You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 4 centimeters, what will be the exact area of each hexagonal shape?

Answer:

120

Step-by-step explanation:

I believe it is, I cant really explain good but trust me :)

\(Answer: \displaystyle\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .\)

Step-by-step explanation:

\(D=12\ \ \ \ O(0;b)\\\displaystyle\\R=\frac{D}{2}\\R=\frac{12}{2} \\ R=6.\\Circle \ equation\ is:\\(x-a)^2+(y-b)^2=R^2.\\a=0\ \ \ \ \ R=6\\x^2+(y-b)^2=6^2\\x^2+(y-b)^2=36\\Henese:\\\displaystyle\\\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .\)

Answer:

Option (1)

Step-by-step explanation:

Given linear inequalities in the graph are,

\(y\geq -\frac{1}{3}x+2\)

y < 2x + 3

Here shaded area above the solid line represents the inequality,

\(y\geq -\frac{1}{3}x+2\)

And shaded area on the right side of the dotted line represents the solution set of the inequality,

y < 2x + 3

And the solution set of the system of linear inequalities will be represented by the common area of these inequalities.

Therefore, ordered pairs (2, 2), (3, 1) and (4, 2) will lie in the common shaded area.

Option (1) will be the answer.

Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.

As given in the question,

Perimeter of the rectangular area encloses for fencing = 3200 yards

Let 'x' and 'y' be the length and width of the rectangle.

2( x + y ) = 3200

⇒ x + y = 3200/2

⇒y = 1600 - x

Area of rectangular field 'A' = xy

⇒ A = x ( 1600 - x )

⇒ A = 1600x - x²

Differentiate both the side of the equation we get,

dA/dx = 1600 - 2x

For Maximum Area dA/dx = 0

1600 -2x =0

⇒ 2x = 1600

⇒ x= 800 yards

Now, y = 1600 - 800

          = 800 yards

Maximum area = (800) (800)

                        = 640,000 square yards

Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.

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In this context, a type I error would occur if the null hypothesis was rejected when it is actually true, meaning that the patient does not have the disease but is diagnosed with it.

This would be a false positive result. It is important to note that a type I error is related to the level of significance chosen for the hypothesis test, and it represents the probability of rejecting the null hypothesis when it is true.

In this case, if the level of significance was set at 0.05, for example, there would be a 5% chance of making a type I error. It is also important to consider the consequences of making a type I error in a medical context, as it could lead to unnecessary treatments or interventions that could harm the patient.

Therefore, it is crucial to carefully design hypothesis tests and choose appropriate levels of significance to minimize the risk of making such errors.

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Answer:

The function H(x) that represents how much you would pay if you use the mall coupon followed by applying the store discount of 25% would be: H(x) = (x-5)*0.25. This function takes the original cost of the jeans (x) and subtracts $5 from it (x-5) to account for the coupon, and then multiplies the result by 0.25 to account for the store discount.

Answer: i need points sorry ‍♀️

Step-by-step explanation:

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Using  given coordinate of the focus and the equation of the directrix, Equation of a parabola is

(y-3)²=4(3)(x-(-1))

(y-3)²=4(3)(x+1)

There are 2 types of parabolas. They are

Left right or up down opening ones

Left right ones are in form (y-k)²= 4p(x-h)

Up down ones are (x-h)²=4p(y-k)

In all of them, the vertex is (h, k)

p is the distance from the vertex to the focus, also the shortest distance from the vertex to the directrix making p half of the distance of the shortest path from focus to directrix

If p is positive, then the parabola opens up or right

If p is negative then the parabola opens down or left

If the directrix is y=something, then it is a up down parabola

If directrix is x=something, then it is a left right parabola

Directrix is outside the parabola, kind of at the back

So lets say we had

Focus = (2,3) and directrix is x = -4

Directrix is x =-4 so left right

From x = -4 to x=2 (focus), that is distance of 6

6/2=3

p=3

So, directrix is on opposite side of opening

-4 is to left of the 2

Then the directrix is at back so the parabola opens to the right

p=3, positive 3

Then we have the vertex is halfway between those

So 3 back from focus is from (2,3) to (-1,3)

So vertex is (-1,3)

Equation of a parabola is

(y-3)²= 4(3)(x - (-1))

(y-3)²= 4(3)(x + 1)

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The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.

