Triangle BKN is shown, where point H is the incenter, m

The conclusion of Clairaut's theorem holds for u = x^4y^3 - y^4, as uxy = uyx.

To verify that the conclusion of Clairaut's theorem holds, we need to show that the mixed partial derivatives of u are equal. We have:

ux = 4x3y3

uy = 3x4y2 - 4y3

Taking the partial derivative of uy with respect to x, we get:

uyx = 12x3y2

Taking the partial derivative of ux with respect to y, we get:

uxy = 12x3y2

Since uxy = uyx, Clairaut's theorem holds for this function u.

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From the hypothesis test conducted, the calculated t-statistic of -3.57 is less than the lower critical t-value of -2.064. This tells us that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level. Therefore, the null hypothesis can be rejected and conclusions can be made that that there is enough evidence to suggest that the average grade of the students in the Algebra 2 class this year is not equal to the average grade of the same students in the Algebra 1 class two years ago.

To determine whether there is enough evidence to reject the teacher's claim, we can conduct a hypothesis test. A one-sample t-test will be us to compare sample mean.

Here are the sample statistics:

Sample size (n) = 25

Sample mean (X) = 87%

Sample standard deviation (s) = 7%

A significance level (α) of 0.05, wil be used

We first calculate the t-statistic, with  (X - μ) / (s/√n),

t = (87 - 92) / (7/√25) = -5 / (7/5) = -3.57

Then, we check this value against the critical t-value for a two-tailed test with 24 degrees of freedom (n-1), and α = 0.05.

The critical t-values for a two-tailed test at α = 0.05 and df = 24 are approximately -2.064 and +2.064.

-3.57 t-test is less than the lower critical t-value of -2.064. This means that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level.

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When using the empirical rule for a set of sample data, the following statements are true: Approximately 68% of all observations are in the interval ± 1s (one standard deviation from the mean),Almost all observations are in the interval ± 3s (three standard deviations from the mean),Approximately 95% of all observations are in the interval ± 2s (two standard deviations from the mean),This statement, "Approximately 95% of all observations are in the interval + S", is incorrect.

When using the empirical rule for a set of sample data, the following statements are true:

a. Approximately 68% of all observations are in the interval ± 1s (one standard deviation from the mean).

b. Almost all observations are in the interval ± 3s (three standard deviations from the mean).

c. Approximately 95% of all observations are in the interval ± 2s (two standard deviations from the mean).

d. This statement, "Approximately 95% of all observations are in the interval + S", is incorrect. The empirical rule states that approximately 68% of all observations are in the interval ± 1s, not just "+ s".

Therefore, the correct answer is (c) Approximately 68% of all observations are in the interval + 2s.

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The surface area of the given right rectangular prism is 288 square inches.

The given dimensions of the right rectangular prism are:

Length = 6 inches

Width = 4 inches

Height = 12 inches

The surface area of a rectangular prism can be calculated using the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values into the formula:

Surface Area = 2(6)(4) + 2(6)(12) + 2(4)(12)

Surface Area = 48 + 144 + 96

Surface Area = 288 square inches

Therefore, the surface area of the given right rectangular prism is 288 square inches.

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Step-by-step explanation:

If x < 0, we consider the absolute value of x/3.

The absolute value is always positive or zero, which means when x < 0, the expression becomes -x/3. This is because we remove the negative sign from negative numbers when finding the absolute value.

So, |x/3| = (-x)/3 when x < 0.

Answer:

-x/3

Step-by-step explanation:

because x < 0 , so lets take x = -3

Then | -3/3 |

    = | -1 | = -(-1) = 1

There fore , | x/3 | for x < 0 = -x/3

According to Census 2000, Utah had the highest proportion of married-couple households.

During the Census 2000, data was collected on the marital status of households in various states across the United States. The analysis revealed that Utah had the highest proportion of married-couple households among the given options of Utah, Mississippi, and Montana. This indicates that a larger percentage of households in Utah consisted of married couples compared to the other states during that time period. The Census data provides valuable insights into the demographic composition of different regions, helping to understand societal trends and patterns.

