1. A rectangular room has an area of 400 sq. ft. The length is 7 ft less than twice the width. Find the
dimensions of the room.

The formula for the area of the trapezoid is A = 1/2(b₁ + b₂)h and the formula for height will be (2A)/(b₁ + b₂).

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

The area of a trapezoid is given as,

A = 1/2(b₁ + b₂)h

The formula for height h will be as,

A = 1/2(b₁ + b₂)h

h = (2A)/(b₁ + b₂)

Hence "The trapezoid's area is calculated using the calculation A = 1/2(b1 + b2)h, and its height is calculated using the formula (2A)/(b1 + b2).".

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It is ''True'' that leagues with larger standard deviation values are more competitively balanced than other leagues.

The standard deviation is a measure of how widely distributed or how much values vary. The expected value occurs when the standard deviation is low, which increases the likelihood that the values will fall within a small range. When the standard deviation is high, on the other hand, the expected value occurs when the values are closer to the mean.

Lets take an example to understand Standard deviation

Let's say the entire target population is comprised of eight students in a specific class. By subtracting the average of the values' squared deviations from it, one can calculate the population standard deviation for a finite set of numbers.

Eight of the following values represent the marks of an eight-student class (or a statistical population):

2,4,4,5,5,5,7,8

These eight data points have the mean (average) of 6;

[tex]\frac{2+4+4+5+5+5+7+8}{8}[/tex] =  [tex]\frac{40}{8}[/tex]

=  5  

First, calculate the deviations of each data point from the mean, and square the result of each:

[tex](2-5)^{2} =[/tex] [tex](-3)^{2}[/tex] = 9                          [tex](5-5)^{2} =[/tex]  [tex]0^{2}[/tex]     = 0

[tex](4-5)^{2} =[/tex] [tex](-1)^{2}[/tex] = 1                           [tex](5-5)^{2} =[/tex]  [tex]0^{2}[/tex]     = 0

[tex](4-5)^{2} =[/tex] [tex](-1)^{2}[/tex] = 1                           [tex](7-5)^{2} =[/tex] [tex]2^{2}[/tex]      = 4

[tex](5-5)^{2} =[/tex]  [tex]0^{2}[/tex]     = 0                           [tex](8-5)^{2} =[/tex] [tex]3^{2}[/tex]      = 9.

The variance is the mean of these values:

[tex](sigma)^{2}[/tex] =  [tex]\frac{9+1+1+0+0+0+4+9}{8}[/tex] =  [tex]\frac{24}{8}[/tex] = 3

and the population standard deviation is equal to the square root of the variance:

sigma = √3 = 1.732

This formula is valid only if the eight values with which we began form the complete population.

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Answer: n+575= total

or n+575=t

Step-by-step explanation:

n is what we start with, plus what she has this year. the total is unknown.

The required number of sessions is obtained as 2.

A linear equation can be balanced by adding or subtracting the same number on both sides of the equality sign. Similarly, multiplication and division is also possible with the same numbers.

Suppose the number of sessions be x.

Then, the expression for the training cost as per the first plan is given as 41 + 83x.

And, for the another plan it is 43x + 82.

As per the question both the expressions has to be equated for the same cost as follows,

43 + 82x = 41 + 83x

=> 43 - 41 = 83x - 82x

=> x = 2

Hence, the number of sessions for both the plans to have same cost is 2.

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Answer:

The perimeter of the quadrilateral is the sum of the four side lengths. If the perimeter is 92 feet, then we can write the equation $x + (x+2) + (x+4) + (x+6) = 92$, where $x$ is the length of the shortest side. Solving this equation, we find that $x = 20$. This means that the side lengths are 20 feet, 22 feet, 24 feet, and 26 feet, so the longest side is 26 feet.

S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7), We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).

The link between lines and points is described by a graph, which is a mathematical description of a network.

The link between lines and points is described by a graph, which is a mathematical description of a network.

Plotting a graph based on the provided data is shown in the attachment.

Given, \s (x,y)=(x+7,y-9)

For example, S(-3,6)=S'(x+7,y-9)=S'(-3+7, 6-9)=S' (4,-3)

T(0, 7) = T' (x+7, y-9) = T' (0+7, 7-9) = T' (7,-2)

According to U(1,4)=U'(x+7,y-9)=U'(1+7, 4-9)=U' (8,-5)

Considering that V(-5,2)=V'(x+7,y-9)=V'(-5+7,2-9)=V' (2,-7)

To create the graph, we must plot the points S'(4,-3), T'(7,-2), U'(8,-5), and V'(2,-7).

S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7)

We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).

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The solution of the given equation is, y = -3.

what is solving an equation?

An effective method for solving linear equations can be found in the steps that follow. By deleting parentheses and combining like terms, each side of the equation can be made simpler. The variable term on one side of the equation can be separated using addition or subtraction. To find the variable, use multiplication or division.

Consider, the given equation

[tex]\frac{y}{y}-5 + \frac{5}{5}-y =0[/tex]

Since, If a/a then it is 1.

⇒ 1 - 5 + 1 - y = 0

-3 - y = 0

Add y on both sides,

-3 - y + y = 0 + y

-3 = y

y = -3

Hence, the solution of the given equation is, y = -3.

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(y2 - y1) / (x2 - x1) is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2.

The slope of the line passing through the points P1 (x1, y1) and P2 (x2, y2) is calculated by: (y2 - y1) / (x2 - x1).

1. Subtract the y-coordinates of the two points: y2 - y1.

2. Subtract the x-coordinates of the two points: x2 - x1.

3. Divide the two results from steps 1 and 2: (y2 - y1) / (x2 - x1).

For example, if the two points are P1 (1, 5) and P2 (3, 8), then the slope is calculated by: (8 - 5) / (3 - 1) = 3 / 2 = 1.5. This means that the line has a slope of 1.5, which means that for every 1 unit increase in x, the y-coordinate increases by 1.5 units. So, for every 2 units increase in x, the y-coordinate increases by 3 units.

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Answer:

C

Step-by-step explanation:

since the dilatation is centred at the origin then multiply the coordinates of the point by scale factor of [tex]\frac{1}{3}[/tex]

(- 3, 6 ) → ([tex]\frac{1}{3}[/tex] (- 3), [tex]\frac{1}{3}[/tex] (6) ) → (- 1, 2 )

The value of all the missing angles in the triangles are;

∠1 = 37°

∠6 = 30°

∠4 = 63°

∠3 = 133°

We know that the sum of angles in a triangle is equal to 180 degrees. Thus, with this knowledge, we can find the angles 1 and 6.

Therefore;

∠1 = 180 - (70 + 73)

∠1 = 180 - 143

∠1 = 37°

∠6 = 180° - (107° + 43°)

∠6 = 180° - 150°

∠6 = 30°

Now, we know that sum of angles on a straight line is 180 degrees. Thus, we can find angle 4 as follows;

∠4 = 180° - (65° + 42°)

∠4 = 180° - 117°

∠4 = 63°

∠3 = 90 + 43

∠3 = 133°

Thus, the conclusion is that the missing angles are ∠1 = 37°, ∠6 = 30°, ∠4 = 63°, ∠3 = 133°

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Answer:

12in

Step-by-step explanation:

Base Area and Volume are proportionalised based on their Height.

Eg. Base Area of Cube = Length × Width

Volume of Cube = Length × Width × Height

Given from the Question:

Base Area of Pyramid =

[tex]25 \: {in}^{2} [/tex]

Volume of Pyramid =

[tex] \frac{1}{3} (base \: area)(height) = 100 {in}^{2} [/tex]

We already knew the Base Area, so we can substitute it into the Volume of Pyramid Formula to find the height.

[tex] \frac{1}{3} (25)(height) = 100 \\ height = \frac{100(3)}{25} \\ = 12in[/tex]

Therefore the height of the Pyramid is 12in.

Bubble cost = $1.49

Beach ball cost = $2.00

Sand bucket cost = $3.50

Bubble = B

Beach Ball = A

Sand bucket = S

total cost = 6B + 2A + 3S

total cost = 6(1.49) + 2(2) + 3(3.5) = 23.44

Hope this helps :)

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- Jeron

A linear function can only have one degree at most but the range of linear function is infinite.

In the given question, we have to explain what is the range of linear function.

A linear function can only have one degree at most. Therefore, it has at least most one x increased by one. The formula for them is f(x) = mx + b.

Nearly invariably, the domains and ranges of linear functions are infinite. When the graph is a horizontal line, there is an exception. This occurs when a function, like f(x) = b, equals a constant. These functions' domains are unlimited, but their range only contains the value b.

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By studying the graph, it can be concluded that

Todd has done three mistakes

He has y increasing when x is between -5 and 0 instead of decreasing.

He has y decreasing when x is between 0 and 5 instead of increasing.

He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.

What is graph of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of points of the form (x, f(x))

Original specifications of the graph

y is decreasing when x is between -5 and 0

y is increasing when x is between 0 and 5

The relationship between x and y is non-linear from x = - 5 to x = 0

The relationship between x and y is linear from x = 0 to x = 5

From the graph it can be seen that Todd has done three mistakes

He has y increasing when x is between -5 and 0 instead of decreasing.

He has y decreasing when x is between 0 and 5 instead of increasing.

He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.

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The tangent planes to the surface are described by the equation "6x + 12y + 48z - 210 = 0" (3, 4, 3).

In this instance, the equation yields the parametrized surface "r(t) = (t², [tex]t^3[/tex], [tex]t^4[/tex]). On the surface, the issue that interests us is (3, 4, 3).

We may use the partial derivative concept to obtain the second derivative of the surface at points (3, 4, 3). Regardless of whether a change in the parameterization approaches zero, the time derivative of the parameter value of a variable serves as the upper estimate of the differentiating quotient.

[(r(3 + h) - r(3)) / h] as h approaches 0

For the x-coordinate of the surface, this limit is given by

[((3 + h)² - 3²) / h] as h approaches 0

which simplifies to

[(9 + 6h + h² - 9) / h] as h approaches 0

which simplifies to

[6h + h²] as h approaches 0

Since h is approaching 0, h2 is approaching it faster than h. As h approaches 0, the limit changes from 0 to 6, and the number of h2 decreases relative to the value of 6h.

Thus, the partial derivative of the x-coordinate of the surface concerning the time at the coordinates (3, 4, 3) is 6.

As a result, the vector is the normal vector to the ground at the location (3, 4, 3). (6, 12, 48). 6x + 12y + 48z + d = 0 is the equation of the tangent planes to the ground at this position.

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The number of times getting an even number on the top of dice if dice is rolled 600 times is 300.

We know that probability is defined as the division of number of favorable outcomes to the total number of outcomes.

Here, favorable outcomes are even number from 6 possible numbers and those are =2,4,6

So, favorable outcomes are={2,4,6)

So, count of favorable outcomes is 3

Total number of outcomes are ={1,2,3,4,5,6}

So, count of total number of outcomes are =6

Therefore, probability of getting an even number on top of dice is =number of favorable outcomes/total number of outcomes

=>P(E) = 3/6

=>P(E)=1/2

Now, dice is rolled 600 times and probability of getting even number is 1/2,so total number of times even number comes on topo of dice is =(1/2)×600=300.

Hence, even number appearance is 300.

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Step-by-step explanation:

16-5= 11

hope it's helpful

The number of possible outcomes when she spins and flips a coin is 8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of sections in the spinner = 4.

The number of possible outcomes in the coin = 2

Now,

The number of possible outcomes when she spins and flips a coin.

= 4 x 2

= 8

i.e

{Red, Green, Blue, Orange} x {H, T}

{Red:H, Red:T, Green:H, Green:T, Blue:H, Blue:T, Orange:H, Orange:T}

______(A)

Thus,

The number of possible outcomes from (A) is 8.

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Answer:

To find out how much money is in Alex's account at the end of the week, we need to add up all of the transactions that he made over the course of the week.

We start by adding the initial amount that Alex had in his account before making any transactions, which is $170.42.

Then we add the first transaction, which is $50.73. This brings the total to $221.15.

Next, we add the second transaction, which is $114.13. This brings the total to $335.28.

Then we add the third transaction, which is $119.69. This brings the total to $455.97.

Finally, we add the fourth and last transaction, which is $226.71. This brings the total to $682.68.

Therefore, at the end of the week, Alex has $682.68 in his account.

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

6x/4 = 12

Multiply 4 on both sides to get rid of it:

6x = 4(12) = 48

Divide 6 on both sides:

x = 48/6 = 8

Answer:

A, C, and E

Step-by-step explanation:

The given statement is true, the minute hand will point to the right of the viewer when the upside down hung clock reads 2:45.

Here, we are given that a round analog clock featuring numbers 1-12 is hung on the wall upside down.

In order to solve this question, we need to visualize the situation very carefully.

When we hang the clock upside down, the numbers will switch their positions among their opposite pair.

For example, number 12 will be at the place of number 6 and vice versa.

Similarly, number 9 will be at the place of number 3.

When the clock strikes 2:45, the minute hand is pointing towards number 9.

However, since the clock is hung upside down, number 9 is at the place of number 3.

Number 3 is on the right side of the viewer who is standing in front of the clock.

Thus, the given statement is true, the minute hand will point to the right of the viewer when the upside down hung clock reads 2:45.

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Answer:

2 inches

Step-by-step explanation:

volume of a cone: 1/3 π r^2 h

h = 12

1/3 π r^2 (12) = 16π

4πr^2 = 16π

r^2 = 16π/4π

r^2 = 4

r = 2

Answer:

No point,One Point.Reflex Angle Formed .

The probability that on any given day the office receives exactly 3 calls is 0.0076.

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, we let

Let X be the number of calls received in an office per day.

X≈Poison(λ=10)

P(X = x) = e^(-λ)λˣ/x!; x = 0, 1, 2.....

= 0, otherwise

The probability that on any given day the office receives exactly 3 calls: 0.0076

P(X = 3) = e^(-10)10³/3!

P(X=3) = 0.0076

Hence, the probability that on any given day the office receives exactly 3 calls is 0.0076.

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Answer:

t = 2

Step-by-step explanation:

First, we have to simplify the equation by multiplying 3 and -2 by everything in the corresponding parenthesis:

3(t+4) simplifies = 3t + 12

-2(2t+3) simplifies = -4t - 6

So:

3t + 12 - 4t - 6 = 4

Now we can combine like terms:

-t +6 = 4

Then we subtract 6 on both sides:

-t = -2

Then we divide by -1 in order to get rid of the negative:

t = 2, final answer.

The Rational number are 7/3, 8 and 72/8.

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that the numerator or denominator doesn't have commonly divisible.

√5 is not rational.

7/3 is rational

√17 is not rational

√64 = 8 is rational

72/8 is rational

Hence, The Rational number are 7/3, 8 and 72/8.

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Answer:

[tex] + - \sqrt{ - 30}[/tex]

Answer:

[tex]\sqrt{30i}[/tex]

Step-by-step explanation:

khan <3