To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.

For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:

Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)

Total fiber = 3x + 2y grams

what is number?

A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.

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Answer:

350,391 is the answer

9514 1404 393

Answer:

  (a) 6² +3² +1² +1² = 47

  (b) 5² +4² +2² +1² +1² = 47

  (c) 3³ +4² +2² = 47

Step-by-step explanation:

It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.

The approach where a cube is required can work the same way.

(a) floor(√47) = 6; floor(√(47 -6^2)) = 3; floor(√(47 -45)) = 1; floor(√(47-46)) = 1

__

(b) floor(√47 -1) = 5; floor(√(47-25)) = 4; ...

__

(c) floor(∛47) = 3; floor(√(47 -27)) = 4; floor(√(47 -43)) = 2

Answer:

Yes, it is correct

Step-by-step explanation:

If the temperature did not drop below 60 degrees, that means that it only stayed at 60 degrees or was higher than 60 degrees.

D is greater than or equal to 60 is the right inequality then.

The area of the region that is bounded by the curve r=5sin(θ) and lies in the sector 0≤θ≤π is 25/2 square units.

To find the area of the region that is bounded by the curve r=5sin(θ) and lies in the sector 0≤θ≤π, we can use the formula for the area of a polar region:

A = 1/2 ∫(b,a) r(θ)² dθ

where a and b are the values of θ that define the region.

In this case, the region is defined by 0 ≤ θ ≤ π and r(θ) = 5\(sin(\theta)^{(1/2)}\), so we have:

A = 1/2 ∫(π,0) [5\(sin(\theta)^{(1/2)}\)]² dθ

Simplifying the integrand:

A = 1/2 ∫(π,0) 25sin(θ) dθ

Using the identity ∫sin(θ)dθ = -cos(θ), we get:

A = 1/2 [-25cos(π) + 25cos(0)] = 25/2

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The volume formula by making substitutions for V and L will be 100 = HW².

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

Suppose that a prism has a volume of 200 cm³ and L = 2W.

The volume formula by making substitutions for V and L will be

V = L x W x H

200 = 2W x W x H

100 = HW²

The volume formula by making substitutions for V and L will be 100 = HW².

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Main Answer:If your friend buys 10 identical boxes, there will be a total of 240 markers.

Supporting Question and Answer:

What is the total number of markers you currently have after purchasing 2 boxes?

The total number of markers you currently have is 48.

Body of the Solution:You purchased 2 boxes of markers, with 24 markers in each box. Therefore, you have a total of 2 boxes × 24 markers per box = 48 markers.

If your friend wants to buy 10 identical boxes, you can multiply the number of markers per box by the number of boxes your friend wants to buy:

10 boxes × 24 markers per box = 240 markers

So, if your friend buys 10 identical boxes, there will be a total of 240 markers.

Final Answer:Therefore,if your friend buys 10 identical boxes, there will be a total of 240 markers.

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If your friend buys 10 identical boxes, there will be a total of 240 markers.

The total number of markers you currently have is 48.

Body of the Solution: You purchased 2 boxes of markers, with 24 markers in each box. Therefore, you have a total of 2 boxes × 24 markers per box = 48 markers.

If your friend wants to buy 10 identical boxes, you can multiply the number of markers per box by the number of boxes your friend wants to buy:

10 boxes × 24 markers per box = 240 markers

So, if your friend buys 10 identical boxes, there will be a total of 240 markers.

Therefore ,if your friend buys 10 identical boxes, there will be a total of 240 markers.

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Answer:

\(\huge\boxed{x \approx 5.4}\)

Step-by-step explanation:

We can break down this problem by first realizing different parts of the circle.

With this, we can find out if we find the radius of the circle, we have our answer.

We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.

What we need is a way to find the radius of the circle. This will get us x. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.

