Question 2
Find the volume.

Answer:

I. Radius, r = 2.90 cm

II. Height, h = 4.10 cm

Step-by-step explanation:

Given the following data;

Volume of cone = 24 cm³

To find the height and radius of the cup that will use the smallest amount of paper;

Mathematically, the volume of a cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]  ......equation 1

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the formula, we have;

[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]

Multiplying both sides by 3, we have;

[tex] 108 = \pi r^{2}h[/tex]

Making radius, r the subject of formula, we have;

[tex] r^{2} = \frac {108}{ \pi h} [/tex]

Taking the square root of both sides, we have;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

Mathematically, the lateral surface area of a cone is given by the formula;

[tex] LSA = \pi rl [/tex]  ......equation 2

Where;

r is the radius of a cone

l is the slant height of a cone.

To find the slant height, we would apply the Pythagorean' theorem;

[tex] l = \sqrt {r^{2} + h^{2}} [/tex]

Substituting r into the above equation, we have;

[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Substituting the values of r and l into eqn 2, we have;

[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Simplifying further, we have;

[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]

[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]

Next, to find the value of h, we differentiate the above mathematical equation with respect to h;

[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]

Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;

[tex] \frac {dS}{dh} = 0 [/tex]

[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]

Rearranging the equation, we have;

[tex] \pi = \frac {216}{h^{3}} [/tex]

We know that π = 3.142

[tex] 3.142 = \frac {216}{h^{3}} [/tex]

Cross-multiplying, we have;

[tex] 3.142h^{3} = 216 [/tex]

[tex] h^{3} = \frac {216}{3.142} [/tex]

[tex] h^{3} = 68.75 [/tex]

Taking the cube root of both sides, we have;

Height, h = 4.10 cm

Lastly, we find the value of r;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]

[tex] r = \sqrt { \frac {108}{12.88}} [/tex]

[tex] r = \sqrt {8.39} [/tex]

Radius, r = 2.90 cm

The height and radius of the cup that will use the smallest amount of paper is;

Radius = 2.52 cm

Radius = 2.52 cmHeight = 3.58 cm

Let us first state some relevant formulas;

Volume of a cone is;

V = ⅓πr²h

Surface area of a cone is;

S = πrL

Where L is Slant height and has a formula;

L = √(h² + r²)

We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³

24 = ⅓πr²h

πr²h = 72

r = √(72/πh)

Putting √(72/πh) for r in the Slant height equation gives;

L = √(h² + (72/πh))

Thus;

S = π × √(72/πh) × √(h² + (72/πh))

Differentiating with respect to h gives;

dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)

At dS/dh = 0,we will have;

(π - 144/h³) = 0

Thus;

h³ = 144/π

h = 3.58 cm

Thus, from r = √(72/πh);

r = √(72/(π × 3.58))

r = 2.52 cm

Read more at; https://brainly.com/question/4405937

Answer: See explanation

Step-by-step explanation:

1. The average recovery time for all heart attack patients that the cardiologist has or will treat. = Parameter

2. All heart attack patients that the cardiologist has cared for or will care for in the future = Population.

3. The average recovery time for the 32 heart attack patients = Statistics

4. The 32 heart attack patients who were observed by the cardiologist = Sample

5. The list of all 32 heart attack patients' recovery times = Data

6. The recovery time for a heart attack patient. = Variable

Answer:

im not sure about this one but my answer is 0.025.

Step-by-step explanation:

if there is a 1 out of 8 chance of getting a free burger,  convert that into 1/8. divide that by 5 and you get 0.025.

Answer:

[tex]Varianve = 3.842[/tex]

[tex]SD = 1.960[/tex]

Step-by-step explanation:

Given

See attachment for data

First, calculate [tex]\sum x^2[/tex]

[tex]\sum x^2 = 18^2 + 17^2 +20^2 + 19^2 + 20^2 + 16^2 + 16^2 + 15^2 + 18^2+14^2 +19^2 + 19^2+18^2+17^2 + 16^2+20^2+16^2+18^2+14^2+20^2[/tex]

[tex]\sum x^2 = 6198[/tex]

Calculate [tex]\sum x[/tex]

[tex]\sum x = 18 + 17 +20 + 19 + 20 + 16 + 16 + 15 + 18+14 +19 + 19+18+17 + 16+20+16+18+14+20[/tex]

[tex]\sum x = 350[/tex]

So, we have:

[tex]SS_x = \sum x^2 -\frac{(\sum x)^2}{n}[/tex]

[tex]SS_x = 6198 -\frac{350^2}{20}[/tex]

[tex]SS_x = 6198 -\frac{122500}{20}[/tex]

[tex]SS_x = 6198 -6125[/tex]

[tex]SS_x = 73[/tex]

Solving (a): The variance

[tex]Varianve = \frac{SS_x}{n-1}[/tex]

[tex]Varianve = \frac{73}{20-1}[/tex]

[tex]Varianve = \frac{73}{19}[/tex]

[tex]Varianve = 3.842[/tex]

Solving (b): The standard deviation

[tex]SD = \sqrt{Variance}[/tex]

[tex]SD = \sqrt{3.842}[/tex]

[tex]SD = 1.960[/tex]

I didn’t undertand the question... mayb ur attachment isnt added! Plz check!