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Therefore, the sample variance is approximately 65 using 95% confidence interval.

To find the sample variance, we need to use the formula for the confidence interval of the mean:

X ± tα/2 (s/√n)

Where:

X is the sample mean

tα/2 is the critical value for the t-distribution at the desired confidence level (with n-1 degrees of freedom)

s is the sample standard deviation

n is the sample size

From the given information, we know that the sample size n = 13, and the confidence interval is (3.5990, 19.0736) with a 95% confidence level. This means that the critical value for the t-distribution at α/2 = 0.025 and 11 degrees of freedom is approximately 2.201.

Using the formula for the confidence interval and the upper and lower bounds of the interval, we can solve for s:

19.0736 = X + 2.201(s/√13)

3.5990 = X - 2.201(s/√13)

Adding the two equations gives:

22.6726 = 2X

Therefore, X = 11.3363

Substituting this value of X into one of the original equations gives:

19.0736 = 11.3363 + 2.201(s/√13)

Solving for s, we get:

s ≈ 8.0587

Rounding to the nearest integer, the sample variance is:

s^2 ≈ 65

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The lateral surface area of a regular prism would be =100cm²

To calculate the lateral surface area of a prism the formula that should be used would be given below such as follows;

Lateral surface area of prism = perimeter of base×height

The base = perimeter of square = 4a

where;

a = side length = 2cm × 4 = 8cm

Height = 125 mm = 12.5cm

Lateral surface area of prism = 8×12.5 = 100cm²

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Answer:

Step-by-step explanation:

You would divide 244.40 by 26%

You would get  63.544.... Now times the 63.544 to the remainder of the 26 from 100...which is 74.  63.544 times 74 equals 4702.256.

Now add the 244.40 to that and u get the answer of 4946.656.

Answer:

Good Luck

Step-by-step explanation:

Let the regular price be "x".

According to the problem, the sofa is being sold for 26% of the regular price, which means the sale price is:

Sale price = 0.26x

The problem also states that the sale price is $244.40, so we can write:

0.26x = 244.40

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.26:

x = 244.40 ÷ 0.26

x = 940

Therefore, the regular price of the sofa is $940.

The statement that represents the equation (x – 3)2 + y2 = 16 is On a coordinate plane, a circle has a center at (3, 0) and radius 4.

The given equation is (x – 3)^2 + y^2 = 16

We solve to obtain:

(x – 3)^2 + (y - 0)^2 = 16

(x – 3)^2 + (y - 0)^2 = 4^2

This is an equation of a circle

Therefore, we can conclude that On a coordinate plane, a circle has a center at (3, 0) and radius 4.

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B

The paper company can produce 785 papers in one day.

(3925÷5=785)

Therefore the paper company can produce 10205 papers in 13 days.

(785×13=10205)

Answer: B. 10,205

Step-by-step explanation: If in 5 days it produces 3,925 notebooks. Then what you should do is divide 3925 by 5. The answer for that equation is 785. So in 1 day they produce 785 notebooks. The last step you should do is multiply 785 by 13. 13 as in days and 785 as in the amount of notebooks made in one day.  That's how you get 10,205 notebooks. Hope this helps :)

False. A rectangle is conventionally used in a process flowchart to represent a storage area or queue. Triangles are typically used in flowcharts to represent decision points, where a choice must be made between two or more alternatives.

Rectangles are used to represent activities or operations, while arrows connecting the shapes indicate the flow or direction of the process. The use of standardized shapes in flowcharts helps to make them easily understandable and accessible to a wide range of individuals, regardless of their background or experience with the specific process being depicted.

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Answer: 135/20=6.75

Step-by-step explanation:

Long division (picture attached below)

The correct answer is D) 4.