If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).

We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:

Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!

Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.

The line X does just that. Therefore, the value of x is also 5.4.

Hope this helped!

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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The first derivative of at x with respect to x is simply the transpose of the matrix a.The first derivative of xt ax with respect to x is 2ax, since taking the derivative of the product of two vectors involves multiplying one of the vectors by the derivative of the other vector, and in this case the derivative of x is the identity matrix (since x is a vector and not a matrix).The second derivative of xt ax with respect to x is simply the matrix 2a, since the second derivative involves taking the derivative of the first derivative.1. Given the vector x and the symmetric matrix A.
2. We need to find the first and second derivatives of the following expressions:
  i. A * x
  ii. x^T * A * x

The question involves vectors, symmetric matrices, and derivatives. Let's break it down step-by-step.

i. First derivative of A * x with respect to x:
To find the derivative of A * x with respect to x, we treat A as a constant matrix. The first derivative is simply the matrix A itself.

Answer: The first derivative of A * x with respect to x is A.

ii. First derivative of x^T * A * x with respect to x:
To find the first derivative of this expression, we'll use the following formula for the derivative of a quadratic form:

d/dx (x^T * A * x) = (A + A^T) * x

Since A is a symmetric matrix, A = A^T. Therefore, the formula becomes:

d/dx (x^T * A * x) = 2 * A * x

Answer: The first derivative of x^T * A * x with respect to x is 2 * A * x.

iii. Second derivative of x^T * A * x with respect to x:
The second derivative of x^T * A * x with respect to x is the derivative of the first derivative (2 * A * x) with respect to x. Since A is a constant matrix, the second derivative is zero.

Answer: The second derivative of x^T * A * x with respect to x is 0.

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Answer:

\(she \: used \: 1.695 \: kg \: of \: flour.\)

Step-by-step explanation:

\(2.64 - 0.945 = 1.695\)

If the actual temperature of steam is 99 °C and is assumed to be 100 °C in calculations, the error introduced can be significant depending on the specific calculations being performed.

Similarly, if the actual temperature of steam is 101 °C and is assumed to be 100 °C, the error introduced can also be significant.

The amount of error introduced when assuming the temperature of steam to be 100 °C instead of the actual temperature of 99 °C or 101 °C depends on the specific calculations being performed.

Similarly, in industrial processes, assuming an incorrect temperature of steam could result in inefficiencies or even safety hazards. Therefore, the difference between the actual temperature of steam and the assumed temperature of 100 °C should not be considered negligible in many cases.

In conclusion, the error introduced by assuming a temperature of 100 °C instead of the actual temperature of steam depends on the specific calculations being performed and can be significant in some cases. It is always best to use accurate and precise measurements in scientific and engineering calculations to minimize the potential for error.

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Complete Question:

1. If you use 100 °C for the temperature of steam in your calculations, how much error do you introduce if it is actually 99 °C or 101 °C? Is this difference negligible?

Jake is considering his career options or career aspirations.

Jake is at a stage in his life where he is contemplating his future and the different career paths he could pursue. He has identified three potential professions: teacher, lawyer, and singer. Jake's talent and intelligence indicate that he has the potential to excel in any of these fields. His vow not to be satisfied in a dead-end job suggests that he is motivated and ambitious, seeking a fulfilling and successful career.

At this point, Jake is likely evaluating various factors such as his interest, skills, personal values, and long-term goals to determine which career path aligns best with his aspirations. He may be considering the level of satisfaction, growth opportunities, financial stability, and societal impact associated with each profession. Exploring these factors will help Jake make an informed decision about his future career and choose a path that will provide him with the fulfillment and success he desires.

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Answer:

Option (C)

Step-by-step explanation:

Given sides of a triangle are 2, \(\sqrt{12}\) and \(\sqrt{19}\).

Option (A).

If the triangle is a right triangle.

By Pythagoras theorem,

(Longest side)² = (Leg 1)² + (Leg 2)²

\((\sqrt{19})^2=2^2+(\sqrt{12})^2\)

19 = 4 + 12

19 = 16

Not true.