Answer:

-10

Step-by-step explanation:

See image below:)

Answer:

x = -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

-4/5x = 8

Step 2: Solve for x

Answer:

2 3 + 1 3 = 3/5 + 3/5 = 1 1/5 + 2+1 = 3 + 1 !/5 = 4 1/5

5 5

Step-by-step explanation: The Slashes mean The number bellow

Please make this answer Brainlist...

9514 1404 393

Answer:

  It satisfies both equations.

Step-by-step explanation:

The points on the graph of an equation are the values of the variables that satisfy the equation (make it true).

In a system of equations, you're generally looking for values of the variables that satisfy all of the equations in the system. That is, the solution will be a point on the graph of every equation in the system.

For a point to be on more than one graph, it must lie at a point of intersection of the graphs. If all of the graphs of a system go through the point of intersection, that point satisfies all of the equations, so is a solution of the system of equations.

Answer:

a person's height

Step-by-step explanation:

thing that you can count

Answer:

a person's height helpful answer

Answer:

n = 1

Step-by-step explanation:

Answer:

n = -4

Step-by-step explanation:

Let's solve your equation step-by-step.

−2(n − 6) = 20

Step 1: Simplify both sides of the equation.

−2(n − 6) = 20

(−2)(n) + (−2)(−6) = 20(Distribute)

−2n + 12 = 20

Step 2: Subtract 12 from both sides.

−2n + 12 − 12 = 20 − 12

−2n = 8

Step 3: Divide both sides by -2.

[tex]\frac{-2n}{-2} = \frac{8}{-2}[/tex]

n = -4

Hope this helps, please mark brainliest if possible. Have a great day.

Answer:

39

Step-by-step explanation:

Find the value of f(x) at both points

f(3) = 3(3)³ + 1 = 82

f(1) = 3(1)³ + 1 =  4

---------------------------

Average Rate of Change is just like slope

Divide the change in f(x) by the change in x

r = (82 - 4) / (3 - 1)

r = 78/2

r = 39

Answer:

67 f

Step-by-step explanation:

Answer:

The answer to 12 is 40 cubic units

Step-by-step explanation:

Answer:

6 meters

Step-by-step explanation:

Area is length times width. If the width is 10 and the area is 60, then you would find 10 times ??? equals 60. Or 60 divided by 10. which is 6

Answer: A. 30 students in the lunchroom.

Step-by-step explanation:

A representative sample simply refers to the sample that has same characteristics just like the population.

A random-based selection is regarded as a representative of the population. In this case, the random sample that represents a representative sample of the number of students who enjoy science class is "30 students in the lunchroom".

When the students in the lunchroom are chosen, then it's a representation of the entire students in the school. This is the best option when compared to other options as they don't represent the students entirely.

Answer:

30 students in the lunchroom

Step-by-step explanation:

Got it right on the test.

I hope this is help full to you

fine ,it is a A ok,I am sorry for using rude words on you

Answer:

x<7

Step-by-step explanation:

See image below:)

Answer:

A

Step-by-step explanation:

6 is a power. So both C and D are wrong because 6 is being treated as an ordinary integer.

So the answer must be either A or B.

B is not correct because to move an expression from the denominator to the numerator changes the sign in the base (which is m in this  question).

A is correct. the power is changed from 6 in the denominator to -6 in the numerator. m is shifted to the numerator as well.

Answer:

30 cookies

Step-by-step explanation:

Reeba sells [tex]\frac{2}{3}[/tex] of [tex]3\frac{3}{4}[/tex] of 12 chocolate chip cookies.

Let us start by finding [tex]3\frac{3}{4}[/tex] of 12. We simply have to multiply the two numbers. However, it would be much easier if we had an improper fraction than a mixed number. Let us make [tex]3\frac{3}{4}[/tex]  an improper fraction first.

[tex]3\frac{3}{4} =\frac{15}{4}[/tex]

Ok! Let's multiply.

[tex]\frac{15}{4} *\frac{12}{1} =\\15*3\\=45[/tex]

Ok, Reeba baked 45 cookies in total. We know that she sells  [tex]\frac{2}{3}[/tex]  of her baked cookies, so we can again multiply the two numbers.

[tex]\frac{2}{3} *\frac{45}{1} =\\2*15=\\30[/tex]

Therefore, Reeba sold 30 cookies.

