Mathematics and science played a role in the design of the Egyptian architecture. Which particular branch of mathematics guided the design?

statistics
geometry
calculus
algebra

Without the historical data or the initial forecast value, it is not possible to provide a direct answer or calculate the forecast for March using exponential smoothing with a smoothing constant of 0.3.

To forecast the value for March using exponential smoothing with a smoothing constant of 0.3, we would need the historical data or the initial forecast value. Without the specific data or the initial forecast, we cannot provide a direct answer.

Exponential smoothing is a forecasting method that assigns exponentially decreasing weights to historical data, with the weights determined by the smoothing constant. The formula for exponential smoothing is as follows:

Forecast for March = Smoothing constant * (Actual value for February) + (1 - Smoothing constant) * (Previous forecast)

To use this formula, we would need the actual value for February and the previous forecast value. Additionally, the initial forecast or an initial value is necessary to begin the exponential smoothing process.

Without the historical data or the initial forecast value, it is not possible to provide a direct answer or calculate the forecast for March using exponential smoothing with a smoothing constant of 0.3. The specific data or the initial forecast value is required to apply the exponential smoothing formula and make an accurate forecast. To obtain a more precise answer, the historical data and the initial forecast value should be provided.

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Answer:

∠A = 120° (180°-60°)

∠W = 60° (b/c ∠W=∠X)

∠Y = 100° (b/c 180°-80°)

∠X = 60° (180°-120°)

∠Z = 120° (180-60°)

Step-by-step explanation:

im unsure about A and W

Answer:

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

How to find the volume of a rectangular prism and pyramid?

The formula for the volume of a rectangular prism is:

Volume = Length * Width * Height

The formula for the volume of a pyramid is:

Volume = (Base Area * Height) / 3

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

This is because the volume of a rectangular prism is calculated by multiplying its three dimensions together, whereas the volume of a pyramid is calculated by multiplying the base area by the height and dividing the result by 3.

Hence, the volume of the rectangular prism is greater than the volume of the pyramid with the same height and base. This is because the rectangular prism has additional volume in the form of its width, which the pyramid does not have.

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Answer:

12 units

Step-by-step explanation:

The side that is on the opposite side of the triangle as angle C is the side labeled as 12 units in length

Step-by-step explanation:

For the set of of each equation, it will be:

y = mx + b

x represents the number of weeks a child saved so we must multiply that by however much they saved during those weeks - hence, why there is an m there

y represents the total amount of money saved

b represents how much money they started off with (which is why we add b instead of multipling)

For Jeanne:

y = mx + b

She started with $1

y = mx + 1

She saved $5 every 3 weeks (this is multiplication)

y = 5(3) + 1

I have to go back to work now, but if you want me to show you the rest of the equations I will be more than happy to do so (I'll be available in 2 hours)

I hope my explanation helps

The correct simplification of the expression is c12 (option c).

The expression (c^4)^3 can be simplified using the exponent rules for powers of a power, which states that when a power is raised to another power, we can multiply the exponents.

Thus, we have:

(c^4)^3 = c^(43) [Using the rule (a^m)^n = a^(mn)]

Simplifying the exponent 4*3, we get:

c^(4*3) = c^12

Therefore, the correct simplification of the expression is c^12.

Option (c) is the correct answer as it correctly represents the simplified form of the given expression. Option (a) c^-1, option (b) c^7, and option (d) c^64 are not correct because they do not follow the exponent rules used to simplify the expression.

In summary, the expression (c^4)^3 simplifies to c^12, which is option (c) in the given options.

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The decomposition of  713 × 49 has been provided below

To multiply 713 and 49, we can use the distributive property and decompose the second number as follows:

49 = 40 + 9

Then, we can multiply each part of the sum by 713:

713 × 40 + 713 × 9

To calculate this, we can use the multiplication table and then add the results:

713

x 40

28520

713

x 9

6417

Then, we add the two results:

713 × 40 = 28520

713 × 9 = 6417

34997

Therefore, the multiplication 713 × 49, decomposed as 713 × 40 + 713 × 9, equals 34,997.

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∠T is congruent or equal to triangle TGA.

option D.

A right triangle is a type of triangle that has one angle measuring 90 degrees (a right angle) while the two remaining angles are known as complementary angles because they sum up to 90 degrees.

For the diagram given in this question, we can conclude that angle PAG is 45 degrees and angle TAG is also 45 degrees, since the line AG bisector angle PGT into two.

