The expression of (²/₃)⁻¹ without an exponent is given as;
3/2
How to use Laws of exponents?The different laws of exponents are;
1) Power Law of Exponents which is expressed as; (x^m)ⁿ = x^(mn)
2) Quotient Law of Exponents is expressed as; x^m ÷ x^n = x^(m - n)
3) Product Law of Exponents is expressed as; x^(m) * x^(n) = x^(m + n)
4) Law of Reciprocal is expressed as; a⁻ⁿ = 1/aⁿ
Now, we want to rewrite the expression (²/₃)⁻¹ without using an exponent.
From the law of reciprocal of exponents we can say that;
(²/₃)⁻¹ = 1/(²/₃)
= 3/2
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52.8 as a fraction in simplest form
Answer:
Step-by-step explanation:
It would be 264/5 or 52^4/5
(^4 is the fourth power)
There are 25 pieces of candy in a bowl, and 15 of them are chocolate. What percentage of pieces of candy in the bowl are chocolate?
60% of the pieces of candy in the bowl are chocolate.
(15/25)*100 = 60%
if PQ+PR=72 cm, then what is the value of sinR? (look at the file)
The exact value of the sine of angle R is equal to 1 / 2.
How to determine the exact value of a trigonometric function
In this problem we find the representation of a right triangle, where two side lengths are known and the exact value of a trigonometric function must be found. First, determine the length of side PR:
PR = 72 cm - PQ
PR = 72 cm - 24 cm
PR = 48 cm
Second, determine the length of side PQ by Pythagorean theorem:
RQ = √[PR² - PQ²]
RQ = √[(48 cm)² - (24 cm)²]
RQ = 24√3 cm
Third, determine the exact value of a trigonometric function of angle R by definition of sine:
sin R = PQ / PR
sin R = (24 cm) / (48 cm)
sin R = 1 / 2
Fourth, determine the exact value of a trigonometric function of angle R by definition of cosine:
cos R = RQ / PR
cos R = (24√3 cm) / (48 cm)
cos R = √3 / 2
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19. In the energy category, Khalil scored low on the intuitive function. Since Khalil has low intuition, he must have
scored high on the function, which involves looking for the facts, focusing on specifics, taking realistic
approaches to problem-solving, planning for the immediate, and embracing practical solutions.
A. observant
B. turbulent
C. judging
D. prospecting
If in the energy category, Khalil scored low on the intuitive function in which he must he have scored high on the function, which involves looking for the facts, focusing on specifics, taking realistic. This is an example of : A. observant
What is Observant?To be observant can be defined as the way in which a person tend to watch others or when a person observe the event happening around him/her .
This scenario is an example of observant based on the fact that this person watch the event happening in Khalil life and this was done by carefully observing Khali and things that happen around Khali.
Therefore the correct option is A.
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Can someone please help?! Appreciated!
The value of the inequality -4(x - 6) < 22 will be x < 1/2.
How to solve the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
The process of solving an inequality using the Distributive Property is similar to solving an equation using the Distributive Property. Both involve simplifying expressions by distributing terms to isolate the variable. However, the only difference is that in an inequality, you have to be careful about the direction of the inequality symbol and make sure to reverse it if you multiply or divide both sides by a negative value.
The value of the inequality will be:
-4(x - 6) < 22
-4x + 24 < 22
Collect the like terms
-4x < 22 - 24
-4x < -2
Divide
x < -2/-4
x < 1/2
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How do you use the definition of continuity and the properties of limits to show that the function h(t) = (2t-3t^2)/(1+t^3) is continuous at the given number a=1?
The function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1 because the limit of h(t) as t approaches 1 is equal to h(1).
First, we need to show that the limit of h(t) as t approaches 1 is equal to h(1).
Since h(t) = (2t-3t^2)/(1+t^3), we can rewrite the limit of h(t) as t approaches 1 as:
lim t->1 (2t-3t^2)/(1+t^3) = lim t->1 (2-3t)/(1+t^3)
We can now use the properties of limits to evaluate the limit.
Substituting t=1 into the expression for the limit, we have:
lim t->1 (2-3t)/(1+t^3) = (2-3(1))/(1+(1)^3) = -1/(2)
Now, we can use the definition of continuity to show that h(t) is continuous at a=1.
Since the limit of h(t) as t approaches 1 is equal to h(1), then h(t) is continuous at a=1.
