The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft. l = ft

Answers

Answer 1

The slant height (l) of this cone is equal to 18.33 feet.

Given the following data:

Surface area of cone = 500π [tex]ft^2[/tex].Radius of cone = 15 ft.

To calculate the slant height (l) of this cone:

How to calculate surface area.

Mathematically, the surface area (SA) of a cone is given by this formula:

[tex]SA = \pi r(l + r)[/tex]

Where:

l is the slant height.r is the radius.

Substituting the given parameters into the formula, we have;

[tex]500 \pi = \pi \times 15(l + 15)\\\\500=15(l + 15)\\\\500=15l+225\\\\15l=500-225\\\\15l=275\\\\l=\frac{275}{15}[/tex]

Slant height, l = 18.33 feet.

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Answer 2
Final answer:

The slant height of a cone with a surface area of 500π square feet and a radius of 15 feet is 275 feet.

Explanation:

The question asks for the slant height of a cone, given that the surface area (S) is 500π square feet and the radius (r) is 15 feet. No explicit formula for the slant height is provided.
We know the formula for the surface area of a cone is S = πrl + πr², where r is the radius, l is the slant height, and π is a constant (approximately 3.14).
By rearranging this equation, subtracting the base area from the surface area and then dividing by πr, we can solve for l: l = (S - πr²)/πr.
Plugging in the provided numbers: l = (500π - π*(15 ft)²)/(π * 15 ft). Simplifying this equation gives: l = (500 - 225) ft = 275 ft. Therefore, the slant height of the cone is 275 feet.

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Related Questions

Max has a monthly salary of $1,100 and also earns 7.5% commission on his sales. If Max had $43,000 in sales last month, what were his total earnings for the month? a. $3,225 b. $4,050 c. $4,325 d. $5,150

Answers

If he makes a base salary of 1100$, then Max's total salary is 1100+<some number>. That <some number> is the amount he makes in commissions, which is 7.5% (or 0.075 by moving the decimal 2 spots to the left). Multiplying 43000 by 0.075 to get his commision money, we get 3225. Remember that we still have to add 1100 to it (as that's his base salary), so we end up with
1100+3225=4325

An equation is formed when two equal expressions. Max's total earnings for the given month are $4,325. The correct option is C.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Max has a monthly salary of $1,100 and also earns a 7.5% commission on his sales. Therefore, the equation that can represent Max's monthly salary for any month is,

y = $1,100 + $(0.075x)

where y is the month's salary and x is the number of sales he made.

Given in the last month Max had $43,000 in sales last month. Therefore, Max's total salary for the given month is,

Max Salary = $1,100 + $(0.075x)

= $1,100 + $(0.075 × 43,000)

= $1,100 + $3,225

= $4,325

Hence, Max's total earnings for the given month are $4,325.

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Choose the answer. 3. (1 pt) Suzanne cut a ribbon into 9 equal pieces. She sewed 5 pieces onto her quilt. Which number line shows a dot representing the fraction of the ribbon that was sewn onto the quilt? A. B. C. D.

Answers

Given that Sussan sew 5 out of 9 cut out ribbins unto her quilt, the number line that shows a dot representing the fraction of the ribbon that was sewn onto the quilt is given by:

A number line with 9 partitions with a dot marked on the 5th partition.

Kyle saves 8% of his income for a new car this year his salary was $2000 less than in the previous year and he saved $3000 what was his salary in the previous year

Answers

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

 

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Answer:

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

 

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Step-by-step explanation:

Richard estimates that he can apply fertilizer to 4,485 square feet of grass in 3/4 of an hour. How many square feet of grass can Richard fertilize per hour?

Answers

We know that Richard can apply fertilizer to 4485 square feet = 3/4 hour

To solve this problem, one approach is to find 1/4 then multiply by 4 to get the whole 4/4 or 1 hour.

So the solution would be:

4485/3=1495
Then multiply this by 4.


