[tex] \Large{\boxed{\sf Height = 58 \: m}} [/tex]
[tex] \\ [/tex]
Explanation:The volume of a cylinder can be calculated using the following formula:
[tex] \Large{\sf V = B \times h} [/tex]
Where:
V is the volume of the cylinder.B is the area of its base.h is the height of the cylinder.[tex] \\ [/tex]
Since we are not given the area of its base, which is a circle, we will have to calculate it applying the following formula:
[tex] \Large{\sf B = \pi \times r^2} [/tex]
Where:
B is the area of the circle (the base of the cylinder).r is its radius.[tex] \\ [/tex]
Combining these two formulas, we can express the volume of the cylinder as follows:
[tex] \Large{\sf V = \underbrace{\sf \pi \times r^2}_{B} \times h} [/tex]
[tex] \\ [/tex]
Now, rearrange the formula to isolate the height, h.
[tex] \sf V = \pi \times r^2 \times h \Longleftrightarrow \dfrac{V}{\pi \times \times r^2} = \dfrac{ \pi \times r^2 \times h}{\pi \times r^2 } \Longleftrightarrow h = \dfrac{V}{\pi \times r^2} [/tex]
[tex] \\ [/tex]
[tex] \Large{\boxed{\sf Given \text{:} } \begin{cases} \sf V &=\sf 492,452.48 \: m^3 \\ \sf r &=\sf 52 \: m \: \\ \sf \pi &= \sf 3.14 \: (approximately) \end{cases} } [/tex]
[tex] \\ [/tex]
Substitute these values into our formula:
[tex] \sf h = \dfrac{492,452.48 \: m^3}{(52 \: m)^2 \times 3.14 } = \dfrac{492,452.48 \: m^3}{8,490.56\: m^2 } \\ \\ \\ \\ \implies \boxed{\boxed{\sf h = 58 \: m}} [/tex]
You and your friend just joined a gym. the gym fee for each member is a linear function of the number of classes that member participates in that month. you took 6 classes and paid $43 in gym fees. your friend took 11 classes and paid $73. what is the average rate of change in cost per class?
The gym fee increases by $6 for each additional class taken. The average rate of change in cost per class is equal to the slope of the linear function, which is $6 per class.
What is average rate ?
Average rate refers to the rate of change of a quantity over a given period of time. It is calculated by dividing the change in the quantity by the time period over which the change occurs.
To find the average rate of change in cost per class, we need to calculate the slope of the linear function that relates the gym fee to the number of classes taken.
Let x be the number of classes taken, and y be the gym fee. We can use the two data points given to find the equation of the line:
When x = 6, y = 43
When x = 11, y = 73
The slope of the line passing through these two points can be calculated as follows:
slope = (change in y) / (change in x)
slope = (73 - 43) / (11 - 6)
slope = 30 / 5
slope = 6
Therefore, the gym fee increases by $6 for each additional class taken.
The average rate of change in cost per class is equal to the slope of the linear function, which is $6 per class.
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Two different models of same rectangle . In first triangle 1 centimeter equals 6.25 feet and in second triangle 1 centimeter equals 1.25 feet. Above are two different models of the same rectangular patio. If the area of the model on the left is 4 sq cm, what is the area of the model on the right?
The area of the model on the right is 6.25 square centimeters.
What is area ?
Area is a measurement of the size of a two-dimensional surface or region. It is the amount of space inside a closed figure or shape, and is typically measured in square units such as square meters, square feet, or square centimeters.
Since the two models represent the same rectangular patio, they must have the same area.
Let A be the area of the model on the right in square centimeters.
Using the ratios given in the problem, we can write:
A/4 = (1.25 ft/1 cm)²
Simplifying the right-hand side, we get:
A/4 = 1.5625 ft²/cm²
Multiplying both sides by 4, we get:
A = 6.25 ft²
Therefore, the area of the model on the right is 6.25 square centimeters.
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Construct Arguments- A human usually has 20 baby teeth, which are replaced by 32 adult teeth. Raul lost 8 of his baby teeth. Raul said he lost 4/10 of his baby teeth. Ana said Raul lost 2/5 of his baby teeth. Which of these conjectures are true? Construct an argument to justify your answer.
Answer:
Step-by-step explanation:
Ana's conjecture that Raul lost 2/5 of his baby teeth is true.
