the combined area of the garden and the walkway when the width of the walkway is 4 feet is LW + 8L + 8W + 64 square feet.
why it is?
Let's assume that the length of the rectangular garden is L and the width is W. Let the width of the walkway be x.
a. The area of the rectangular garden is L x W. The combined area of the garden and the walkway is the area of the larger rectangle formed by the outer boundary of the walkway. The length of this larger rectangle is (L + 2x) and the width is (W + 2x). Therefore, the polynomial that represents the combined area of the garden and the walkway is:
(L + 2x)(W + 2x)
Expanding this expression, we get:
LW + 2Lx + 2Wx + 4x²2
So, the polynomial that represents the combined area of the garden and the walkway is LW + 2Lx + 2Wx + 4x²2.
b. If the width of the walkway is 4 feet, then x = 4. Substituting this value in the polynomial we obtained in part (a), we get:
LW + 2L(4) + 2W(4) + 4(4)²2
Simplifying this expression, we get:
LW + 8L + 8W + 64
Therefore, the combined area of the garden and the walkway when the width of the walkway is 4 feet is LW + 8L + 8W + 64 square feet.
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I'm learning probability in geometry but haven't learned it for percentage. Can someone help me?
Answer:
Step-by-step explanation:
a. 100 divided by 75 = 1.3333333333333333333333333333333
1.3333333333333333333333333333333 times 43 = 57.333333333333333333333333333332
round it to the nearest whole number: ≅ 57%
Three divided by six hundred twenty two (remainder included
the answer is 207 Remainder 1
an open rectangular gutter is made by turning up the sides of a piece of metal 20 in wide. the area of the cross section of the gutter is 50 in^2 find the depth of the gutter
Shade in the region represented by the inequalities.
The length οf the hypοtenuse AC is 10 units.
What is graph?In mathematics, a graph is a visual representatiοn οf data οr infοrmatiοn that cοnsists οf pοints, called vertices οr nοdes, and lines, called edges οr arcs, that cοnnect them.
Graphs are οften used tο represent relatiοnships between οbjects, events, οr quantities.
They can be used tο mοdel and sοlve prοblems in variοus fields, such as cοmputer science, engineering, ecοnοmics, and sοcial sciences. There are many types οf graphs, including bar graphs, line graphs, scatter plοts, pie charts, and netwοrk graphs, amοng οthers. Each type οf graph is suited fοr visualizing different types οf data οr relatiοnships.
Based οn the given diagram, we can use the Pythagοrean theοrem tο find the length οf the hypοtenuse AC οf the right triangle ABC:
[tex]AC^2 = AB^2 + BC^2[/tex]
Substituting the given side lengths, we get:
[tex]AC^2 = 6^2 + 8^2[/tex]
[tex]AC^2 = 36 + 64[/tex]
[tex]AC^2 = 100[/tex]
Taking the square rοοt οf bοth sides, we get:
AC = 10
Therefοre, the length οf the hypοtenuse AC is 10 units.
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In an arithmetic sequence, the tenth term is 28. The sum of term 5 and term 7 is 32. Calculate the sum of the first 50 terms
The sum of the first 50 terms is 3775. Let a be the first term and d be the common difference of the arithmetic sequence.
Then, the tenth term is a + 9d = 28, and the sum of the fifth and seventh terms is 2a + 12d = 32.
Solving these equations simultaneously, we get a = 2 and d = 3.
To find the sum of the first 50 terms, we use the formula for the sum of an arithmetic sequence:
S50 = (50/2)(2a + (50-1)d) = 25(2 + 49(3)) = 3775.
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Help me with the even numbers. 2,4,6,and8
2= 2
4=10
i cant see 6 or 8
the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is:
The probability that the number of calls between 2:00 pm and 2:10 pm is exactly 200 is 0.000002204.
This can be calculated using the Poisson distribution. The Poisson distribution is used to model the probability of a given number of events occurring in a given time interval.
The Poisson equation is P(x) = (λ^x e^-λ)/x!
where λ is the expected number of occurrences per interval.
