The shape and the circumference of the base created by the rotation is; Cone and Circumference of 63 mm
What shape is created by rotation?We are given;
Each side of equilateral triangle = 20 mm
Now, when the triangle is rotated about the line ‘a’ which passes through the midpoint of any of the 3 sides of the equilateral triangle we will get a conical shape.
The distance from the line a which cuts one side of a triangle to one vertex of the triangle is the radius = 10 mm
We know that;
Circumference of a circle = 2πr
Thus;
C = 2 × 3.14 × 10
C = 6.28 × 10
C = 62.8 mm
C = 63 mm
Thus, the approximate circumference of the base is 63 mm.
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Find the solutions for a triangle with a =11.4, b =13.7, and c =12.2.
The solutions for the triangle are: ∠A = 51.833...° , ∠B = 70.880...° and ∠C = 57.286...°
Explanation
For finding the unknown angles, we need to use Cosine rule. The formulas are...
[tex]cos A = \frac{b^2+c^2-a^2}{2bc} \\ \\ cos B= \frac{a^2+c^2-b^2}{2ac}\\ \\ cos C= \frac{a^2+b^2-c^2}{2ab}[/tex]
Given that the length of three sides of the triangle as : [tex]a= 11.4, b= 13.7[/tex] and [tex]c=12.2[/tex]
Thus,
[tex]cosA= \frac{(13.7)^2+(12.2)^2 -(11.4)^2}{2(13.7)(12.2)} \\ \\ cosA= \frac{206.57}{334.28} \\ \\ cosA= 0.61795... \\ \\ A= cos^-^1 (0.61795...)= 51.833... degree\\ \\ \\ \\ cos B= \frac{(11.4)^2+(12.2)^2 -(13.7)^2}{2(11.4)(12.2)}\\ \\ cos B= \frac{91.11}{278.16} \\ \\ cos B= 0.3275...\\ \\ B= cos^-^1 (0.3275...)= 70.880... degree \\ \\ \\ \\ cos C= \frac{(11.4)^2+(13.7)^2 -(12.2)^2}{2(11.4)(13.7)}\\ \\ cos C= \frac{168.81}{312.36} \\ \\ cos C= 0.54043...\\ \\ C= cos^-^1 (0.54043...)= 57.286... degree[/tex]
Answer
To simplify the answer above this one, it is
C) A=51.8 B=70.9 C=57.3
Step-by-step explanation:
I got it right on edge
Determine the measure of an angle (in radians) that cuts off an arc length of 6.4 inches in a circle with a 6.4 inch radius.
A line passes through the ordered pairs (4,1) and (2,8) . What is the slope? Please help
Final answer:
The slope of the line that passes through the points (4,1) and (2,8) is calculated using the slope formula and results in a slope of -3.5.
Explanation:
To find the slope of a line passing through the ordered pairs (4,1) and (2,8), you can use the slope formula:
m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is the first point (4,1) and (x2, y2) is the second point (2,8).Plugging in the values, we get:
m = (8 - 1) / (2 - 4) = 7 / (-2) = -3.5Therefore, the slope of the line that passes through the points (4,1) and (2,8) is -3.5.
The slope of the line passing through the given points is -3.5.
Let’s find the slope of the line passing through the points (4, 1) and (2, 8).
The slope of a line can be calculated using the following formula:
[tex]\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where:
• [tex](x_1) and (y_1)[/tex] are the coordinates of the first point (in this case, (4, 1)).
• [tex](x_2) and (y_2)[/tex] are the coordinates of the second point (in this case, (2, 8)).
Let’s compute the slope:
1. Difference in (x)-coordinates: [tex](x_2 - x_1 = 2 - 4 = -2)[/tex]
2. Difference in (y)-coordinates:[tex](y_2 - y_1 = 8 - 1 = 7)[/tex]
Now, calculate the slope:
[tex]\text{slope} = \frac{7}{-2} = -3.5[/tex]
Therefore, the slope of the line passing through the given points is -3.5.
which situation is represented by the following equation?45w+123.95=753.95
A sandwich shop offers the following toppings. How many two topping sandwiches can you make? -lettuce -tomato -bacon -cheese -mustard
A) 8
B) 10
C) 12
D) 20
Please include steps or explain how you got your answer! :)
The correct answer is: B) 10
Step 1:
To calculate the number of two-topping sandwiches you can make from the given toppings, you can use the combination formula:
[tex]\[C(n, k) = \frac{n!}{k!(n-k)!}\][/tex]
Where:
- [tex]\(n\)[/tex] is the total number of toppings available (5 in this case).
- [tex]\(k\)[/tex] is the number of toppings you want to choose (2 in this case).
- [tex]\(C(n, k)\)[/tex] represents the number of combinations.
Step 2:
Substituting the values:
[tex]\[C(5, 2) = \frac{5!}{2!(5-2)!}\][/tex]
[tex]\[C(5, 2) = \frac{5!}{2!3!}\][/tex]
[tex]\[C(5, 2) = \frac{5 × 4}{2 × 1}\][/tex]
[tex]\[C(5, 2) = \frac{20}{2}\][/tex]
[tex]\[C(5, 2) = 10\][/tex]
So, you can make [tex]\(10\)[/tex] two-topping sandwiches from the given toppings.
i need help finding the perimeter of a rectangle
we have 8 yards of wrapping paper if we use two feet for each present how many presents can we wrap
The mean of a normal distribution is 12.3 with the standard deviation is 1.7. find the 73th percentile
who help me is a genius
y = |x| translated half a unit to the left
Answer:|
y=|x+.5|
Step-by-step explanation:
I found my answer by drawing a graph and then moving 2 spaces left then you need to do absolute values
you also need to plot some points on the graph to see where there is a straight line
I hope this helps
Experts/ace/geniuses helppp
PLEASE Help!! What is the solution of the equation? Eliminate any extraneous solutions.
hey can you please help me posted picture of question
What is the answer to the problem i am very confused...
PLEASE HELP
1. What is the length of the unknown leg in the right triangle? with sides
sqrt 23yd and sqrt 87 yd
a. 8yd
b. sqrt 110yd
c. 64 yd
d. sqrt 7040yd
Mias dog weighs 32.6 pounds. Letties dog weighs 3.8 times as much as Mias you. What does Letties dog weigh in pounds?
Final answer:
Lettie's dog weighs 123.88 pounds, calculated by multiplying Mia's dog's weight of 32.6 pounds by 3.8.
Explanation:
Calculating Lettie's Dog's Weight:
To find out how much Lettie's dog weighs, we need to perform a simple multiplication calculation because we are told Lettie's dog weighs 3.8 times as much as Mia's dog. Mia's dog weighs 32.6 pounds, so the weight of Lettie's dog will be:
32.6 pounds × 3.8 = 123.88 pounds.
It's important to remember that when we're dealing with measurements such as weight, we need to ensure that we stick to the same unit for a proper comparison. Given that we're talking about the weight of dogs, the pound is the most suitable unit of measurement for this context. Thus, we would not be using ounces or tons here, as those units are suitable for much lighter or heavier items, respectively.
hey can you please help me posted picture of question
Osman broke the unusually shaped picture window and his parents living room. The figure shows the dimensions of the window. replacement glass cost $8 per square foot, and there will be a $35 installation fee. Find the cost to replace the window to the nearest cent.
Osman can calculate the cost to replace the unusually shaped picture window by determining its area and then using the formula C = (Area of the window × $8) + $35 to find the total cost. The final total should be rounded to the nearest cent. However, without the window's dimensions, an exact cost cannot be calculated.
Explanation:To calculate the cost to replace the unusually shaped picture window in Osman's parents' living room, we must first determine the area of the window to find out how many square feet of glass are needed. Once we have the area, we can multiply by the cost per square foot and add the installation fee. Unfortunately, the question does not provide the necessary dimensions of the window, so we cannot proceed with the exact calculations. However, I will provide a general formula that Osman could use to calculate the replacement cost.
Let's assume that the dimensions of the window are provided and that we have managed to calculate the area, A, in square feet. The cost of the replacement glass will then be A × $8. After calculating this, Osman would need to add the installation fee, which is $35. So the total cost to replace the window, C, would be calculated using the formula:
C = (A × $8) + $35
Once Osman replaces the window, if the total calculated cost is not a whole number, he should round it to the nearest cent.
Solve the system using the substitution method
2x+y=6
3x+5y=9
branliest offered
A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $41,949.00 each year, and $28,826.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,483,249.00. How many people does the company intend to employ next year?
Answer:
50
Step-by-step explanation:
Let
x = number of employees each yeary = labor costsThe relationship between x and y can be represented through a linear equation.
y = a . x + b
where,
a is the slope
b is the y-intercept
The slope represents the cost per each person employed, that is, a = $28,826.00/person.
Then,
y = ($28,826.00/person) . x + b
Even if no person is hired (x = 0), there is a fixed cost of $41,949.00 (y = $41,949.00).
$41,949.00 = ($28,826.00/person) . 0 + b
b = $41,949.00
The final equation is
y = ($28,826.00/person) . x + $41,949.00
If the company will spend $1,483,249.00 (y = $1,483,249.00.),
$1,483,249.00 = ($28,826.00/person) . x + $41,949.00
1,441,300 = ($28,826.00/person) . x
x = 50 person (50 people)
The company intends to employ 50 people next year.
My son is trying to figure out how to decompose 8/12 and what he has to work with is x/2 + x/2 =8/12
Find the surface area of regular prism with height 6 cm, if the base of the prism is a Regular quadrilateral with side 4 cm.
Judy squeezes 140 mm of lemonade to make 1 liter of lemonade how many millimeters of lemon juice are in 2 L of lemonade
If two cylinders are similar and the ratio between the lengths of their edges is 2:5 what is the ratio of their volumes
Answer: Thou answer shalt be Le letter B. 8:125
lori is 3 times as old as 7 more than ron's age if ron is a years old how old is lori
ASAP
The equation of the linear regression line represents the relationship between the number of cars washed for charity, x, and the amount earned for charity, y. yˆ=10x+20 How much money can the charity expect to earn if 50 cars come in for a wash?
Two cable ferries start moving towards each other from shores A and B. When the pass each other for the first time the distance to shore B is 100 meters. Once they reach their destinations and start traveling back at the same time. When they meet for the second time, the distance to shore A is 50 meters. What is the distance between the shores Aand B?
The first meeting point of the ferries represents half of the total roundtrip, while the second meeting point represents a quarter of it. Knowing this proportion and the distances at which the meetings happen, we conclude that the distance between shores A and B is 200 meters.
Explanation:This problem can be solved using rates and proportions. Consider the total round trip of each ferry. The first meeting is at 100 meters from shore B and the second meeting is 50 meters from shore A.
Imagine a full roundtrip travel, from A to B and back to A. When the ferries meet for the first time, they have collectively completed one full round trip (distance A to B and B back to A). At their second meeting, they have collectively made two full round trips.
This means that the first meeting happened at 1/2 of the round trip distance and the second meeting happened at 1/4 of the round trip distance, meaning that the second meeting point was half the distance of the first meeting point. Based on where the second meeting point is (50 meters from shore A), we know that the first meeting point (100 meters from shore B) is twice the distance of the second meeting point from shore A.
Now, we understand the distances as follow: the total distance from shore A to shore B is the sum of the distance from the first meeting point to shore B (100 meters) and twice the distance from the second meeting point to shore A (2*50 meters), which sums up to 200 meters. Therefore, the distance between shores A and B is 200 meters.
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The lengths of the base of a trapezoid is 12ft and 5ft the height is 96 in what is the area of the trapezoid
Answer:
the area is 816
Step-by-step explanation:
Step-by-step
12 + 5 = 17
17 / 2 = 8.5
8.5 * 96 = 816
the area is 816
Q # 6 find the measure please
Bianca and Dave are a married couple filing a joint tax return. They have a combined gross income of $81,031 and claim four exemptions. They can make an adjustment of $2,914 for business expenses, an adjustment of $1,939 for business losses, a deduction of $4,140 for medical expenses, an adjustment of $4,825 for contributions to their retirement fund, and a deduction of $2,420 for charitable donations. If exemptions are worth $3,650 apiece and the standard deduction for a joint return is $8,350, what is their total taxable income?
a.
$50,193
b.
$41,843
c.
$48,403
d.
$52,793
Answer:
C
Step-by-step explanation:
Gross income(81,031) - adjustments(9,678) - exemptions(3,650•4 = 14,600) - STANDARD deduction(8,350)
$81,031 - $2,914 - $1,939 - $4,825 - $14,600 - $8350 = $48,403
itemized deductions = $6,560 which is less than the Standard deduction of $8,350, so you would use the Standard deduction
The total taxable income is b. $41,843..
To find Bianca and Dave's taxable income, we'll follow these steps:
Calculate the Total Exemptions:
They have 4 exemptions worth $3,650 each.
Total exemptions = 4 × $3,650 = $14,600.
Calculate Adjustments and Deductions:
Business Expenses: $2,914 Business Losses: $1,939 Medical Expenses: $4,140 Retirement Contributions: $4,825 Charitable Donations: $2,420Total adjustments and deductions = $2,914 + $1,939 + $4,140 + $4,825 + $2,420 = $16,228.
Determine the Standard Deduction:
For married filing jointly, the standard deduction is $8,350.
Calculate Adjusted Gross Income (AGI):
AGI = Combined Gross Income - Adjustments
AGI = $81,031 - (Business Expenses + Business Losses + Retirement Contributions)
AGI = $81,031 - ($2,914 + $1,939 + $4,825) = $81,031 - $9,678 = $71,353.
Calculate Total Deductions:
In this case, we will take the higher of the total adjustments/deductions calculated or the standard deduction.
Total official deductions = max(Total adjustments and deductions, Standard Deduction)
Total deductions = max($16,228, $8,350) = $16,228.
Calculate Taxable Income:
Taxable Income = AGI - Total Deductions - Total Exemptions
Taxable Income = $71,353 - $16,228 - $14,600
Taxable Income = $71,353 - $30,828 = $40,525.