To see why, consider that Raul originally had 20 baby teeth. If he lost 8 of these teeth, that means he has 20 - 8 = 12 baby teeth remaining. To determine what fraction of his baby teeth he lost, we can calculate:
8 baby teeth lost / 20 baby teeth total = 2/5
So, Raul lost 2/5 of his baby teeth, which supports Ana's conjecture.
On the other hand, Raul's statement that he lost 4/10 of his baby teeth is not correct, since 4/10 can be simplified to 2/5, which is the same as Ana's conjecture that he lost 2/5 of his baby teeth.
Subtract. Express your answer in the simplest from. negative 3/9 - 6/9
Answer:
-1/3
Step-by-step explanation:
When adding or subtracting fractions, you don't add or subtract the denominators.
So, Start by subtracting the numerators
3/9 - 6/9 = -3/9
you can simplify this fraction by dividing both the numerator and denominator by 3
-3 ÷ 3 = -1
9 ÷ 3 = 3
So, the answer is:
-1/3
Hope this helps!
Which of the following rational functions is graphed below?
A. F(x) =(x-2)/(x+5)
B. F(x) =1/(x-2)(x + 5)
C. F(x) =1/(2x + 5)
D. F(x)= 1/(x+2)(x-5)
The graph of the rational equation is solved and f ( x ) = 1/ ( x + 2 ) ( x - 5 )
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 1/ ( x + 2 ) ( x - 5 )
The function will have increasingly large values as the denominator approaches zero. When x -2, the denominator is positive and the function tends to the upside. When x -2 x 5, the function is negative. When x 5, the function becomes positive once more.
Hence , the rational function is f ( x ) = 1/ ( x + 2 ) ( x - 5 )
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The complete question is attached below :
Which of the following rational functions is graphed below?
A. F(x) =(x-2)/(x+5)
B. F(x) =1/(x-2)(x + 5)
C. F(x) =1/(2x + 5)
D. F(x)= 1/(x+2)(x-5)
pls show work im struggling
Answer:
The flag pole is 12 feet tall
Option C.
Step-by-step explanation:
We can use the Pythagorean theorem to evaluate the height of the flagpole.
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of each of the legs squared and can be written as
[tex]a^2+b^2=c^2[/tex]
Numerical Evaluation
In this example we are given the value of the hypotenuse and the value of one of the legs.
[tex]b=16\\c=20[/tex]
Substituting our values into the equation yields
[tex]a^2+16^2=20^2[/tex]
Lets solve for [tex]a[/tex].
Evaluate [tex]16^2[/tex].
[tex]a^2+256=20^2[/tex]
Evaluate [tex]20^2[/tex].
[tex]a^2+256=400[/tex]
Subtract [tex]256[/tex] form both sides of the equation.
[tex]a^2=144[/tex]
Take the square root of both sides to eliminate the exponent.
[tex]a=\sqrt{144}[/tex]
Evaluate [tex]\sqrt{144}[/tex].
[tex]a=12[/tex]
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better picture for the other question
A table that represents the function y = -3x/4 + 3 is: B. table B.
How to complete the table?In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;
When the value of x = -2, the linear function is given by;
y = -3x/4 + 3
y = -3(-2)/4 + 3
y = 9/2 (False).
When the value of x = -4, the linear function is given by;
y = -3x/4 + 3
y = -3(-4)/4 + 3
y = 6 (True).
When the value of x = 0, the linear function is given by;
y = -3x/4 + 3
y = -3(0)/4 + 3
y = 3 (True).
When the value of x = 4, the linear function is given by;
y = -3x/4 + 3
y = -3(4)/4 + 3
y = 0 (True).
When the value of x = 8, the linear function is given by;
y = -3x/4 + 3
y = -3(8)/4 + 3
y = -3 (True).
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A new automobile is purchased for $20,000. If V = 20,000(0.8)x, gives the car’s value after x years, about how long will it take for the car to be worth $8,200?
Answer:
Step-by-step explanation:
We can start by setting up an equation to solve for x, the number of years it will take for the car to be worth $8,200:
8200 = 20000(0.8)^x
Dividing both sides by 20,000, we get:
0.41 = 0.8^x
Taking the logarithm of both sides (using any base, as long as we're consistent), we get:
log(0.41) = log(0.8^x)
Using the property of logarithms that allows us to bring down the exponent as a coefficient, we get:
log(0.41) = x log(0.8)
Dividing both sides by log(0.8), we get:
x = log(0.41) / log(0.8)
Using a calculator, we find:
x ≈ 5.92
Therefore, it will take about 5.92 years for the car to be worth $8,200.
