The franklin room is 49 ft by 49 ft how many 5 ft diameter round tables could you fit in the aisles in the Franklin Room?

What would be the maximum number of chairs you could fit in the Franklin room for 5 foot round tables

Answer:

Probability of an even number product as requested = 7/10 = .7 = 70%

Step-by-step explanation:

Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4) and 3 odd digits, (1,3,5).

Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 exact digits = 1*1 = 1. Thus, 6+1 = 7 different 2-digit products result in even numbers from among 10 possible 2-digit products.

Probability of an even number product as requested = 7/10 = .7 = 70%

The two quadrilaterals TUVW and EFGH are similar.

Those polygons look the same but are different in size.

And in similar polygons,

the corresponding sides are in constant proportion to each other and the corresponding angles are equal to each other.

Given:

TUVW and EFGH are the two quadrilaterals.

The sides of the polygon TUVW are equal.

And the sides of the polygon EFGH are equal.

That means the corresponding sides will have a constant ratio.

And corresponding angles are congruent.

So, the polygons are similar.

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24

24x3.14

75.36

75.36/3.14

= 24 its b

Answer: 36pi(cm)^2 Answer B

Step-by-step explanation:

Answer:

3,115

Step-by-step explanation:

900 + 275 + 490 + 1450 = 3,115

The angle measures of each vertex of the garden are 53.13 degrees.

In Parallelogram ABCD, diagonals AC and BD intersect at point A = √7.

Angle is a geometric figure that can be described as the amount of rotation between two straight line or planes and angle is measured in degree with a full circle being 360°.

1. To determine the angle measures of each vertex of the garden, we must first calculate the angles formed by each side. For example, the angle formed by sides AB and BC can be found by using the inverse tangent function. The equation would be

arctan(BC/AB) = arctan (4/3) = 53.13 degrees.

The angles for the other sides can be calculated in the same way. We can then use the sum of angles theorem to calculate the angles at each vertex. Since the garden is an irregular shape, the angles at each vertex will be different.

2. In Parallelogram ABCD, diagonals AC and BD intersect at point A. To calculate , we can use the distance formula.

The equation would be = √((x2 – x1)2 + (y2 – y1)2).

For the coordinates given, we would have

= √((2 – 5)2 + (5 – 1)2)

= √(-9 + 16)

= √7.

Answer 3: To determine whether quadrilateral ABCD is a rectangle, rhombus, or square, we must first calculate the slope.

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Answer:

x ≥ 3

Step-by-step explanation:

3x ≥ 9

x ≥ 3

Answer:

D(t) = 20 * sin(B * t - B * 3 + k * 2π) + 45 = 20 * sin(B * (t - 3) + k * 2π) + 45

Step-by-step explanation:

The temperature over a day can be modeled by a sinusoidal function of the form:

D(t) = A * sin(Bt + C) + D

Where A is the amplitude (half the difference between the high and low temperatures), B is the angular frequency, C is the phase shift, and D is the vertical shift.

From the given information, we know:

The high temperature is 85 degrees.

The low temperature of 45 degrees occurs at 3 AM, or 3 hours after midnight.

So, the amplitude is (85 - 45)/2 = 20

The temperature at 3 AM can be found by setting t = 3:

D(3) = 20 * sin(B * 3 + C) + 45

So, the vertical shift is 45.

Finally, we can find the phase shift by using the fact that the low temperature occurs at 3 AM:

C = -B * 3 + k * 2π

Where k is an integer.

Putting it all together, we get:

D(t) = 20 * sin(B * t - B * 3 + k * 2π) + 45 = 20 * sin(B * (t - 3) + k * 2π) + 45

This is the equation for the temperature, D, in terms of t.

Answer: Depends on the unit. IF INCHES: 6 1/2 = 78 Inches

Step-by-step explanation:

6.5 x 12 = 78

Please reply if not inches, I can try to help you after ^^

By  simple interest , 2108 is the balance after 6 years.

What does compound and simple interest mean?

Simple interest and compound interest are the two methods that can be used to compute interest. The principal, or initial amount of a loan, is used to compute simple interest.

                                Compound interest is often referred to as "interest on interest" since it is computed using the main amount and the interest that has accrued over the course of previous periods.

annual simple interest = 4%

principal = $1700

 Time = 6 years

  interest = PRT/100

            = 1700 * 6 * 4/100

            =   408

 the balance after 6 years  = 1700 + 408

                                               =    2108

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The equation for the rate of change of concentration is Δc/Δt, and this is equal to the rate of change of concentration over a given interval, -0.0680 m/s.

To calculate the final concentration, we must use the equation Δc = rate × time, where Δc is the change in concentration, and rate and time are the rate of change of concentration and the interval, respectively. Plugging in our values, Δc = -0.0680 m/s × 3.0 s = -0.204 m. This means that the final concentration of c is 2.700 m - 0.204 m, which is equal to 2.496 m.

To summarize, the rate of change of concentration equation is Δc/Δt = rate of change, and the equation to calculate the final concentration is Δc = rate × time. Plugging in the rate of change and interval, we get Δc = -0.0680 m/s × 3.0 s = -0.204 m, which gives us the final concentration of c at the end of the same interval as 2.496 m.