For this question, λ = 3/min, since the rate of calls to the computer software help desk is 3 per minute.
Plugging λ = 3/min into the Poisson equation, we get
P(x) = ((3/min)^200 e^-(3/min))/200!.
This simplifies to
P(x) = 0.000002204.
The probability of having exactly 200 phone calls to a computer software help desk in the 10-minute period from 2:00 pm to 2:10 pm is 0.000002204.
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Do the Cauchy-Schwarz Inequality and the triangle inequality hold for the given vectors and inner product?u = (5, 3), v = (14, 4), (u, v) = u · v(a) the Cauchy-Schwarz Inequality Yes / No(b) the triangle inequality Yes / No
a) Yes, the Cauchy-Schwarz Inequality holds for the given vectors and inner product. Since 74 ≤ 76.84, the Cauchy-Schwarz Inequality holds.
b) Yes, the triangle inequality holds for the given vectors and inner product. Since 20.25 ≤ 23.21, the triangle inequality holds.
How do we know the Cauchy-Schwarz Inequality and the triangle inequality hold given vectors and inner product?Cauchy-Schwarz Inequality:
Using the given inner product, we have:
|u · v| ≤ ||u|| ||v||where ||u|| and ||v|| denote the norms of the vectors u and v, respectively.
We can calculate:
||u|| = sqrt(5^2 + 3^2) = sqrt(34)||v|| = sqrt(14^2 + 4^2) = sqrt(212)Then, applying the Cauchy-Schwarz Inequality, we have:
|u · v| = |(5)(14) + (3)(4)| = 74||u|| ||v|| = sqrt(34) sqrt(212) ≈ 76.84Triangle Inequality:
The triangle inequality states that for any vectors u, v, and w, we have:
||u + v|| ≤ ||u|| + ||v||Using the given vectors, we can calculate:
||u + v|| = ||(5 + 14, 3 + 4)|| = ||(19, 7)|| = sqrt(19^2 + 7^2) ≈ 20.25||u|| + ||v|| = sqrt(5^2 + 3^2) + sqrt(14^2 + 4^2) ≈ 23.21Learn more about Triangle Inequality
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a bond is worth 100$ and grows in value by 4 percent each year. f(x) =
To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).
Book I, Problem 18. Find three numbers such that the sum of any pair exceeds the third by a given amount; say the given excesses are 20, 30, and 40. (Hint: Let the sum of all three numbers be 2x. Add number (3) to both sides of the equation (1) + (2) = (3) + 20 to get (3) = x – 10. Obtain expressions for (1) and (2) similarly.]
a = 5, b = 25, c = 0
step by step explanation:
Let the three numbers be a, b, and c. Then, we have the following system of equations:
a + b = c + 20 (1)
a + c = b + 30 (2)
b + c = a + 40 (3)
Adding all three equations together, we get:
2(a + b + c) = 90
Simplifying, we get:
a + b + c = 45
Now, using the hint given in the problem, we can write:
c = x - 10
b = a + 20
a + (a + 20) = (x - 10) + 30
Simplifying this equation, we get:
2a + 20 = x + 20
Solving for x, we get:
x = 2a
Substituting this value of x in the equation c = x - 10, we get:
c = 2a - 10
Now we can express b and c in terms of a:
b = a + 20
c = 2a - 10
Therefore, three numbers that satisfy the given conditions are:
a = 5, b = 25, c = 0
We can verify that the sum of any pair exceeds the third by the given amounts:
a + b = 30 > c + 20 = 20
a + c = 5 > b + 30 = 25
b + c = 15 > a + 40 = 45
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16. Movie tickets for an adult and three children cost $29. An adult's
ticket is $3 more than a child's ticket. Find the cost of an adult's ticket.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points)
Answer:
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given the diameter of both the cylinder and the cone is 8 inches, the radius is 8/2 = 4 inches.
The volume of the cylinder is Vcyl = π(4)²(3) = 48π cubic inches.
The formula for the volume of a cone is V = (1/3)πr²h.