1495 multiplied by 4 is equal to 5980 square feet.

So Richard can apply fertilizer to 5980 square feet in 1 hour.

First find f+g, f-g, f-g and f\g. Then determine the domain for each function f(x)=3×+7,g(×)=×+9 (f+g)(×)=

Answers

I'll do f+g, you try the others on your own and comment if you need help with them! For f+g, you're just going to add the two functions together:
[tex]f(x)=3x+7[/tex]
[tex]g(x)=x+9[/tex]
[tex](f+g)(x)=(3x+7)+(x+9)=4x+16[/tex]

Final answer:

To find (f+g)(x), add the functions f(x) and g(x), substituting x into both functions and then adding the results together. The result is (f+g)(x) = 4x + 16.

Explanation:

To find (f+g)(x), we need to add the two functions f(x) and g(x). f(x) = 3x + 7 and g(x) = x + 9. To determine (f+g)(x), we substitute x into both f(x) and g(x) and then add the results together.

So, (f+g)(x) = f(x) + g(x) = (3x + 7) + (x + 9) = 4x + 16.

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Find the simple interest. Principal ​$2300 rate 20​% time 27 months The interest is ​$ ?

Answers

[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$2300\\ r=rate\to 20\%\to \frac{20}{100}\to &0.20\\ t=years\to \frac{27}{12}\to &\frac{9}{4} \end{cases} \\\\\\ I=2300\cdot 0.2\cdot \cfrac{9}{4}[/tex]

the value of the 7 in 507,264 is 10 times the value of the 7 in which number?

Answers

The value of seven is in the thousands place and is 10 time the number seven if it were at the hundreds place, which is where 2 is.

7000=10 x 700
7000=7000

Answer:

The value of the 7 in 507,264 is 10 times the value of the 7 in number 2

Step-by-step explanation:

Given Number : 507,264

To find : Number in which the value of the 7 in 507,264 is 10 times the value of the 7 .

Starting from the left ,

4 is in ones place

6 is in tens place

2 is in hundreds place

7 is in thousands place

0 is in ten thousands place

5 is in lakhs place

Here, 7 is in thousands place

7000 = 10 x 700

2 is in hundreds place

200 = 2 × 100

Therefore, the value of the 7 in 507,264 is 10 times the value of the 7 in  number 2 .

Carol, Ann, and Liz each bought a toy fish. Carol’s fish is 9 inches longer than Ann’s fish. Liz’a fish is 9 inches longer than twice the length of Ann’s fish. Ann’s fish is 17 inches long. Find the length of each toy fish.

Answers

Ann= 17
Carol= 17+9
Liz= (17x2) +9

Ann- 17 in.
Carol-26 in.
Liz- 34+ 9= 43 in.

suppose an isosceles triangle abc has a=pi/6 and b=c=5. what is the length of a^2?

Answers

5^2(2-sqrt3) is the right answer

A data firm records a large amount of data. historically, 1.0% of the pages of data recorded by the firm contain errors. if 200 pages of data are randomly selected?
a. what is the probability that six or more pages contain errors?
b. what is the probability that more than 10 pages contain errors?
c. what is the probability that none of the pages contain errors?
d. what is the probability that fewer than five pages contain errors?

Answers

a) P(X >= 6) = 0.0160

b) P(X > 10) ≈ 6.88 x 10^-6

c) P(X = 0) ≈ 0.1339

d) P(X < 5) ≈ 0.9482

a. Probability of six or more pages with errors:

This is the sum of probabilities for 6, 7, 8, ..., 200 errors:

P(X >= 6) = 1 - [P(X < 6)] = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

Using a calculator or statistical software, we can find these individual probabilities and sum them up. Alternatively, we can use binomial distribution tables or functions available in programming languages.

P(X >= 6) ≈ 0.0160

b. Probability of more than 10 pages with errors:

Similar to part (a), but calculating from 11 errors onwards:

P(X > 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=10)]

P(X > 10) ≈ 6.88 x 10^-6 (very small probability)

c. Probability of none of the pages containing errors:

P(X = 0) = (0.99)^200 ≈ 0.1339

d. Probability of fewer than five pages containing errors:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

P(X < 5) ≈ 0.9482

Prove the quotient of any two rational numbers is a rational number

Answers

That is not possible, a quotient or any equation for that fact can only be rational when it lacks repeating {x} values. Take for instance this 2x11x2^2+(1+10)=

In the equation the {x} values would be most likely described as {2}. Since 2 was the quotient that was being repeating hence that equation not being rational. Hope this helps!



The quotient of any two rational numbers is always a rational number. This can be proved by expressing the division as multiplication by the reciprocal and demonstrating that the result is a rational number. Therefore, the property of being rational is preserved under division.

Let's define rational numbers first. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. Mathematically, if a and b are integers and b ≠ 0, then r = a/b is a rational number.

Consider two rational numbers r1 and r2.
Suppose r1 = a/b and r2 = c/d, where a, b, c, and d are integers, and b ≠ 0 and d ≠ 0.To find the quotient q of these two rational numbers, we compute r1 ÷ r2:
q = (a/b) ÷ (c/d)This division can be written as multiplication by the reciprocal:
q = (a/b) × (d/c) = (a × d) / (b × c)Since the product of two integers is also an integer, a × d and b × c are integers.We can write the quotient as:
q = (a × d) / (b × c), where (b × c) ≠ 0 because neither b nor c is zero.Therefore, q is the quotient of two integers where the denominator is not zero, which means q is a rational number.

Thus, we have proved that the quotient of any two rational numbers is a rational number.

A car is traveling at a rate of 40 miles per hour. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.

Answers

1 mile = 1.6 kilometers

 multiply 40 mph by 1.6 = 64

car's rate = 64 kilometers per hour


multiply kilometers per hour by 4 = 256

 car will travel 256 kilometers in 4 hours

What he said. Multiply 40 by the numbers

Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 3 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)

Answers

Calculate the z-score of the given by the equation,

   z-score = (x - m)/s

where x is the data point, m is the mean, and s is the standard deviation. Substituting the known values,

    z-score = (11 - 8)/ 3 = 1

This translates to 0.84. 

ANSWER: 0.84. 

A protective cover for a wireless tablet has a height of 8 inches and base of 7 inches. What is the area of the cover?

Answers

So to find the answer of the area, you have to multiply 7 and 8 which would equal to 56.

Answer: The area of the cover = 56 square inches.

Step-by-step explanation:

We know that the shape of a tablet is rectangle.

Thus to calculate the area of the protective cover we apply the formula to calculate area of rectangle.

The area of rectangle is given by :-

[tex]\text{Area}=\text{Length*width}\\\\\Rightarrow\text{Area}=8\times7\\\\\Rightarrow\text{Area}=56\text{ inches}^2[/tex]

Therefore, the area of the protective cover is 56 square inches.

George spent 70 % of his saving to buy a camera. The camera cost $574 . How much did he originally have in savings?

Answers

574 : 70 * 100 =
820 $

the difference of twice a number and 3

Answers

2n/3
the difference means divide 2 times(multiply)a number 

If the product of two numbers is 14 and one of the numbers is 3 ½ times the other, then what is the sum of the two numbers?

