Bill needs to find the area of the ground covered by a conical tent. The tent is 12 feet tall and makes a 70° angle with the ground. Which expression can be used to find the area?
a) π · (12 · tan 70°)2
b) 36 · π
c) π · (12tan 70°12tan 70°)2
d) π · (tan 70°12tan 70°12)2
Answers
a) π · (12 · tan 70°)2. To find the area of the ground covered by the conical tent, use the formula for the surface area of a cone, A = πr(r+√(r^2+h^2)).
Explanation:To find the area of the ground covered by the conical tent, we can use the formula for the surface area of a cone. The formula is A = πr(r+√(r^2+h^2)), where r is the radius and h is the height of the cone.
In this case, the height of the cone is 12 feet and the angle it makes with the ground is 70°. To find the radius, we can use trigonometry. The radius is given by r = h tanθ, where θ is the angle with the ground. Plugging in the values, we get r = 12 tan(70°).
Now, substituting the value of r into the formula for the surface area of the cone, we get A = π(12 tan(70°))(12 tan(70°)+√((12 tan(70°))^2 + 12^2)). This simplifies to option a) π · (12 · tan 70°)2.
Related Questions
What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?
y = x + 3
y = x + 7
y = 3x – 13
y = 3x + 5
Answers
Answer:
b
Step-by-step explanation:
The equation of the line parallel to y = x + 4 passing through the point (6, 5) is y = x - 1, which has the same slope as the given line but a different y-intercept, determined by the given point.
Explanation:The question asks for the equation of a line that is parallel to y = x + 4 and passes through the point (6, 5). Since the line we are looking for must be parallel, it will have the same slope as the given line, which in this case is 1 (since the coefficient of x is 1 in the given equation). The general form of the line we're looking for is y = x + b, where b is the y-intercept. To find the specific equation, we substitute the point (6, 5) into the equation to solve for b:
5 = (1)(6) + b5 = 6 + b
b = 5 - 6
b = -1
Thus, the equation of the line that meets the conditions is y = x - 1, which is not represented in the options given. Since none of the options match, it's possible that there might have been a mistake in the options provided or an error in the transmission of the question. However, based on the information given, this is the correct equation for the line parallel to y = x + 4 that passes through (6, 5).
f(t)=5t−7 please help
lllll
Answers
-7
t= - -----
f-5
how can you find x in the equation ax-bx+y=z
Answers
A human hair was measured to be 8.0×10−4 inch thick. A cat hair was measured to be 4.0×10−1 inch thick. How much greater is the thickness of the cat hair than the human hair? Write the answer in standard form.
Answers
Human hair: 8.0 x 10-4 = 0.00080
Cat hair: 4.0 x 10-1 = 0.40
Subtracting: 0.40 - 0.00080 = 0.3992
Using rules of precision, the answer becomes 0.40
Answer:
time 4learning answer is 500
Step-by-step explanation:
Rami sold concessions during a concert. He sold bottled water for $3.50 each and bags of trail mix for $4 each. By the end of the evening, Rami sold 400 items for a total of $1,475. How many bottles of water and how many bags of trail mix did Rami sell?
Answers
price of bag of trail mix - $4 each
number of bottles of water sold - x
number of bags of trail mix sold - y
cost spent for bottles - 3.5x
cost spent for bags - 4y
total cost;
3.5x + 4y = 1475 ----> 1)
total number of items
x + y = 400---2)
multiply 2nd equation by 4
4x + 4y = 1600 ---> 3)
Subtract third equation from the 1st
0.5x = 125
x = 250
when x = 250
x + y = 400
250 + y = 400
y = 150
number of bottles - 250
number of bags - 150
Rami sold 250 bottles of water and 150 bags of trail mix at the concert, totaling $1,475 in sales.
To solve the problem of how many bottles of water and bags of trail mix Rami sold, we need to set up and solve a system of linear equations based on the given information.
