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Al-Khwarizmi made significant contributions to the world of mathematics, particularly in the field of algebra. His major accomplishment was the development of algebra as an independent mathematical discipline.

Al-Khwarizmi, a Persian mathematician and scholar, wrote the book titled "Kitab al-Jabr wal-Muqabala," which laid the foundation for modern algebra. In this influential work, he introduced systematic methods for solving linear and quadratic equations. Al-Khwarizmi's algebraic techniques, including the use of variables and equations, greatly advanced mathematical understanding and problem-solving. His work also contributed to the development of algorithms and mathematical notation, such as the concept of the "zero" and the decimal system. Overall, al-Khwarizmi's contributions revolutionized mathematics and had a profound impact on subsequent generations of mathematicians and scientists.

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Answer:

Step-by-step explanation:

Givens

If two internal angles of two triangles are congruent, then the third angle is also congruent.

Therefore, the similarity is proven by AAA postulate, which states that if we have three corresponding angles congruent, then those triangles are similar.

Remember that similarity is about proportion between sides and congruence between angles.

The component of the weight parallel to the inclined plane is approximately 34.72 pounds, and the component perpendicular to the inclined plane is approximately 196.96 pounds.

To analyze the situation, we need to break down the weight of the object into its components parallel and perpendicular to the inclined plane.

Given:

Weight of the object = 200 pounds

Angle of the inclined plane with the horizontal = 10 degrees

First, we find the component of the weight parallel to the inclined plane. This component can be determined using trigonometry:

Component parallel to the inclined plane = Weight * sin(angle)

Component parallel to the inclined plane = 200 pounds * sin(10 degrees)

Component parallel to the inclined plane ≈ 200 pounds * 0.1736

Component parallel to the inclined plane ≈ 34.72 pounds

Next, we find the component of the weight perpendicular to the inclined plane:

Component perpendicular to the inclined plane = Weight * cos(angle)

Component perpendicular to the inclined plane = 200 pounds * cos(10 degrees)

Component perpendicular to the inclined plane ≈ 200 pounds * 0.9848

Component perpendicular to the inclined plane ≈ 196.96 pounds

Therefore, the component of the weight parallel to the inclined plane  and the component perpendicular to the inclined plane is approximately 34.72 pounds and 196.96 pounds respectively.

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We can use the analysis of variance procedure to test hypotheses about three or more groups and their mean differences. ANOVA is a powerful tool for testing hypotheses about differences among group means, variability within and between groups, and interaction effects in multifactor studies.

The procedure compares the variability between the groups to the variability within the groups, and determines whether the observed differences in means are statistically significant. This can be used to test hypotheses about the effect of a treatment, the comparison of multiple groups, or the relationship between an independent variable and a dependent variable. Overall, the analysis of variance procedure provides a powerful tool for hypothesis testing in research, and can be used to draw conclusions about the population from a sample of data. The analysis of variance (ANOVA) procedure is a statistical method used to test hypotheses about:

Differences among group means: ANOVA helps to determine if there are significant differences among three or more group means, enabling researchers to compare multiple groups simultaneously. Variability within and between groups: ANOVA compares the variability of data points within each group to the variability between groups. This analysis helps identify if the variation is due to factors of interest or random chance. Interaction effects: In a multifactor ANOVA, the procedure can test for interaction effects between independent variables. This helps to understand if the effect of one factor on the dependent variable is dependent on the levels of another factor.

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What is speed?

Velocity is defined as the speed of movement of an object along its direction. Velocity tells you how fast an object is moving and the direction it's moving. Similar to velocity, but also adds direction. Therefore, velocity is directed velocity, although velocity has no direction.

how to calculate speed

Find the initial velocity of an object by dividing the time it took the object to travel the specified distance by the total distance. In the formula V = d/t, V is velocity, d is distance, and t is time.

According to the question given data,

Distance=3000miles

Time=4.5hours

Put the value of formula

V=3000/4.5

V=666.66m/s

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Answer:

x = 111; y =36; z = 76

Step-by-step explanation:

The sum of the interior angles of a triangle will add up to zero and a line that divides a straight line into to parts will have a sum of angles of 180 degrees. Use this information to add and subtract the angles to find x, y, and z.

Answer:

-61

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write expression

-18/-6 + 8 × - 8

Step 2: Divide

3 + 8 × -8

Step 3: Multiply

3 - 64

Step 4: Subtract

-61

Answer:

If instructed to simplify the question, your answer is -5+8x.

Step-by-step explanation:

-18 divided by -6 equals positive 3.

3 + 8x -8 would become -5+8x, because 3 minus 8 is -5. Hope this helps!

The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The expression are

        \(\Delta E  = \Delta E _1 + \Delta E_2\)

and

     \(\Delta E  = \Delta E _3 + \Delta E_4\)

Step-by-step explanation:

Generally from the diagram  the energy change from state A to  state B is  

        \(.\  \ \Delta E_2 \ \ \ \ \  \  \ \ \Delta E_2  \\A  \ \ \to \ \ \  C \ \ \ \to \ \ \  B\\\)

Also  

\(.\  \ \Delta E_3 \ \ \ \ \  \  \ \ \Delta E_4  \\A  \ \ \to \ \ \  D \ \ \ \to \ \ \  B\\\)

So  two expressions for the difference in internal energy between state a and state b are  

      \(\Delta E  = \Delta E _1 + \Delta E_2\)

and

     \(\Delta E  = \Delta E _3 + \Delta E_4\)

The rank of a matrix is the number of linearly independent columns or rows in the matrix.