I hope this helps! Let me know if you have any questions :)

Answer:

Sin(E) = 7/25

Sin(D) = 24/25

Tan(D)= 24/7

Step-by-step explanation:

Sin=opp/hyp

Tan=opp/adj

Cos=adj/hyp

The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

The given parameters are:

EF = 24

DF = 7

Start by calculating the length DE using:

DE²= EF² + DF²

So, we have:

DE²= 24² + 7²

Take the square root of both sides

DE= 25

The sine of the angles is calculated using:

sin(Ф) = opp/hyp

So, we have:

sin(E) = 7/25

sin(D) = 24/25

The tangent of the angles is calculated using:

tan(Ф) = opp/adj

So, we have:

tan(D)= 24/7

Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

Read more about trigonometric ratios at:

https://brainly.com/question/11967894

Answer and Step-by-step explanation:

First, multiply the parentheses, then add everything together.

-- (5x + 24)(9x +  12)

-- 45[tex]x^2\\[/tex] + 60x + 216x + 288 (Simplify)

-- 45[tex]x^2\\[/tex] + 276x + 288

--- (3x + 9)(8x + 6)

--- 24[tex]x^2\\[/tex] + 18x + 72x + 54 (Simplify)

--- 24[tex]x^2\\[/tex] + 90x + 54

---- (2x + 7)(24[tex]x^2\\[/tex] + 90x + 54)

---- 48[tex]x^{3}[/tex] + 180[tex]x^2\\[/tex] + 108x + 168[tex]x^2\\[/tex] + 630x + 378 (Simplify)

---- 48[tex]x^{3}[/tex] + 348[tex]x^2\\[/tex] + 738x + 378

----- 45[tex]x^2\\[/tex] + 276x + 288 + 48[tex]x^{3}[/tex] + 348[tex]x^2\\[/tex] + 738x + 378

----- 48[tex]x^{3}[/tex] + 393[tex]x^2\\[/tex] + 1014x + 666

48[tex]x^{3}[/tex] + 393[tex]x^2\\[/tex] + 1014x + 666 is the final answer.

#teamtrees #PAW (Plant And Water)

Answer:

[tex] \rm \displaystyle {48x}^{3} + 393 {x}^{2} +1014x + 660[/tex]

Step-by-step explanation:

we would like to simplify the following:

[tex] \rm \displaystyle (5x + 24)(9x + 12) + (3x + 9)(8x + 6)(2x + 7)[/tex]

there're two parts the multiplication the whole part to solve the multiplication part we can consider FOIL and for the whole, PEMDAS which can be represented as

[tex] \rm\displaystyle \rm \displaystyle \underbrace{\underbrace{(5x + 24)(9x + 12) } _{ \text{FOIL - 1}}+ \underbrace{ (3x + 9)(8x + 6)(2x + 7)} _{ \text{FOIL - 2}}} _{ \text{PEMDAS}}[/tex]

let's figure out FOIL-1 part

By FOIL we obtain:

[tex] \displaystyle {45x}^{2} + 60x + 216x + 288[/tex]

simplify addition:

[tex] \displaystyle {45x}^{2} + 276x+ 288[/tex]

let's figure out FOIL-2:

By FOIL and PEMDAS we acquire:

[tex] \rm \displaystyle {48x}^{3 } + {348x}^{2} + 738x + 378[/tex]

finally the whole part

[tex] \rm \displaystyle {45x}^{2} + 60x + 216x + 288+ {48x}^{3 } + {348x}^{2} + 738x + 378[/tex]

combine like terms:

[tex] \rm \displaystyle {48x}^{3} + 393 {x}^{2} +1014x + 660[/tex]

and we are done!

Answer:

36 ounces.

Step-by-step explanation:

The ratio being 24:8 can be simplified to 3:1

Multiply the one (the vinegar) by a factor of 12

What happens to one side has to happen to the other

12(3:1)

36 ounces.

Answer:36

Step-by-step explanation:

Answer:

33/55

Step-by-step explanation:

Total applicants, n(T) = 350

Female applicants, n(F) = 158

Female and Graduate applicants, n(FnG) = 66

Graduates, n(G) = 110

Probability of female Given that applicant has graduate degree; this is a conditional probability problem;

Recall :

P(A given B) = P(A|B) = P(AnB) / P(B)

Therefore ;

P(F|G) = P(FnG) / P(G) = 66 / 110 = 33/55

We're given the one-sided limit,

[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}[/tex]

Evaluating the limand directly at x = 1 gives the indeterminate from

(sin(1 - 1) - exp(1 - 1) + 1) / ln(1) = 0/0

so we can potentially solve the limit by applying L'Hopital's rule. Doing so gives

[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}=\lim_{x\to1^+}\frac{-\cos(1-x)-e^{x-1}}{\frac1x}=\frac{-\cos(0)-e^0}{\frac11}=\boxed{-2}[/tex]

Answer:

x ≤ 6.25

Step-by-step explanation:

8x + 10  ≤  60

Subtract 10 from both sides

8x ≤ 50

Divide both side by 8

x ≤ 6.25

If my answer is incorrect, pls correct me!

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-Chetan K