Let's define the variables:
- [tex]\( x \)[/tex] = the number of bottles of water sold
- [tex]\( y \)[/tex] = the number of bags of trail mix sold
From the problem, we have two pieces of information that we can turn into equations:
1. The total number of items sold is 400.
2. The total revenue from the items sold is $1,475.
We can write these two statements as equations:
1. [tex]\( x + y = 400 \)[/tex]
2. [tex]\( 3.50x + 4y = 1475 \)[/tex]
We now have a system of linear equations:
[tex]\[\begin{cases}x + y = 400 \\3.50x + 4y = 1475\end{cases}\][/tex]
Step 1: Solve the first equation for [tex]\( y \)[/tex]
[tex]\[y = 400 - x\][/tex]
Step 2: Substitute [tex]\( y \)[/tex] in the second equation
Replace [tex]\( y \)[/tex] in the second equation with [tex]\( 400 - x \)[/tex]:
[tex]\[3.50x + 4(400 - x) = 1475\][/tex]
Step 3: Simplify and solve for [tex]\( x \)[/tex]
Expand and simplify the equation:
[tex]\[3.50x + 1600 - 4x = 1475\][/tex]
Combine like terms:
[tex]\[3.50x - 4x + 1600 = 1475\][/tex]
[tex]\[-0.50x + 1600 = 1475\][/tex]
Subtract 1600 from both sides:
[tex]\[-0.50x = 1475 - 1600\][/tex]
[tex]\[-0.50x = -125\][/tex]
Divide both sides by -0.50:
[tex]\[x = \frac{-125}{-0.50} = 250\][/tex]
So, Rami sold 250 bottles of water.
Step 4: Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex]
Substitute [tex]\( x = 250 \)[/tex] back into the first equation:
[tex]\[y = 400 - 250 = 150\][/tex]
So, Rami sold 150 bags of trail mix.
Conclusion
Rami sold:
- 250 bottles of water
- 150 bags of trail mix
To verify, we check the total revenue:
[tex]\[3.50 \times 250 + 4 \times 150 = 875 + 600 = 1475\][/tex]
The numbers match the given total revenue, confirming our solution is correct.
Rosa has 5 pounds of apples how many pies with 8 ounces of apples can Rosa make
Answers
80 divided by 8 is 10.
Hope this helps, sorry if wrong :)
16 ounces are in 1 pound. So, [tex]16*5=80[/tex]
Next you divide [tex] \frac{80}{8} =10[/tex]
The answer is 10 pies.
Colby and Jaquan are growing bacteria in an experiment in a laboratory. Colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. Jaquan has a different type of bacteria that doubles every 3 hours. How many bacteria should Jaquan start with so that they have the same amount at the end of the day?
Answers
Colby will have 50 X (2 ^ 12) = 204,800
Jaquan finishes with 204,800 after its doubled 8 times (24 / 3). So she needs to start with 204,800 / 2 ^ 8 = 800
Answer:
800
Step-by-step explanation:
204,800 / 2 ^ 8 = 800
James believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received math class requested 315 64 379
Did not get math class requested 41 80 121
Total 356 144 500
Help James determine if all students at his school have an equal opportunity to get the math class they requested. Show your work and explain your process for determining the fairness of the class assignment process.
Answers
Based on the table:
Honor students:
315/356 = 88.48% is the total number of people who got the math class requested whereas
Non-honor students:
64/144 = 44.44% did not get the math class requested
So…
They will not have equal chance to get the math class they demanded, if both percent’s were equal, it would be just. For honors students, 88% of them will get the class they demanded, but for non honors students it's 44%.
A trinket company has a warehouse that contains 50,000 trinkets. At the end of each day, a truck picks up 4,000 trinkets to deliver to the trinket store. When the warehouse drops below 15,000 trinkets, the company will begin producing more trinkets to restore the inventory. 1) Write an equation for the number of trinkets in the factory after days. 2) After how many days will the factory begin producing trinkets?
Answers
The expression for the number of trinkets in the company after d days would be 50000-4000d. The inequality going along with it would be:
50000-4000d<15000
We start by cancelling 50000 from both sides by subtracting:
50000-4000d<15000-50000
-4000d<-35000
Divide both sides by -4000:
-4000d/-4000 < -35000/-4000
d > 8.75
This would round up to 9 days.
where do the graphs Of linear equations 2x+3y=4 and 5x+6y=7 intersect
Answers
The graphs of the linear equations 2x+3y=4 and 5x+6y=7 intersect at the point (2, 0).
Explanation:The graphs of linear equations 2x+3y=4 and 5x+6y=7 intersect at a single point. To find the point of intersection, we can solve the two equations simultaneously.
Start by rearranging the equations to solve for y in terms of x:Now, set the two expressions for y equal to each other:(-2/3)x + 4/3 = (-5/6)x + 7/6Simplify and solve for x:
-2x + 8 = -5x + 143x = 6x = 2Substitute the value of x in either original equation to find y:
2(2) + 3y = 4
4 + 3y = 4
3y = 0
y = 0
Therefore, the graphs of the two equations intersect at the point (2, 0).
Which situation CANNOT be represented by this equation? −14x+14=8
A hot-air balloon has a 14-foot diameter that each 14 of an hour gets steadily smaller.At what rate, x, does the balloon have to shrink per hour before it has shrunk to a diameter of 8 feet?
A hot-air balloon has a 14-foot diameter that is getting smaller at a rate of 14 foot per minute. How many minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet?
A hot-air balloon has an 8-foot diameter that is changing at a rate of 14 foot per minute. How long in minutes, x, will it take until the balloon has a diameter of 14 feet?
Answers
A hot-air balloon has an 8-foot diameter that is changing at a rate of 14 foot per minute. How long in minutes, x, will it take until the balloon has a diameter of 14 feet?
We observe that when we clear x we have:
-14x = 14-8
-14x = 6
Which means that the balloon will not reach a diameter of 14 feet
Answer:
The third option is the answer.
Step-by-step explanation:
[tex]-14x+14=8[/tex]
A hot-air balloon has an 8-foot diameter that is changing at a rate of 14 foot per minute. How long in minutes, x, will it take until the balloon has a diameter of 14 feet?
The equation in this case will be : [tex]8-14x= 14[/tex]
a rectangular fish pond is 21 ft squared in area. if the owner can surround the pond with a 20 ft fence what are the dimensions of the pond
Answers
THE ANSWER IS 41 FEET
In Marissa's Calculus course, attendance counts for 5% of the grade, quizzes count for 10% of the grade, exams count for 60% of the grade, and the final exam counts for 25% of the grade. Marissa had 100% average for attendance, 93% for quizzes, 86% for exams, and 85% on the final exam. Determine Marissa's course average.
Answers
Quizzes: 10% value × 93% ( Marissa grade )
= 9.3%
Exams : 60% value × 86% ( Marissa grade )
= 49.6%
Final Exam : 25% value × 85% ( Marissa grade)
= 21.25%
Add all the grades:
5 + 9.3 + 49.6 + 21.25 = 85.15
Marrissa's average grade is 85.15%
I hope you understood my brief explanation. And please consider marking this awnser as Branliest if you think it deserves it. Thank you :) !
Marissa's course average is calculated by weighting each grade by its importance and then summing. This results in an overall average grade of 87.15%.
Explanation:To calculate Marissa's course average given the percentage weight of each grading category and her averages in each category, we multiply each of her grades by the respective weight, then add the weighted grades together.
So, the calculation would be as follows:
Attendance grade: 100% * 0.05 = 5
Quiz grade: [tex]93 * 0.10 = 9.3[/tex]
Exams grade: [tex]86 * 0.60 = 51.6[/tex]
Final exam grade: [tex]85 * 0.25 = 21.25[/tex]
Adding these up, we get [tex]5 + 9.3 + 51.6 + 21.25 = 87.15[/tex]
So, Marissa's course average is 87.15%
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Please help me pleaseee
Answers
the answer is D
what fraction of the letters in the word MUSHROOM are not vowels? show me how you got the answer please
Answers
a proportion relationship is represented by the equation 2x=18y.If y=kx,where k is the constant of proportionlaity,then what is the value of K?
