The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone.
(a) Sketch the roof of the castle tower. Label the known lengths as described and label the unknown length as x.
(b)What is the slant height of the roof?
Answers
Answer:
a) See the attachment (measurements are in meters).
b) x = √(12² + 16²) = √(144 + 256)
= √400 = 20
The slant height of the roof is 20
meters.
Related Questions
Can someone help me with this question me and my friends are fighting over it?
13.The letters R, W, A, and E are arranged in a random order. What is the probability that the arrangement forms the
words WEAR or WARE?
A. 1/2
B. 1/6
C.1/12
d.1/24
Answers
Because if you rearrange all the letters so that W is is the beginning you get 6 different combinations.
Then I multiplied those 6 combinations by 4 because there are 4 letters.
Once I multiplied I got 2/24 because there are 24 possibilities in total, and we are looking for the probability of getting those 2 combinations.
I simplified 2/24 to its lowest form and I got 2/24 = 1/12.
So the correct answer is C.1/12, hope this helps!
- Alyssa T.
Julie works for 48 hours per week for 12 weeks during the summer, making $5000. If she works for 48 weeks during the school year at the same rate of pay and needs to make another $5000, how many hours per week must she work?
Answers
Since she only needs to make the same amount of money, if she works for 4 times as many weeks, she can work 4 times fewer hours per week, meaning she can work 1/4*48= 12 hours per week.
During the academic year, Julie needs to put in about 12 hours per week of work to earn an additional $5,000 at the same rate of compensation.
To find out how many hours per week Julie must work during the school year to make another $5000,
set up a proportion using the information we already have.
Let's use the ratio of her earnings to the number of hours worked to create the proportion.
During the summer:
Earnings = $5000
Hours worked = 48 hours/week
Weeks worked = 12 weeks
Summer rate of pay = Earnings / (Hours worked × Weeks worked)
Summer rate of pay = $5000 / (48 hours/week × 12 weeks)
Summer rate of pay = $5000 / 576 hours
Summer rate of pay ≈ $8.68 per hour (rounded to two decimal places)
Now, during the school year, she needs to make another $5000.
So, set up the proportion:
School year earnings = $5000
School year rate of pay = $8.68 per hour (same as the summer rate)
School year rate of pay = School year earnings / (Hours worked × Weeks worked)
$8.68 per hour = $5000 / (Hours worked × 48 weeks)
Now, solve for the number of hours worked per week during the school year:
Hours worked × 48 weeks = $5000 / $8.68 per hour
Hours worked × 48 weeks = 576.036
Hours worked ≈ 12 hours per week (rounded to the nearest whole number)
Therefore, Julie must work approximately 12 hours per week during the school year to make another $5000 at the same rate of pay.
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Approximate the value of 5 pie
Answers
We can see that pi is a little bit more than 3. Multiplying this times 5 gives a lil bit more than 15.
D
A Ford is traveling 20 mph slower than a Buick. The Buick is traveling at a rate of 65 mph. Let F = the the speed of the Ford. Which formula below would correctly calculate the speed of the Ford?
Answers
Since the Ford is 20 mph slower than the Buick, all you have to do is subtract 20 from the speed of the Buick. We know the speed of the Buick, it is 65.
Therefore, the speed of the Buick is 65 - 20 or 45 mph.
Use benchmarks to choose the customary unit you would use to measure each height of a computer with a fit length of a semi truck the amount of liquid a bathtub holds.
Answers
For the height of a computer, it would be best to use inches. Most screens would be about 10 -15 inches.
For the length of a semi-truck, we could use feet or yards. Inches would be too small and miles would be way too long.
For the amount of liquid in a bathtub, we should use gallons.
Final answer:
Choose the best units of measurement for a variety of items based on benchmarks and size considerations.
Explanation:
When considering the size of a bathtub, the best unit for measuring capacity would be liters.
To choose the best unit of measurement for each item:
The volume of a water balloon: Milliliters
The length of a basketball court: Yards
The weight of an apple: Ounces or grams
The volume of a milk carton: Cubic centimeters
For the height of a light switch, the appropriate unit would be inches.
For the width of a refrigerator, the appropriate unit would be feet.
List three values that make this inequality true 3n≤18
___,___,___
Answers
18/3=6
N is less than or equal to 6. So any number less than 6 would work.
Although there’s infinite values that could make this true, I will list only 3.
6,0,-6
Since it can be equal to, 6 would work. For 0 and -6, they’re both less than 6 so they would work.
The three values that make this inequality true 3n ≤ 18 are 6, 5, and 4.
We have,
To find three values that make the inequality 3n ≤ 18 true, we can simply substitute different values of n and check if the resulting statement is true or false.
Here are three values that satisfy the inequality:
n = 6:
3n = 3(6) = 18, which is equal to the upper bound of the inequality. Therefore, 3n ≤ 18 is true for n = 6.
n = 5:
3n = 3(5) = 15, which is less than 18. Therefore, 3n ≤ 18 is true for n = 5.
n = 4:
3n = 3(4) = 12, which is less than 18. Therefore, 3n ≤ 18 is true for n = 4.
Note that there are infinitely many values of n that satisfy this inequality, but these three values are enough to demonstrate that the inequality is true for at least three specific values of n.
Thus,
The three values that make this inequality true 3n ≤ 18 are 6, 5, and 4.
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Which of the following Has a value of 8(4)
A) 4,096
B)32
C)83
D)512
Answers
8(4) means to multiply 8 and 4. 8 x 4 = 32
8(4) = 8 x 4
8 x 4 = 32
Suppose a bay window is a perfect semicircle with an area of 4.5 square feet. If the architect wants to use a scale of 0.5 inch = 1 ft on the floor plan, what is the radius of the bay window on the floor plan?
A) 0.85 inches
B) 1.7 inches
C) 3 inches
D) 3.4 inches
Answers
The answer is A) .85 inches
Step-by-step explanation:
A =
1 /2 πr2 4.5 = 1 2 πr2 1.6926 = r
thus, 0.50 in
1 ft = x in 1.6926 ft x = 0.8463
Final answer:
To find the radius of the bay window on the floor plan, calculate the radius of the actual bay window first, apply the scale factor, resulting in a radius of 3.4 inches that is option D is correct.
Explanation:
To find the radius of the bay window on the floor plan, you need to calculate the radius of the actual bay window first. Given the area of the bay window as 4.5 square feet in a semicircle shape, you can use the formula for the area of a semicircle, A = 1/2 * π * r².
Once you find the actual radius, you can then convert it to the scale of 0.5 inch = 1 ft to determine the radius on the floor plan. Remember, the scale factor is the ratio of a length on the drawing to the actual length it represents.
After the calculation, the radius of the bay window on the floor plan is 3.4 inches (Option D).
If your starting salary is $50,000 and you receive a 4% increase at the end of every year, what is the total amount, in dollars, you will earn over the first 16 years that you work?
Answers
50000(1 + 1.04 + 1.04^2 + 1.04^3 + .... + 1.04^15) = 50000 * (1.04^16 - 1) / (1.04 - 1) = 1,091,226.56
Final year's salary = 90047.17
86,583.82 * 1.04 = 90047.17
There are only 15 table when there should be 16.
a_N = 50000(1.04)^15 = 90047.17
And if we add 90047.17 to the previous total of 1001179.38 we get
$1,091,226.55
Answer:
The correct answer is $1091227
Douglas is placing strings of lights around the edge of a circular patio with a diameter of 7.5 meters. The lights are in lengths of 1.45 meters.
What is the best approximation for how many strings of lights Douglas needs?
Use 3.14 to approximate for π .
A. 5
B.11
C.17
D.122
Answers
Answer: C: 17
Step-by-step explanation:
The solution to 5.2x = 14.04 is x = ___.
0.37
2.7
8.84
73.01
Answers
x = 14.04 / 5.2
x = 2.7
answer
2.7
Consider U = {x|x is a positive integer greater than 1}.
Which is an empty set?
{x|x ∈ U and 1/2 x is prime}
{x|x ∈ U and 2x is prime}
{x|x ∈ U and 1/2 can be written as a fraction}
{x|x ∈ U and 2x can be written as a fraction}
Answers
Justification:
U = {x|x is a positive integer greater than 1} = {2, 3, 4, 5, 6, ...}
1) {x|x ∈ U and (1/2) x is prime}
Take x = 4 => (1/2) 4 = 4 / 2 = 2 = prime, so this is not empty.
{x|x ∈ U and 2x is prime}
2) 2x = {4, 6, 8, 10, 12, } so none of them is prime, hence this is an empty set.
3) {x|x ∈ U and (1/2) x can be written as a fraction}
Take any x that is odd. For example x = 3
=> (1/2)x = (1/2)3 = 3/2 which is a fraction, so this is not an empty set.
2) {x|x ∈ U and 2x can be written as a fraction}
Take any value of x, for example x = 7 => 2 = 14, and 14 = 28 / 2 so this is not an empty set.
Answer:
{x|x ∈ U and 2x is prime}
Step-by-step explanation:
got 100%
here is a sketch of y=x^2 + bx + c. the curve intersects the x-axis at (2,0) and point P. the y-axis at (0,14) work out the x-coordinate of the turning point of the graph
Answers
Finding the x-coordinate of the turning point of a quadratic equation requires knowledge of its coefficients. Given a function y = x^2 + bx + c, and points (2,0) and (0,14), we need further calculations or information to precisely identify b to use the vertex formula -b/2a effectively.
Explanation:To find the x-coordinate of the turning point of the graph of the quadratic equation y = x^2 + bx + c, we can use the fact that the vertex of a parabola given by the general form ax^2 + bx + c is at x = -b/2a. Since the quadratic intersects the x-axis at (2,0), we can plug x = 2 into the equation to find one relation between b and c.
Another given point is (0,14), which when plugged in gives c = 14. To find b, we need more information from the question or an understanding of quadratic functions more deeply. However, without b, we can use the vertex formula derivatively, knowing that a in our equation is 1 (since the coefficient of x^2 is 1).
We also know that for any quadratic function, the x-coordinate of the vertex (turning point) can be found using -b/2a. Without the exact value of b, we cannot find the exact x-coordinate directly from the information given.
However, the general methodology would involve using the known points to first find equation coefficients and then apply the vertex formula. This highlights the importance of understanding quadratic functions and their graphical representations, such as vertices and intercepts, to solve these types of problems efficiently.
The x-coordinate of the turning point of the graph is 4.5
How to determine the x-coordinate of the turning point of the graph
From the question, we have the following parameters that can be used in our computation:
[tex]y = x^2 + bx + c[/tex]
It intersects the y-axis at (0, 14)
This means that
[tex]0^2 + b(0) + c = 14[/tex]
c = 14
So, we have
[tex]y = x^2 + bx + 14[/tex]
It intersects the x-axis at (2, 0)
So, we have
[tex]2^2 + 2b + 14 = 0[/tex]
4 + 2b + 14 = 0
2b = -18
b = -9
So, we have
[tex]y = x^2 - 9x + 14[/tex]
The x-coordinate of the turning point of the graph is then calculated as
x = -b/2a
So, we have
x = 9/2
x = 4.5
Hence, the x-coordinate of the turning point of the graph is 4.5
A fair charged $2.50 admission for adults and a dollar for children. The receipts for 1 day were $1951 on 1300 paid admissions. How many adults attended the fair that day?
Answers
y = children
x + y = 1300
2.5x + y = 1951 Subtract these two equations.
-1.5x = - 651
x = -651/-1.5
x = 434 Adults
y = 1300 - x
y = 1300 - 434
y = 866 children
1300 x 1 = $1300
Extra collection:
1951 - 1300 = $651
Difference in price = $2.50 - $1.00 = $1.50
$651 ÷ 1.5 = 434 adults
1300 - 434 = 866 children
Ans: 434 adults and 866 children
A figure has a vertex at the point (-4, -6) the figure is dilated with the center at the Irgun with a scale factor of 5
Answers
Jane is thinking of a number between -10 and 10. if you multiply Jane's number by -2, then subtract 2, the result is greater than 6. What is Jane's number
Answers
what is the area of square HIJK
Answers
hope this helps:)
10y-12=4
Help??? Confused??? Trying to make this twenty letters long lol
Answers
10y-12=4
10y=12+4
10y=16
y=16/10=8/5=1 3/5 or 1.6
HELP!!! SIN/COS
What is the value of x?
sin49 degrees = cos x
Answers
[tex] \sin(45 \: degrees) = \: \cos(x) [/tex]
[tex] \frac{ \sin(45 \: degrees) }{cos} = \: x[/tex]
[tex] \frac{ sin}{cos } = tan[/tex]
[tex]therefore \: \: \: \tan(45 \: degrees) = x[/tex]
[tex]but \: \: \: \tan(45 \: degrees) = 1 [/tex]
[tex]therefore \: \: \: x = 1[/tex]
[tex]hope \: this \: helps[/tex]
Answer:
cos 41°
Step-by-step explanation:
this is the correct answer, not the one above.
if entered on the calculator (texas instruments TI-30X2S)
sin (49)= 0.75470958
2nd → cos → 2nd → (-)
which would look like this→ cos-1(0.75470958)
answer= cos 41
4x7/8 will be —————7/8 is it greater than or equal or less than
Answers
4 x 7/8 > 7/8 because 4 x 7/8 = 3 1/2 which is larger than 7/8.
In a school library, 52% of the books are paperback. If there are 2,658 books in the library, how many of them are nit paperback to the nearest whole number?
Answers
48/100 x 2,658
= 1275 books are not paperbacks.
Please help quick if you know the answer
Answers
C. 8,240,000
Brainliest pts
De una botella de 4 L se utilizaron 2 4/5. ¿Cuánto aceite queda?
Answers
A Gardener has 560 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river so it does not need any fencing. What dimensions would guarantee that The Gardener has the greatest possible area
Answers
To maximize area and minimize perimeter, you make the figure as close to equilateral as possible. 560/3 = 186 2/3. We would rather use whole number dimensions, so we would have 186 for one side. 560-186 = 374. 374/2 = 187 for the other dimension.
Answer:
Each side of the garden should be 186.67 feet
Step-by-step explanation:
We know that the biggest area of a rectangular prism is when it closer to a square, and we know that a square is a special kind of rectangle with all equal sides, so we want all the sides to be equal.
To do this we know that the Gardener has 560 feet of fencing and he is only going to fence 3 sides because the other side is bordered by a river.
So we have to divide the fencing by the sides to have equal sides:
560 feet / 3 sides = 186.67 feet per side.
So the garden will be a square with each side of 186.67 feet, and the area will be:
186.67 * 186.67 = 34,845.70 square feet.
Please find x: 3x − 1 = 2x − 1
Answers
3x - 1 = 2x - 1
Start by subtracting 2x on both sides
3x - 1 - 2x = 2x - 1 - 2x
x - 1 = - 1
Then add 1 on both sides
x - 1 + 1 = -1 + 1
x = 0
I hope this helps!
As always, it is my pleasure to help students like you.
======================================================================
SOLVING.....
3x − 1 = 2x − 1
Subtract 2x from each side
3x − 1 − 2x = 2x − 1 − 2x
x − 1 = −1
Add 1 to each side
x − 1 + 1 = −1 + 1
x = 0
====================================================================
CHECKING.....
Substitute 0 for x in 3x − 1 = 2x − 1
3(0) − 1 = 2(0) − 1
0 - 1 = 0 - 1
-1 = -1
This is true so x does equal 0
A painting crew reported that a job is 3/5 completed. what fraction of the job remains to be done.
Answers
The required fraction of the job that remains to be done is 2x / 5.
Given that,
A painting crew reported that a job is 3/5 completed. what fraction of the job remains to be done is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Let the whole fraction of the job be x.
A painting crew reported that a job is 3/5 completed = 3/5x
The job remains to be done = x - 3/5x
= 2x / 5
Thus, the required fraction of the job that remains to be done is 2x / 5.
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The formula for electrical power is p=iv Which is the equivalent equation solved for i?
Answers
we are given
[tex] p=v*i [/tex]
Since, we have to solve for i
so, we will isolate i on anyone side
we can divide both sides by v
[tex] \frac{p}{v}= \frac{vi}{v} [/tex]
[tex] \frac{p}{v}= i [/tex]
[tex] i=\frac{p}{v} [/tex]..............Answer
Answer:
p/v=I
Step-by-step explanation:
hope i helped. :} its also on edge
Sergei says that 10% of a number will always be less than 20% of any other number.
Answers
This isn't true, because if you were to take 10% of, let's say, 100 (which is 10), and if you were to take 20% of 20 (which is 5), 5 is still smaller than 10.
Hope this helps!
A. How many phone plans have national long distance B. How many customized phone plans include 100 minutes per month talking time and paging capabilities?
Answers
A right triangle had one leg of length 84 units. The hypotenuse is 91 units long. What is the length of the other leg?
HELP ASAP FOR BRAINLIEST (:
A. 49 Units
B. ^(178 units
C. 7 Units
D. 35 Units