The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. What is the area of the roof? What is the lateral area of the roof?
Answer:
The area of the roof: ≈2287.44 ft^2, the lateral area of the roof:≈1580.58 ft^2
Step-by-step explanation:
The area of the roof is computed by the equation of the area of a cone:
A = πr(r + [tex]\sqrt{h^{2}+r^(2) }[/tex])
(r: radius, h: height, πr^2 is the area of the base of the cone, πr[tex]\sqrt{h^{2}+r^(2) }[/tex] is the lateral area of the cone). So:
A = [tex]15\pi (15 + \sqrt{30^{2} +15^{2} } )[/tex] ≈ 2287.44 ft^2.
As I stated earlier, the lateral area of the roof can be computed:
A[tex]L[/tex]=[tex]15\pi \sqrt{30^{2} +15^{2} }[/tex] ≈ 1580.58 ft^2.
Noah's Diner offers its clients a choice of regular and diet soda. Last night, the diner served
18 regular sodias and 57 diet sodas. What percentage of the sodas served were regular?
Answer: 24%
Step-by-step explanation:
for these problems you can use this equation: [tex]\frac{x}{n} *100=p[/tex]
where x=given quantity, n=total amount, and p is your answer.
for this problem x=18 (regular sodas)
we add the amount of regular and diet sodas to get n=75 (18+57)
when we plug it in we have [tex]\frac{18}{75} *100[/tex] which gives us our answer, p, 24%
hope this helped ♡
What percent of 1/4 is 1/5
5%
16%
24%
80%
[tex]\text{Let it be x percent}\\ \\\dfrac 14 \times x\% = \dfrac 15\\\\\\\implies\dfrac 14 \times \dfrac x{100} = \dfrac 15\\ \\\\\implies x = \dfrac{400}{5} = 80\\\\\\\text{Hence the answer is}~ 80\%[/tex]
Two boys, Brady and Quinn, are running a 100 meter race. In the race, Brady beats Quinn by 5 meters.
They decide to race again. To make things fair, in the second race, Brady stands 5 meters behind the
starting line. The two boys run at the same speed as they did in the first racy. Who wins the second race?
Answer:
It states they ran the same speed in the first race so that means only the distance they ran would be different. Thus that means Brady only ran 95 meters instead of 100 meters. If Brady was put 5 meters back that means it will be a tie if they ran at the same speed the entire race.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
It would be a tie. Brady is 5 meters faster then Quinn. So if Brady were to stay behind 5 meters and they ran the same speed as they did before, then it would be a tie.
How do I get the answer??
Answer:
4√10
Step-by-step explanation:
Hello!
Let's first simplify the radical.
We can do this by expanding the radical:
We need to pull out a perfect square factor to expand a radical and simplify it. In 45, we have 9 and 5 multiplied, and 9 is a perfect square.
Let's work with √45:
√45 can be written as √9 * √5 (using the rule √ab = √a * √b)√9 simplifies to 3, so it is 3√5Now we can simplify the operation in the parenthesis by combining like terms:
3√5 + √5√5 + √5 + √5 + √54√5Now using the same rule as above, we can multiply the values:
√2(4√5)4√10Your solution is 4√10
Please solve with explanation
Try this option, all the details are in the attachment. Note the equation a) is performed with green, the equation b) with red line.
With break green line is the cureve y= -x²; with break red line is y=2x².
solve this problem pls don't spam
#3
Did solve that in one of your question
#4
Total spent
10-1/4+25-3/4+16-1/210.25+25.75+16.536+16.5₹52.5PLEASE EXPLAIN
Why is the unit in volume measured with units cubed instead of units squared?
Answer:
It's cubic because volume occupies a three dimensional space. Area is measured in a second unit of length
Step-by-step explanation:
Answer:
Volume is 3 dimensions
Step-by-step explanation:
Cubed is 3 dimensions: length, width, and height - like measuring how much water will fit in a cup. Squared is only 2 dimensions - like when you measure a piece of paper or a floor tile or a piece of fabric.
Which of the following equations has no solution?