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Answer:

16

Step-by-step explanation:

Any number to the power of 0 is 1

1/4^-2 -> 4^2 -> 16

Answer: 16

Step-by-step explanation:

-2^0 = 1

y^-2 => 1/y^2 => 1/4^2 = 1/16

1/ (1/16)

1 x 16/1 = 16

Answer:

3

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\=\frac{f(1)-f(-1)}{1-(-1)}\\ \\=\frac{3-(-3)}{1+1}\\\\=\frac{3+3}{2}\\ \\=\frac{6}{2}\\ \\=3[/tex]

The value of a, A and C are 12.31 cm,44.07° and 34.68° respectively

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find C:

b/sinb = c/sinC

17.23/sin101.25 = 10/sinC

17.23 × sin C = sin101.25 × 10

17.23× sin C = 0.98 ×10

sinC = 9.8/17.23

sinC = 0.569

C = sin^-1(0.569)

C = 34.68°

The sum of angle in a triangle is 180

A = 180-(101.25+34.68)

A= 180-135.93

A = 44.07°

a/sinA = b/sin B

a/sin 44.07 = 17.23/sin101.25

a= sin 17.23 × sin 44.07/sin101.25

a =( 17.24× 0.70)/0.98

a = 12.31 cm

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Answer:

x = Approximately 4.92. (Tech: 4.923076923076923)

Step-by-step explanation:

To solve for x in the equation,

x - 1/4(12 - x) = x + 3(4 - x) - 2x

Expand the terms on the right side:

x - 1/4(12 - x) = x + 12 - 3x - 2x

Combine like terms:

x - 1/4(12 - x) = -3x + 12

Isolate x on one side of the equation:

1/4(12 - x) + 3x = 12 + x

Combine like terms:

1/4(12 - x) + 3x = 13

Distribute 3x:

1/4(12 - x) + 3x = 13

3x = 13 - 1/4(12 - x)

Multiply both sides by 4:

12x = 52 - (12 - x)

Combine like terms:

13x = 64

Finally, divide both sides by 13:

x = 4.923076923076923

So the value of x is approximately 4.92.

As a result, the vector a = pi+qj, where p and q are positive constants, has p=0.573 and q=11.991 so that |a| = 15.

A vector is an quantity with direction and magnitude but no controlling idea in mathematics. Examples of such statistics include shock and velocity. A vector is something that has both and direction. A vector can be thought of technically as a pointed line segment, whose length relates to the vector's magnitude and whose motion is indicated by an arrow. A quantity or phenomenon known as a vector has two distinct assets: size and direction. The phrase also refers to a mathematical or geometrical representation of these numbers. Emfs, weight, momentum, power, and velocity are examples of vectors in nature.

Given

ā= pi +qj =      and    |al = p2 +q2 = 15

\vec{a}  makes an angle of 55  with i    i.e.  (pi +9]). = cos55

(pi +bj]). = cos55  = 0.573

=>p = 0.573

:.q2 = 15^2 – (0.573)2 = 224.64

=> q = 11.991  

As a result, the vector a = pi+qj, where p and q are positive constants, has p=0.573 and q=11.991 so that |a| = 15.

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The number of the one-point shot is 17 and the number of the 2 point shot is 36.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that at a basketball​ game, a team made 53 successful shots. They were a combination of​ 1- and​ 2-point shots.

Let the one-point shot is x and the 2 point shot is y. The equations can be written as below:-

x + y = 53

-x - 2y = -89

_________

y = 36

The value of x will be calculated as:-

x + y = 53

x + 36 = 53

x = 53 - 36

x = 17

Hence, the one-point shot number is 17, and the two-point shot number is 36.

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Question 1

We can say that [tex]P=a \cdot b^w[/tex] for constants [tex]a[/tex] and [tex]b[/tex].

Substituting the given points into this equation yields [tex]ab=900[/tex] and [tex]ab^3=8100[/tex]. We need to find the value of [tex]b[/tex] in this system.

[tex]\frac{ab^3}{ab}=\frac{8100}{900} \implies b^2=9[/tex]

Since the graph shows exponential growth, take the positive square root. So, [tex]b=\boxed{3}[/tex].

Question 2

We need to find the value of [tex]a[/tex].

[tex]ab=900 \implies 3a=900 \implies a=\boxed{300}[/tex]

Answer:

The area of a parallelogram is given by the formula A = base x height. In this case, the base has a length of x meters, and the height is x - 1 meters. So we can write:

A = x(x - 1)

We are told that the area is 306 square meters, so we can set up an equation:

x(x - 1) = 306

Expanding the left side gives:

x^2 - x = 306

Bringing all the terms to one side gives a quadratic equation:

x^2 - x - 306 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = -1, and c = -306, so:

x = (1 ± sqrt(1 - 4(1)(-306))) / 2(1)

x = (1 ± sqrt(1 + 1224)) / 2

x = (1 ± sqrt(1225)) / 2

x = (1 ± 35) / 2

So x is either (1 + 35) / 2 = 18 or (1 - 35) / 2 = -17/2. Since x represents a length, it cannot be negative, so the value of x is 18 meters.

