There are twenty one pictures. They will be hung in three equal groups. How many pictures will be in each group ?

A. 3 pictures

B. 7 pictures

C. 18 pictures

D. 24 pictures

So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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The probability that the taxi was actually blue is 0.61.

Witnesses are right 77% of the time. This means that they are incorrect 23% of the time. Furthermore, 25% of the taxis were blue while the rest were green. Since these are the only two choices, it follows that 75 percent of the taxis are green.

Using Bayes' Theorem, we can calculate the probability that the taxi was blue:

P (Taxi is blue|Witness said it was blue)

P (Witness said it was blue|Taxi is blue)

P (Taxi is blue)

P (Witness said it was blue|Taxi is green)

P (Taxi is green)

To begin, we must determine the probabilities of each of these:

P (Taxi is blue) = 0.25

P (Taxi is green) = 0.75

P (Witness said it was blue|Taxi is blue) = 0.77

P (Witness said it was blue|Taxi is green) = 0.23

To get the result we multiply all of them together:

P (Taxi is blue|Witness said it was blue) = P (Taxi is blue) × P (Witness said it was blue|Taxi is blue) / [P (Taxi is blue) × P (Witness said it was blue|Taxi is blue) + P (Taxi is green) × P (Witness said it was blue|Taxi is green)]P (Taxi is blue|Witness said it was blue) = 0.25 × 0.77 / (0.25 × 0.77 + 0.75 × 0.23)

P (Taxi is blue|Witness said it was blue) = 0.61

Therefore, the probability that the taxi was actually blue is 0.61.

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Answer:   I think it is A or C

hope this helps!

Step-by-step explanation:

\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

The fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

A fraction represents a part of a whole.

1. Let's say Alexa had a total of 5x crayons in the bag.

the number of blue crayons in the bag is 2x,

There is one triangle for every two round crayons,

(1/2) × 2x = x (By condition)

So, the fraction of crayons that are blue triangle is x / 5x = 1/5.

The number of blue round crayons is 2x.

The number of non-blue crayons is 5x - 2x = 3x,

The ratio of blue rounds to non-blue crayons is 2x / 3x = 2/3.

2.

4 out of 5 wall footballs are rubber, 4/5 of the footballs in the bag are rubber.

The fraction of rubber footballs that are brown is 2/3.

The fraction of footballs that are brown rubber footballs is (4/5) × (2/3) = 8/15.

The fraction of non-brown rubber footballs is (4/5) - (8/15) = 4/15.

The ratio of rubber footballs to non-rubber footballs is (4/5) / (1/5) = 4.

So there are 4 times as many rubber footballs as non-rubber footballs

Hence,  the fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

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Answer:

27/100?

Step-by-step explanation:

(a) This is a partition of the set of integers because every integer is either even or odd, and no integer can be both even and odd at the same time.

(b) This is not a partition of the set of integers because it does not include 0, which is an integer that is neither positive nor negative.

(c) This is a partition of the set of integers because every integer is either divisible by 3, leaves a remainder of 1 when divided by 3, or leaves a remainder of 2 when divided by 3, and no integer can belong to more than one of these sets at the same time.

(d) This is a partition of the set of integers because every integer belongs to exactly one of these sets.

(e) This is not a partition of the set of integers because the set of integers that leave a remainder of 3 when divided by 6 includes both even and odd integers, which means that some integers would belong to more than one of these sets at the same time.

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Answer:

GOODMORNING!!!

Step-by-step explanation:

I pray you, have a wonderful day!!  

The average movie ticket cost in Japan is approximately $17.73, while the average movie ticket cost in Switzerland is approximately $13.45.

To find the average movie ticket prices in Japan and Switzerland, we can set up a system of equations based on the given information.

Let's assume the cost of one movie ticket in Japan is represented by the variable J, and the cost of one movie ticket in Switzerland is represented by the variable S.

From the given information, we can establish two equations:

Equation 1: 3J + 2S = $80.09

Equation 2: 3S + 2J = $75.81

We can solve this system of equations to determine the values of J and S.

To eliminate one variable, we can multiply Equation 1 by 3 and Equation 2 by 2:

Equation 3: 9J + 6S = $240.27

Equation 4: 6S + 4J = $151.62

Now, subtract Equation 4 from Equation 3 to eliminate the S variable:

(9J + 6S) - (6S + 4J) = $240.27 - $151.62

9J + 6S - 6S - 4J = $88.65

5J = $88.65

Divide both sides of the equation by 5:

J = $88.65 / 5

J = $17.73

So, the cost of one movie ticket in Japan is approximately $17.73.