If the columns of an n × n matrix A are linearly independent as vectors in ℝn, then the rank of A is n. This is because linearly independent vectors are not multiples of each other, and therefore do not reduce to a smaller set of linearly independent vectors when the matrix is put in reduced row echelon form. As a result, the rank of the matrix is equal to the number of columns, which is n. Therefore, the rank of A is n.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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The 95% confidence interval estimate of the population mean rating for Miami International Airport is approximately 5.50 to 6.74 (rounded to two decimal places).

To develop a 95% confidence interval estimate of the population mean rating for Miami International Airport, we can use the sample data provided. Here are the steps to calculate the confidence interval:

Step 1: Calculate the sample mean and sample standard deviation (s) from the given ratings.

Step 2: Determine the critical value (t*) for a 95% confidence level. Since the sample size is small (n = 50), we need to use the t-distribution. The degrees of freedom (df) will be n - 1 = 50 - 1 = 49.

Step 3: Calculate the standard error (SE) using the formula: SE = s / √n, where n is the sample size.

Step 4: Calculate the margin of error (ME) using the formula: ME = t* * SE.

Let's proceed with the calculations:

Step 1: Calculate the sample mean and sample standard deviation (s).

Sample ratings: 7 7 3 8 4 4 4 5 5 5 5 4 9 10 9 9 8 10 4 5 4 10 10 10 11 4 9 7 5 4 4 5 5 4 3 10 10 4 4 8 7 7 4 9 5 9 4 4 4 4

Sample size (n) = 50

Sample mean = (Sum of ratings) / n = (306) / 50 = 6.12

Sample standard deviation (s) = 2.18

Step 2: Determine the critical value (t*) for a 95% confidence level.

Using a t-distribution with 49 degrees of freedom and a 95% confidence level, the critical value (t*) is approximately 2.01.

Step 3: Calculate the standard error (SE).

SE = s / √n = 2.18 / √50 ≈ 0.308

Step 4: Calculate the margin of error (ME).

ME = t* * SE = 2.01 * 0.308 ≈ 0.619

Step 5: Construct the confidence interval.

Confidence Interval = 6.12 ± 0.619

Lower bound = 6.12 - 0.619 ≈ 5.501

Upper bound = 6.12 + 0.619 ≈ 6.739

The 95% confidence interval estimate of the population mean rating for Miami International Airport is approximately 5.50 to 6.74 (rounded to two decimal places).

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Based on the given information and significance levels, the conclusion that should be made is option b: For only alpha = 0.01, we would reject H0. There is convincing evidence that the lightbulbs last less than 1000 hours at alpha = 0.01, but not at alpha = 0.05.

In hypothesis testing, the significance level (alpha) is the threshold used to determine whether to reject the null hypothesis (H0). A smaller alpha value indicates a stricter criterion for rejecting the null hypothesis.

In this case, the null hypothesis (H0) assumes that the true mean time the lightbulbs last is 1000 hours. The alternative hypothesis (H1) suggests that the lightbulbs last less than 1000 hours.

The resulting p-value of 0.028 is the probability of obtaining a sample mean time equal to or more extreme than 990 hours, assuming that the null hypothesis is true. If the p-value is less than the significance level, we reject the null hypothesis.

Option b states that only at alpha = 0.01 (a stricter significance level), we would reject H0. This means that there is convincing evidence that the lightbulbs last less than 1000 hours at alpha = 0.01. However, at alpha = 0.05, the evidence is not strong enough to reject the null hypothesis.

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It is called the y-coordinate

The point itself is called a coordinate, vertically, the vertical component of the coordinate is called the y-coordinate, while horizontally, the horizontal component of the coordinate is called the x-coordinate.

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Given

\( \text{Length of the tree= 25 feet} \\ \text{Angle of Elevation= 30°}\)

\( \text{Height Of The Tree}\)

\( \text{Let The Height of the Tree be ‘x’}\)

We Know:-

\( \tan\theta = \frac{ \text{perpendicular}}{ \text{base} }\)

\( \tan \theta = \frac{ \text{height of the tree}}{ \text{length of the base}} \\ \\ \implies \tan30 = \frac{ \text{x}}{25} \\ \\ \implies \text{x }= 25 \times \tan30 \\ \\ \implies \text{x }= 25 \times 0.577 \\ \\ \implies \text{x} = 14.425 \\ \\ \implies \text{x} = 14.43\)

\( \therefore \text{height of the tree(\text{x})} = \red{14.43 \: \text{feet}}\)

Option C is the correct answer

Answer:

\(y=3\)

Step-by-step explanation:

\(-2(7 - y) + 4 = -4\)

➱ Subtract 4 from both sides:

➱ Divide both sides by -2:

➱ Subtract 7 from both sides:

➱ Divide both sides by -1:

OAmalOHopeO

The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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The given ordered pairs satisfy a linear function f(x) = mx + b.

