What contribution did al-khwarizmi make to the world of mathematics?.

Answer:

49a²b² - 9c²

Step-by-step explanation:

(7ab+3c)(7ab-3c)

= 49a²b² - 21abc + 21abc - 9c²

= 49a²b² - 9c²

So, the answer is 49a²b² - 9c²

Answer: 49a²b² - 9c²

Step-by-step explanation:

     We will apply the difference of two squares formula:

(7ab+3c)(7ab-3c)

(7ab)² - (3c)²

49a²b² - 9c²

Answer:

the value is 120 i think and 2 x-intercepts for the graph of f

Step-by-step explanation:

sorry if it's wrong

Answer:

Start at 13, then count 5 more to the right. You will end at 18, which is your answer.

Step-by-step explanation:

Answer:

the anser is 18

Step-by-step explanation:

you would start at the mark that indicates 13 and go up or to the right 5 more marks or to whichever mark indicates 18

Answer:

The plane can fly 760 miles in 4/3 hours.

Step-by-step explanation:

Given that:

An airplane can cruise at 570 miles per hour.

We have to find the distance travelled by train in 4/3 hours.

Distance = Speed * Time

Distance = \(570*\frac{4}{3}\)

Distance = \(\frac{2280}{3}\)

Distance = 760 miles

Hence,

The plane can fly 760 miles in 4/3 hours.

The smallest possible inside length of the cubical steel tank that can hold 600 L of water is approximately X meters. This calculation is based on the assumption that 1 liter of water occupies 1 cubic decimeter.

To determine the smallest possible inside length of the tank, we need to calculate the volume of the tank and then find the side length of the cube. Given that the tank needs to hold 600 L of water, we can convert this volume to cubic meters by dividing by 1000 (since 1 cubic meter is equal to 1000 liters). So, the volume of the tank in cubic meters is 600/1000 = 0.6 cubic meters.

Since the tank is cubic in shape, the volume can be calculated by raising the length of any side to the power of 3. Let's denote the side length of the cube as 's'. Therefore, we have the equation s^3 = 0.6.

Taking the cube root of both sides, we find s = ∛0.6. Evaluating this expression, we get s ≈ 0.824 m (rounded to three decimal places).

Therefore, the smallest possible inside length of the cubical steel tank that can hold 600 L of water is approximately 0.824 meters.

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Tanya yearly salary is

$35000 + 8% of her sales

Let her sales be x

Since, her sales is x

35000 + 0.08x > salary

To determine her necessary sales to earn over $50, 000

Let $50, 000 be her benchmark salary

35,000 + 0.08 * x > 50000

35000 + 0.08x > 50000

0.08x > 50000 - 350000

0.08x > 15000

Divide both sides by 0.08

0.08x/0.08 > 15000/0.08

x > 15000 / 0.08

x > 187,500

Therefore, she will need a sales of 188,000 and above to earn above $50,000

Answer:

Degree measure of each angle is 90⁰, 47⁰ and 43⁰

Step-by-step explanation:

since the triangle is right angled, we assume that Q and S are the other angles of this triangle R

Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰

5x - 13 + 4x - 5 = 90⁰

9x = 108

x = 12

We now replace x in Q and S to get the angles

Q = 5(12) -13

= 47⁰

S = 4(12) - 5

= 43⁰

The regular expression is ^(a(aa)*b)$.

To create a regular expression for the language L = {w = {a,b}* | w has an odd number of 'a's and ends with 'b'}, we can use the following expression:

^(b|(a(aa)*b))$

Breaking it down:

^ indicates the start of the string.

(b|(a(aa)*b)) matches either 'b' or a sequence of 'a's followed by an odd number of 'a's and 'b'.

(aa)* matches zero or more pairs of 'a's.

$ indicates the end of the string.

This regular expression ensures that the string starts with 'b' or a sequence of 'a's, followed by an odd number of 'a's, and ends with 'b'. Any additional characters or sequences in between are not allowed.

Please note that regular expressions can have different notations and conventions depending on the context or programming language you're using. The expression provided here follows a general pattern that should work in most cases.

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Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.

Direct Materials: It includes the cost of raw materials used in manufacturing a product.

Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.

Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process

Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.

To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.

