The rate of return on the $10,000 bond purchased at $8750 with a 10% coupon is 24.29%. The answer closest to this value is option C, 11.43%.
The rate of return on a bond is determined by the coupon rate and the difference between the purchase price and face value of the bond.
The coupon rate is the amount of interest paid annually on a bond expressed as a percentage of the face value of the bond.
In this case, the coupon rate is 10%, and the bond was purchased at $8750.
The face value of the bond is $10,000,
So the difference between the purchase price and face value is $1250.
The rate of return can be calculated as follows:
rate of return = (coupon rate + (face value - purchase price) / purchase price) * 100
rate of return = (0.10 + ($10,000 - $8750) / $8750) * 100
rate of return = (0.10 + ($1250 / $8750)) * 100
rate of return = (0.10 + 0.1429) * 100
rate of return = 0.2429 * 100
rate of return = 24.29%
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The area of a rectangular outdoor stage has been extended on one side. The entire new area in square meters can be written as 216+12x. Factor the expression to find the dimensions of the extended stage.
Answer:12(x+18)
Step-by-step explanation:
Find the ymmetric equation of the line that pae through the point P(−2,1,0)
and i parallel to the vector v⃗ =⟨0,2,−3⟩
x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
This is the symmetric equation of the line that passes through the point P and is parallel to the vector .
What is symmetric equation?
A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:
x = -2 + 0t
y = 1 + 2t
z = 0 - 3t
where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:
d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v
So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:
(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t
x + 2 = -2t
y - 1 = 2t
z + 3 = 3t
Rearranging the above equations, we get:
x = -2 - 2t
y = 2t + 1
z = 3t - 3
Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:
x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
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x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
This is the symmetric equation of the line that passes through point P and is parallel to the vector.
What is the symmetric equation?
A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:
x = -2 + 0t
y = 1 + 2t
z = 0 - 3t
where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:
d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v
So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:
(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t
x + 2 = -2t
y - 1 = 2t
z + 3 = 3t
Rearranging the above equations, we get:
x = -2 - 2t
y = 2t + 1
z = 3t - 3
Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:
x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
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True or False : The magnitude of a vector is zero if all of its components are zero.
True , a vector cannot have zero magnitude if one of its components is not zero.
If all of a vector's components are zero, is the vector's magnitude also 0?
A vector's magnitude cannot ever be smaller than any of its components' magnitudes. Only when all of a vector's components are 0 can the vector's magnitude be zero.
Their northward components are also equal, and the eastward component of vector A is equal to the westward component of vector B.
What is the vector's magnitude?
A vector's magnitude, represented by the symbol |v|, is used to determine a vector's length. The distance between the vector's beginning point and endpoint is what this amount essentially represents.
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Find the value of x for which // m.
105°
(3x - 18)
m
The value of x is 3.
What are Parallel lines?parallel lines are coplanar infinite straight lines that do not intersect at any point.
The lines l and m are the parallel lines.
3x-18+105=180
3x+87=180
Subtract 87 on both sides
3x=180-87
3x=93
Divide both sides by 3
x=31
Hence, the value of x is 3.
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Decreasing the sample size, while holding the confidence level the same, will do what tothe width of your confidence interval?a.make it bigger b.make it smaller c.it will stay the same d.cannot be determined from the given information
Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.
The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.
When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.
Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.
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Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.
The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.
When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.
Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.
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While on a beach, your friend discovers a different genie. This genie also offers two purses to choose from and he gives you the following graph to show how the money in each purse will grow. The set of triangular marks that lie on a line represent values in Purse A, and the set of square marks that make a curve represent those in Purse B.
The genie is still deciding how many days he will let the money in the purses grow. Help your friend plan a strategy for picking the purse with the most money while the genie thinks.
Strategy should be, choosing purse A if number of days is less than 10,if it is more than 10 , he should choose purse B.
If there are 10 days, he can choose any of the purse.
What is an inequality?Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
Given,
Genie provides friend two purses,
Purse A and Purse B
Graph of Growth in amount to number of days is given.
By the graph,
Intersection point is on 10th day
Till 10th day Amount of purse A is grows more than amount of purse B.
After 10th day amount of purse B starts growing more than amount of purse A
Let no. of days be x
If x < 10, he should choose purse A.
If x > 10 he should choose purse B.