As per the given data we have to determine the given ordered pairs satisfy a linear function.

If the information about the function is given in the algebraic form, then it is linear if it is of the form f (x) = mx + b.

Let the linear function be f (x)=a x + b

From the table f (4)=2 ; f (3)=4

a(4) + b = 2

4a + b = 2....(1)

a(3) + b = 4

3a + b = 4....(2)

Solving (1), (2)

4a - 3a + b - b = 2 - 4

a = - 2

Put a = - 2 in equation (2)

3(-2) + b = 4

b = 4 + 6

b = 10

Therefore f(x)= -2 x + 10

f(5)= -2(5) + 10

f(5)= -10 + 10

f(5)= 0

(x, y) = (5, 0)

f(4) = -2(4) + 10

f(4) = - 8 + 10

f(4) = 2

(x, y) = (4, 2)

So, ordered pairs satisfy the linear function

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Option C) is the correct graph that best represents the combination of both functions.

The graph, which plots time on the x-axis and temperature on the y-axis, displays an increasing function that depicts the temperature. The graph is divided into two sections: one shows a straight line with a positive slope to reflect the heater's contribution, and the other shows a curve to show the sun's contribution.

Option A) depicts a straight line that illustrates the rise in temperature brought on by the heater, but it omits the sun's influence. The intersection of these two functions is not depicted in this graph.

Option B) displays a curve that depicts the rise in temperature brought on by the sun, but it omits the impact of the heater. The intersection of these two functions is not depicted in this graph.

The sum of the two functions h(t) and s(t), which model the rise in pool temperature, can be written as follows:

c(t) = h(t) + s (t)

The specific functions h(t) and s(t) and their values at various times t would affect the graph of c(t).

Both the function h(t) and the function s(t) model the rise in temperature brought on by the sun and the heater, respectively.

As a result, Option C) is the correct graph that accurately depicts the union of the two functions.

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Answer:

Its A.

Step-by-step explanation:

it just looks like a combination of the other 2

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 descending values of the numbers is 0.98 > 0.925 > 0.88 > 0.7

Given data ,

Let the numbers be represented as A

Now , the value of A is

A = { 0.98 , 0.925 , 0.88 , 0.7 }

And , arranging in the descending order means from the greatest to the least value

So , the value of A is 0.98 > 0.925 > 0.88 > 0.7

Hence , the descending order is 0.98 > 0.925 > 0.88 > 0.7

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Answer:

0.65

Step-by-step explanation:

\(13.00*5%=0.65\)

Answer:

Price before tax: $ 13.00

+ Sales tax (5%): $ 0.65

Total price including tax: $ 13.65

Good luck <33

To solve for e in the equation 5.16 = 4e, we need to isolate e on one side of the equation.

We can start by dividing both sides of the equation by 4:

5.16/4 = (4e)/4

1.29 = e

Therefore, 5.16 = 4e is equal to e = 1.29.

Applying the scale factor of 1:5, Lisa del Giocondo's face was 1.6 inches long in the sketch.

If the scale factor from the sketch to real life is 1:5, then it means that every inch in the sketch represents 5 inches in real life.

Therefore, to find out how long Lisa del Giocondo's face was in the sketch, we need to multiply the real-life length of her face by the inverse of the scale factor, which is 1/5.

If her face was 8 inches long in real life, then her face in the sketch would be:

8 inches * (1/5) = 1.6 inches

Therefore, based on the scale factor given, Lisa del Giocondo's face was 1.6 inches long in the sketch.

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Answer:

(2n+3)(2n+5)

Step-by-step explanation:

This question is asking about the sampling distribution of a proportion for a study where the president of a company believes that 30% of their orders come from first-time customers. The question provides options for the type of distribution and asks for the probability of certain sample proportions.

In this case, the sample size is 100 and the proportion of first-time customers is p = .30. To determine the sampling distribution of the proportion, we need to consider whether np and n(1-p) are both greater than 5. In this case, np = 30 and n(1-p) = 70, so both are greater than 5, indicating that the sampling distribution of the proportion is approximately normal.

To find the probability that the sample proportion will be between .20 and .40, we need to calculate the z-scores for both values and find the area between them under the standard normal distribution. Using the formula for the standard error of the proportion, we can calculate the z-score for .20 as (0.20 - 0.30) / √((0.30 * 0.70) / 100) = -2.53 and the z-score for .40 as (0.40 - 0.30) / √((0.30 * 0.70) / 100) = 2.53. Looking up these z-scores in a standard normal distribution table, we find that the area between them is approximately 0.9858, rounded to 4 decimals.

Similarly, to find the probability that the sample proportion will be between .25 and .35, we calculate the z-score for .25 as (0.25 - 0.30) / √((0.30 * 0.70) / 100) = -1.33 and the z-score for .35 as (0.35 - 0.30) / √((0.30 * 0.70) / 100) = 1.33. The area between these z-scores is approximately 0.6827, rounded to 4 decimals.

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