Please someone help I keep getting this wrong. :/
The equation that represents the graph will be x = (1/12) y². Then the correct option is A.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of the upward parabola is written as,
y = 4ax²
The equation of the downward parabola is written as,
y = - 4ax²
The equation of the rightward parabola is written as,
x = 4ay²
The equation of the leftward parabola is written as,
x = - 4ay²
From the graph, the parabola opens rightward, then the equation is written as,
x = (1/12) y²
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solve 6(3x/2 - 4) = 30 you may use the flowchart to help you if you wish
If f(x) is a linear function and the domain of f(x) is the set of all real numbers, which statement cannot be true? The graph of f(x) has zero x-intercepts. The graph of f(x) has exactly one x-intercept. The graph of f(x) has exactly two x-intercepts. The graph of f(x) has infinitely many x-intercepts. Mark this and return
"The graph of f(x) has exactly two x-intercepts" - For a linear function whose domain is the set of all real numbers, this assertion cannot be accurate.
Any function with the formula f(x) = mx + b is referred to as linear.
Setting f(x) = 0, we get:
mx + b = 0
Solving for x, we get:
x = -b/m
Depending on the slope m and y-intercept b values, there are an unlimited number of x-intercepts.
What are linear functions?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function. A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nonetheless, calculus and linear algebra are also used to represent linear functions. The function notation is the only distinction. It is also important to understand an ordered pair written in function notation.
from the questions:
A function with the formula f(x) = mx + b, where m and b are constants, is referred to as a linear function. When f(x) = 0, the point where a linear function intersects the x-axis is known as the x-intercept.
Setting f(x) = 0, we get:
mx + b = 0
Solving for x, we get:
x = -b/m
As a result, the x-intercept of a linear function is a single point, (-b/m, 0), and depending on the slope m and y-intercept b values, there may only be zero, one, or infinitely many x-intercepts.
As a result, for a linear function whose domain is the set of all real numbers, it is not possible for the statement "The graph of f(x) has precisely two x-intercepts" to be true.
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Can someone help me please? Thank you
Answer:
1. 6/18 = 1/3
9/21 = 3/7
2. 4/6 = 2/3
2/4 = 1/2
3. 6/12 = 1/2
8/12 = 2/3
4. 2/8 = 1/4
3/6 = 1/2
5. 7/21 = 1/3
8/10 = 4/5
6. 9/12 = 3/4
12/20 = 3/5
7. 8/16 = 1/2
10/25 = 2/5
The value of the 9 in 964,352 is how many times the value of the 9 in 290,481?
A. 10
B. 100
C. 10,000
D. 1,000
Answer:
A. 10
Step-by-step explanation:
The 9 in 290,481 is in the ten thousands place (10⁴)
The 9 in 964,352 is in the hundred thousands place (10⁵)
10⁵/10⁴ = 10
Answer:
A. 10
The value of 9 in 964,352 is 10,000 times greater than the value of 9 in 290,481, because it is positioned in the hundreds of thousands place versus the tens place.
Explanation:The value of a digit in a number is determined by its position or place value. In the number 964,352, the value of the 9 is 900,000, because it is in the hundreds of thousands of places. In the number 290,481, the value of the 9 is 90, because it is in the tens place. To find out how many times greater the value of the 9 in 964,352 is than the value of the 9 in 290,481, we divide 900,000 by 90, which gives us 10,000. Therefore, the answer is C. 10,000.
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(3x^5)(√x) = ????????
Answer:[tex]3x^{5} \sqrt{x}[/tex]
Step-by-step explanation:
Given: AABC with altitude h
Prove: sin(B) sin(C)
B
sin (B)
csin (B)
sin(B)
=
Statements
AABC with altitude h
=
a
h
b
sin(C)
с
given
h, sin (C) = definition of sine
= h, bsin (C) =
Reasons
h
transitive property of equality
1st drop down: multiplication property of equality, substitution property of equality, division, property of equality
2nd drop down: cSIN(A)=bSIN(C), cCOS(B)=bCOS(C), cSIN(B)=bSIN(C)
3rd drop down: substitution property of equality, division, property of equality, multiplication property of equality
So, it is proven that the area of triangle ABC is 1/2*a*b*sinC .