If x = 10, he can choose any purse.
Hence, Friend should choose purse A if number of days is less than 10.
Friend should choose purse B if number of days is greater than 10.
If number of days is 10, he can choose any of the purse.
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For each positive integer n, consider the pair (3^n −1, 5^n −1). For n = 1, this is the pair (2, 4) and for n = 2, it is (8, 24). Can you find a value for n such that both numbers in the pair (3^n − 1, 5^n − 1) are divisible by d = 7? Can you find more than one such n? Do you think there are finitely or infinitely many n such that 3n − 1 and 5n − 1 are both divisible by d = 7? Why? Explain your reasoning as carefully as you can.
Now, what if we replace d = 7 with d = 11? Or with d = 13? What if we take d = 77
or d = 1001? Describe any patterns you think are interesting
There is no value of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by 7.
For d=7, we can see that:
3² - 1 = 8 is divisible by 7, but 5² - 1 = 24 is not divisible by 7.
For larger values of d such as 11, 13, 77, and 1001, we can use a similar approach to see if there are any values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. However, finding an exact value of n for larger values of d may be difficult without using more advanced mathematical methods.
In general, the number of values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by a given integer d will depend on the properties of the numbers 3, 5, and d. For example, if d is a prime number that is not a divisor of either 3 or 5, it is likely that there are only a few values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d.
However, if d is a composite number or a divisor of either 3 or 5, there may be more values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. Whether there are finitely or infinitely many such n will depend on the specific values of 3, 5, and d.
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Select all the abiotic factors.
Group of answer choices
Grass
Parasites
Whale
Mushroom
Mold
Bacteria
Trees
Competition between organisms
Sunlight
Oxygen
Carbon Dioxide
Nitrogen
Clouds
Rain
Desert
Snow
Plastic
Dirt
Rock
The abiotic factors are Sunlight, oxygen, Carbon Dioxide, Nitrogen, Clouds, Rain, Desert, Snow, Plastic, Dirt and Rock
How to determine abiotic factors?Abiotic factors are non-living physical and chemical elements and conditions in the environment that influence the survival and growth of living organisms. The abiotic factors in the given list are:
Sunlight: The light energy from the sun that drives photosynthesis and provides energy to living organisms.
Oxygen: A colorless, odorless, tasteless gas essential for respiration in many organisms.
Carbon Dioxide: A colorless, odorless gas that is produced by respiration, combustion and decay of organic material and is used by plants during photosynthesis.
Nitrogen: An odorless, tasteless gas that makes up a major component of the Earth's atmosphere and is essential for plant growth as a component of amino acids and nucleic acids.
Clouds: A visible mass of water droplets or ice crystals suspended in the atmosphere.
Rain: Precipitation that falls from clouds as water droplets.
Desert: An area characterized by little rainfall and high temperature, often with limited vegetation.
Snow: Precipitation that falls from clouds as ice crystals.
Plastic: A synthetic or semi-synthetic material made from various organic polymers.
Dirt: The naturally occurring material that covers the surface of the earth, made up of organic and inorganic matter.
Rock: A naturally occurring solid composed of one or more minerals.
These are all abiotic factors, while the other items in the list are biotic factors, which are living or once-living elements in the environment.
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The point given lie on a line. (-1,3) (2,-1)(5,-5) (8,-9) Find the lope of the line
Rise divided by run gives you the slope. A line's rise and run can be used to calculate the slope of a line from its graph. A line's continuous slope is one of its defining characteristics. The slope is (-1,3).
What is meant by slope?The slope is defined as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites.A line's slope is determined by how steeply it slopes from LEFT to RIGHT. Slope is the ratio of a line's rise, or vertical change, to run, or horizontal change. No matter which 2 locations on the line you choose, the slope of a line is always constant (it never changes).A surface (such a road or railroad track) has a 2% slope if it changes elevation by 2 units over a run of 100 units.To learn more about slope refer to:
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eight thousand one hundred and five four divided by two seven equals three two remainder not true two false
Answer:
False.
Step-by-step explanation:
8154 = eight thousand one hundred and five four
27 = Two seven.
Now we divide.
8154/27 = 302
Now you get 302 if you divide.
So therefore, its false.