1: 3x=5
2: 5x+7=3
3: 4x=9x
4: x=x−2
Answer:
4
Step-by-step explanation:
3x = 5:
x = 1 ⅔
5x + 7 = 3
5x = 3- 7
5x = -4
x = -⅘
4x = 9x
9x - 4x = 0
5x = 0
x = 0 / 5
x = 0
x = x - 2:
x -x = -2
0 = -2?
Answer:
4
Step-by-step explanation:
Its because x=x-2 =-2 subtract x from both sides and you get 0 so theres no solution and you get -2
4 2/3 divided by 1 1/9
Answer:
4.2 or 21/5
Step-by-step explanation:
i used demos
Answer:
4 1/5
[tex]\frac{14 * 9}{3 * 10} = \frac{126}{30}~which~is~also~4\frac{1}{5}[/tex]
enter the correct value in each box to write the equation of the trend line in slope-intercept form
Answer:
y = -3x +15
Step-by-step explanation:
(2,9) (4,3)
slope is -6/2 or -3
use slope intercept form to solve for y-intercept
y = mx + b
9 = (-3)(2) + b
9 = -6 + b
15 = b
y = -3x + 15
Help picture below problem 8
Solution :-
Here, we have been given that lines f and g are parallel. Thus, the angle measuring 135° and ∠2 are vertically opposite angles.
And we know that vertically opposite angles measure same. Thus,
∠2 = 135°
Hope that helps ~~~
solve following problem
Answer:
p²=h²-b²
p² =10²-6²
p² =100-36
p²=64
p=( √8)²
p=8
Let [tex]x[/tex] and [tex]y[/tex] be the length and height, respectively, of the rectangle.
Let the bottom left vertex be the origin (0, 0), and position the triangle so that the bottom leg lies on the horizontal axis in the [tex]x,y[/tex]-plane. The hypotenuse of the triangle then lies on the line through (0, 0) and (6, 8), with slope 8/6 = 4/3. Then for some [tex]x[/tex] between 0 and 6, we have [tex]y = \frac43x[/tex].
This means for some fixed distance [tex]x[/tex] from the origin, the rectangle has length [tex]6-x[/tex] and height [tex]\frac43x[/tex]. Thus the area of the rectangle can be expressed completely in terms of [tex]x[/tex] as
[tex]A(x) = (6-x) \times \dfrac43x = 8x - \dfrac43 x^2[/tex]
Non-calculus method:
Complete the square to get
[tex]8x - \dfrac43 x^2 = -\dfrac43 (-6x + x^2) = 12 - \dfrac43 (9 - 6x + x^2) = 12 - \dfrac43 (x-3)^2[/tex]
which is maximized when the quadratic term vanishes at [tex]x=3[/tex], giving a maximum volume of [tex]\boxed{12\,\mathrm{in}^2}[/tex].
Calculus method:
Differentiate [tex]A(x)[/tex] and find the critical points.
[tex]A'(x) = 8 - \dfrac83 x = 0 \implies x = 3[/tex]
Differentiate again to check the sign of the second derivative at the critical point.
[tex]A''(x) = -\dfrac83 \implies A''(3) = -\dfrac83 < 0[/tex]
which indicates a local maximum at [tex]x=3[/tex]. Hence the maximum area is [tex]A(3) = 12[/tex], as before.
how many part time and full time employees does the company have?
Answer:
there are 36 part time employees and there are 144 full time employees
Step-by-step explanation: multiply 45 by 4
then multiply 180 by 0.2 to get 36 and 180 by 0.8 and get 144
Tim will buy a pair of shoes that cost $120.He received a 35% discount coupon. Luckily his friend Mario gets an additional 15% discount being an employee of the store. If Mario buys the shoes for Tim, how much will Mario pay if the tax is 8%? Round your answer to the nearest centavo
Answer:
$69.60
Step-by-step explanation:
A trough contains a certain amount of sand. After Jamie used it to fill 2.4-kilogram bag, a 650- gram bowl, and a 3-kilogram, 125- gram pail, she realized she had a kilogram of sand left in the trough. How much sand was in the trough at first?Give your answer in grams, using a comma.
Explain how you got your answer
Answer:
7kg 275g
Step-by-step explanation:
hope this helps
Answer:
7kg 275g
Step-by-step explanation:
Add all of them together and then add what's left. Hope this helps! :)
How to be good at math???