Now, we can substitute the value of J into one of the original equations to find the cost of one movie ticket in Switzerland:

3S + 2J = $75.81

3S + 2($17.73) = $75.81

3S + $35.46 = $75.81

3S = $75.81 - $35.46

3S = $40.35

Divide both sides of the equation by 3:

S = $40.35 / 3

S = $13.45

Therefore, the cost of one movie ticket in Switzerland is approximately $13.45.

To summarize, the average movie ticket cost in Japan is approximately $17.73, while the average movie ticket cost in Switzerland is approximately $13.45.

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From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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The rank of the matrix A is equal to the dimension of its column space. Therefore, the rank of A cannot be determined solely based on the given characteristic polynomial.

The rank of a matrix is a measure of the linear independence of its columns. It represents the maximum number of linearly independent columns in the matrix.

On the other hand, the characteristic polynomial of a matrix is a polynomial equation obtained by subtracting the identity matrix multiplied by the scalar variable λ from the given matrix A, and then taking the determinant.

The characteristic polynomial provides information about the eigenvalues of the matrix, which are the values of λ that satisfy the equation αλ^5 + βλ^4 + γλ^3 = 0.

While there may be some connections between the rank of the matrix and the characteristic polynomial, it is not possible to determine the rank of the matrix A solely based on the given characteristic polynomial equation.

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Answer:

A im guessing sorry if wrong hope i help

Step-by-step explanation:

Answer:

Step-by-step explanation:

If Galena had $16 in her bank and $28 in her wallet. after her aunt gave her some more money, she had $60. So, Galena's aunt gave her $16.

To solve the problem, let's break it down step by step using algebra. Let x represent the amount of money Galena's aunt gave her. According to the information given, Galena received $16 and $28 from her parents. We can write this as:

$16 + $28 + x = $60

To find the amount Galena's aunt gave her, we need to isolate the variable x. We can do this by simplifying the equation:

$44 + x = $60

Next, we want to isolate x on one side of the equation. We can do this by subtracting $44 from both sides:

x = $60 - $44

Simplifying further, we have:

x = $16

So, Galena's aunt gave her $16.

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Answer:

24π in³/75.36 in³

Step-by-step explanation:

We are looking for the volume of a cone with a diameter of 6 inches and a height of 8 inches.

First, divide the diameter by 2 to get the radius.

6 in/2 = 3-in. radius

Now, incorporate the formula for the volume of a cone. That is πr²h/3.

3.14 * 3² * 8/3

Square 3 to get 9.

3.14 * 9 * 8/3

Multiply 3.14 by 9 to get 28.26.

28.26 * 8/3

I recommend turning 28.26 into a improper fraction. That would be 1413/50.

1413/50 * 8/3

Can any cross-cancellation be done? Yes!

50 and 8 share a GCF of 2.

1413/25 * 4/3

1413 and 3 share a GCF of 3.

471/25 * 4/1

Multiply 471 by 4, and put it over 25.

1884/25

Simplify your answer.

75 9/25 = 75.36 in³, which is about 24π in³.

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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Answer:

AB and BC are the sides of a parallelogram, ABCD. AB = 5 cm, BC = 7 cm and ABC = 60 degrees. Draw the lines AD and CD to complete the parallelogram.

Step-by-step explanation:

Answer:

27.6%

Step-by-step explanation:

See the attached worksheet. Find the total number of marbles (29) and then take the green marbles and divide by the total and multiply by 100%.  (8/29)*(100%) = 27.6% to the nearest tenth.

The limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity is 0.

To find the limit of the function (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity, we will divide both the numerator and denominator through the highest power of x. In this case, the highest power of x is x², so we can divide both the numerator & the denominator through x²:

\([(2x-1)/(x^2)] * [(3-x)/((x-1)/(x^2)(x+3))]\)

Now, as x approaches infinity, every of the fractions within the expression procedures zero except for (2x-1)/(x²). This fraction techniques 0 as x procedures infinity because the denominator grows quicker than the numerator. therefore, the limit of the expression as x strategies infinity is:

0 * 0 = 0

Consequently, When x gets closer to infinity, the limit of (2x-1)(3-x)/(x-1)(x+3) is 0.

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Answer:

Step-by-step explanation:

A formula is a method that has been proven to work when solving specific types of problems.

Let’s explore some of those familiar formulas by looking at rectangles, squares, area and perimeter.

The perimeter of a figure is the distance around the figure. Perimeter is the sum of all of the sides in a square or rectangle. Since a rectangle has two sets of parallel sides, the formula for determining perimeter  of a rectangle is:

and

Let’s look at an example.

[Figure 2]

The rectangle above shows its dimensions. Find the perimeter.

First, substitute the values for the width  and the length  into the perimeter formula.

Next, complete the multiplication and addition to find the perimeter.

The answer is 42.

The perimeter of the rectangle is 42 inches.