How To Get The Domain And Range From The Graph Of A Function
The input values displayed on the x-axis make up the entirety of a graph's domain. The collection of potential output values that make up the range is represented by the y-axis.
How do you find the range of a graph of a function?All y's potential values are referred to as the function's range. Using the formula y = f, one can determine a function's range (x). If every x value in a relation has exactly one corresponding y value, then it is merely a function.The codomain in relations and functions is the collection of all potential results of the specified relation or function. How to determine a function's domain and range f(x) = 3x2 - 5 The set of input values for f, in which the function is real and defined, is known as the domain of a function. All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.To learn more about values refer to:
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Kaeya need to ave at leat $600 for a trip. She ha already aved $45. She plan to ave $35 per week
Kaeya need to save at least $600 for a trip. She ha already saved $45. She plan to save $35 per week she will need 16 week to completely save money for her trip.
Kaeya need to save at least $600 for a trip
She has already saved $45.
so she now has to save 600 - 45 = $555
She plan to save $35 per week
So she have to save 555/35 no of weeks to collect the remaining no of money for her trip
= 555/35
= 15.85
≈ 16 weeks
Therefore, she will need 16 week to completely save money for her trip if she need to save at least $600 for a trip.
Savings are the funds that remain after subtracting a person's consumer spending from their disposable income during a specific time period. Savings, then, is what's left over after all bills and commitments have been fulfilled for an individual or household.
Cash or cash equivalents (such as bank deposits) are used to store savings since they carry no danger of loss but also offer very low returns. Savings can increase through investing, but doing so involves putting money at risk.
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What is the measure of angle W ?
Answer:
Angle W is 100 degrees
---------------------------------
Angle W is the exterior angle of the given triangle.
We know that exterior angle is the sum of remote interior angles.
It gives us:
W = 33 + 67 = 100PLEASE HELP SOLVE THIS QUESTION
The slope of this line is m = 1.
An equation of this line is y = x.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (0, 1).Substituting the given data points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 0)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1
At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.Substituting the parameters, we have:
y - 1 = 1(x - 1)
y = x - 1 + 1
y = x
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find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x 1, y = 0, x = 0, x = 5; about the x-axis v =
The volume v of the solid obtained by rotating the region bounded by the curves y = x + 1, y = 0, x = 0, x = 5 about the x-axis is 215π/3.
We have to determine the volume v of the solid obtained by rotating the region bounded by the curves about the specified line.
The line is y = x + 1, y = 0, x = 0, x = 5; about the x-axis.
The volume of the solid disk is;
V = [tex]\int\limits^a_b A(x) \, dx[/tex], where A(x) = π(radius)^2
So, V = [tex]\pi\int\limits^{5}_{0} (x+1)^2 \, dx[/tex]
Now simplifying the value of (x + 1)^2 as x^2 + 2x + 1. So
V = [tex]\pi\int\limits^{5}_{0} (x^2+2x+1) \, dx[/tex]
Now integrating
V = [tex]\pi \left(\frac{x^3}{3}+\frac{2x^2}{2}+x\right)^{5}_{0}[/tex]
V = [tex]\pi \left[\left(\frac{5^3}{3}+\frac{2(5)^2}{2}+5\right)-\left(\frac{0^3}{3}+\frac{2(0)^2}{2}+0\right)\right][/tex]
V = [tex]\pi \left[\left(\frac{125}{3}+\frac{50}{2}+5\right)-\left(0+0+0\right)\right][/tex]
V = π(125/3 + 25 + 5)
V = π(125/3 + 30)
V = π(125 + 90)/3
V = 215π/3
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9/15x5/10 simplify explain how you did the work
Answer:
3/10 or 0.3
Step-by-step explanation:
(9/15)(5/10)
= (3/5)(1/2)
3x1=3 and 5x2=10
= 3/10 or 0.3
What is the answer to this question?
The value of x in the triangle is 75°
What is triangle Geometry?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.
The sum of angles in a triangle is 180°. Also the sim of angles on a straight line is also 189°
One of the triangle theorem is that the exterior angle of a triangle is equal to the sum of the opposite angles.
Therefore with this, we can say that
120= 57+x
collect like terms
120-57 = x
x = 75°
therefore the value of x in the triangle is 75°
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what is the least common denominater of 1-8 5-12 and 7-18?