Answer:
Step-by-step explanation:
To get good at math is to pay attention to the formulas and quiz yourself with what ever your learning over and over until you get it.
Which number is an irrational number?
A) 3.5
B) √ 36
C) √ 148
D)
37
—
100
Answer:
C) √ 148
Step-by-step explanation:
The difference is
Part B 287
Find the product of the expressions.
Answer:
12
Step-by-step explanation:
70 points and brainliest if the answer is correct
5^4x5^7
A. 125^11
B. 15^11
C. 5^28
D. 5^11
Answer:
Option D
Step-by-step explanation:
If the bases are the same in a multiplication problem, then you can simply add the exponents. (i.e., a² × a⁶ = a²⁺⁶ = a⁸)
[tex]\bullet \rightarrow 5^4\times5^7[/tex]
[tex]\bullet\rightarrow 5^{4 + 7}[/tex]
[tex]\bullet \rightarrow \boxed{5^{11}}[/tex]
Answer: D
Step-by-step explanation:
5^4 x 5^7
You will add the exponent 4 + 7 = 11
You will keep your base 5^11
Shannon has a paper cone filled with water. The cone has a diameter of 8 centimeters and a height of 9 centimeters. Select the containers that could hold all of the water in Shannon's paper cone
In the United States we measure fuel economy in miles per gallon. At the beginning of a trip a car's odometer read 23,450 miles, and the fuel tank was full. At 23,742 miles the fuel tank was refilled with 9.87 gallons of gas. Estimate the number of miles per gallon the car averaged on that portion of the trip.
Answer:
About 30 miles per gallon of gas
Step by step:
First you subtract 23,742 - 23,450
and then you divide it by 9.87 and then you round
A dotted piece of cloth is 4 feet wide and 2 yards long. A plaid piece of cloth is 3 feet wide and 8 feet long. Show how to find the number of 1-foot squares in each cloth by drawing an array and using multiplication.
Answer:
Step-by-step explanation:
1. Change all the units to be the same. 1yd= 3 feet so 2yd x 3ft =6ft
new Dimensions 4x8 and 3x8
2. View images
Brainliest if correct
Answer:
correct answer here
Step-by-step explanation:
Find the smallest side of APQR, given that mZP = 46°, mZR = 97°, and m2Q =37°,
Answer:
|PR|
Step-by-step explanation:
The smallest side is the side that sees the angle with the smallest measure:
If we were to draw a triangle with the given information we can see that the side length with the smallest value is the one that sees angle Q, |PR|
Q13
A man has a flight at 19:15 on Thursday. He must arrive at the airport 2 hours before this time to
check in.
He needs to know what time he should leave home.
He will park his car at the airport car park and it will take 15 minutes to get to the check in counter.
The distance from his house to the airport is 90 miles.
He will drive at an average of 60miles per hour.
Answer: around 6 or 5 o clock
Step-by-step explanation: hope this helps
Given P(E or F) = 0.69, P(E) = 0.49, and P(E and F) = 0.06, what is P(F)?
Answer:
P(F) = 0.26
Step-by-step explanation:
Given:
P(E ∪ F) = 0.69P(E) = 0.49P(E ∩ F) = 0.06Using formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒ P(E ∪ F) = P(E) + P(F) - P(E ∩ F)
⇒ 0.69 = 0.49 + P(F) - 0.06
⇒ 0.69 = 0.43 + P(F)
⇒ P(F) = 0.69 - 0.43
⇒ P(F) = 0.26
help plsssssssssssssssssssssssssssssssssssssssssss
Answer:
g(40 or more)
Step-by-step explanation:
30 represents the median or the 50% mark so it cant be this
60 represents the highest amount of minutes. so this is unlikly
40 represents the hqr or the median between 30 and the max. this means that you now have 50% of 50% or 25%
A manager drew this box-and-whisker plot to represent the ages of the company’s 240 employees. How many employees are younger than 42?
24
48
60
75
Answer:
its 60, need proof?
Step-by-step explanation:
Answer: 60
Step-by-step explanation: I took the test and got it right. Goodluck with the rest!
Arkansas is __________ of Oklahoma?
Answer:
East
Step-by-step explanation:
Arkansas is East of Oklahoma.
Refer to the image below:
Answer: East
Step-by-step explanation: