The expression [tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}[/tex] is equivalent to 10 for [tex]x = 10^{(8/15)}[/tex].
What are exponents?In mathematics, an expοnent (alsο called pοwer οr index) is a shοrthand nοtatiοn used tο represent the repeated multiplicatiοn οf a number by itself.
We can simplify the given expressiοn using the prοperties οf expοnents and rοοts.
First, we can simplify the expression inside the first square root as:
√√x1⁰ = [tex]\rm \sqrt{(x^{10})^{(1/4)} }= (x^{10})^{(1/8)} = x^{(10/8)} = x^{(5/4)}[/tex]
Next, we can simplify the expression inside the second square root as:
[tex]\sqrt{(\sqrt{x\³})} = \sqrt{(x^3)^{(1/4) }}= (x^3)^{(1/8)} = x^{(3/8)[/tex]
Therefore, the entire expression becomes:
[tex]\sqrt{(\sqrt{x1\⁰)}} (\sqrt{(\sqrt{x\³})} = x^{(5/4)} * x^{(3/8) }= x^{(15/8)}[/tex]
Now, we need to find the value of x that makes this expression equal to 10.
[tex]x^{(15/8) }= 10[/tex]
Taking the eighth power of both sides:
[tex]x^{15} = 10^8[/tex]
Taking the 15th root of both sides:
[tex]x = (10^8)^{(1/15)}[/tex]
[tex]x = 10^{(8/15)}[/tex]
the equivalent expression is:
[tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}= x^{(5/4) }* x^{(3/8)} = x^{(15/8)} = (10^{(8/15)})^{(15/8)} = 10[/tex]
Therefore, the expression [tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}[/tex] is equivalent to 10 for [tex]x = 10^{(8/15)}[/tex].
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1. Suppose that there is a forest with 10,000 rabbits. We randomly select 100 of them, place a nonremovable mark on them, and set them free in the forest. After a couple of days, the marked rabbits mixed well with other living ones in the forest, and we randomly catch 50 rabbits from the forest. Find the probability that the sample of 50 rabbits contains exactly 2 marked rabbits.
The probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.
Explain about the hypergeometric distribution?When sampling from either a small population without replacement, the hypergeometric distribution consists of a discrete probability distribution which determines the likelihood that an event occurs k times in n trials.
The absence of replacements in the hypergeometric distribution sets it apart from the binomial distribution.As a result, it is frequently used in random sampling to ensure statistical quality. A straightforward, indication would be choosing team members at random from a population of males and girls.The given data:
Total market sample of rabbits = 100.
Randomly selected rabbits = 50.
Let the probability that the sample of 50 rabbits contains exactly 2 marked rabbits be P(E).
Then, using hypergeometric distribution;
P(E) = ⁵⁰C₂ / ¹⁰⁰C₂
Solve the probability using the combination.
P(E) = 25*49 / 50*49
P(E) = 25/50
P(E) = 1/2
Thus, the probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.
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On Sunday, the owners of the Middletown Café are giving away muffins. The owners budgeted $75 to spend on muffins for the event, and each muffin costs $0.82. The inequality 75≥0.82m 75 ≥ 0 . 82 , where m is the number of muffins, represents the situation. How many customers could possibly get a muffin? Select all that apply.
Answer:
We can solve the inequality for m to find the maximum number of muffins that can be purchased within the budget of $75:
75 ≥ 0.82m
Divide both sides by 0.82:
m ≤ 91.46
Since m must be a whole number, the maximum number of muffins that can be purchased is 91. Therefore, 91 customers could possibly get a muffin.
Step-by-step explanation:
14x +5y = 31 slve for x
Answer: x = 31 over 14 − 5y over 14
Step-by-step explanation: Move all terms that don't contain x to the right side and solve.
A persons lung capacity can be modeled by the function C(t) = 250sin(2x/5 * t) + 2450 where C(t) represents the volume in mL present in the lungs after t seconds. State the maximum value of this function over one full cycle and explain what this value represents
The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath. The function C(t) = 250sin(2I/5(t))+2450.
It shows the capacity of the lung of a person at any point of time t in milliliters (mL).
We not only need to find the one full cycle but also determine the period of function and it is given by:
T = 2I/(2I/5)
T = 5 seconds.
This means that the function completes one full cycle every 5 seconds.
To find the maximum value of the function over one full cycle, we need to find the maximum value of sin(2π/5(t)). The maximum value of sin(2π/5t) is 1, this happens at 2π/5(t) = π/2 + nπ, and n is considered as an integer.
So, the maximum value of the function occurs when sin(2I/5(t)) = 1, Substituting this into the original function, we get maximum value, Cm:
Cm = 250(1) + 2450
= 2700 mL.
The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath.
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Please help superrr confused :(
Step-by-step explanation:
Week 1, you eat 10 out of 95
Week 1 r ( 1) = 95 - 10(1) =85
Week 5 r(5) = 95 - 10r
=95 - 10(5)
=95 - 50
=45lbs
Week 8 r(8) = 95 - 10.r
=95 - 10(8)
=95 - 80
= 15 lbs
Week w r(w) = 95 - 10.w
= 95 - 10W (lbs)
f(r) = 95 - 10r
Where r is the number of weeks.
r(w) =35 means that at the end of w weeks, there were 35 candies left.
If the original candy was 95 and 35 was left after w weeks
r(w) = 95 - 10w
35 = 95 - 10w
Subract 95 from both sides
-60 = - 10w
Divide both sides by - 10
6= w
The solution means that 35 candies were left after w weeks and w represents 6weeks.
(you can c compare my answer with a second response)
Given that the measurement is in centimeters, find the area of the circle to the nearest tenth. (use 3.14 for π) circle with a radius of 3 cm
The area of the circle to the nearest tenth is 28.3 square centimeters.
To find the area of a circle with a given radius, we use the formula
A = π[tex]r^2,[/tex]
where A is the area and r is the radius.
In this case, the radius is 3 cm, so we can substitute it into the formula to get:
A = 3.14 x [tex]3^2[/tex]
Simplifying this equation, we get the following:
A = 3.14 x 9
A = 28.26
To round this to the nearest tenth, we look at the digit in the hundredth place, 6. Since 6 is greater than or equal to 5, we round up the number in the tenth place, which is 2. Therefore, the final answer is:
A ≈ 28.3 [tex]cm^2[/tex]
So, the area of the circle to the nearest tenth is 28.3 square centimeters.
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Of the 90 families in our barangay,60 are engaged in farming and the rest are in fishing. What percent of the families are engaged in farming?
Answer:
66.67%
Step-by-step explanation:
There are two ways to solve this problem depending on which way you like. Percentages are based on a 0-100 system and thus you can start by dividing 100/90. This will give you an amount of 1 family. We are looking for 60 families, so multiply that value by 60 to get how much of a percentage 60 families is.
The other way is to divide 90 by 60, and then multiply that result by 100 to give you a percent.
Regardless of your preferred method, both answers are the same.
Mabel has $30,000 in a savings account that earns 11% annually. The interest is not compounded. How much interest will she earn in 2 years?
please help :(
Step-by-step explanation:
If the interest is not compounded, it means that Mabel will earn a simple interest of 11% per year on her principal amount of $30,000.
The formula for calculating simple interest is:
Interest = (Principal x Rate x Time)
Where:
Principal = $30,000
Rate = 11% = 0.11 (as a decimal)
Time = 2 years
So, substituting the values in the formula, we get:
Interest = (30,000 x 0.11 x 2) = $6,600
Therefore, Mabel will earn $6,600 in interest over a period of 2 years.
Can someone write this 0.698, 0.2, 0.099, 0.18 in order please?
Answer:
0.099, 0.18, 0.2, 0.698.
Step-by-step explanation:
What is the value of sinD?
The value of sin(D) is 7/25 after the application of the Pythagoras theorem.
What is a Pythagoras theorem?The Pythagorean theorem is a fundamental theorem in geometry that describes the relationship between the sides of a right triangle. It claims that the hypotenuse's square length, which is the side that faces the right angle, is equivalent to the total of the squares of the lengths of the other two sides in a right triangle. The theorem can be formulated mathematically as:
c² = a² + b²
where, even the lengths for the remaining two sides (the legs) of the right triangle are a and b, and c is the length of the hypotenuse.
The Pythagorean theorem may be employed to determine the triangle's third side's length:
DE²= FD² + EF²
25² = 24² + EF²
625 = 576 + EF²
EF² = 49
EF = 7
Now, we can use the definition of sine to find sin(D):
sin(D) = opposite/hypotenuse = EF/DE = 7/25
Therefore, the value of sin(D) is 7/25.
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Given the equation 6x + 18 = 72:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)
The solid shown here is a cube. Count the number of faces, edges, and vertices. Remember, you can use the formula V – E + F = 2 to make sure that you counted correctly.
Vertices
Edges
Faces
In the given cube, the required data is as follows:
Faces = 6
Edges = 12
Vertices = 8
What is a cube?A cube is a solid three-dimensional form with six square faces that all have the same length sides. It is one of the five platonic solids and is also referred to as a regular hexahedron.
Six square faces, eight vertices, and twelve edges make up the form.
Here in the question as asked,
Faces = 6
Edges = 12
Vertices = 8
Now to prove that we are correct,
V -E + F =2
= 8 - 12 + 6
=2
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Find each quotient using synthetic division. (m^(4)-7m^(3)-39m^(2)-28m-3)-:(m+3)
The quotient using a synthetic method of division is m³ - 10m² - 9m - 1
How to evaluate the quotient using a synthetic methodThe quotient expression is given as
(m⁴ -7m³ -39m² - 28m - 3) divided by m + 3
Using a synthetic method of quotient, we have the following set up
-3 | 1 -7 -39 -28 -3
|__________
Bring down the first coefficient, which is 1:
-3 | 1 -7 -39 -28 -3
|__________
1
Multiply -3 by 1 to get -3, and write it below the next coefficient and repeat the process
-3 | 1 -7 -39 -28 -3
|____-3__ 30__27__3____
1 -10 -9 -1 0
So, the quotient is m³ - 10m² - 9m - 1
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determine whether or not the distribution is a probability distribution and select the reason(s) why or why not. x 2 4 6 p(x) 15 15 15 select all that apply: the given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. the given distribution is a probability distribution, since the sum of probabilities is equal to 1. the given distribution is not a probability distribution, since at least one of the probabilities is greater than 1 or less than 0. the given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1.
The given distribution is not a probability distribution.
The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. A probability distribution must satisfy two conditions: 1) the probabilities must lie inclusively between 0 and 1, and 2) the sum of probabilities must be equal to 1.
In this case, the sum of probabilities is 15+15+15 = 45, which is not equal to 1. Therefore, the given distribution is not a probability distribution. The other options are incorrect because they do not accurately describe the given distribution.
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PLEASE SHOW WORK!!!!!!!!!
If point A is the starting position, how high Is a rider after 3 seconds?
After 3 seconds, the rider is still at their starting height of 0 metres.
The height of a rider after 3 seconds can be calculated using the equation h(t) = v₀t - (1/2)gt², where h(t) is the height of the rider in metres at time t, v₀ is the initial velocity in metres per second, and g is the acceleration due to gravity in metres per second squared.
Assuming v₀ is 0, since the rider is just starting, and g is 9.81, then the height of the rider after 3 seconds is h(3) = 0 - (1/2)(9.81)(3²) = -44.355. Since this is a negative number, the rider is still at their starting height of 0 metres after 3 seconds.
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a function is said to be differentiable at if exists. for some -values the derivative may not exist and we say that the function is not differentiable there. at which of the following locations is a function not differentiable? discontinuity cusp horizontal tangent line vertical tangent line
The location at which a function is not differentiable is a Vertical tangent line
A function may not be differentiable at some points. Such points are known as non-differentiable points. Let's take a look at each of the given terms to figure out the non-differentiable points. Discontinuity: A discontinuity is when a function's graph is interrupted by a break or hole.
It occurs when a function is undefined at a certain point. It may be classified into three categories: removable, jump, and infinite. Functions may not be differentiable at removable discontinuities but are differentiable at jump and infinite discontinuities. A discontinuous point is not the same as a non-differentiable point because it may be differentiable at other points of the function.
Cusp: A cusp is a sharp corner formed by a curve. It happens when the slope of the function approaches infinity. The curve is not differentiable at the cusp. Horizontal Tangent Line: When the slope of a function approaches zero, it creates a horizontal tangent line. The function may or may not be differentiable at this point depending on the shape of the graph.
It may be differentiable or not differentiable. Therefore, it is not a non-differentiable point. Vertical Tangent Line: When a function's slope approaches infinity, it creates a vertical tangent line. The function is non-differentiable at this point. A vertical tangent line is always a non-differentiable point.
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Where have i gone wrong?
I need an answer!
Answer:
a)6
b)15 and -15
Step-by-step explanation:
a)5*5*5*5*5*5 there is 6 5's so, we can show it as, [tex]5^{6}[/tex]
[tex]5^{6}[/tex]=[tex]5^{x}[/tex]
x=6
b) in this one you found one of the answers of y which is 15.
but [tex]15^{2}=-15^{2}\\so y=15\\and y=-15[/tex]
Answer:
The answer is down below
Step-by-step explanation:
a) 5×5×5×5×5×5=5^x
5×5×5×5×5×5=5⁶
b)y²=225
square both sides
√y²=√225
y=15
the shape is formed from two straight lines and two arcs. work out the total shaded area correct to the nearest 0.1cm^2.
Check the picture below.
so we're really looking for the area of a sector of a circle with 63° and a radius of 3, twice.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =63\\ r=3 \end{cases}\implies A=\cfrac{(63)\pi (3)^2}{360} \\\\\\ A=\cfrac{63\pi }{40}\implies \stackrel{\textit{now let's double that}}{2\cdot \cfrac{63\pi }{40}}\implies \cfrac{63\pi }{20}\implies 9.9~cm^2[/tex]
the physician orders digoxin 0.25 mg po daily. the pharmacy supplies the following medication. the dosage strength of the digoxin can be expressed as: ? m g 1 t a b l e t
To calculate the dosage strength of digoxin, which is supplied by the pharmacy in mg per tablet, the physician orders digoxin 0.25 mg po daily.
In other words, The physician ordered 0.25 mg of digoxin to be administered orally every day. The medication provided by the pharmacy is to be taken in tablet form. To calculate the amount of digoxin in each tablet, you need to divide the ordered dose by the amount of tablets.
The equation is:Dose Ordered / Tablets = Dose per tablet
Substitute the known values:Dose Ordered = 0.25 mgTablets = 1 tablet0.25 mg / 1 tablet = 0.25 mg per tablet.
Therefore, the dosage strength of the digoxin supplied by the pharmacy is 0.25 mg per tablet.
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3/10 Students go for the music class and 2/3 students go for the dance class. which class has more students?
Answer: The dance class has more students
Step-by-step explanation:
3 divided by 10 = 0.3
2 divided by 3 = 0.66
Since 0.66 is more than 0.3, we can say that more students entered the dance class than the music class.
pls help meee 100 points
Explain why this comparison is either reasonable
3.4< 3.36
WHAT DO I PUT IN
100 points if you help mee
Answer: The comparison "3.4 < 3.36" is reasonable because 3.36 is greater than 3.4.