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Answer:

y = 47

Step-by-step explanation:

All of the angles in a triangle must add up to 180. The angle marked 3y can help us find the missing angle of the triangle: 180-3y
Then you can make an equation to help solve for y:
50 + (2y-3) + (180-3y) = 180
Combine like terms:
227-y=180
y = 47

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: y=47 \degree\)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \:(2y - 3) + 50 = 3y\)

\(\qquad \tt \rightarrow \:2y - 3 + 50 - 3y = 0\)

\(\qquad \tt \rightarrow \:2y - 3y + 47 = 0\)

\(\qquad \tt \rightarrow \: - y = - 47\)

\(\qquad \tt \rightarrow \:y = 47 \degree\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The percentage of adult spiders that have carapace lengths exceeding a certain value is equal to the area under the standard normal curve that lies to the right of that value.

This is because the normal distribution is symmetric around its mean, and the area to the right of a certain value represents the proportion of data points that are greater than that value. Therefore, by calculating the area under the standard normal curve to the right of a certain value, we can determine the percentage of adult spiders with carapace lengths exceeding that value.

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The volume of the rectangular prism can be found using the 6x6x7 option (A) 6x6x7 is correct.

It is defined as the six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.

It is given that:

The volume of the rectangular prism is given by:

V = L×W×H

Here, V is the volume of the rectangular prism

L is the length of the rectangular prism

W is the width of the rectangular prism

H is the height of the rectangular prism

From the figure:

L = 6 cm

W = 7 cm

H = 6 cm

V = 6x7x6

or

V = 6x6x7

Thus, the volume of the rectangular prism can be found using the 6x6x7 option (A) 6x6x7 is correct.

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Answer:

1,267,200

Step-by-step explanation:

Given that the map reported that the scale is 1 inch to 20 miles.

Recall that there are 63,360 inches in 1 mile, thus, in 20 miles, we have 20 x 63,360 = 1,267,200

Therefore, the scale of 1 inch to 20 miles can also be represented as 1 to 1,267,200

Based on the visual representation of the data sets, we can make an educated guess about which data set has the greatest and least sample standard deviation.

Data set (i) appears to have the greatest sample standard deviation because it has the widest spread of values, ranging from 14 to 19.

Data set (iii) appears to have the least sample standard deviation because it has the smallest range of values, only ranging from 2 to 4.

Data set (ii) appears to have the same range of values as data set (i), so it is likely to have a similar sample standard deviation.

Dataset (ii) appears to have a sample standard deviation that is in between the other two datasets, with the data points slightly more spread out than in dataset (iii), but less spread out than in dataset (i).

However, without calculating the actual standard deviations, we cannot be completely certain about which data set has the greatest or least sample standard deviation. Calculating the standard deviations would provide more precise information about the variability of each data set.

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The claim that a drug is effective at 1% is not sufficiently supported by the available data.

Participant 1 2 3 4 5 6

Before 185 220 190 158 227 211

After 175 215 195 155 230 207

Difference = Before - After = 10 5 -5 3  -3 4

Participant 7 8 9 10 11 12

Before 260 156 201 300 180 270

After 258 159 201 290 172 272

Difference = Before - After = 2 -3 0 10  8 -2

Participant 13 14 15 16 17 18

Before 293 183 205 151 291 166

After 290 185 200 146 287 166

Difference = Before - After = -7 -2 5 5  4 0

Hypothesis :

H0 : μd = 0

H0 : μd ≠ 0

10+5-5+3-3+4+2-3+10+8-2+3-2+5+5+4+0 = 44

The mean of d, \(d`\) = Σd / n = 44 / 18 = 2.44

The standard deviation, S.d = 4.45 (using calculator)

The test statistic, T : \(d`\) / (S.d/√n)

T = 2.44 / (4.45/√18)

T = 2.44 / 1.0488750

T = 2.326

Degree of freedom, df = n - 1 ; 18 - 1 = 17

P value = 0.0326

α = 0.01

Since P value < α ; we fail to reject H0

So the claim that a drug is effective at 1% is not sufficiently supported by the available data.

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Answer:

Rationalize the denominator of the expression. Then simplify your answer.

Step-by-step explanation:

.1/√3

Answer: About 84.261 degrees

Step-by-step explanation:

To find the angle of elevation, we can create a triangle and solve for the angle.