What is a triangle?A triangle is a 2D shape having three sides and the sum of all angles is 180°. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
We have,
A ΔABC,
And,
AB = c
BC = a
CA = b
H = Altitude of the triangle,
Now,
Area of triangle = 1/2* base* height
i.e.
Area of triangle ABC =1/2*a*h .....(i)
Now,
Using trigonometric ratios,
sinC = perpendicular/hypotenuse
i.e. sinC = h/b
We get,
h = b * SinC
Now,
putting this value in equation (i),
We get,
Area of triangle ABC=1/2*a*b*sinC
So, It is proved that area of triangle ABC =1/2*a*b*sinC ,
Hence, we can say that it is proven that the area of triangle ABC is 1/2*a*b*sinC , using trigonometric ratios and the triangle's area formula.
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50 Points!! Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum of the given function for this region. Photo attached
The maximum and minimum of the given function are 22 and -2, respectively
Graph the system of inequalities.The system of inequalities is given as
y ≥ -x - 2
y ≥ 3x + 2
y ≤ x + 4
See attachment for the graph
Name the coordinates of the vertices of the feasible region.From the graph, we have the following coordinates
(-1, -1), (-3, 1) and (1, 5)
The maximum and minimum of the given functionSubstitute (-1, -1), (-3, 1) and (1, 5) in f(x, y) = -3x + 5y
So, we have
f(-1, -1) = -3(-1) + 5(-1) = -2
f(-3, 1) = -3(-3) + 5(1) = 14
f(1, 5) = -3(1) + 5(5) = 22
Hence, the maximum is 22 and the minimum is -2
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30 POINTS! Help is appreciated! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this
composite figure? Use 3.14 for . Round to the nearest hundredth. Show your work.
The area of the composite figure is approximately 57.51 square centimeters.
By calculating the area of the triangle and the sector, and then adding them together, we may determine the area of the composite figure.
The following formula can be used to determine the sector's area:
Sector area is equal to (central angle / 360) x r2.
The sector's radius is 8 cm, and its central angle is 60°, resulting in:
Sector area equals (60/360) x 3.14 x 82
Sector size: 33.51
The following formula can be used to get the triangle's area:
Area of triangle Equals base x height x half.
The Pythagorean theorem can be used to determine the triangle's height given that its base is 8 cm:
a² + b² = c²
8² + h² = 10²
64 + h² = 100
h² = 36
h = 6
As a result, given that the triangle's height is 6 cm, we have:
Triangle's area equals 1/2 x 8 x 6.
Triangle has a 24 area.
By combining the areas of the triangle and the sector, we can determine the area of the composite figure.
33.51 + 24 times the composite figure's area
The composite figure's area is 57.51.
Hence, the composite figure has a surface area of roughly 57.51 square centimetres.
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What do we call the 3D shape below and what is it's SURFACE AREA? Explain how you determined your answer and show your work!!!!
Please help me fast
Math 6th grade 4.10
Answer:
Step-by-step explanation:
Square pyramid (since the base is a square)
Area base [tex]= 8^2=64mm^2[/tex] (area of square)
Area each side [tex]= \frac{1}{2} base[/tex]×[tex]height[/tex] (area triangle formula)
= [tex]\frac{1}{2}[/tex]×[tex]8[/tex]×[tex]10[/tex]
= [tex]40 mm^2[/tex]
Total area [tex]= 4triangles + square base[/tex]
[tex]=4[/tex]×[tex]40+64[/tex]
[tex]=224 mm^2[/tex]
Q.4. Mandy babysits and makes $8.50 per hour. To commute to the job, she spends $40 per
week on the bus and subway. Which inequality can be used to determine how many hours,
h, she must work to make more than $300 per week?
A. 8.50x + 40 > 300
B. 8.50x40 > 300
C. 40x+8.50 > 300
D. 40x8.50 > 300
Answer:
A is the correct answer
Step-by-step explanation:
Dora bought 4 1/2 pounds of carrots for $3.60.
Question: What is the price per pound of the carrots Dora bought?
The price per pound of the carrots Dora bought is $0.80.
What is the unit rate?
Unit rate is a ratio that compares the amount of one unit of measure to the corresponding amount of another unit of measure. It is a special case of a ratio, in which the second term is always one. For example, if a car travels 120 miles in 2 hours, the unit rate of speed is 60 miles per hour, which means that the car travels 60 miles for every hour of driving.