Angle TAG = 90⁰

angle TGA + angle GTA = 90 (complementary angles)

TGA = 45⁰ ≅ ∠T

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Answer:

3t-10

Step-by-step explanation:

g(h(t))=g(t-4)

=3(t-4)+2

=3t-12+2

=3t-10

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Graph

Center = ( - 7 , 2)

Radius = 2

equation of the circle = ?

Step 02:

equation of the circle

(x - h) ² + (y - k) ² = r ²

( h , k) = ( - 7 , 2)

r = 2

( x - (-7)) ² + (y - 2)² = 2 ²

(x + 7)² + (y - 2)² = 4

The answer is:

The equation of the circle is (x + 7)² + (y - 2)² = 4

New Ratio = 19:21

This deals with ratios, fractions and basic arithmetics'.

Thus, the total part for each of them will be;

Zoe; 3/10

Yolansa; 7/10

Zoe; 3x/10

Yolansa; 7x/10

\(\frac{7x}{10}\) - \(\frac{3x}{10}\) = 64

Simplifying this gives;

\(\frac{4x}{10}\) = 64

Rearranging gives;

4x = 640

x = 640/4

x = $160

Thus, originally;

Yolanda has \(\frac{7}{10}\) × 160 = $112

Zoe has \(\frac{3}{10}\) × 160 = $48

Yolanda now gives \(\frac{1}{4}\) of her money to Zoe.

Thus, she gives out \(\frac{1}{4}\) × 112 = $28

Thus,

Zoe now has; 48 + 28 = $76

Yolanda now has; 112 - 28 = $84

76:84

Simplifying this ratio gives;

19:21

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We are required to find the new ratio of zoes money to yolanda

the new ratio of zoes money to yolanda is 19:21

Ratio of zoes money to Yolanda's = 3:7.

Zoes = 3

Yolanda = 7

Total ratio = 3 + 7 = 10

let

x = Total money

Zoes = 3/10

Thus, the total part for each of them will be;

Zoe= 3/10x

Yolanda = 7/10x

Yolanda has $64 more than Zoe.

Therefore,

7/10x - 3/10x = 64

(7x - 3x) / 10 = 64

4x/10 = 64

cross product

4x = 64 × 10

4x = 640

divide both sides by 4

x = 640/4

x = $160

Original share:

Zoe = 3/10x

= 3/10 × 160

= 0.3 × 160

= $48

Yolanda = 7/10x

= 7/10 × 160

= 0.7 × 160

= $112

If Yolanda gives 1/4 to zoe

= 1/4 of 112

= 1/4 × 112

= 0.25 × 112

= $28

New Zoe's share = $48 + $28

= $76

New Yolanda's share = $112 - $28

= $84

Their new ratio = 76 : 84

divide by 4

= 19 : 21

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The area of the frame is D. 252 in².

It should be noted that the frame 2 inches wide surrounds a painting that is 18 inches wide and 14 inches tall.

The area will be:

= Length × Width

= 18 × 14

= 252 in²

The area is 252 inches².

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These functions are facilitated by the hardness of the skin in specific areas and a distinct pattern of lines.

These surfaces' hard exteriors resist abrasion, have high mechanical strength, and are highly impermeable to bacteria and fungi, which helps to avoid infection. To assist with performing simple and complex jobs, the hands and feet can be folded and unfolded appropriately thanks to the distinct patterns of lines on their surfaces.

The thick skin on the palms of the hands and soles of the feet, also known as the "glabrous skin," is adapted to withstand the constant friction and pressure that these areas are subjected to.

Here are some structural features of the skin that make it suited for its function:

Epidermal ridges: The skin on the palms and soles has a unique pattern of ridges and valleys that form fingerprints and footprints. These ridges increase the surface area of the skin in contact with the environment, which provides better grip and traction.

Thick stratum corneum: The outermost layer of the skin, called the stratum corneum, is thicker in the palms and soles than in other parts of the body. This layer is composed of many layers of dead, flattened skin cells (keratinocytes) that are filled with a tough protein called keratin. The thick stratum corneum provides mechanical strength and protection against abrasion.

Dermal papillae: The dermal layer of the skin contains small, finger-like projections called dermal papillae. These papillae interlock with the epidermal ridges to anchor the skin in place and prevent it from sliding around too much.