The decimal point separates the whole number part of a number from the fractional part. In this case, 3.36 has a greater whole number part (3) than 3.4, and both have the same decimal part (0.36). So, 3.36 is greater than 3.4.
Therefore, the statement "3.4 < 3.36" is a true and reasonable comparison.
Step-by-step explanation:
Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a
monthly fee and a charge for each minute of calling time. In June she used 350 minutes and the cost
was $177.00. In July she used 900 minutes and the cost was $397.00.
A) Express the monthly cost C as a function of x, the number of minutes of calling time she used.
Answer: c(x) = 4x +
syntax error.
B) If Jane used 622 minutes of calling time in August, how much was her bill?
Answer: $
5, 6, 8, ___ , 15, ___
18, 20, 24, ___ , 38, ___
25, 28, 34, ___ , ___ , 70
55, 54, 51, 46, ___ , ___ , 19
82, 81, 78, ___ , 66
0 + 6 = ___+ 0
___ + 9 = 9 + 14
20 x ( 4 + ___) = ( 20 x 4 ) + (20 x 3)
9 + ( 6 + 5 ) = (9 + 6) + ___
10 x (___ + 6) = (10 x 8) + (10 x ___)
Answer:
5, 6, 8, 11, 15, 20
5+1=6+2=8+3=11+4=15+5=20
18, 20, 24, 30, 38, 48
18+2=20+4=24+6=30+8=38+10=48
55, 54, 51, 46, 39, 30, 19
55-1=54-3=51-5=46-7=39-9=30-11=19
82, 81, 78, 73, 66
82-1=81-3=78-5=73-7=66
0+6=6+0
6=6
14+9=9+14
23=23
20x(4+3)=(20x4)+(20x3)
20x7=80+60
140=140
9+(6+5)=(9+6)+5
9+11=15+5
20=20
10x(4+6)=(10x8)+(10x2)
100=100
Step-by-step explanation:
Question 7 What equation is parallel to y=-(1)/(4)x+5 and passes through (2,-3)?
The equation of the line that is parallel to y = -(1/4)x + 5 and passes through (2, -3) is y = -(1/4)x - 5/2.
To find the equation of the line that is parallel to the line y = −(1/4)x + 5 and passes through the point (2, −3), follow these steps:Step 1: Determine the slope of the given line.The slope-intercept form of the equation of the line is y = mx + b where m is the slope of the line. y = −(1/4)x + 5 is already in slope-intercept form, so its slope is −1/4. Step 2: Determine the slope of the line that is parallel to the given line. The slope of a line parallel to another line is the same as the slope of the given line. Therefore, the slope of the line we need to find is also −1/4. Step 3: Determine the y-intercept of the line we need to find. We already know that the line passes through the point (2, −3). To determine the y-intercept of the line, substitute x = 2 and y = −3 into the slope-intercept form of the equation of the line. −3 = −(1/4)(2) + b b = −3 + 1/2 = −5/2 Therefore, the y-intercept of the line we need to find is −5/2. Step 4: Write the equation of the line in slope-intercept form. The equation of the line we need to find is y = mx + b where m = −1/4 and b = −5/2. y = −(1/4)x − 5/2 is the equation of the line that is parallel to y = −(1/4)x + 5 and passes through (2, −3).Answer: The equation of the line that is parallel to y = -(1/4)x + 5 and passes through (2, -3) is y = -(1/4)x - 5/2.
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Help plsss
Determine if it’s linear
The functions are classified as follows:
a) Linear.
b) Linear.
c) Linear.
d) Non-linear.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.Hence, from the definition, a function is classified as linear if the highest exponent of both x and y is of one.
A term x on the denominator has an exponent of -1, hence item d is not a linear function.
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The linear equations in the options are:
a) 5x - 9 + 7y = x - 4
b) 0.01x - 0.7y = 2.2
c) -3x = 4
How to deterimine if it is linear?We say that an equation is linear if the dependence with the veriables is only of first degree.