Unit rate is commonly used in everyday life, such as in shopping (price per unit) or in cooking (ingredients per serving).
To find the price per pound of the carrots, we need to divide the total cost by the total weight.
First, we need to convert the mixed number 4 1/2 to an improper fraction:
4 1/2 = (4 x 2 + 1) / 2 = 9/2
Next, we divide the total cost by the total weight in pounds:
Price per pound = Total cost / Total weight
Price per pound = $3.60 / 4.5 pounds
Price per pound = $0.80
Therefore, the price per pound of the carrots Dora bought is $0.80.
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Graph y = 6X
This is all we have along with a graph that we have to move the line.
The graph of the equation is added as an attachment
How to determine the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 6x
The above expression is a linear equation that implies that
The product of 6 and x is equal to the the value of y
Note that:
A linear graph is a straight line on a two-dimensional coordinate plane that represents a linear equation
Where the equation is in the form y= mx + b, where m is the slope and b is the y-intercept.
This also means that
The slope of the equation is 6The y-intercept is 0Next, we plot the graph
See attachment for the graph of the linear equation and few points on it
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nine times the input minus seven is equal to the output. if the input is -1, what is the output?
Answer:
the output is −16
Step-by-step explanation:
x=-1
9·x-7
9·-1-7
-9-7
-16
You and a friend are hiking and find yourselves near the top of a waterfall. There is a path to hike down that takes 1.8 miles to reach the bottom safely and go swimming. There is also a path that is 1.3 miles down to a great place to eat lunch. Your friend wants to stay at the top of the waterfall and fly his drone overhead to take pictures from the sky. A drone is a flying robot that can be remotely controlled with computer software or technology. Draw a vertical number line to help you answer the questions.
Part A: the drone would need to fly up 1.3 miles Part B: the drone would need to fly up 1.8 miles. Part C: the value of zero represents the top of the waterfall . Part D: the absolute value of -1.8 is the same as the absolute value of 1.8, we have shown that you hiked the same distance in both directions.
Describe Distance?It can be measured in various units such as meters, kilometers, feet, miles, etc. In mathematics, the distance between two points in a coordinate plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:
d = √[(x2 - x1)² + (y2 - y1)²]
Where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them
Part A: The distance from the top of the waterfall to the place where you eat lunch is 1.3 miles, so the drone would need to fly up 1.3 miles
Part B: The distance from the top of the waterfall to the place where you go swimming is 1.8 miles, so the drone would need to fly up 1.8 miles
Part C: In this problem, the value of zero represents the top of the waterfall where you and your friend are currently located.
Part D: Let x be the distance you hiked to go swimming, and let y be the distance you hiked to go back to the top to meet your friend. Then, the total distance you hiked is the sum of the absolute values of x and y, which can be written as |x| + |y|. Since you hiked down 1.8 miles to go swimming and then hiked back up 1.8 miles to the top, x = -1.8 and y = 1.8. Substituting these values, we get |(-1.8)| + |1.8| = 1.8 + 1.8 = 3.6. Since the absolute value of -1.8 is the same as the absolute value of 1.8, we have shown that you hiked the same distance in both directions.
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The complete question is :
Find the slope of the line. Describe how one variable changes in relation to the other. A. 2; distance increases by 2 miles per hour B. 2; distance decreases by 2 miles per hour C. 1/2; distance increases by 1 mile every 2 hours D. 1/2; distance decreases by 1 mile every 2 hours
The line's slope is [tex]\frac{1}{2}[/tex] and the distance increases by 1 mile every 2 hours.
What is a good example of a line's slope?
The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.
A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.
B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.
C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.
D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.
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Graph the following feature
Y intercept =2
Slope = -6/5
The equation of line is y = ( -6/5 )x + 2 , where the slope is m = ( -6/5 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -6/5 )
The y intercept of the line is b = 2
So , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
On simplifying , we get
y = ( -6/5 )x + 2
Hence , the equation of line is y = ( -6/5 )x + 2 and the graph is plotted
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QUESTION 15
Consider the following argument: If seven clowns are squeezed into a small car, we are at the circus. Seven clowns are
not squeezed into a small car. So, we are not at the circus. What is the logical form of this argument?