Sweat glands: The palms and soles contain a high density of sweat glands that produce sweat, which helps to cool the skin and maintain a good grip. The sweat glands also secrete a specialized type of sweat called "eccrine sweat,".

Meissner's corpuscles: These are specialized sensory receptors located in the dermis of the glabrous skin. They are sensitive to touch and pressure and help us to detect fine textures and shapes with our fingertips and toes.

Overall, the structure of the thick skin on the palms and soles is well-suited to its function of providing a strong, durable, and sensitive surface for gripping and manipulating objects, as well as for supporting the weight of the body during standing and walking.

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The structure of the thick skin on the palms and soles is well-suited to its function of providing a strong, durable, and sensitive surface for gripping and manipulating objects, as well as for supporting the weight of the body during standing and walking.

The thick skin on the palms of the hands and soles of the feet, also known as the "glabrous skin," is adapted to withstand the constant friction and pressure that these areas are subjected to.

Here are some structural features of the skin that make it suited for its function:

Epidermal ridges: The skin on the palms and soles has a unique pattern of ridges and valleys that form fingerprints and footprints. These ridges increase the surface area of the skin in contact with the environment, which provides better grip and traction.

Thick stratum corneum: The outermost layer of the skin, called the stratum corneum, is thicker in the palms and soles than in other parts of the body. This layer is composed of many layers of dead, flattened skin cells (keratinocytes) that are filled with a tough protein called keratin. The thick stratum corneum provides mechanical strength and protection against abrasion.

Dermal papillae: The dermal layer of the skin contains small, finger-like projections called dermal papillae. These papillae interlock with the epidermal ridges to anchor the skin in place and prevent it from sliding around too much.

Sweat glands: The palms and soles contain a high density of sweat glands that produce sweat, which helps to cool the skin and maintain a good grip. The sweat glands also secrete a specialized type of sweat called "eccrine sweat,".

Meissner's corpuscles: These are specialized sensory receptors located in the dermis of the glabrous skin. They are sensitive to touch and pressure and help us to detect fine textures and shapes with our fingertips and toes.

Overall, the structure of the thick skin on the palms and soles is well-suited to its function of providing a strong, durable, and sensitive surface for gripping and manipulating objects, as well as for supporting the weight of the body during standing and walking.

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Answer:

Step-by-step explanation:

polygons are closed figures with straight sides:

A, C, and D are polygons

B is an open figure

E and F have curved sides

Answer:

A,C and D are polygons.The others are not.

The time taken by the student to complete the weekly quiz if she had 91 is 3.55 hours

Given the linear relationship between the  amount of time students spends on their homework and their weekly quiz scores expressed as:

y = 6.2s + 69

If the value of y is 91, we need to get the value of "s"

Substitute s = 91 into the function to have:

91 = 6.2s + 69

6.2s = 91 - 69

6.2s = 22

s = 22/6.2

s = 3.55

Hence the value of s when y is 91 is 3.55

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One possible transformation is a reflection in the x-axis followed by a dilation centered at the origin with a scale factor of 3.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

Before the dilation, the figure was reflected from the first quadrant to the second quadrant, which is a lateral reflection, hence the figure was reflected over the x-axis.

The height of the blue triangle is of 1 unit, while the height of the larger triangle is of 3 units, hence the scale factor is given as follows:

k = 3/1

k = 3.

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Answer:

To solve this problem, we need to add up the amounts saved by each person and then order the total amounts from smallest to largest. Here's the solution in Python code:

python

Copy code

mary = [2, 4, 8, 16]

jane = [10, 12, 14, 16]

tom = [7, 13, 19, 25]

andy = [3, 6, 9]

mary_total = sum(mary)

jane_total = sum(jane)

tom_total = sum(tom)

andy_total = sum(andy)

totals = {"Mary": mary_total, "Jane": jane_total, "Tom": tom_total, "Andy": andy_total}

# Sort the totals in ascending order

sorted_totals = sorted(totals.items(), key=lambda x: x[1])

# Output the names in order of how much they saved

names = [x[0] for x in sorted_totals]

result = "".join(names)

print(result)  # Output: AJTM

So the answer is "AJTM".

Step-by-step explanation:

AJTM

To minimize total storage and setup costs, Jesaki Publishing should print approximately 224 books during each printing run.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

To minimize total storage and setup costs for Jesaki Publishing, we need to consider both the storage costs and the setup costs involved in printing additional copies of the book.

Let's break down the costs involved:

Storage costs: It costs $1 to store a book for one year, and Jesaki sells 50,000 copies of the book each year. So the total storage cost per year can be calculated as 50,000 * $1 = $50,000.

Setup costs: Each time Jesaki prints additional copies, it costs $1,000 to set up the presses. The number of printing runs needed can be calculated as the total number of books printed divided by the number of books printed during each printing run (x). So the number of printing runs (y) is given by y = 50,000 / x.

Now, we can express the total cost (C) as a function of x and y:

C(x, y) = setup costs + storage costs

C(x, y) = $1,000 * y + $50,000

To minimize the total cost, we need to minimize the function C(x, y). Let's substitute the value of y in terms of x into the equation:

C(x) = $1,000 * (50,000 / x) + $50,000

C(x) = $50,000 + $50,000 / x

To find the value of x that minimizes the total cost, we can take the derivative of C(x) with respect to x and set it equal to zero:

C'(x) = -50,000 / x² = 0

Solving for x, we find x = √(50,000) ≈ 223.61.

Therefore, to minimize total storage and setup costs, Jesaki Publishing should print approximately 224 books during each printing run.

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The values that satisfy sin(π/2-θ)=secθ for 0 ≤ θ<2π are θ = 0, θ = π, and θ = 2π.

To solve the equation sin(π/2-θ)=secθ, we can first rewrite secθ as 1/cosθ.

Then, we can use the identity sin(π/2-θ) = cosθ to get:

cosθ = 1/cosθ

Next, we can multiply both sides of the equation by cosθ to eliminate the fraction:

cos²θ = 1

Taking the square root of both sides, we get:

cosθ = ±1

Since 0 ≤ θ<2π, we know that cosθ = 1 for θ = 0 and θ = 2π, but we need to find values of θ where cosθ = -1.

For cosθ = -1, we can use the unit circle to find that θ = π.

Therefore, the values that satisfy sin(π/2-θ)=secθ for 0 ≤ θ<2π are θ = 0, θ = π, and θ = 2π.

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In the final arrangement, Angela is to the left of Eric.

Given the initial arrangement of Joan, Emmanuel, Andrew, and Angela from left to right, we need to determine who is to the left of Eric after the swaps.

First, Janet changes places with Eric. So the new arrangement becomes:

Joan, Emmanuel, Andrew, Janet, Angela.

Next, Eric changes places with Marcus. Considering the updated arrangement:

Joan, Emmanuel, Andrew, Janet, Marcus, Angela.

Now, we need to identify who is to the left of Eric. Looking at the arrangement, we see that Marcus is to the left of Eric. Therefore, Marcus is the answer.

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The actual width of the plane = 6.5 feet and the actual length of the plane = 8.5 feet.

Provided that the die-cast plane toy is scaled at an inch to 1 foot, we can determine the dimensions of the actual plane by converting the measurements from inches to feet.

The width of the toy plane is 6.5 inches.

To obtain the actual width, we divide this measurement by the scale of 1 inch to 1 foot:

Actual width = 6.5 inches / 1 inch/1 foot = 6.5 feet.

Therefore, the actual width of the plane is 6.5 feet.

Similarly, the length of the toy plane is 8.5 inches.

Converting this measurement to feet, we have:

Actual length = 8.5 inches / 1 inch/1 foot = 8.5 feet.

Therefore, the actual length of the plane is 8.5 feet.

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Answer:

The symbol ⊥ means is perpendicular to

Step-by-step explanation:

(brainliest)

Answer:

perpendicular to

Step-by-step explanation:

(a)Probability that a person could give up cell phone = 0.48

(b)Probability that a person who could give up her cell phone also could give up television is 0.65

(c) Probability that a person who could not give up a cell phone could give up television is 0.73

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

According to  the given question:

a. Probability that a person could give up cell phone = 0.48

b. Probability that a person who could give up her cell phone also could give up television

= P(give up cell phone and TV)/p(give up cell phone)

= 0.31/0.48

= 0.6458

= 0.65

c. Probability that a person who could not give up a cell phone could give up television is

= P(could not give up cellphone and could give up TV)/P(could not give up cell phone)

= 0.38/0.52

= 0.73

d. The probability a person could give up television is higher for persons who couldn't give up cell phones than for those who could give up their cell phones.