First, we can imagine a triangle with side A being the ground between the base of the ladder and the wall, side B being the wall (from the base of the wall to where it touches the top of the ladder), and side C being the ladder (from where it touches the ground to where it touches the wall).

In the problem, it has already given us two of the side lengths we need to solve for the angle of elevation:

1. We know that the ladder is 10 feet tall, so we can say that side C is 10.

2. We know that the ladder base is placed 1 foot from the wall, so we can say that side A is 1.

The angle of elevation is the angle that the ladder is tilted from the ground, or the angle between the ground (side A) and the ladder (side C). These sides relative to the angle would be the adjacent (side A) and the hypotenuse (side C).

To calculate for the angle, we can use the cosine function. (cos = adjacent / hypotenuse)

To find the angle of elevation (which we can call angle b), we can use:

cos(b) = A / C

arccos(A / C) = b

(Note: arccos is the inverse of the cos function)

Then, we can plug in the values and get:

b = arccos(1 / 10)

b = 1.471 radians OR 84.261 degrees

Answer:

6

Step-by-step explanation:

The population is the collection of parents of 13- to 17-year-olds. The sample is the 1720 parents surveyed.

The population in this survey is option D: the collection of responses of parents of 13- to 17-year-olds. The sample in this case is option C: the 1720 parents of 13- to 17-year-olds who were surveyed.

In this scenario, the population refers to the entire group of interest, which is parents of 13- to 17-year-olds. The survey aims to gather information about this entire group, so the population is defined as the collection of responses from all parents of 13- to 17-year-olds.

On the other hand, the sample is a subset of the population that is selected and surveyed. In this case, the sample consists of the 1720 parents of 13- to 17-year-olds who participated in the survey. The sample is used to gather data and draw conclusions about the larger population.

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Answer:

The ratio of the volume of the triangular prism to the volume of the cuboid is 3: 20

Step-by-step explanation:

The volume of the triangular prism V\(_{T}\) = \(\frac{1}{2}\) bh × H, where

The volume of the cuboid V\(_{C}\) = L × W × H, where

∵ The base of the triangular prime is a right triangle with legs 5 cm, 4 cm

∴ b = 5 cm and h = 4 cm

∵ Its height is 9 cm

∴ H = 9 cm

→ Substitute them in the rule of the prism above

∵ V\(_{T}\) = \(\frac{1}{2}\) (5)(4) × 9

∴ V\(_{T}\) = 90 cm³

∵ The dimensions of the base of the cuboid are 6 cm and 5 cm

∴ L = 6 cm and W = 5 cm

∵ Its height is 20 cm

∴ H = 20 cm

→ Substitute them in the rule of the cuboid above

∵ V\(_{C}\) = 6 × 5 × 20

∴ V\(_{C}\) = 600 cm³

→ Find the ratio between them

∵ V\(_{T}\): V\(_{C}\) = 90: 600

→ Divide each term of the ratio by 30 to simplify them

∴ V\(_{T}\): V\(_{C}\) = 3: 20

∴ The ratio of the volume of the triangular prism to the volume of

   the cuboid is 3: 20

Answer:

"X: 3: 9/2 =15/4: 9/2 :Yask" is difficult for me to understand.

The best I can find is x = 11 1/4 or 11.25

I'll assume:

X: 3: 9/2 means X/3/(9/2) and that is equal to 15/4/(9/2)

Step-by-step explanation:

X/3/(9/2) = 15/4/(9/2)

X/3/(9/2) = 15/4/(9/2)   [Multiply both sides by (1/(9/2)

X/3 = 15/4

4x = 45

x = 11 1/4 or 11.25

Answer:

12 Miles is the answer! Hope you do Great!

Step-by-step explanation:

Answer:

the answer is 864 in3

Step-by-step explanation:

Jerome photographed an aquarium that measured 12 inches by 18 inches by 24 inches.

So V=LxWxH....

12 x 18 x 24= 5,184

Then...

Lim photographed an aquarium that was 12 inches by 30 inches by 12 inches.