A.9
B.2
C.1/2
D.1/9
Answers
.. 18y/18 = 2x/18
.. y = (1/9)x
selection D is appropriate
In questions 1-5, help the developer name the streets if the entrance street is y=2/3x-7, by using the patterns you discovered in the opening activity and the chart you filled in for the closing questions. All the streets that run parallel to the entrance street ( Oak Street) were given tree names, while all those that run perpendicular to the entrance street were given flower names. If it is neither parallel nor perpendicular to the main street, then the street was labeled with an animal name.
1. Street equation: y=-3/2x-2
weeping willow street
hibiscus street
oak street
Panther street
2.Street equation: y=2/3x+4
weeping willow street
hibiscus street
oak street
gray squirrel
3. Street equation: y=8/12x-7
silver maple street
hibiscus street
oak street
raccoon street
4. Street equation: y=-2/3x-16
elm street
daffodil street
oak street
panther street
5. Street Equation: y=4/6 x+5/3
elm street
camilla street
oak street
brown bear street
Answers
2.oak street (parallel)
3.raccoon street (Neither)
4.panther street (Neither)
5.oak street (parallel)
I'm not 100% sure with the names because I was getting confused but I put what type of line it was so you can check the name yourself.
Angle ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 110°, what is the measure of angle ABC?
Answers
A circle has 360 degrees, so to find the measure of the major arc, subtract 110 from 360 to get 250.
ABC = 1/2(250 - 110)
ABC = 1/2(140)
ABC = 70
The measure of angle ABC is 70 degrees.
Hope this helps =)
Answer:
Step-by-step explanation:
Given that two tangents to a circle intersect at a point B outside the circle
A and C are points of contact.
By theorem on circles we have angle ABC is equal to 1/2 the difference of intercepted arcs.
Angle of minor arc =110 and hence major arc [tex]= 360-110 = 250[/tex]
Difference = [tex]250-110 =140[/tex]
Measure of angle ABC 1/2 of 140 = 70 degrees.
In △DEF, DF = 17 and m∠F=32. Find DF to the nearest tenth.
Answers
ED=9.01
angle D=58
hope this helps
A tee box is 48 feet above its fairway.
Answers
Part A:
Factoring we have:
0 = -16 (t ^ 2 - 2t + -3)
0 = (t ^ 2 - 2t + -3)
0 = (t + 1) * (t-3)
t> 0
t-3 = 0
t = 3
Answer:
The ball is in the air for 3 s.
Part B:
h (t) = - 16t ^ 2 + 32t + 48
We evaluate for t = 1
h (1) = - 16 * (1) ^ 2 + 32 * (1) + 48
h (1) = 64
Answer:
The height of the ball at 1 second is:
h (1) = 64 feet
Part C:
We derive the equation and we equate to zero:
h '(t) = - 32t + 32
0 = -32t + 32
32t = 32
t = 1
h '' (t) = - 32 <0 (t = 1 is a maximum)
Answer:
Yes, The ball at its maximum height at t = 1 second.
find (g o f)(x) where f(x)= x^2-2, g(x)=5x-8
Answers
The composite function (g o f)(x) of f(x) and g(x) is 5x^2-18.
We have given that,
f(x)= x^2-2, g(x)=5x-8
What is the value of (g o f)(x)?The value of (g o f)(x)=g(f(x)
g(f(x)=5(f(x))-8
=5(x^2-2,)-8
=5x^2-10-8
=5x^2-18
Therefore the composite function of f(x) and g(x) is 5x^2-18.
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Least to greatest 1/2, 2/5, 6/10
Answers
1/2=0.50
2/5=0.40
6/10=0.60
Least to greatest: 2/5, 1/2, 6/10
Hope this helped☺☺
Nayati wants to swim 50 miles this school year. She plans to swim 1/4 mile each day. How many days will it take her to swim 50 miles. Show your work.
Answers
200 x 1/4 = 50
which scale facor would produce an expansion under a dilation of the original image
Answers
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Please explain how you got the answer.
Answers
1. using the property of the inscribed quadrilateral it is possible to make up the system of linear equations:
2.