Area is the amount of square units inside the figure. Area is found by multiplying the . The formula for finding the area of a rectangle is:

You can use the dimensions from the rectangle above to find the area of this rectangle.

First, fill the values for  and  into the formula for area.

Next, solve for the area by multiplying.

The answer is 108.

The area of the rectangle is .

Notice that the unit of measurement for area is squared. That is because you multiplied a unit measure times itself: . Area is always written in square units.

You can also find the perimeter and area of a square. Remember that a square has four equal sides given the symbol . You can use the following formula for finding the perimeter of a square:

Let’s look at an example.

A rectangle has a length of 12 feet and a perimeter of 72 feet. Write and solve an equation to determine the width of the rectangle.

First, substitute the values for the perimeter  and the length  into the perimeter formula.

Next, complete the multiplication.

Then, subtract 24 from both sides to get your variable alone on the right side.

Then, multiply both sides by the reciprocal of 2 to isolate your variable.

The answer is 24.

The width of the rectangle is 24 feet.

Examples

Example 1

Earlier, you were given a problem about Raj and his garden fence.

He knows that the area of the land is 240 square feet, the length of one side is 15 feet, and needs to know the width of the land.

First, substitute the values for the area and the side length into the area formula.

Next, multiply both sides by the reciprocal of 15 in order to isolate the variable .

The answer is 16.

The width of Raj’s garden is 16 ft. Therefore the dimensions of the garden are 16 ft by 15 ft.

Example 2

A square has a perimeter of 196 inches. Determine the length of one side of the square.

First, substitute the value for the perimeter  into the perimeter formula.

Next, multiply both sides by the reciprocal of 4 to isolate your variable.

The answer is 49.

Example 3

Find the perimeter of the following square if the side length is 4.5 inches.

First, substitute the value for the side length into the perimeter formula.

Next, multiply by 4 to solve for the perimeter.

The answer is 18.

Example 4

Can you find the area of the square in Example 1?

First, substitute the value for the side length into the area formula.

Next, multiply to solve for the area.

The answer is 20.25.

The area of the square is .

Example 5

A square has an area of 144 sq. meters. What is the side length?

First, substitute the value for the area into the area formula.

Next, take the square root of the area to isolate . Remember that the opposite of square is square root.

The answer is 12.

Answer:

55

Step-by-step explanation:

165 / 3 = 55 therefore, one inch is equal to 55 miles. Hope this helps

The correct set of hypotheses for testing the effect of the bonus plan is:

To test the effect of the new bonus plan on increasing sales at the automobile dealership, the manager can use the following set of hypotheses:

Null Hypothesis: The mean sales rate per salesperson remains the same or less than five automobiles per month (H0: μ ≤ 5)

Alternative Hypothesis: The mean sales rate per salesperson increases with the implementation of the bonus plan (HA: μ > 5)

These hypotheses will help determine if the bonus plan has a significant impact on increasing sales.

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Answer:

(13, 16)

Step-by-step explanation:

Point A has coordinates (3,2) Point b has the coordinates (27,30)

Therefore the width of the diagram = 27 - 3 = 24 units and the height of the diagram = 30 - 2 = 28 unit

The length of the square = 28 unit / 4 square = 7 unit

Also, half of the height of the diagram = 28/2 = 14 unit

Therefore the x coordinate is given by:

27 - (2 × 7) = 27 - 14 = 13 or 27 - 14 (=13) or 3 + 7 + (24 - 3 × 7) = 13

Also, the y coordinate is given by:

30 - (2 × 7) = 30 - 14 = 16 or 30 - 14 (=16) or (30 + 2)÷2 = 16

Therefore the coordinate for point C is given by (13, 16)

Answer:

8 is the atomic number

Step-by-step explanation:

Atomic number = 8  (meaning it has 8 protons in its nucleus)

Atomic weight = 15.999

O = symbol for oxygen

Answer:

6 quarts

Step-by-step explanation:

8 bags

--------

2 quarts

Multiply top and bottom by 3

8*3 bags

--------

2*3 quarts

24 bags

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

6 quarts

Answer:

6

Step-by-step explanation:

2 quarts of iced tea = 8 tea bags.

x quarts of Iced tea = 24 tea bags

=> 2/8 = x/24

=> Multiply the extremes and means

=> 8x = 48

=> 8x / 8 = 48 / 8

=> x = 6

6 quarts of iced tea can be made with 24 tea bags.

Answer:

Step-by-step explanation:

Scalene (no equal side): 4th triangle

Isosceles (two equal sides): 1st, 2nd, and 4th triangle

Equilateral (all equal sides): 3rd triangle

Hope this helps!

Answer:

6.73 x 1\(0^{2}\)

Step-by-step explanation:

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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