Therefore, the answer is x = 18.

The proof that the angles are similar have been done below

To prove that two triangles are similar, we need to show that they have congruent angles.

We can use the Angle-Angle (AA) Similarity theorem, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

In triangle ABC, angles A and B are equal to angles A and D in triangle ADE. So, according to the AA Similarity Theorem, triangles ABC and ADE are similar.

Thus, we can write:

ABC ~ ADE

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If each container held 8 ounces of salad, then Larry purchased a total of number of 96 ounces of pasta salad.

1. First, determine the number of containers of pasta salad purchased. In this case, it is 12 number of containers.

2. Next, determine the amount of salad contained in each container. In this case, each container holds 8 ounces of salad.

3. Finally, multiply the number of containers purchased (12) by the amount of salad contained in each container (8 ounces). This gives us a total of 96 ounces of pasta salad purchased.

the complete question is :

Larry bought 12 containers of pasta salad for a school picnic. Each container held the same number of ounces of salad. If the total weight of the 12 containers was 6 pounds, how many ounces of pasta salad did each container hold?

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Answer:

54,736

Step-by-step explanation:

22+44+556=622 × 88

Answer:

7.068....................

Answer:

6x-6y=0

Step-by-step explanation:

The discount is $30 and the rate of discount for the truckload of Kurt's Dirt selling for $120 but bought for $90 is 25%.

The discount rate refers to the percentage of price reduction offered to retail customers.

To compute the discount rate, we first determine the amount of discount.  Then the result is expressed as a percentage of the initial price before the discount.

The selling price of a truckload of Kurt's Dirt = $120

The discounted price = $90

The amount of discount = $30 ($120 - $90)

Discount rate = 25% ($30/$120 x 100).

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The minimum size of a cut where size is number of edges in the cut, for a graph that has more than one connected component is 1.

In graph theory, a bridge, also known as a cut-edge, is a fundamental concept that refers to an edge in a graph that has the property of disconnecting the graph when it is removed. This means that when an edge is considered a bridge, the removal of that edge would result in an increase in the number of connected components in the graph. The importance of bridges in graph theory lies in the fact that they provide a way to break down a complex graph into smaller, simpler components that can be analyzed and understood individually. Bridges can be found in many different types of graphs, including undirected graphs, directed graphs, and weighted graphs. It is also important to note that in a graph with more than one connected component, there must exist at least one bridge, meaning that the minimum size of a cut in a graph is 1. This is because a bridge is the edge that separates the graph into two or more separate components.

The minimum size of a cut in a graph is 1. This occurs in the case of a "bridge", where removing a single edge from the graph would result in two separate connected components. In any graph with more than one connected component, there must exist at least one bridge, meaning that the minimum size of a cut is 1.

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Answer:

Jim gets 16 Tim get 40

Step-by-step explanation:

The largest domain of f(x)=x²+1 is ∝

From the question, we have the following parameters that can be used in our computation:

f(x)=x²+1

The above expression is a quadratic function

The domain of a quadratic function is the set of all real values

This means that the input value can be as large as possible

So, the largest domain is ∝ (infinity)

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The testing strategy important in the design of an experiment because a good strategy will produce accurate results. So the option a is correct.

The Design of Experiments (DOE) method is a statistical methodology for planning, carrying out, and analyzing tests. Any program based on DOE principles should start early in the test planning process.

The test planners should assemble a group of subject matter experts who can identify the primary quantitative mission-focused measures of interest (in DOE parlance: response variables) that will characterize the system's performance in the context of a mission-oriented evaluation.

Environmental and operational factors that are expected to drive system performance, as well as their levels, should be identified by test planners.

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The complete question is:

Why is the testing strategy important in the design of an experiment?

Multiple Choice

a. A good strategy will produce accurate results.

b. Good testing strategy will always disprove the hypothesis.

c. Good testing strategy will allow you to prove your hypothesis to be true.

The value of the trigonometry identity is tan(2x) = 4/7[√2]

From the question, we have the following parameters that can be used in our computation:

cos(x) = 2√5/5 and 3π/2 < x < 2π

Start by calculating the sine function sin(x) using

sin(x) = √[1 - cos²(x)]

So, we have

sin(x) = √[1 - (2√5/5)²]

This gives

sin(x) = 1/10[√10]

The tangent is then calculated as

tan(2x) = (2sin(x)cos(x))/(cos²(x) - sin²(x))

This gives

tan(2x) = (2 * 1/10[√10] * (2√5/5))/(((2√5/5))² - (1/10[√10])²)

Evaluate

tan(2x) = 4/7[√2]

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The solution to the figure shown is Option D.

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the figure be represented as A

Now , the front part of the figure is shown

And , on reflection , the position of the figure will be changed

The top part of the figure has 4 cubes

And , the side view of the figure has 2 cubes

From the options , we can see that the Option D satisfies the figure shown in the question

As , the front view will have a cube above the second cube and top view will show 4 cubes and the side view will show 2 cubes respsectively

Hence , the figure is solved

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