In a two-way analysis of variance, we are examining the effects of two independent variables (or factors) on a dependent variable. We must calculate four F-ratios to test the significance of these effects: two for the main effects of each factor, and two for the interaction effect between the two factors.

The F-ratio is a statistical test that compares the amount of variability between groups to the amount of variability within groups. By calculating F-ratios for each effect, we can determine whether the differences between groups are statistically significant and whether the independent variables have a significant impact on the dependent variable.

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Answer: 100

hope this helps

(0, 0) is the y-intercept of the given line.

To detect the y-intercept of a line in a graph, you need to find the point where the line intersects the y-axis. In other words, it's the point where the value of x is zero.

To find the y-intercept of a line on a graph:

If the equation of the line is in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept, then the value of b is the y-coordinate of the point where the line intersects the y-axis.

In the given graph line is paasing through origin (0, 0).

Thus, the value of y where the value of x will be zero is zero.

So the y-intercept is 0.

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The probability that the randomly selected patient had a blood test requested during their visit is approximately 0.120

In this case:

We can calculate the overall probability as the weighted average of the probabilities from each doctor:

Probability = (Probability from Dr. Sarabia) * (Percentage of patients seen by Dr. Sarabia) + (Probability from Dr. Tran) * (Percentage of patients seen by Dr. Tran) + (Probability from Dr. Jackson) * (Percentage of patients seen by Dr. Jackson)

Probability = (0.10 * 0.27) + (0.10 * 0.32) + (0.15 * 0.41)

Probability ≈ 0.027 + 0.032 + 0.061

Probability ≈ 0.12

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The surface area of the prism is 520 in².

The area of the prism is 750 in³.

We have,

The given figure is a rectangular prism.

The surface area can be calculated by adding all the areas of the surfaces.

Now,

There are two types of surfaces.

Top and bottom surfaces and the side surfaces

So,

Top surface = Bottom surface

Area = 2 x (8 x 7(1/2)) = 8 x 15 = 120

Side surface.

Area = 4 x (8 x 12(1/2)) = 4 x (8 x 25/2) = 4 x 4 x 25 = 16 x 25 = 400

The surface area.

= 120 + 400

= 520 in²

And,

The area of the prism.

= 8 x 7(1/2) x 12(1/2)

= 8 x 15/2 x 25/2

= 2 x 15 x 25
= 30 x 25

= 750 in³

Thus,

The surface area of the prism is 520 in².

The area of the prism is 750 in³.

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Answer: 50

Step-by-step explanation:

Greatest common factor of 200 and 150 is 50

200/50=4

150/50=3

Answer:

31/40

Step-by-step explanation:

3/8+2/5

Find the common denominator.

15/40+16/40

Add.

=31/40

Answer: 31/40

Step-by-step explanation:

3/8+2/5

make denominators equal, multiply by 8and 5

15/40+16/40=31/40

The expression that is equivalent to 42x - 48 is: 6(7x - 8)

An algebraic expression is defined as a mathematical phrase that includes both variables, constants, coefficients, and algebraic operations.

An algebraic expression is also considered as a variable expression described using its terms, and operations on the terms. For example, x + 3 can be described as "3 more than x".

We want to factorize the expression 42x - 48

The number that is common to both numbers is 6 and as such we have the expression factorized as:

6(7x - 8)

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Answer:

The piece left over is 10 cm long

Step-by-step explanation:

1 metre = 100 cm

Each piece = 30 cm long

Number of piece = 3

30 × 3 = 90

100 - 90 = 10 cm

Therefore, the piece left over is 10 cm long

1.) For the triangle with sides 9 and 5, the third side must satisfy the inequality:

9 - 5 < x < 9 + 5

which simplifies to:

4 < x < 14

So the range of possible measures for the third side is 4 < x < 14.

2.) For the triangle with sides 5 and 8, the third side must satisfy the inequality:

8 - 5 < x < 8 + 5

which simplifies to:

3 < x < 13

So the range of possible measures for the third side is 3 < x < 13.