So= V=LxWxH

12 x 30 x 12=4,320

And they need to see who has more so 5,184-4,320=864in3

I hope this helps also Into Math said it was correct :)

The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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Part 1: To write the given parametric equations into one rectangular equation, we can eliminate the parameter \(\(t\)\)by solving one equation for\(\(t\)\) and substituting it into the other equation. we can start with \(\(x = 8t\):\)

And the isolated part is to be  \(t\) as follows:

\(\(t = \frac{x}{8}\)\)

\(now \(t\)will be classified \(y = t + 2\):\)

\(\(y = \frac{x}{8} + 2\)\)

So, the resulting rectangular equation is\(\(y = \frac{x}{8} + 2\).\)

Part 2:Straight line is the rectangular equations graph\(\(\frac{1}{8}\)\)and a y-intercept of 2. It has a positive slope, indicating that the line is ascending from left to right.

Part 3: The rectangular equation is\(\(y = \frac{x}{8} + 2\).\)

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The distance between the fountain and the playground is approximately 10.8 yards.

To find the distance between the fountain and the playground, we can use the Pythagorean theorem.

Given:

Coordinates of the center of the park: (0, 0)

Fountain is 4 yards north of the center: (0, 4)

Playground is 10 yards east of the center: (10, 0)

Let's consider the distance between the fountain and the playground as the hypotenuse of a right triangle formed by the fountain, playground, and the center of the park.

Using the Pythagorean theorem, the distance between the fountain and the playground (hypotenuse) can be calculated as follows:

Distance^2 = (Difference in x-coordinates)^2 + (Difference in y-coordinates)^2

Difference in x-coordinates = 10 - 0 = 10 yards

Difference in y-coordinates = 4 - 0 = 4 yards

Distance^2 = (10)^2 + (4)^2

Distance^2 = 100 + 16

Distance^2 = 116

Taking the square root of both sides to find the distance:

Distance = sqrt(116)

Distance ≈ 10.8 yards (rounded to the nearest tenth)

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The rectangular coordinates of the point are ( 19.7, -3.5)

We know the radius and the corresponent angle, so we have the polar coordinates of a point (R, θ).

The rectangular coordinates of that general point are:

x = R*cos(θ)

y = R*sin(θ)

We know the radius is 20 units, and the angle is 350°, replacing that we will get:

x = 20*cos(350°) = 19.7

y = 20*sin(350°) = -3.5

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Answer:

The equation of the parabola is (x - 4)² = -16(y - 1)

Step-by-step explanation:

The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where

∵ The focus of the parabola is (4, -3)

∵ The focus is (h, k + p)

∴ h = 4

∴ k + p = -3 ⇒ (1)

∵ It has a directrix of y = 5

∵ The directrix of the parabola is y = k - p

∴ k - p = 5 ⇒ (2)

→ Add equations (1) and (2) to find k and p

∵ (k + k) + (p - p) = (-3 + 5)

∴ 2k + 0 = 2

∴ 2k = 2

→ Divide both sides by 2

∴ k = 1

→ Substitute the value of k in equation (1)

∵ 1 + p = -3

→ Subtract 1 from both sides

∴ 1 - 1 + p = -3 - 1

∴ p = -4

∵ The form of the equation of the parabola is (x - h)² = 4p(y - k)

→ Substitute the values of h, k, p in it

∴ (x - 4)² = 4(-4)(y - 1)

∴ (x - 4)² = -16(y - 1)

∴ The equation of the parabola is (x - 4)² = -16(y - 1)

a) The total number of different sequences of process and control samples each day is 823,543. b) The total number of different sequences of process and control samples each day is 120. c) The total number of different sequences of process and control samples each day, considering the first test as a control sample, is 46656.

a) To calculate the number of different sequences of process and control samples each day, we can consider the samples as distinguishable. We have 5 process samples and 2 control samples.

For each position in the sequence, we have 7 choices (5 process samples or 2 control samples). Since the samples are independent and can be selected in any order, we can use the multiplication principle.

Therefore, the total number of different sequences of process and control samples each day is 7⁷ = 823,543.

b) Now, let's consider the five process samples to be different and the two control samples to be identical.

We have 5! (5 factorial) ways to arrange the process samples among themselves. However, the two control samples are identical, so they remain fixed in their positions.

Therefore, the total number of different sequences of process and control samples each day is 5! = 120.

c) If the first test of each day must be a control sample, we need to consider the control sample fixed in the first position. We have 1 choice for the first position (control sample) and 6 choices for the remaining 6 positions (5 process samples and 1 control sample).

Therefore, the total number of different sequences of process and control samples each day, considering the first test as a control sample, is 1 * 6⁶ = 46656.

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