O a. Modus Tollens
O b. Denying the antecedent
O c. Affirming the consequent
O d. Disjunctive Syllogism
O e. Modus Ponens
The logical form of this argument is -
Denying the Antecedent.
What is them meaning of "Denying the antecedent"?Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement.
It is committed by reasoning in the form :
If P, then Q. Therefore, if not P, then not Q.
Given is the argument as -
"If seven clowns are squeezed into a small car, we are at the circus. Seven clowns are not squeezed into a small car. So, we are not at the circus"
The logical form of this argument is -
Denying the Antecedent
Therefore, the logical form of this argument is -
Denying the Antecedent.
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Create a Venn diagram to illustrate the following:
(D ⋃ E) ⋃ F
The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.
What exactly is a Venn diagram?A Venn diagram is a graphical representation of set theory that uses circles or other closed shapes to show the relationships between sets of objects. In a Venn diagram, each set is represented by a circle or other shape, and the area of the circle represents the total number of objects in that set.
The circles are usually drawn so that they overlap, with the overlapping region representing the objects that belong to both sets. Venn diagrams can be used to illustrate set operations such as union, intersection, and complement.
Now,
As i can not draw here
so i will explain it
To create the Venn diagram, we first draw three overlapping circles to represent the sets D, E, and F. We then shade the regions corresponding to the set operations in the expression, starting from the innermost operation and working our way out.
The expression (D ⋃ E) represents the union of sets D and E, so we shade the region where the circles for D and E overlap. This region represents all the elements that are in D or E or both.
Next, we take the union of (D ⋃ E) with F. This means we shade the region where the circle for F overlaps with the region we shaded in the previous step. This region represents all the elements that are in D or E or F or any combination of these sets.
The final Venn diagram should have three overlapping circles, with the region where all three circles overlap shaded to represent (D ⋃ E) ⋃ F.
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Given cos 0 = √2/5and sin 0 < 0.
What is the value of sin ?
assume the heights of men are normally distributed with a mean 67 inches and standard deviation 4 inches. if a random sample of sixteen men is selected, what is the probability that the mean height is between 66 and 68 inches?
The required probability that the mean height of a sample of sixteen men falls between 66 and 68 inches is approximately 0.6827.
How to find probability using normally distribution?We know that the sample size n = 16, the population mean μ = 67 inches, and the population standard deviation σ = 4 inches.
The sampling distribution of the sample mean can be approximated by a normal distribution with mean μ and standard deviation σ/√n.
Thus, the distribution of the sample mean can be expressed as:
[tex]$\bar{X} \sim \mathcal{N}(\mu, \frac{\sigma}{\sqrt{n}})$$[/tex]
Substituting the given values, we have:
[tex]$\bar{X} \sim \mathcal{N}(67, \frac{4}{\sqrt{16}})$$[/tex]
[tex]$\bar{X} \sim \mathcal{N}(67, 1)$$[/tex]
To find the probability that the sample mean falls between 66 and 68 inches, we need to find the z-scores corresponding to these values and calculate the area under the normal curve between these z-scores.
The z-score corresponding to a sample mean of 66 inches is:
[tex]$z = \frac{66 - 67}{1} = -1$$[/tex]
The z-score corresponding to a sample mean of 68 inches is:
[tex]$z = \frac{68 - 67}{1} = 1$$[/tex]
Thus, we need to find the probability that the z-score falls between -1 and 1. Using a standard normal distribution table or calculator, we can find that this probability is approximately 0.6827.
Therefore, the probability that the mean height of a sample of sixteen men falls between 66 and 68 inches is approximately 0.6827.
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Help me out pls. I have been trying to solve this forevrr but can find out how to work it since its not a true circle
The area of the composite figure is equal to 63.270 square feet.
How to find the area of a composite figure
In this problem we need to compute the area of a composite figure, which is the result of adding the areas of a semicircle and a right triangle. The area formulas of the figures mentioned above are introduced below:
Semicircle
A = 0.5 · r²
Right triangle
A = 0.5 · b · h
Where:
r - Radius, in feetb - Base, in feeth - Height, in feetA - Area, in square feetIf we know that r = 5 ft, b = 8 ft and h = 6 ft, then the area of the composite figure is:
A = 0.5π · (5 ft)² + 0.5 · (8 ft) · (6 ft)
A = 12.5π + 24 ft²
A = 63.270 ft²
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