On solving the provided question, we can say that Equivalent Fractions with the LCD 1/8 = 9/72 and 5/12= 30/72
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
LCD = 72
Equivalent Fractions with the LCD
1/8 = 9/72
5/12= 30/72
7/18 = 28/72
Rewriting input as fractions
1/8, 5/12, 7/18
For the denominators (8, 12, 18) the least common multiple (LCM) is 72.
LCM(8, 12, 18)
Therefore, the least common denominator (LCD) is 72.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
1/8 = 1/8 × 9/9 = 9/72
5/12 = 5/12 × 6/6 = 30/72
7/18 = 7/18 × 4/4 = 28/72
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how many degrees are there on both the celsius and kelvin temperature scales, between the normal freezing and boiling points of water?
There are 100 degrees between the normal freezing and boiling points of water.
On the Celsius temperature scale, the difference between the normal freezing point (0°C) and the normal boiling point (100°C) of water is 100°C - 0°C = 100°C.
Celsius, also called centigrade, scale based on 0° for the freezing point of water and 100° for the boiling point of water.On the Kelvin temperature scale, the equivalent temperatures for the normal freezing and boiling points of water are 273.15 K and 373.15 K, respectively. The difference between these two temperatures on the Kelvin scale is 373.15 K - 273.15 K = 100 K.
So, in both Celsius and Kelvin scales, there are 100 degrees between the normal freezing and boiling points of water.
Therefore, there are 100 degrees between the normal freezing and boiling points of water.
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Please help very urgent! A fair maiden can sew the border of a tapestry in six hours. Her sister works twice as fast. If they are working together, how long will it take them to finish the border?
Let's call the time it takes the fair maiden to sew the border of the tapestry "t". So, her sister can sew the border in t/2 hours.
Working together, they can sew the border in t + t/2 = 1.5t hours.
Since we know the fair maiden can sew the border in 6 hours, we can substitute this into the equation to find t:
6 + 6/2 = 1.5t
Simplifying the right side of the equation:
6 + 3 = 1.5t
9 = 1.5t
Dividing both sides of the equation by 1.5:
t = 6
So the fair maiden can sew the border in 6 hours and her sister can sew the border in 6/2 = 3 hours.
Working together, it would take them 6 + 3 = 9 hours to sew the border of the tapestry.
What is the measure of angle B in this triangle?
Enter your answer in the box.
Answer:
it is probably 70° of the triangle
(FOR 100 POINTS!) MY ANSWER PROBABLY WASNT RIGHT, JUST COMMENT THE CORRECT THING IN SIMPLEST RADICAL FORM.
Answer:
6
Your answer is correct, but since √1 = 1
we can simplify this as 6 · 1 = 6
Step-by-step explanation:
Since the given figure is a square, all four sides are equal.
Each side = 3√2
For a square of side a, the diagonal is given by
d = √(a²+a²) = √(2a²) = a√2
Here we have a = 3√2
So diagonal = x = 3√2 (√2) = 3 · 2 = 6
What is the correct statement for three
The definition that justifies the congruence of angle measures GJH and GJI is given as follows:
Definition of Angle Bisector.
What is the definition of Angle Bisector?A bisection is defined as a segment that splits an angle measure into two equal measures.
Hence an angle bisector means that an angle is divided into two angles of equal measure.
For this problem, we have that segment GJ is the angle bisector of angle G, meaning that the angle measures GJH and GJI are congruent.
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A baketball tournament tarted at 12:15pm and ended at 4:00pm did the tournament lat more than 4 hour? i put 3:45 min. Am i right
No, you're incorrect. The tournament lasted from 12:15pm to 4:00pm, which is a duration of 3 hours and 45 minutes. So, the tournament lasted less than 4 hours.
To calculate the duration, you subtract the start time from the end time:
4:00pm - 12:15pm = 3 hours and 45 minutes
Therefore, the tournament lasted for 3 hours and 45 minutes, which is less than 4 hours.
Here's a step-by-step breakdown of the calculation:
Start by calculating the number of whole hours between the start and end time.
4:00pm - 12:15pm = 3 hours
Next, calculate the number of remaining minutes.
4:00pm - 12:15pm = 45 minutes
So the total duration of the tournament was 3 hours and 45 minutes, which is less than 4 hours.
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Select all the correct answers.