[tex] \left \{ {{A+C=180} \atop {B+D=180}} \right. \ =\ \textgreater \ \ \left \{ {{2x+3+C=180} \atop {3x+9+2x-4=180}} \right. \ =\ \textgreater \ \ \left \{ {{C=107} \atop {x=35}} \right. [/tex]
answer: 107°
Sue plays on a soccer team. In one game this season, she scored 8 goals, which was one-fourth of the goals she scored for the whole season. How many goals in all did she score this season? (Please show work)
Answers
or
8 ÷ 1/4 = 32
or
x = number of goals Sue scored this season
x × 1/4 = 8
now divide both sides by 1/4
x × 1/4÷1/4 = 8÷1/4
x = 32
Answer: 32 goals in all scored Sue this season.
Sue scored 8 goals in one game, which was one-fourth of her total goals for the season. Multiply 8 goals times 4, we find that Sue scored a total of 32 goals for the season.
Explanation:The problem describes Sue's performance in soccer which tells us that the 8 goals she scored in one game are equivalent to one-fourth of the total goals she scored for the season. To find the total score for the whole season, we have to multiply the periods' score by 4 which is the quotient of the total goals to the periods' goals. So, if 8 goals equals to one-fourth, her total score for that season is 8 goals * 4 = 32 goals. So, Sue, who plays on a soccer team, scored a total of 32 goals for the season.
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Kyle bought a pair of socks for $6. Last month, his friends bought the same socks for $5. What is the percent increase in the price of the socks?
Answers
Price this month = $6
Increase in price = $6 - $5 = $1
Percentage increase = 1/5 x 100 = 20%
---------------------------------------------------
Answer: Percentage increase = 20%
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The owner of a bike shop sells unicycle and bicycles and keeps inventory by counting seats and wheels. One day she counts 20 seats and 28 wheels. The equation representing the total number of seats is u+b=20 where u is the number of unicycles and b is the number of bicycles. Select the equation representing the number of wheels.
Answers
A bicycle has 2 wheels. b bicycles have 2b wheels.
In u unicycles and b bicycles, there are a total of
u + 2b wheels.
We are told there are 28 wheels, so u + 2b must equal 28.
The answer is choice C. u + 2b = 28
The equation u+2b=28 represents the number of wheels, which is correct option(C).
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels. One day, she counts 20 seats and 28 wheels.
u is the number of unicycles and b is the number of bicycles.
There are total 20 seats
⇒ u+b=20
unicycle has 1 wheel and bicycle has 2 and total there are 28 wheels
⇒ u+2b=28
Hence, this equation represents the number of wheels.
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A pentagon has angle measures of 102°, 100°, 115° and 110°. What must the fifth angle measure?
Answers
540 - 102- 100 - 115 - 110= 113°
ANSWER:
The fifth angle measures 113°.
Hope this helps! :)
A pentagon has angle measures of 102°, 100°, 115°, and 110°. Therefore, The fifth angle measures 113°.
What is the sum of angles in pentagon?The sum of all the angles of Pentagon angles is 540°.
A pentagon has angle measures of 102°, 100°, 115°, and 110°.
To find the fifth angle so we subtract all angles above from 540°
102 + 100 + 115 + 110 = 540
540 - 102- 100 - 115 - 110 = 113°
Therefore, The fifth angle measures 113°.
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Let x be a random variable with pareto distribution with parameter α . determine the probability distribution function of the random variable y = ln ( x ) . what kind of distribution does y have?
Answers
[tex]F_X(x)=\mathbb P(X\le x)=\begin{cases}1-\dfrac1{x^\alpha}&\text{for }x\ge1\\\\0&\text{otherwise}\end{cases}[/tex]
and so
[tex]F_Y(y)=\mathbb P(Y\le y)=\mathbb P(\ln X\le y)=\mathbb P(X\le e^y)=F_X(e^y)[/tex]
[tex]\implies F_Y(y)=\begin{cases}1-e^{-\alpha y}&\text{for }y\ge0\\\\0&\text{otherwise}\end{cases}[/tex]
[tex]\implies f_Y(y)=\dfrac{\mathrm d}{\mathrm dy}F_Y(y)=\begin{cases}\alpha e^{-\alpha y}&\text{for }y>0\\0&\text{otherwise}\end{cases}[/tex]
which is the PDF of an exponential distribution with rate parameter [tex]\alpha[/tex].