Answers

x=number1 and y=number2
product of the two numbers is 14 which translates to
xy=14
either x or y are 3.5 times big as the other one
so 3.5x=y
substituting in xy=14
x(3.5x)=14
[tex]3.5 {x}^{2} = 14[/tex]
[tex] {x}^{2} = \frac{14}{3.5} = 4 [/tex]
then x must be equal to 2 or -2
x+y=
by substituting
x+3.5x=
if x =2 then 2+7=9 or if x=-2 then -2-7=-9

Find the limit, if it exists. (if an answer does not exist, enter dne.) lim (x, y, z)→(0, 0, 0) xy + 3yz2 + 4xz2 x2 + y2 + z4

Answers

Consider what happens along the line through the origin with [tex]x=y=z[/tex]. The limit reduces to

[tex]\displaystyle\lim_{(x,y,z)\to(0,0,0)}\frac{xy+3yz^2+4xz^2}{x^2+y^2+z^4}=\lim_{x\to0}\frac{x^2+7x^3}{2x^2+x^4}=\lim_{x\to0}\frac{1+7x}{2+x^2}[/tex]

but this limit does not exist.
Final answer:

The question is about calculus and requires finding the limit of a multivariable function as it approaches a particular point. Evaluating such limits can be very complex and typically requires application of theorems and techniques from multivariable calculus. In this specific case evaluation of limit goes beyond the scope of this platform.

Explanation:

The subject of this question is mathematics, specifically it is about

Calculus

and more specifically about finding limits of functions of multiple variables. In this case, the function given is f(x, y, z) =  (xy + 3yz2 + 4xz2) / (x2 + y2 + z4). To determine the limit of the function (if it exists) as (x, y, z) approaches (0, 0, 0), we would use substitution method. When we substitute x=0, y=0, and z=0 to the function, we get undefined format (0/0) which means we need to apply the L'Hopital's rule. But application of this rule to multivariable function involves evaluating multiple partial derivatives of function which is beyond the scope of this platform. Hence, a full evaluation of the limit of this particular function requires use of theorems and techniques from

multivariable calculus

.

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Joshua earns $8.20 per hour when he works at the college library. How much money does he earn by working at the library for $4.5 hours.



PLEASE HELP!!!

Answers

8.20 x 4.5   36.9

he earns $36.90
36.9 is the answer that should be it

What is m∠PTS?
Enter your answer in the box.


Answers

Angles PTS and RTQ are vertical angles, so they are congruent.
Their measures are equal.

11(y - 10) = 4y - 5

11y - 110 = 4y - 5

7y = 105

y = 15

m<PTS = 11(y - 10) = 11(15 - 10) = 11(5) = 55

m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°.

What is an angle?

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

Angle is shown by the sign

Given the line segments, PQ and SR is intersecting at T

Thus m∠PTS and m∠RTQ will be vertically opposite angles

m∠PTS = m∠RTQ

Given that,

m∠PTS = 11(y - 10)

m∠RTQ  = 4y - 5

11(y - 10) = 4y - 5

11y - 110 = 4y - 5

11y - 4y = -5 + 110

7y = 105

y = 15

Therefore m∠PTS = 11(15 - 10)

m∠PTS = 55°

Hence "m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°".

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Find two consecutive odd integers such that their product is 71 more than 3 times their sum.

Answers

Let's put this in terms of a system of equations. Let's call the numbers x and y, with x being the larger integer and y the smaller one. Since they are consecutive odd integers, we know that:
x = y + 2
The constraint is:
xy= 3(x+y) + 71         Simplify
xy = 3x + 3y + 71       Plug in (y+2) for x:
(y + 2) y = 3(y + 2) + 3y + 71         Simplify
y² + 2y = 3y + 6 + 3y + 71              Subtract 6y from  both sides, add 71+6
y² -4y = 77
y² - 4y - 77 = 0
Factor:
(y - 11) (y+7) = 0
y = 11 or y=-7

When y = 11, x = 13, since x = y+2
Plug in to make sure:
xy = 3(x+y) + 71
11*13 = 3 (11 + 13) + 71
143 = 3 (24) + 71
143 = 72 + 71
143 = 143               
Our values work! 
Answer: 11, 13

Can u simplify and convert these please and thank you

Answers

1/13 = 0.0769 = 7.7%

9/26 = 0.346 = 34.6%

5/26 = 0.192 = 19.2%

3/13=.23= 23%
1/13=.08=8%
9/26=.35=35%
5/26=.19=19%

Mrs blanda truck holds 19.7 gallons of gas she used 4 full tanks of gas last month and paid $3 for each gallon how much did mrs blanka spend on gas last month

Answers

multiply 19.7 x 4 for total gallons

19.7 * 4 = 78.8 total gallons

 multiply that by price:

78.8 * $3 = $236.40 total price

Final answer:

Mrs. Blanka spent $236.4 on gas last month by filling up her truck's 19.7-gallon tank 4 times at a price of $3 per gallon.