Which three pairs of side lengths are possible measurements for the triangle?
45
B
45
AB=16, AC=16
AB= 6, AC= 6√/2
BC=7√2, AC = 14
AB= 15, BC = 15
OBC=8, AC = 8√3
AB= 11, AC = 22
The possible measurements for the triangle are given as follows:
AB = 6, AC = 6√2.AB = 15, BC = 15.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For this problem, we have an angle of 45º, which has the same value for sine and cosine, hence:
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A doctor's office is deciding between buying 2 different sized cups. The 2 cups are shown. -1.5in -2 in- Before deciding which size cup to buy, they determine how much water each size cup can hold. How much more water, in cubic inches, can the larger cup hold than the smaller cup? Round your answer to the nearest hundredth. Use the pi key on your calculator for pi. (On the EOC, this problem specifically says - in cubic inches so you need to add that to your answer. EX. 5.81 cubic inches) N
The larger cup can hold 144.51 in³ more water than the smaller cup.
How to obtain the volume of a cone?The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:
V = 3.14r²h/3
V = 1.0472r²h.
For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:
V = 1.0472 x 2² x 3
V = 12.57 in³.
For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:
V = 1.0472 x 5² x 6
V = 157.08 in³.
Then the difference is of:
157.08 - 12.57 = 144.51 in³.
Missing InformationThe cones are given by the image presented at the end of the answer.
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MWhat is the measure of ∠F?
Answer:
Angle F i= 48 degrees
Step-by-step explanation:
Sum of angles in a triangle= 180°
8x -18+ 6x-4+5x-7= 180
Collect like terms
8x +6x +5x -18 -7-4=180
19x-29=180
19x = 180 +29
19x=209
x=209/19
x= 11
⇒Angle F= 5x-7
= 5(11)-7
= 55-7
=48 degrees
Answer:
48°
Step-by-step explanation:
A/C, 6x - 4 + 8x - 18 + 5x - 7 = 180°
or, 19x - 29 = 180°
or, x = 209 ÷ 19 = 11
So, x equals 11.
Now, Angle F = (5 × x) - 7 = (5 × 11) - 7 = 55 - 7 = 48°
Hence, Angle F measures 48°.
HOPE IT HELPED BUDDY!
Please help!
What is the geometric mean of 48 and 12? (Put ONLY the number as your answer) If it is not a whole number, round to decimal 1 place.
The geometric mean of two or more numbers is the same as their average. In this case, we have the numbers 48 and 12.
[tex]\dfrac{48+12}{2}=\dfrac{60}{2}=30[/tex]
Hence, the geometric mean of 48 and 12 is 30. Let me know if you have any questions, thanks!
we turn over the cards of a well-shuffled standard deck of 52, and we observe the sequence. (a) how many sequences have all cards of the same suit together? (b) how many sequences have all the clubs together?
There are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.
A standard deck of 52 cards contains 4 suits: spades, hearts, diamonds, and clubs.
(a) To find how many sequences have all cards of the same suit together, we need to find the number of sequences where all the cards of the same suit are together.
There are 4 possible suits, and each suit contains 13 cards.
So, the number of sequences where all the cards of the same suit are together is 13! x 4.
(b) To find how many sequences have all the clubs together, we need to find the number of sequences where all the clubs are together.
There are 13 clubs, and each club card can be placed in any order.
So, the number of sequences where all the clubs are together is 13!
Therefore, there are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.
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exact shape function of tapered bar element
In FEM, nodal displacement is calculated using the matrix equation shown below: [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces.
Describe function.A function is something that connects an input to an output.
Then, they are interpolated over entire elements using shape functions, which are essentially polynomials of different orders. Although quadratic shape functions, like a quadratic curve, are becoming common, linear shape functions, like a straight line used to approximate a distance between two locations, are the most fundamental. Even higher order shape functions (like cubic) exist, but they are rarely used in practical settings. The calculation of an element's stress uses Gauss Points rather than nodes. You can look up the GP locations for any given kind of element, but for the purposes of this discussion, let's just talk about singles.
Since [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces, the matrix equation presented below is used to determine nodal displacement.
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Complete question -
Given the tapered bar/axial element below, determine the exact displacement interpolation function and the associated exact shape functions. Show all intermediate steps.