The volume of the cone is Vcone = (1/3)π(4)²(18) = 96π/3 = 32π cubic inches.
Therefore, the relationship between the volume of the cylinder and the cone is that the volume of the cone is exactly two-thirds of the volume of the cylinder.
We can see this by dividing the volume of the cylinder by the volume of the cone:
Vcyl/Vcone = (48π) / (32π) = 3/2
So, the volume of the cylinder is 1.5 times greater than the volume of the cone.
f(x) =
=
x— + 2x
कर
- 4x + 8
Answer:
The slope is "m"
m= -5
Step-by-step explanation:
x-- Axis interception points of x- 2x - 4x +8 ( 8 over 5, 0)
y-- Axis interception points of x - 2x - 4x +8 (8,0)
x-2x-4x+8
y=-5x+8
what is the probability of getting all tails? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.
Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.
To calculate the probability of getting all tails in three flips, we need to multiply the probabilities of getting tails on each individual flip. Since the flips are independent events (i.e. the outcome of one flip does not affect the outcome of another flip), we can simply multiply the probabilities together:P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)
= (1/2) x (1/2) x (1/2)
= 1/8
Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.
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A triangle has an area of 19.68 sqaure millimeteres and a height of 4.8 millimeteres. What is the length of the base?
Answer:
8.2mm
Step-by-step explanation:
Formula for area of triangle is 1/2 base x height
Since we are trying to find base, we must work in reverse.
19.68mm / 4.8 = 4.1mm (1/2 the base)
To find base we must multiply by 2
2 x 4.1mm = 8.2mm
Base = 8.2mm
16. A savings account was worth $1250 at the end of 2010 and worth $1306 at the end of 2011. The linear model
for the worth of the account is w = 56t+1250, where t is the number of years since the end of 2010.
Find an exponential model, in the form of w= a(b)', for the worth of the savings account. Round b to the
nearest thousandth.
How much greater is the worth predicted by the exponential model than predicted by the linear model at the
end of 2020? Round to the nearest cent.
An exponential model for the worth of the savings account is [tex]W = 1250(1.045)^t[/tex]
The worth predicted by the exponential model is greater than predicted by the linear model at the end of 2020 by $131.2.
What is an exponential function?In Mathematics, an exponential function can be modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.Based on the information provided about the savings account, we would determine the growth rate as follows;
[tex]W = P_{0}e^{rt}[/tex]
Growth rate, r = 1/(1 - 0)ln(1250/1306)
Growth rate, r = ln(1250/1306)
Growth rate, r = 0.0438
In the form [tex]W = a(b)^t[/tex], the required exponential function is given by;[tex]W = 1250(1.045)^t[/tex]
Years = 2020 -2010 = 10 years.
From the linear function, we have:
W = 56t + 1250
W = 56(10) + 1250
W = $1,810.
From the exponential function, we have:
[tex]W = 1250(1.045)^t\\\\W = 1250(1.045)^{10}[/tex]
W = $1,941.2
Difference = $1,941.2 - $1,810
Difference = $131.2.
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in the number 240.149, how does the value of the 4 in the hundredths place compare to the value of the 4 in the tens place?
The 4 in the hundredths place has a smaller value than the 4 in the tens place.
In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.
In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.
Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.
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in a causal study of the effect of shelf placement on sales of a brand of cereal, which is the dependent variable? group of answer choices where the cereal was placed on the shelf sales of the cereal concomitant variation of the cereal none of the above
A causal study is a study that seeks to determine whether one variable causes another variable.
The independent variable is the variable that is believed to cause the change in the dependent variable, while the dependent variable is the variable that is believed to be influenced by the independent variable.
In a causal study of the effect of shelf placement on sales of a brand of cereal, the independent variable is where the cereal was placed on the shelf. The dependent variable is sales of the cereal.
This is because the sales of the cereal are influenced by where it is placed on the shelf.The answer to the question is sales of the cereal.