Thus, we have successfully shown that the function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1.
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What is the value of P(X=3 or X=0)?
Enter your answer in the box.
P(X=3 or X=0) = __________
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a) Factorise x²-2x-3
b) Hence, simplify 2x-1
x²²-2x-3
+
1
x-3
By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets.Answer is x = 5/2, -4.
How do you factorise ?By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets.Finding the highest common factor between each term in the phrase is the simplest method of factorization.
In front of any brackets, indicate the highest common factor (HCF).The Grouping method, the difference in two squares, and the sum or difference in cubes are the four primary methods of factoring. The Greatest Common Factor (GCF) is another.
2x^2 + 3x - 20
Since 2 * -20 equals -40, we require two numbers whose total is +3 and whose product is -40.
We write this as + 8 and -5.
Factor by grouping: = 2x2 + 8x - 5x - 20
= 2x(x + 4) - 5(x + 4)
= (2x - 5)(x + 4)
So, the roots are x = 5/2 and -4.
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please fill in the "if ___" part!
The expression can be simplified as follows:
2(x - y)/[y(x + y)]
The condition for the expression is given as follows:
x ≠ y, y ≠ 0.
How to simplify the expression?The expression for this problem is defined as follows:
[(x - y)²]/(2xy + 6y) x (4x + 12)/(x² - y²)
The factors of the expression can be simplified as follows:
2xy + 6y = 2y(x + 3).4x + 12 = 4(x + 3).x² - y² = (x + y)(x - y).The terms that can be simplified are given as follows:
4(x + 3)/2y(x + 3) = 2/y.(x - y)²/[(x + y)(x - y)] = (x - y)/(x + y).Hence the product is given as follows:
(x - y)/(x + y) x 2/y
2(x - y)/[y(x + y)]
As the expression is a fraction, the denominator cannot be zero, hence the conditions are given as follows:
x ≠ y, y ≠ 0.
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-9x + 1 = -9x+1 is it no solution one solution or infinite solutions
Answer: Infinite Solutions
Step-by-step explanation:
When an equation is the exact same as the other, they have an infinite amount of solutions.
I hope I helped :D
Answer: This equation has infinite solutions.
Step-by-step explanation: There are all real numbers on both sides of the equation. I hope this helps!
A measure computed from the entire population is called
a. a statistic.
b. a qualitative value.
c. a mean.
d. a parameter.
A measure computed from the entire population is called a parameter. Option D is the correct answer.
A parameter is a numerical characteristic of the population, and it is usually estimated from a sample of the population. Parameters are usually unknown and are estimated using a variety of mathematical methods.
Examples of parameters include the population means, median, and standard deviation. Parameters can also be used to describe the characteristics of a population, such as the percentage of people who are a certain color, race, or gender.
Parameters are usually reported in summary form, such as the mean or median of a population. In contrast, a statistic is a measure computed from a sample and is not representative of the entire population. Statistics are used to make estimates and predictions about a population and are usually reported in the form of a confidence interval.
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a transformation is applied to a figure to create a new figure on a coordinate grid. which transformation does not preserve congruence?
a. A reflection across the x-axis
b. A translation 7 units down
c. A dilation by a scale factor of 5
d. A rotation of 90° clockwise
When x is -1.5, what value of y makes the equation true?
The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation is given below.
y = - 3x + 2.5
The value of the equation at x = 1 will be given as,
y = - 3 × (1) + 2.5
y = - 3 + 2.5
y = - 0.5
The value of the equation at x = - 1.5 will be given as,
y = - 3 × (-1.5) + 2.5
y = 4.5 + 2.5
y = 7
The value of the equation at x = 8.5 will be given as,
y = - 3 × (8.5) + 2.5
y = - 22.5+ 2.5
y = - 20
The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.
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Complete question:
On parallelogram PQRS, P is located at (-1, 6) and S is located at (-7,-3). What is the
slope of segment QR?
P Р
R
rimblr an impronar fraction
How do I solve this?
According to the parallelogram, the slope of the segment QR is 3/2
In math the term called parallelogram is a closed quadrilateral with parallel and congruent opposite sides is referred to as a parallelogram and the opposite pairs of sides have the same slope and the sum of two adjacent angles is 180 degrees.