3.) For the triangle with sides 6 and 10, the third side must satisfy the inequality:

10 - 6 < x < 10 + 6

which simplifies to:

4 < x < 16

So the range of possible measures for the third side is 4 < x < 16.

4.) For the triangle with sides 6 and 9, the third side must satisfy the inequality:

9 - 6 < x < 9 + 6

which simplifies to:

3 < x < 15

So the range of possible measures for the third side is 3 < x < 15.

5.) For the triangle with sides 11 and 8, the third side must satisfy the inequality:

11 - 8 < x < 11 + 8

which simplifies to:

3 < x < 19

So the range of possible measures for the third side is 3 < x < 19.

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Step-by-step explanation:

y = x^3 + 1     switch x and y....then solve for y

x = y^3 + 1

x-1 = y^3

y = cubrt ( x-1)     <====this is the inverse function

Each line in every set of lines of the same color intersects with each line in two other sets. Because of that fact, there's a segment formed on each line in every set. Therefore, by tracing any segment from every set, we get a closed shape, which is a pentagon, as a result. Since there are 3 segments in each set and a pentagon has 5 sides, the number of pentagons we can trace is [tex]3\cdot3\cdot3\cdot3\cdot3=3^5=243[/tex].

Using number theory, the difference between the smallest and largest is 8998.

In order to determine the difference between the largest and smallest 4-digit in which the values do not change when their digits are reversed, we can start with;

This problem falls under number theory and we can apply some insight here;

In this case, the smallest value will be 1000 while the largest will be 9999

We can add 1 from 1000 till we reach 9999. For each number, we compare it with its reversed form. If they are equal, we store that number as a candidate for the smallest and largest numbers.

After checking all the numbers, we find that the smallest and largest numbers that meet the given criterion are:

Smallest number: 1001 (remains the same when digits are reversed)

Largest number: 9999 (remains the same when digits are reversed)

Now, we can calculate the difference between the smallest and largest numbers:

Difference = Largest number - Smallest number

Difference = 9999 - 1001

Difference = 8998

Therefore, the difference between the smallest and largest 4-digit numbers that do not change when their digits are reversed is 8998.

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The Decimal 0.612 and the 12 is repeating as a fraction is 20.346/33.

Step 1: Let x = 0.612

Step 2: Multiply both sides by 1000 to remove the decimal point: 1000x = 612

Step 3: Since the 12 is repeating, we can subtract the non-repeating part from the repeating part to get 12 - 0 = 12. Then we can write the repeating part as a fraction with a denominator of 99 (which is one less than 100, the number of repeating digits). So we have: 0.12 = 12/99

Step 4: Rewrite the equation from step 2 using the value from step 3: 1000x = 612 + 12/99

Step 5: Simplify the right-hand side: 1000x = 61038/99

Step 6: Divide both sides by 1000 to solve for x: x = 61.038/99

Step 7: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 3: x = 20.346/33

Therefore, the decimal 0.612 and the 12 is repeating as a fraction is 20.346/33.

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Answer:The circle has a center at (5,5) and a radius of 2. Therefore, the equation is (x-5)2+(y-5)2=22, or (x-5)2+(y-5)2=4.

Step-by-step explanation:

i did the qestion on my test

The solution is: 5 in hours did Ben work that Saturday​.

The number of hours that Ben worked at the restaurant can be calculated by the expression, Xpm - Xam.

The number of hours that Ben worked can be represented as:

= Time he finished working - Time he started working

= X pm - X am

If for instance, he started work at 7 am and finished at 12 pm, he would have worked:

= 12 - 7

= 5 hours

The expression that shows the length of time he worked can therefore be concluded to Xpm - Xam.

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complete question:

Ben is a waiter at a restaurant. on Saturday, Ben got up at 6:30am, started work at X.am and finished work at X.pm. how long in hours did Ben work that Saturday​