Explanation:

To calculate how much Mrs. Blanka spent on gas last month, we need to consider the amount of gas her truck holds, the number of times she filled up her tank, and the price per gallon of gas. Mrs. Blanka's truck holds 19.7 gallons of gas, and she used 4 full tanks of gas last month. Given the price of gas was $3 per gallon, the calculation would be as follows:

First, find the total gallons of gas used: 19.7 gallons/tank × 4 tanks = 78.8 gallons.Next, calculate the total cost: 78.8 gallons × $3/gallon = $236.4.

Therefore, Mrs. Blanka spent $236.4 on gas last month.

A group of friends are going to see the newest action movie. The price of a ticket is $6.25. As a group, they spent $12 on refreshments. If they spent a total of $30.75 on tickets and refreshments, how many people went to the movies? Which equation represents the scenario?

Answers

Answer:

Which equation represents the scenario?

✔ 6.25x + 12 = 30.75

How many people went to the movies?

✔ 3

Step-by-step explanation:

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The price of a ticket = $6.25

As a group, they spend $12 on refreshments.

Total spent money = $30.75

Now,

Let number of people go to the movie = x

Then, Total price spent on ticket = $6.25x

And, As a group, they spend $12 on refreshments.

So, Total spent money is equal to $30.75, as;

$6.25x + $12 = $30.75

This equation represents the scenario.

Now, Solve the equation for number of people as;

$6.25x + $12 = $30.75

Subtract 12 both side,

6.25x + 12 - 12 = 30.75 - 12

6.25x = 18.75

Divide by 6.25,

x = 3

Thus, There are 3 peoples go to the movie.

Therefore,

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

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Use place value to find the product 3x600=3x

Answers

x = 600 because 3x600 = 1800 meaning x needs to be 1800 and 3 x 600 is 1800 

Four friends split equally a lunch bill of 36.96 plus 20% tip. How much did each person pay

Answers

Let P = how much each person paid.

P = [(36.96)(0.20) + 36.96]/4

Solve for P to find your answer.

The basic recipe for split pea soup serves 8 people. Find the amount of each ingredient needed to serve 32 people.

Answers

[tex]\bf \begin{array}{ccll} \stackrel{basic}{recipe}&people\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&8\\ r&32 \end{array}\implies \cfrac{1}{r}=\cfrac{8}{32}\implies \cfrac{1\cdot 32}{8}=r[/tex]

so, 4 time as much the recipe, or 4 times as much of each ingredient.

Round 354,738 to the nearest thousand?

Answers

your answer is 400,000.

Hope this helps!

354,738 rounded to the nearest thousand is 355,000.

What is a place value?

In Mathematics and Euclidean Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

TenthsHundredthsThousandthsUnitTensHundredsThousands.

The number in the thousand place in the number 354,738 is 7 and it is greater than or equal to 5. This ultimately implies that, we would round up the number 4 to 5.

354,738 ≈ 355,000.

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You walk north for 2.5 miles. then you walk east a distance of 3.0 miles. how many miles from the starting point are you?

Answers

All you do is add 3.0 and 2.5
This would give u 5.5

Correct me if i'm wrong, but i hope it helps

Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of jonah's freinds pick the same amount as Jonah, how many apples do Jonah and his friemds pick in all?

Answers

5x15= 75 4x15= 60 
75 + 60 = 135
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