For example, equations of the form:
a*x + b*y = c
Are linear, because the variables x and y have an exponent of 1.
Then, the options that show linear equations are:
a) 5x - 9 + 7y = x - 4
b) 0.01x - 0.7y = 2.2
c) -3x = 4
The last option is non linear, because x is on the denominator.
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15 The table shows values of s and t.
S
t
0.2
7.5
0.5
1.4
0.9
Is s inversely proportional to f? Explain why.
(2 marks)
Answer:
s is inversely proportional to t
Step-by-step explanation:
As s increases, t decreases. They are inversely proportioanl when that happens.
Dos ingenieros deciden medir la altura de una montaña cercana a un pueblo que está a 1200 msnm. Miden la cima de la montaña desde el punto "A" señalado en el gráfico con un ángulo de elevación de 37°, luego avanzan hacia al punto "B" que dista 480 m del punto "A" y vuelven a medir la cima con un ángulo de elevación de 45°. ¿Cuál es la altura de la montaña respecto al nivel del mar?
The height of the mountain above sea level is 777.94 m.
The two engineers can calculate the height of the mountain by using the principle of trigonometry. Firstly, they must calculate the altitude of the mountain from the point A, which can be done by using the formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point A and d is the distance between point A and the mountain. In this case, the altitude from point A is h = tan(37°) * 1200 = 1645.58 m. Secondly, they can calculate the altitude from point B, which can be done by using the same formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point B and d is the distance between point B and the mountain. In this case, the altitude from point B is h = tan(45°) * 480 = 867.64 m. Finally, the height of the mountain above sea level can be calculated by subtracting the altitude from point B from the altitude from point A, i.e. h = 1645.58 m - 867.64 m = 777.94 m.
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the domain for the first input variable to predicate t is a set of students at a university. the domain for the second input variable to predicate t is the set of math classes offered at that university. the predicate t(x, y) indicates that student x has taken class y. sam is a student at the university and math 101 is one of the courses offered at the university. give a logical expression for each sentence. (a) sam has taken math 101. (b) every student has taken at least one math class. (c) every student has taken at least one class other than math 101. (d) there is a student who has taken every math class other than math 101. (e) everyone other than sam has taken at least two different math classes. (f) sam has taken exactly two math classes.
The logical expressions for each sentence can be written as follows:
(a) t(Sam, Math 101)
This expression states that Sam has taken Math 101.
(b) ∀x∃y t(x, y)
This expression states that for every student x, there exists a math class y such that the student x has taken the math class y.
(c) ∀x∃y (t(x, y) ∧ y ≠ Math 101)
This expression states that for every student x, there exists a class y such that the student x has taken the class y and the class y is not Math 101.
(d) ∃x∀y (t(x, y) ∧ y ≠ Math 101)
This expression states that there exists a student x such that for every math class y, the student x has taken the math class y and the math class y is not Math 101.
(e) ∀x∃y∃z (t(x, y) ∧ t(x, z) ∧ x ≠ Sam ∧ y ≠ z)
This expression states that for every student x, there exists two different math classes y and z such that the student x has taken the math classes y and z and the student x is not Sam.
(f) ∃y∃z (t(Sam, y) ∧ t(Sam, z) ∧ y ≠ z ∧ ∀w (t(Sam, w) → (w = y ∨ w = z)))
This expression states that there exists two different math classes y and z such that Sam has taken the math classes y and z and for every math class w, if Sam has taken the math class w, then the math class w is either y or z.
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A circle has a radius of 5.4 cm. What is the exact length of an arc formed by a central angle measuring 45°?
The length of the arc with a central angle of 45° is 4.24 cm
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The length of an arc formed on a circle with a central angle Ф and radius r is:
Length of arc = (Ф/360) * 2πr
Given the circle radius is 5.4 cm and the central angle is 45°, hence:
Length of arc = (Ф/360) * 2πr = (45/360) * 2π(5.4) = 4.24 cm
The length of the arc is 4.24 cm
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