Here we have know that values of P is located at (-1, 6) and S is located at (-7,-3). Then the slope of QR is calculated by using the the slope formula for a line segment passing through two points,
It can be calculated as,
=> m = (-3 - 6) / (-7 - (-1)
When we simplify this one then we get,
=> m = -9/-6
=> m = 3/2
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PLEASE HELP ASAP
The table represents a linear relationship.
x −2 0 2 4
y −1 0 1 2
Which of the following graphs shows this relationship?
A graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
B graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
C graph of a line passing through the points negative 2 comma 4 and 0 comma 0
D graph of a line passing through the points negative 2 comma 1 and 0 comma 0
A graph which shows this relationship is: B. graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0.
How to determine the linear function?In order to determine the ordered pairs and linear function that could represent a linear relationship in the given table, we would have to determine the slope of based on the data points.
In Mathematics, the slope of a linear function can be calculated by using this this mathematical expression;
Slope = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (0 + 1)/(0 + 2)
Slope = 1/2
Slope = 0.5.
At data point (-2, -1), a linear function of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.y + 1 = 0.5(x + 2)
y = 0.5x + 1 - 1
y = 0.5x
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It costs $4 per ride at an amusement park, plus a $10 fee to get in. Write an equation to represent the total cost (y) for any number of rides (x).
An equation to represent the total cost (y) for any number of rides (x) is y = 4x + 10.
How to write an equation to represent the total cost (y)?In order to write an equation that model this situation, we would assign variables to the number of rides at an amusement park and the total cost respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of rides.Let the variable y represent the total cost.Next, we would translate the word problem into an algebraic equation based on the fact that it cost $4 per ride, plus a $10 fee to get in as follows;
y = 4x + 10.
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Determine the solutions of the equation. What solution makes sense for the situation?
x =
What are the dimensions of the rectangle?
width =inches
length =inches
The dimensions of the rectangle are 8 inches as width and 13 inches as length.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The equation is given as:
x² + 5x - 104.
x² + 13x - 8x - 104
x(x + 13) - 8 (x + 13).
x - 8 = 0
x = 0 + 8
Width = 8
Length = x + 5
= 8 + 5.
= 13
The width is 8 inches and length is 13 inches.
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Determine the solutions of the equation. What solution
makes sense for the situation?
A rectangle has a length that is 5 inches greater than its
width, and its area is 104 square inches. The equation (x
+5)x = 104 represents the situation, where x represents
the width of the rectangle.
(x + 5)x = 104
x2 + 5x - 104 = 0
What are the dimensions of the rectangle?
Find the solution to the system of equations.
Answer: (-5, -2)
Step-by-step explanation:
We will substitute the first equation into the second and then solve for x. Then we will substitute x into the equation and solve for y.
Given:
5x + 3y = -31
Substitue:
5x + 3(x + 3) = -31
Distribute:
5x + 3x + 9 = -31
Combine like terms:
8x + 9 = -31
Subtract 9 from both sides of the equation:
8x = -40
Divide both sides by 8:
x = -5
Given:
y = x + 3
Substitute x into the equation and solve for y.
y = (-5) + 3
Combine like terms:
y = -2
We can also graph it. The point of intersection is the solution, see below.
Subtract x² - 6x from 5x² - 7x - 10.
Answer:
-4x^2 + x + 10
Step-by-step explanation:
see the image below for further details. Hopefully, it’s correct! :)
Square root of 50 in simplist radical form
Answer:
The square root of 50 can be simplified to the radical form of 5*sqrt(2)
Step-by-step explanation:
To simplify the square root of 50, we factor the number 50, which is 50 = 510 = 552. The square root of any number that is a perfect square, such as 55, is equal to the number inside the square root, which is 5 in this case. The square root of any number that is not a perfect square, such as 2, remains under the radical sign.
Therefore, the simplified radical form of the square root of 50 is √50 = 5√2.
The square root of 50 in simplest radical form is 5√2.
To find the square root of 50 in simplest radical form, we need to determine if there are any perfect square factors in 50 that can be taken outside the square root symbol.
The prime factorization of 50 is 2 × 5².
We can see that 5² is a perfect square factor of 50.
Therefore, we can rewrite the square root of 50 as the square root of (2 × 5²).
Using the property of square roots, we can split the square root of a product into the product of the square roots of each factor:
√(2 × 5²) = √2 × √(5²)
The square root of 5² simplifies to 5, so we have:
√(2 × 5²) = √2 × 5
Therefore, the square root of 50 in simplest radical form is 5√2.
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2. A manufacturer of flashlights wants to know how well one of their newer styles is selling in a chain of large home-improvement stores. They select a simple random sample of 20 stores, record how many of the flashlights were sold in a 30-day period, and construct a 95% confidence interval for the mean number of flashlights sold.
(a) If, instead of constructing a 95% confidence interval, the flashlight manufacturer constructed a 98% confidence interval, would the 98% interval be wider, narrower, or the same width as the 95% interval? Explain.
(b) How would the width of confidence interval change if the flashlight manufacturer took a larger sample? Explain.
(c) The 20 stores in the sample were actually the only stores who provided sales figures from 36 stores that were randomly chosen to be in the sample. Can the manufacturer adjust the confidence interval to take this nonresponse into account? If so, how? If not, why not?
A: (a) The 98% confidence interval would be wider than the 95% interval. As the confidence level increases, the margin of error increases, thus making the interval wider.
(b) The width of the confidence interval would decrease as the sample size increases. This is because a larger sample size will result in a more accurate representation of the population, thus allowing for a narrower confidence interval.
(c) The manufacturer cannot adjust the confidence interval to take this nonresponse into account, as the nonresponse does not affect the accuracy of the sample. The confidence interval is based on the sample itself and not the population from which it was drawn.
What is mean by random sample?Random sampling is a method of selecting a sample of individuals from a population such that each member of the population has an equal chance of being selected.
Random sampling is often used in research studies to ensure that the sample is representative of the population as a whole.
Random sampling is also used to minimize bias and ensure that the sample is not influenced by any particular group or individual.
Random sampling is important because it helps ensure that the results of the study are accurate and valid.
Random sampling helps to ensure that the sample is representative of the population and that the results are not influenced by any particular group or individual.
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polygon ABCDE is on a coordinate plane with point A at 2, 4 and point B at 4, 3 and point C at 3, 2 and point D at 1, 2 and point E at 0, 3 Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A′ is at (−2, 4) and the image of D′ is at (−1, 2). Which transformation can be used to show that ABCDE and its image are congruent?
Answer: When a polygon is transformed so that the image of A′ is at (−2, 4) and the image of D′ is at (−1, 2), it means that the image of the polygon is congruent to the original polygon and has undergone a transformation of a horizontal reflection.
A horizontal reflection is a transformation in which the shape is reflected over the x-axis, resulting in a mirror image of the shape with the same size and orientation but reflected horizontally. In this case, the image of the polygon is congruent to the original polygon and has undergone a horizontal reflection with a horizontal translation of 3 units to the left.
The transformation can be described as a composition of the horizontal reflection over the x-axis and a translation of -3 units horizontally.
Step-by-step explanation:
in the year 2000, there were a reported 7,867 cases of whooping cough in the us, while in the year 2002, there were 9,771 cases, according to the cdc. what might be misleading about concluding from these data that more people were getting whooping cough in 2002?
The data does not take into account population increases over the two years. It is possible that there were more people in 2002, so the number of cases could have gone up without there being an actual increase in the rate of infection.
It could also be the case that better reporting and the more accurate diagnosis were responsible for the increase in numbers. The two-year period could also be too short to draw any meaningful conclusions. Diseases can have long-term cycles of increase and decrease, so it is possible that the increase in numbers was just part of a longer-term cycle that had already been in progress.
To accurately assess the situation, it would be necessary to look at longer-term data and take into account changes in population size.
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12. Estimate the average rate of change of p between peak, p(8), and closing, p(14). What is
the meaning of the rate of change in the context of this problem? Show all work.
The meaning of the rate of change in the context of this problem is 4/7.
What is the change's speed?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another.The term "rate of change" (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or slowdown of changes (i.e., the pace). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.The formula R = D/T may often be used to tackle rate-of-change problems.P-8 / p(14)
8p / p(14) =4/7
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Match the correct angle pairs.
Matching the correct angle pair, we have;
i. Example of corresponding angles - Angle 1 and Angle 5
ii. Example of alternate interior angles - Angle 3 and Angle 6
iii. Example of alternate exterior angles - Angle 2 and Angles 7
iv. Example of Vertical angles - Angle 5 and Angle 8
Angles formed by a transversal.A transversal is a straight line which intersect two parallel lines, thus forming a series of angles with some common properties. Some of the common properties are: alternate angles, vertically opposite angles, corresponding angles, etc.
Considering the given choices in the question, matching the correct angle pairs; we have;
i. Example of corresponding angles - Angle 1 and Angle 5
ii. Example of alternate interior angles - Angle 3 and Angle 6
iii. Example of alternate exterior angles - Angle 2 and Angles 7
iv. Example of Vertical angles - Angle 5 and Angle 8
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Ashley invested $59,000 in an account paying an interest rate of 3 (1/8)% compounded
daily. Fwam invested $59,000 in an account paying an interest rate of 2 (3/4)%
compounded annually. After 15 years, how much more money would Ashley have in
her account than Fwam, to the nearest dollar?
Answer:
5650
Step-by-step explanation:
3 (1/8)% =3.125% but compound daily = 3.125% /365 = 0.00856%
so everyday the money grows at 1.00856%, so compound 365 times, it'll become 1.00856%^365 =3.1742% annually equivalent.
so now you can compare the 2 - apples to apples.
so 3.1742%^15years * 59000 = $94,279.80
2.75%^15years * 59000 = $ $88,629.74
diff is 5650$
Dr johnson is a clinical physiologist looking to test out a new therepy to help people that are scared of spiders he measured each person fear of spiders before the therapy and after the therapy in both colums of data he used the pulse rate of people when confronted by an actual spiders
Answer: Dr. Johnson is conducting an experimental study to test the effectiveness of a new therapy for individuals with arachnophobia, which is the fear of spiders. He is measuring the pulse rate of the participants before and after the therapy as an indicator of their fear response when confronted by an actual spider. The data collected will likely be used to determine if the therapy is effective in reducing the participants' fear of spiders as measured by their pulse rate.
It is important to note that while pulse rate is a good indicator of fear response, it is not the only indicator of fear and it is also not a definitive measure of the effectiveness of the therapy. Other factors such as self-reported fear, behavioral changes, and physiological changes should also be considered to get a comprehensive understanding of the therapy's effectiveness.
Step-by-step explanation:
Please answer!.
.............
∠2 and ∠7 -Interior Alternate angles
∠1 and ∠3 -Corresponding angles
∠4 and ∠5 -Exterior Alternate angles
∠3 and ∠5 -Corresponding angles
What is an angle?An angle is a measure of the amount of rotation between two lines or planes. It is typically measured in degrees or radians. An angle can be formed by two rays that share a common endpoint, known as the vertex of the angle. The rays are called the sides of the angle, and the endpoint is called the vertex. Angles can be classified as acute, right, obtuse, or straight, depending on their measure.
Everyday objects contain some of the everyday examples of angles. Angles are formed by the shapes of objects like chairs, pizza, fingers, and scissors. The vertex point, a common vertex that connects the two lines that make up the angle sign, is present.
In the given figure
∠2 and ∠7 -Interior Alternate angles
∠1 and ∠3 -Corresponding angles
∠4 and ∠5 -Exterior Alternate angles
∠3 and ∠5 -Corresponding angles
Hence, the answer is:
∠2 and ∠7 -Interior Alternate angles
∠1 and ∠3 -Corresponding angles
∠4 and ∠5 -Exterior Alternate angles
∠3 and ∠5 -Corresponding angles
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Which is a correct solution for the following system of Inequalities
Answer:
I think the answer is C
-3,-2
26.
(Pythagoras / Trigonometry] *
For this triangle use Pythagoras' theorem
c? = a² + b2. Find the length of the hypotenuse.
a=9
b=40
32.
C = ?
The length of the hypotenuse is 43.37 .
Now, According to the question:
Pythagorean triples are [tex]a^2+b^2 = c^2[/tex] where a, b and c are the three positive integers. These triples are represented as (a, b, c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle. The most known and smallest triplets are (3,4,5).
Now, Solving the problem:
There are two sides :
a = 9
b = 40
and, to find the length of the hypotenuse.
According to the Pythagoras formula:
[tex]a^2+b^2 = c^2[/tex]
Plug the values in above formula:
[tex]9^2+40^2=c^2[/tex]
81 + 1600 = [tex]c^2[/tex]
[tex]c^2[/tex] = 1681
c = [tex]\sqrt{1681}[/tex]
c = 43.37
Hence, The length of the hypotenuse is 43.37 .
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