Hence,

(a)Probability that a person could give up cell phone = 0.48

(b)Probability that a person who could give up her cell phone also could give up television is 0.65

(c) Probability that a person who could not give up a cell phone could give up television is 0.73

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Answer:

Based on the confidence interval, Sheldon's claim is plausible

Step-by-step explanation:

The number of customers in the sample, n = 620 customers

The number of customers that replied that they had moved at least once in the last five years = 201 (32.4%)

The 90% confidence interval for the sample = (0.293, 0.355)

Let 'p' represent the proportion of all customers who have moved in the past five years

The proportion of customers Sheldon claimed have moved in the past five years, p > 1 in 4 (0.25)

The proportion Zachary urges Sheldon to claim is, p > 1 in 3 (0.\(\overline 3\))

Given that the lower estimate of the confidence interval is 0.293 (>0.25) and upper bound of the confidence interval is 0.355 (> 0.\(\overline 3\)), and that 0.26 in also more than 1 in 4 but less than 0.293, but however that 0.293 which is within the 90% confidence interval is less than 0.\(\overline 3\) or 1 in 3, as opposed to what Zachary urges Sheldon to claim, Sheldon's claim is more plausible.

Answer:D

Step-by-step explanation:

a. The probability that a flaw is detected by the end of the second fixation is given by the formula: P(flaw is detected by the end of the second fixation) = 1 - P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation).

b. Similarly, the probability that a flaw will be detected by the end of the nth fixation is given by the formula: P(flaw is detected by the nth fixation) = 1 - P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation) * ... * P(flaw is not detected in n-th fixation).

c. To calculate the probability that a flawed item will pass inspection, we can use the formula: P(B'|A), where A is the event that an item has a flaw and B is the event that the item passes inspection. Thus, P(B'|A) is the probability that the item passes inspection given that it has a flaw. Since the item is passed if a flaw is not detected in the first three fixations, and the probability that a flaw is not detected in any one fixation is 1 - p, we have P(B'|A) = P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation) * P(flaw is not detected in third fixation) = (1 - p)³.

d. To find the probability that an item is chosen at random and passes inspection, we can use the formula: P(C) = P(item is not flawed and passes inspection) + P(item is flawed and passes inspection). We can calculate this as (1 - 0.1) * 1 + 0.1 * P(B|A'), where A' is the complement of A. Since P(B|A') = P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation) * P(flaw is not detected in third fixation) = (1 - p)³, we have P(C) = 0.91 + 0.1 * (1 - p)³.

e. It's important to note that all of these formulas assume certain conditions about the inspection process, such as the number of fixations and the probability of detecting a flaw in each fixation. These assumptions may not hold in all situations, so the results obtained from these formulas should be interpreted with caution.

The given problem deals with calculating the probability that an item is flawed given that it has passed inspection. Let us define the events, where D denotes the event that an item has passed inspection, and E denotes the event that the item is flawed.

Using Bayes’ theorem, we can calculate the probability that an item is flawed given that it has passed inspection. That is, P(E|D) = P(D|E) * P(E) / P(D). Here, P(D|E) is the probability that an item has passed inspection given that it is flawed. P(E) is the probability that an item is flawed. And, P(D) is the probability that an item has passed inspection.

Since the item is passed if a flaw is not detected in the first three fixations, we can find P(D|E) = (1 - p)³. Also, given that 10% of all items contain a flaw, we have P(E) = 0.1.

Now, to find P(D), we can use the law of total probability. P(D) = P(item is not flawed and passes inspection) + P(item is flawed and passes inspection). This is further simplified to (1 - 0.1) * 1 + 0.1 * (1 - p)³.

Finally, we have P(E|D) = (1 - p)³ * 0.1 / [(1 - 0.1) * 1 + 0.1 * (1 - p)³], where p = 0.5. Therefore, we can use this formula to calculate the probability that an item is flawed given that it has passed inspection.

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Using the formula for lines intersecting in a circle, we get the value of x to be = 8.4units.

A diameter is a line segment that traverses a circle by going through its centre.

The radius is twice as long as the diameter.  A chord is a segment that does not have to pass through the centre and has endpoints on the circle.

We know that in a circle when lines are intersecting each other than the lines divided are in the formula:

a/b = c/d

Here in the question,

Given AB = 14.

One part = x

Other part = 14 - x

Now as per the formula,

x/14-x = 6/4

⇒ 4x = 84 - 6x

⇒ 4x + 6x = 84

⇒ 10x = 84

⇒ x = 8.4

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