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a manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 9 inches and standard deviation of 1 inches. if a sample of 50 items are chosen at random, what is the probability the sample's mean length is greater than 9.1 inches? round answer to
If a sample of 50 items are chosen at random. the probability that the sample mean length is greater than 9.1 inches is 0.0571, or 5.71%.
How to find the probability?The sample mean of the 50 items follows a normal distribution with mean equal to the population mean (μ), and standard deviation equal to σ/√n, where n is the sample size.
Substituting the given values, we have:
= μ = 9 inches
= σ/√n = 1/√50 inches
Now, we need to standardize the sample mean distribution to find the corresponding z-score using the formula:
z = (X- μX) / σX
Substituting the given values, we have:
z = (9.1 - 9) / (1/√50) = 1.58
The probability of getting a z-score of 1.58 or less is 0.9429. Therefore, the probability of getting a z-score of 1.58 or greater is:
P(z > 1.58) = 1 - P(z ≤ 1.58) = 1 - 0.9429 = 0.051
Therefore the probability that the sample mean length is greater than 9.1 inches is 0.0571.
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What is the value of y in the solution to the system of equations?
²x+y=1
-X
2x - 3y = -30
-8
-3
3
O 8
So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75. As a result, the answer is y = 31/4.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
the system of equations,
[tex]y = 1 - 2x\\2x - 3(1 - 2x) = -30\\2x - 3 + 6x = -30\\8x = -27\\x = -27/8\\2(-27/8) + y = 1\\-27/4 + y = 1\\y = 1 + 27/4\\y = 31/4[/tex]
So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75.
As a result, the answer is y = 31/4.
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Select the three correct ways to describe an angle with a measure of 13° .
Answer:
The three correct ways to describe an angle with a measure of 13° are:
Thirteen degrees
An acute angle with a measure of 13°
An angle that is less than a right angle and has a measure of 13°
The sum of Joy's age and her brother's age is $24$ . Her brother's age is $3$ years older than twice Joy's age.
What is the difference, in years, between Joy's age and her brother's age?
Answer:
please give question properly
when we make inferences about one population proportion, what assumptions do we need to make? mark all that apply.
The data should come from a binomial distribution. There should be no non-response or other forms of bias. The sample size should not be more than 10% of the population size, and the sample should be independent of one another.
When making inferences about one population proportion, the following assumptions need to be made:
Option 1: The sample is a simple random sample from the population.
Option 2: The sample size should be large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
Option 3: The data comes from a binomial distribution.
Option 4: There is no non-response or other forms of bias.
Option 5: The sample size is no more than 10% of the population size.
Option 6: The sample is independent of one another.In order to make inferences about one population proportion, the assumptions mentioned above need to be made. It is vital to make sure that the sample is a simple random sample from the population, and that the sample size is large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
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i dont know how yo do this question
Step-by-step explanation:
2x + 2y = 28 <=====given
x * y = 40 <===given ..... re-arrange to :
y = 40 / x <===substitute this 'y' into the first equation
2x + 2 ( 40/x) = 28 <=====solve for x
2x^2 -28x + 80 = 0
x^2 -14x +40 = 0
(x -10)(x-4) = 0 shows x = 10 or 4 then y = 4 or 10
dimensions 10 and 4 inches
Answer:
4 or 10 inches
Step-by-step explanation:
I added a photo of my solution
the shortest side of a triangle with angles 50o, 60o, and 70ohas length of 9 furlongs. what is the approximate length, in furlongs, of the longest side?
The longest side of a triangle with angles of 50°, 60°, and 70° and a length of 9 furlongs on the shortest side is approximately 12.2 furlongs.
What is the Law of Cosines?The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle are known (SAS) or the lengths of the three sides (SSS) are known.
To calculate this, using the Law of Cosines formula,
which is:
[tex]c^2 = a^2 + b^2 - 2abcosC[/tex]
where c is the longest side, a is the shortest side, b is the other side of the triangle, and C is the angle
between a and b.
In this case, c = 12.2 furlongs,
a = 9 furlongs,
b is the side opposite the angle 70°, and C = 70°.
So the formula becomes:
[tex]c^2 = 92 + b^2 - 2(9)(b)cos70^{o}[/tex]
Solving for b gives us b = 12.2 furlongs, which is the length of the longest side.
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Find the HEIGHT of a cylinder if the volume is 1607 and the radius is 4.
Answer:
Step-by-step explanation:
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
We are given that V = 1607 and r = 4. We can plug these values into the formula and solve for h:
1607 = π(4^2)h
1607 = 16πh
h = 1607/(16π)
h ≈ 25.5
Therefore, the height of the cylinder is approximately 25.5 units. Note that we rounded the answer to one decimal place since the radius was given to one decimal place.
a cylindrical tank with radius m is being filled with water at a rate of . how fast is the height of the water increasing?
The height of the water is increasing at the rate of 3 meters per minute.
We know that a cylindrical tank with radius r and height h has a volume of V = πr²h.
The rate at which the water is being filled in the tank is given as dV/dt = 2πr²( dh/dt).
On rearranging the above equation we get dh/dt = (dV/dt) ÷ (2πr²)
Given: Radius of the cylindrical tank, r = 3 m
Rate at which the water is being filled,
dV/dt = 54π cubic meters per minute.
we
Height of the cylindrical tank, h = ?
We need to find out how fast is the height of the water increasing.
This can be calculated using the formula.
dh/dt = (dV/dt) ÷ (2πr²)
Substitute the values of dV/dt and r in the above formula,
we get,
dh/dt = (54π) ÷ (2π x 3²)
dh/dt = 54/18
dh/dt = 3 m/min
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A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation
The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25
Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.
The amount of medicine in the 10 grams of 15% solution is
0.15 × 10 = 1.5 grams
The amount of medicine in the 25 grams of 10% solution is
0.10 × 25 = 2.5 grams
So the total amount of medicine in the original mixture is,
1.5 + 2.5 = 4 grams
Now let x be the amount of pure medicine added.
The total amount of medicine in the final mixture is,
4 + x
The total amount of solution in the final mixture is,
10 + 25 + x
So the concentration of the final mixture is,
(4 + x) / (10 + 25 + x)
We know that this concentration is 25%, so we can write:
(4 + x) / (10 + 25 + x) = 0.25
This is the equation that represents the situation.
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The given question is incomplete, the complete question is:
A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation
any process that generates well-defined outcomes is . a. an event b. an experiment c. a sample point d. a probability
Every procedure that produces predictable results is considered an experiment, and the sample space (S) for an experiment is the collection of all possible results.
What does probability mean in its simplest form?The possibility or chance that a particular occurrence will occur is expressed numerically as a probability. Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range.
What is probability research, exactly?Probability theory, a branch of mathematics, is concerned with the study of random events. A random occurrence can take on any number of distinct shapes, but its conclusion cannot be predicted before it occurs. The way things came out is thought to have been influenced by chance.
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what is the measure of the larger acute angle of the triangle? round your answer to the nearest tenth of a degree.
The measure of the larger acute angle of the triangle can be calculated using trigonometric ratios or by subtracting the measure of the smaller acute angle from 90 degrees. Without further information or given measurements, it is not possible to determine the exact measure of the angle.
Let's consider the general formula for a right triangle where A, B, and C are the angles and a, b, and c are the corresponding sides opposite to each angle:
sin A = a/c, sin B = b/c, and sin C = a/b.
For an acute triangle, we know that the sum of all the angles is equal to 180 degrees, so A + B + C = 180. If the triangle is a right triangle, then one of the angles, say C, is equal to 90 degrees, and A + B = 90 degrees.
In this case, we are only given that the angles of the triangle are acute. Therefore, we can use the formula sin A = a/c, sin B = b/c and sin C = a/b to solve for the angles or use the fact that A + B + C = 180 degrees and A + B = 90 degrees to find the measure of the larger acute angle by subtracting the measure of the smaller acute angle from 90 degrees. However, without specific measurements or additional information, we cannot determine the exact measure of the angle.
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