locate the vertices of a square inscribed in a circle, follow these steps: draw the circle, choose a point on the circumference, create a radius, find the midpoint, and connect the points to form a square.

To locate the vertices of a square inscribed in a circle, you can follow these steps:

Now you have located the vertices of a square inscribed in circle C.

The simplified form of the expression  [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] is [tex]6\sqrt{120}[/tex] which corresponds to answer choice A.

Given: [tex]2\sqrt{10} \times 3\sqrt{12}[/tex]

To find: simplify

We can break down the expression  [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] and multiply the roots and whole numbers as follows:

[tex]\text{product is} = 2\sqrt{10} \times 3\sqrt{12} \\\text{product is} = 2 \times 3 \times \sqrt{10} \times \sqrt{12}\\\text{product is} = 6 \times \sqrt{120}\\\text{product is} = 6\sqrt{120}[/tex]

The simplified form of the given expression is 6√120, which corresponds to answer choice A.

Answer:

The 3 in the hundreds place has 10 times the value of the 3 in the tens place.

Step-by-step explanation:

In a base-10 place-value number system such as the one we customarily use, the value of a given digit is multiplied by 10 when it is placed one position farther to the left of the decimal point.

The threes in this number are in adjacent positions—one is in the tens place, and the one to its left is in the hundreds place. The digit in the hundreds place has a value of 300, which is 10 times the value of 30 that the digit in the tens place has.

Paul must increase the temperature by 216 degrees Fahrenheit to boil his ice and be able to cook his pasta.

Paul needs to raise the temperature of the ice he has from -4 degrees Fahrenheit to the boiling point of water, which is 212 degrees Fahrenheit. To determine how many degrees Paul needs to change the temperature, we subtract the current temperature of the ice from the desired temperature to boil water. Here is the step-by-step calculation: Subtract -4 from 212. The result is that Paul needs to increase the temperature by 216 degrees Fahrenheit for the ice to reach the boiling point and cook his pasta.

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The individual pipes can fill the pool in 4 hours and 12 hours respectively then using both pipes together, it will take 3 hours to fill the pool.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Give that,

One pipe can fill the pool in 4 hours.

Another pipe can fill the pool in 12 hours.

The first pipe fills the pool in 4 hours,

So its rate is 1/4 of the pool per hour.

Similarly,

The second pipe fills the pool in 12 hours,

So its rate is 1/12 of the pool per hour.

To find the combined rate, when both pipes are used together,

Add their individual rates:

(1/4 + 1/12)  = 3/12 + 1/12 of the pool per hour.

(1/4 + 1/12)  = 1/3 of the pool per hour.

Now, to find the time it takes to fill the pool using both pipes,

Take the reciprocal of the combined rate,

1 / (1/3) = 3 hours.

Hence,

Using both pipes together, it will take 3 hours to fill the pool.

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Answer:

a=1 b=5 c=-5

We solve by using the quadratic formula.

x = -5 +- sq root (5² - 4*1*-5) / (2 * 1)

x = [-5 +- sq root (25 + 20)]/ 2

Step-by-step explanation:

The correct numbers to use in solving problems about spans of time like B.C. and A.D. should be “integers”.

Integers are whole numbers (not a fractional number or not a decimal number) which can take a value of negative, zero, or positive number. Example of integers would be -1, 0 and 1.

In calculations, the time period would be on the x-axis. Since B.C. and A.D. are two different spans of time, therefore in the calculations, the date of BC should be negative (negative x-axis) while the date of AD should be positive (positive x-axis). This would place the origin as the common reference.

To solve problems about spans of time that include B.C. and A.D. dates, Integers will be used .

The terms A.C. and B.C. stands for anno Domini and before Christ

These are used to label  years in the Gregorian calendars.

For solving a Problem that involve B.C and A.D. , Integers will be used

As the time span are neither in fraction or decimal

It can be negative , 0 and positive

B.C will be on the negative side of the x axis and A.D. will be equal to the positive side of the x axis.

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Final answer:

The standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink is approximately 4.564 mg.

Explanation:

To calculate the standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink, we can use the concept of the sampling distribution of the sample mean.

When independent random samples of a fixed size are taken from a population, the standard deviation of the sample means (σx-bar) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is also known as the standard error of the mean.

The formula to find the standard deviation of the sample means is:

σx-bar = σ / √n

In this case, the population standard deviation is given as 25 mg of caffeine, and the sample size is 30 bottles.

So, we calculate the standard deviation of the average amount of caffeine as follows:

σx-bar = 25 mg / √30

σx-bar ≈ 25 mg / 5.477

σx-bar ≈ 4.564 mg (rounded to three decimal places)

Thus, the standard deviation of the average amount of caffeine in a carton containing 30 bottles is approximately 4.564 mg.

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This question is solved using proportions.

Thus, to find the number of boxes, we use a rule of three.

1 box - 12 cookies.

x boxes - 168 cookies.

Applying cross multiplication:

[tex]12x = 168[/tex]

[tex]x = \frac{168}{12}[/tex]

[tex]x = 14[/tex]

Thus, 14 boxes can be packaged.

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Now, we find the amount of money she made.

Thus:

[tex]T = 14 \times 1.2 = 16.8[/tex]

She made $16.8.

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100/5 =20

16 + 18 +20 +22 +24 = 100

middle number is 20