Therefore, its not a right triangle.

Option (B).

If it is a triangle following conditions will be followed.

1). a + b > c

2). b + c > a

3). a + c > b

For the given sides of the triangle,

1). 2 + √12 > √19 [True]

2). 2 + √19 > √12 [True]

3). √12 + √19 > 2 [True]

Therefore, the given measures of the sides will form a triangle.

Option (C)

By Pythagorean inequality theorem,

If c² =  a² + b² → Right triangle

If c² > a² + b² → Obtuse triangle

If c² < a² + b² → Acute triangle

Since, (√19)² > 2² + (√12)² → 19 > 4 + 12

Therefore, the given triangle is an Obtuse triangle.

Option (D).

Not true. It's an obtuse triangle.    

Answer:

Free fall acceleration 10m/s/s approx.

So in ten seconds after acceleration, it would be 100 m/s

Answer:

100 m/s

..........

To determine if the given points are part of the (200) plane, we need to check if their coordinates satisfy the equation of the plane.

The equation of a plane in three-dimensional space is typically written in the form Ax + By + Cz + D = 0, where A, B, C, and D are constants. For the (200) plane, the equation would be 2x + 0y + 0z + 0 = 0, which simplifies to 2x = 0. Let's check the given points: a) (1/2, 0, 0): When we substitute x = 1/2 into the equation 2x = 0, we get 2(1/2) = 0, which is true. Therefore, point a) lies on the (200) plane. b) (-1/3, 0, 0): Substituting x = -1/3 into the equation 2x = 0 gives us 2(-1/3) = 0, which is also true. So, point b) is part of the (200) plane. c) (0, 1, 0):When we substitute x = 0 into the equation 2x = 0, we get 2(0) = 0, which is true. Thus, point c) lies on the (200) plane. All three given points (a), b), and c)) are part of the (200) plane.

In conclusion, all three given points (a), b), and c)) are part of the (200) plane.

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Answer:

here!

Step-by-step explanation:

"In decimal form, the value of pi is approximately 3.14."

hope this helps! :)

Answer:

pi equal 3.141492654 ................. and more but that is the standard answer

Step-by-step explanation:

Answer:

22 bird legs

20 hamster legs

24 beetle legs

+

____________

66 legs

Step-by-step explanation:

BOOM! QUICK MAFS

Answer:

Each card will have a value of $15 when they equal after 600 days which also is 20 30-day periods.

Step-by-step explanation:

Card1: \(85 - \frac{3.50}{30} x\)

Card2: \(75 - \frac{3}{30} x\)

x is number of days

\(85 - \frac{3.50}{30} x = 75 - \frac{3}{30} x\)

2550 - 3.50x = 2250 - 3x

2550 - 0.50x = 2250

-0.50x = -300

x = 600 days

Card1: \(85 - \frac{3.50}{30} (600)\)

         85 - 70 = 15 dollars

Card2: \(75 - \frac{3}{30} (600)\)

         75 - 60 = 15 dollars

The value of each card will be when they have equal value is $15.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now, Let x be the number of time periods for which the gift card is not used, then

For the gift card $ 85 if it is not used for x periods, then the amount that will be lost is

85 - 3.50 x---------------------(1)

For the gift card $ 75 if it is not used for x periods, then the amount that will be lost is

75 - 3x---------------------- (2)

Now when both the amount lost is equal

85 - 3.50 x = 75 - 3x

solving the equation, we get

or, 3.50 x - 3x = 85 -75

or, 0.50 x = 10

or,  x = 20

Thus the value of gift cards will be equal for 20 ,30 day periods.

Now,the value of each card be when they have equal​ value

The two cards  will have equal value after 20, 30 day periods, this denotes that at this time, the value of each card will be equal.

Then

85 - 3.50 x = 75 - 3x

substituting  x = 20, we get

85 - 3.50*20 = 75 - 3*20

85 - 70  = 75 - 60

15  = 15

So, when they have equal​ value, the value of each card will be $15.

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